[
{"source_document": "", "creation_year": 1946, "culture": " English\n", "content": "Produced by Sankar Viswanathan, Greg Weeks, and the Online\n    This etext was produced from If Worlds of Science Fiction July 1952.\n    Extensive research did not uncover any evidence that the U.S.\n    copyright on this publication was renewed.\n                     Hoiman and the Solar Circuit\n     _They lifted Hoiman's scratch, thus causing him to lose much\n      smoosh. So he grabbed his bum and hit the high orbit._\nPay day! I scrawled my Larry Maloney across the back of the check and\nhanded it to Nick, the bartender. \"Leave me something to operate on,\"\nI told him.\nNick turned it over. \"Still with the _News_?\"\nThe question was rhetorical. I let it pass without swinging at it. I\nwas mentally estimating the total of the pile of tabs Nick pulled out\nof the cash register, like a fighter on percentage trying to count the\nhouse. I didn't like the figure it gave me.\nNick added them up, then added them again before he pulled some bills\nout of the money drawer and said, \"Here's thirty skins. Your rent\ndue?\"\n\"This'll cover it. I'll do my drinking here.\"\nI went over to a booth and sat down. I lit a cigarette. I smoked. And\nwaited. Presently Sherry, tall, dark and delicious, decided I was\nmaking like a customer, and strolled over. \"Would you like a menu, Mr.\nMaloney?\" she trilled.\n\"Larry to you,\" I reminded her. \"No menu. Bring me a steak. Big.\nThick. Rare. And a plate of french fries. No salad. Bread and butter.\nCoffee.\"\nShe managed at last to pull her writing hand out of mine, and I had to\nrepeat the order. Unless it could be turned into money, Sherry's\nmemory was limited strictly to the present instant.\nShe put in the order, then brought me a set-up. I let my eyes go over\nher, real careful, for maybe the thousandth time. No doubt of it--the\nlassie had a classy chassis. If she just wouldn't yak so damn much.\n[Illustration: _It looked as though Hoiman's Bum would be remembered\non Mars._]\n\"Did you see the matches last night?\" She didn't wait for my answer,\njust went on with the yat-a-ta. \"I spent the whole evening just glued\nto my television set. I was simply enthralled. When the Horrible\nHungarian got the Flying Hackensack on--\"\n\"Standing Hackenschmidt, Sherry!\"\n\"--poor little Billie McElroy I wanted to--to scratch his eyes out.\"\nI pointed out that McElroy weighed in at two forty-one and had gone on\nto win the match. Sherry never heard me.\n\"And the way the Weeping Greek kept hitting the other fellow--the\nannouncer said he was throwing Judo cutlets.\"\n\"_Cuts_, not cutlets.\"\n\"But aren't Judo cutlets illegitimate?\" The barest hint of a puzzled\nfrown tugged at her flawless brows as she poured ice water into my\nglass.\n\"The word,\" I repeated, \"is _cuts_. And the blow is not illegal.\" I\ngave my eyes another treat. What a chassis. And _what_ a mind.\n\"Anything these days, so long as you don't kill your opponent, is\nlegal in wrestling.\"\nSuddenly we had company: a little man who made scarcely a sound as he\nslid into my booth and sat facing me. \"Rassling, yet,\" he said, in\nbitter tones. \"What a woid. Dun't be saying it.\" He helped himself to\na cigarette from my pack lying on the table, and put the pack in his\npocket. He lit the cigarette, using my lighter, which he held a moment\nlonger than necessary before replacing it--regretfully--on the table.\nHe inhaled deeply. \"Rassling!\" he repeated. \"Leave us not discuss it.\"\nHe was thin, haggard, unkempt, and his brown suit--in which the chalk\nstripes were beginning to blend with the background--was threadbare.\nHe needed a shave, and his fingernails were dirty. He was vaguely\nfamiliar. The beady little eyes flicked up at me, and all uncertainty\ndissolved.\n\"Oh, no!\" I said. \"Not you. Not--\"\nHe exhaled a great cloud of smoke. \"Hoiman Katz,\" he said, in dejected\ntones. \"It is me, again. The same as like always, only not so better.\"\nHe sighed.\nSherry's tongue had been shifting from one foot to the other, waiting\nfor an opening. \"Are you a wrestler, Mr. Katz?\" she asked brightly.\nHoiman half rose from his seat, and the cigarette dropped from his lax\nmouth. Then he slumped down again, spread his hands, shrugged, and\nsaid, \"Now I esk you!\"\nSherry said, \"I guess not.\" Then, \"Shall I bring you something?\" Her\neyes were on me as she asked. She hadn't worked on Vine Street for six\nyears without learning the ropes--about people at least.\nI nodded.\nKatz was waiting for the nod. He licked his lips. \"I'll have a--\"\n\"Planet Punch?\"\n\"No. I'll have a--\"\n\"Solar Sling? Martian Mule?\"\nHoiman's eyes squinted shut, and he winced eloquently. \"Martian!\" he\ngroaned. \"With rassling, too! Bring me a bottle of beer. Two bottles!\"\nAfter a moment he peered cautiously through slitted lids. \"Is she\ngone?\" he whispered. \"Such woids. Rassling. Martian. Better I should\nhave stood in Hollywood.\"\nI laughed. \"What's the matter with wrestling, Hoiman? Last I heard you\nwere managing a good boy--what was his name?\"\n\"Killer Coogan? That bum!\"\nI had to do some thinking back. \"Yeah,\" I said, \"that's the boy.\nStarted wrestling back in the fifties. Good crowd pleaser. Took the\nJunior Heavyweight Championship from Brickbuster Bates. Had a trick\nhold he called the pretzel bend--hard to apply, but good for a\nsubmission every time when he clamped it on. Right?\"\n\"Okay, so he won some bouts with it. But that was twenty-five years\nago. He's slower, can't use that holt any more. We ain't had no main\nevents for a long time, and my bum is a big eater, see?\"\n\"So?\"\n\"So Hoiman Katz is not sleeping yet at the switch. He's got it up\nhere.\" A grimy forefinger tapped his wrinkled brow. \"I says, Hoiman,\nif we don't get it here, we gotta go where we _can_ get it.\"\nSherry came back with Hoiman's two bottles of beer, and my steak and\nfrench fries. The steak was a dream, and the french fries were a\ncrisp, rich golden brown that started my mouth watering.\nSherry wanted to talk. I waved her down, and she went away pouting. If\nthere was a story in Hoiman I wanted to get it without interference.\nHe was pouring a second glass of beer. His beady eyes swivelled up to\nmine, then quickly away. \"You want I should tell you about my bum?\"\nI mumbled something through a mouthful of good juicy steak.\nHoiman sighed, reminiscently, and a grimy paw swooped into my french\nfries. I moved them to the other side of my steak platter.\nWe woiked all up and down the Coast, (Hoiman said). My bum took all\ncomers. Slasher Slade had his abominal stretch. Crusher Kane had his\nrolling rocking horse split; Manslaughter Murphy had his cobra\nholt--but none of those guys had anything like my Bum's pretzel bend.\nHe trun 'em all, and they stayed trun.\nThat was fine. All through the fifties, and the sixties we made plenty\nscratch. Maybe it slowed down, but we was eating regular. In the\nseventies my bum was slowing up. I shoulda seen it when he started\nmissing his holt. That leaves him wide open, see? And twict the other\nbum moiders him.\nThat was recent--they was just putting in regular passenger service on\nthe space lines, so you could buy tickets to the Moon, or Venus or\nMars. Depended on whether you was ducking a bill or some broad.\nBy this time my bum is getting pinned to the mat too regular, and\nwe're slipping out of the big dough. I counts up our lettuce one day,\nand I says to my bum, I says, Ray, I says, you and me are going to the\nMoon.\nSo what if they didn't have a rassling circuit there yet, I tell him.\nJust leave it to your uncle Hoiman. We'll make our own circuit.\nI figured that the ribbon clerks wouldn't be taking space rides for\nawhile, and if we went to the Moon we'd find some bums there who could\ngive my bum a good bout, but not fast enough to toss him.\nSo we went there.\nHoiman's eyes, looking into the past, had lost their beadiness. He'd\nshifted his third glass of beer to his right hand, and his left,\nseemingly of its own volition, had found my plate of french fries. The\npile had dwindled by half, and tell-tale potato crumbs were lodged in\nthe whiskers on Hoiman's unshaven chin. Neither beer nor potatoes in\nhis mouth seemed to matter--he went right on talking at the same rate.\nIt takes me two weeks, (Hoiman continued), to ballyhoo up a bout, line\nup another bum, fix up the ring and hall and everything. We was down\nto our last lettuce that night. I gets my bum by the ear, and I tells\nhim, I says, make it a good show. But don't take no chances--this is\nwinner take all, and we better not lose. Don't use your pretzel bend\nunlessen you have to.\nThis bum we rassle was a big miner, see?--hard as the rocks he juggles\naround in the daytime. He was stronger'n my bum, but he don't know\nnothing about rassling. My bum tried a step-over toehold on him, but\nhe knows how to kick. My bum goes through the ropes. He don't try that\nno more.\nThey rassle around, and eight minutes later my bum takes first fall\nwith a body press after flattening the miner with a hard knee lift. I\ntold my bum to let him take the second fall, which he does. The big\nminer gets a head scissors on him and like to moiders him before he\ncan submit.\nRay isn't liking it, and he takes the third one quick with a abominal\nstretch, which surprises the big guy and takes all the fight outa him.\nHe didn't know they was holts like that, and he passes the word around\nthat my bum has plenty moxie. So we get only one more bout on the\nMoon--but outa the two we get enough scratch to take us to Venus.\nHoiman paused, trying hard to pour more beer out of the empty second\nbottle. He licked his lips like they were real dry, and his beady eyes\nflicked a glance at me that came and went as fast as the tip of a\nswinging rapier. I signalled Sherry to bring two more bottles of beer.\nHoiman relaxed, sighed, gazing almost affectionately at the new crop\nof french fries which had appeared suddenly in his clutching fist.\nSherry, still pouting, came with the beer, and ten seconds later\nHoiman was talking again.\nWe did okay on Venus, (he said). Before long I have a regular little\ncircuit woiked up in the three spaceports, and they is plenty bums\nthere what think they can rassle. Some of them can--my bum has to use\nhis pretzel bend oftener and oftener. He's lucky, and he don't slip\nnone clamping it on--at first.\nI have ta tell you about them Venusians. Them dustlanders, I mean.\nThey got big flat wide feet for padding through the dust, and their\nnoses are like a big spongy thing all over their puss, to filter the\ndust out. So they got no expression on their pans. A guy like me,\nwhich has got a real expressive face, could get the willies just\nlooking at them. And their eyes--round and flat, big as silver\ndollars.\nThem dustlanders was nuts about rassling. They flock to the rassling\nshows and buy good seats. They don't do no hollering and waving like\npeople do. Just sit there, staring out of them big flat eyes and\nmaking funny _chuffing_ noises at each other when some bum would get a\ngood hold on the other.\nMy bum didn't pay them no never mind at foist, but one day he tells me\nhe keeps feeling them eyes on him while he's rasslin'. I give him the\nold razz--but that night he tries for his pretzel bend, and misses.\nThe other bum is young and fast, and my bum gets trun, but good!\nSo this happens a few more times, and my bum says we gotta move on--he\ncan't rassle no more with them dustlanders staring at him and\n_chuffing_ about him.\nSome of them ear benders on Venus are studying up on the side, anyhow,\nand the outlook for my bum ain't so good no more nohow. So we go to\nMars.\nI signalled Sherry for my coffee, as Hoiman ground to a stop while he\nrefilled his glass. I swear my eyes weren't away from the table for\nmore than a half second, but in that moment all the french fries left\nmy plate. I yielded to Fate--it wasn't meant to be that I eat french\nfries this pay day.\nThings are primitive like on Mars, (Hoiman was saying), on accounta\nthe troubles they have with power there. We rassled under some funny\nset-ups, but that's okay with me as long as my bum tosses his man.\nThis time they ain't none of them screwy Venusians to put the whammy\non him, and he's doing okay. Until--I gotta admit it--I get deluges of\ngrandeur, or something.\nI gotta tell ya about them Martians. They are about seven feet tall,\nnot too heavy, but they got plenty moxie. And an extra pair of arms,\nso I get to thinking they oughta be terrific in the ring. Just so they\nain't _too_ terrific.\nI ask my bum, I says to him, I says, could he, does he think, trun one\nof them Martians? He says iffen he has to he'll use his pretzel bend,\nand they ain't no Martian on six legs, or eight, what won't say uncle.\nSo I check with the Colony Administrator, and he says it's okay for a\nmatch perviding we don't interfere with any of their beliefs or\ncustoms or conventions. I ast him what were they, and he told me the\nMartians never talked about them, so we'd just have to be careful.\nWhat the hell, I says to my bum. A bout's a bout. So I start\npromoting. First I find out do them Martians have a bum what wants to\nrassle my bum, winner take all--which is the way we like to rassle,\nwhen I know my bum can trun the other bum. Natch.\nI don't mean we talk to the Martians--I don't savvy them squeaks they\nuse on each other. We hire an interpreter--we have to take his word\nfor it that everything is woiking out.\nSo the night of the match comes around and them Martians insist on\nhaving it in their own town, Meekweek it sounds like, near as I can\nsay it in people talk. Remember I told you it was primitive? You never\nseen nothing like this. They don't live with people by the way. They\nlive off by theirselves in their own town.\nThe ring and mat and ropes are okay--not regulation, but nothing to\nsquawk about. Them lights was what get me. The Martians got no power,\nso they make a deal with some insecks. Cross my heart--'sa fack. You\nnever see such insecks. Round, big as a dinner plate, flat on top,\nrounded off on the bottom. They stay up in the air by spinning like a\nwheel--just like them flying saucers the Rigellians was spying on us\nin the fifties. You wouldn't remember about that.\nAt night the bottom part of them insecks lights up like a big electric\nbulb, almost as bright, too. They was enough of them _zinging_ around\nover the ring to make it look like it was floodlighted. My bum says\nthey remind him of them dish-eyed Venusians, but I quick change the\nsubjeck. That shoulda tipped me off--shoulda give me a freemonition\nthat the party was gonna get rough. If I'da known how rough, we'da\nstood in town.\nThe Martian bum is a big mug, and those four arms of his look mighty\nplural. I quick tells my bum, I says to him, I says, watch out for arm\nlocks and leg strangles. If that overgrowed spider ever gets one on\nyou he'll double keylock it!\nThe two bums go in the ring, and get their instructions. Mostly the\nref makes motions. The Martian nods his head like he understands fine.\nWhen the ref is telling them about trunnin' each other outen the ring,\nthe Martian makes a motion like can he trun his man up in the rafters?\nThe ref shakes his head no, and that seems to satisfy the Martian. The\ntimekeeper blows a whistle, and things start to moving. That Martian\nMangler puts down his two middle limbs, uses them like legs, and is\nacross the ring and swarming all over my bum while he is still taking\nhis foist step.\nBefore you know it the ref is counting one, two, three, and my bum is\ntrun for the foist fall. The Martian is using his middle limbs like\narms, and he has a hammerlock and an arm strangle both on my bum--and\nboth of them keylocked!\nThe ref gets them untangled, and I quick tell my bum we ain't hurt\nuntil we get trun twict. So I tell him how to get that next fall--to\nkeep away from them four arms and keep circling until he gets a chance\nto clamp on the pretzel bend.\nThe whistle blows, and this time my bum uses my head. When the Martian\nMangler gallops over to his corner, my bum has went through the ropes\nand quick runs around on the apron to the other side and comes at the\nMartian from behind before the goof knows what's happening.\nHe lets the Martian have a rabbit punch, then a forearm smash, then a\nknee to his stomach. The Martian leans over, kinda sick, maybe, and\ngets a knee lift to the smoosh. This softens him up good, and my bum\nclamps the pretzel bend on him. That Martian squirms like an octopus,\nwith arms and legs flying in all directions. And you coulda knocked me\nover with a subpoena when he got out of it!\nYour guess is as good as mine, how he done it. But my bum is moving\nfast, and he gives him some more knee lifts and a drop kick or two,\nand then a hair mare, and he falls on him for a body press and gets\nthe count.\nEach bum has got a fall. You shoulda heard them Martians there\nsqueaking this time--ten times as loud as when their bum won the foist\nfall. But they had no squawks. These flying chandeliers they had, they\nkinda bunched up to follow the action, and the light was good so the\nref couldn't make no mistake about it.\nThat Martian squirming out of the pretzel bend don't look so good, so\nI tell my bum not to use it for the thoid fall. I tell him to give the\nMartian some more of them knee lifts--he don't get along with them at\nall. I tell him to folly that up with a airplane spin and a body slam.\nMy bum follys instructions to the alphabet, and that is just what\nhappens. He bangs that Martian around with elbow smashes and knee\nlifts till he don't know is he on one leg or six. Then he goes in fast\nand grabs him by a coupla legs and arms, holds him up in the air, and\nspins him like a pinwheel.\nRight away I knowed something was in the air besides that Martian\nMangler. Oi! Did things happen all to onct!\nMy bum slams the Martian and falls on him for the count, and wins the\nthoid fall and the match. That part is okay. But while the Martian is\nstill up in the air I notice that all the squeaking from the Martians\nhas stopped all of a sudden.\nSo from the Martians we are getting nothing but silence, strictly\nwholesale. I think maybe that's natural when their bum gets trun.\nAnd then--plop! plop! plop!--and them flying light bulbs all drop down\nflat on the mat and lay there just like the Martian bum, until they\nisn't enough light in the house to see to strike a match. And then the\nsqueaking starts again, like a million hungry rats, and I can just\nbarely see them Martians starting for the ring.\nI gets my bum by the arm and tells him something tells me we better\nblow the joint. We blow, fast. Them Martians is mad about something\nwhich I ain't had time to figure out, yet. My bum steps on one of them\nanimated light fixtures when he gets out of the ring and squashes it.\nA puddle of light squirts out, and natch he steps in it. We are\nscramming through that crowd like mad, and we are in the clear. But we\nhear them squeaks behind us for a long time. They are follyin' the\nglowing footprints my bum is leaving to point the way.\nHe emptied the last bottle of beer, holding it upended for a long time\nwaiting for the final laggard drop to detach itself. He stalled over\nhis drink, waiting for me to ask him what happened, so I did. He put\non his most wounded expression, and I knew then that he'd suffered a\nmortal blow--to his purse.\nYeah, we got away, I made my bum trun away his flashy shoes so they\ncouldn't track us by them. We walked all the way back to Neopolis, the\npeople city. All kinds of plain and fancy rumors beat us there, so the\nColony Cops put us in protective custody until they got the straight\nstory.\nNobody ever saw another Martian. It seems that they got some trick\nnotions about theirselves. They are proud because they can walk on the\nground and don't have to fly, so they got a hearty contemp for things\nthat fly, like them insecks which they used for house lights.\nNow, them insecks is dopes too and would give anything if they could\nwalk like the Martians. And the Martians know the insecks can think a\nlittle, and it makes them feel good to have the insecks looking up to\nthem. Lord knows nobody else does.\nSo when my bum lifted their bum up in the air and spun him around like\na pinwheel it was a big insult to them. They took it that my bum was\nas much as telling them that he didn't think they was any better than\nthem insecks flying around over the ring. And the insecks took it as a\ninvite to come down and try the Martians racket so that's why they all\nflop into the ring and the lights go out. They was trying to walk.\nThat's more than the Martians can take. They swarm into the ring and\nkill all the insecks. They'da killed us too, but I got smart brains\nand we didn't hang around asking for it.\nAnd now they won't have nothing to do with no people from Earth on\naccount of they have lost so much smoosh, the way they look at it.\nWe got no take from that bout. And the Colony Administrator lifts all\nour scratch--said we'd gummed up Martian trade and he'da trun us in\nthe clink too only he didn't want to see no more of us. He wouldn'ta\neven give us fare back to Earth except he said he didn't want us\nanywhere on Mars.\n\"So that,\" the little promoter concluded sadly, \"is why I don't like\nMars and rasslin' and Martian Mules and people who talk about such\nthings.\" His beady eyes flicked a baleful glance at Sherry, who\nhovered nearby on the chance that he'd stop talking and give her an\ninning.\nHoiman stood up, carefully shook the bottles to be sure that they were\nempty, extracted a cigarette from the pack he'd stuck into his pocket,\nand used my lighter again. He hefted it carefully, reluctantly putting\nit back on the table. Then his little black eyes swivelled to the last\npiece of potato on my plate--the piece he'd spared in previous raids.\n\"What's the matter with them fries?\" he asked.\nIt disappeared into his mouth and he went away, munching, a dingy\nlittle man padding along on silent, predatory feet.\nHe'd scarcely slipped out through the door when Sherry moved in.\n\"Is he really a wrestler, Larry?\" she asked breathlessly.\n\"Him?\" Even Sherry, vintage Vine Streeter that she was, should have\ngot the pitch. \"The only thing,\" I told her solemnly, \"that Hoiman\never got a hammerlock on was a dollar bill!\"\nBut Sherry wasn't listening, \"Don't you just _love_ wrestling?\"\nI let my eyes have a treat, taking their time as they went over that\nclassy chassis. Then I said it. Fervently.\n\"Any time, Sherry! Any time.\"\nTHE END\nEnd of Project Gutenberg's Hoiman and the Solar Circuit, by Gordon Dewey", "source_dataset": "gutenberg", "source_dataset_detailed": "gutenberg -  Hoiman and the Solar Circuit\n"},
{"source_document": "", "creation_year": 1946, "culture": " English\n", "content": "Produced by Stephen Hutcheson and the Online Distributed\n                     BURIED TREASURE OF CASCO BAY:\n                     A Guide For The Modern Hunter\n                      Forest City Printing Company\n   All rights reserved, including the right of reproduction in whole\n                 Copyright \u00a9 1963 by B. F. Kennedy, Jr.\nThe following people helped me greatly in the compilation of this book.\n                        Miss Jessie B. Trefethen\nThis little endeavor of mine that follows, is a small effort in a\nliterary way, to acquaint the reader with modern methods and information\non the art of treasure hunting and various facts and locations of same.\nThe Author sincerely hopes that you gather some information and\nentertainment from the reading of this book.\n             _Now City Historian for South Portland, Maine_\nB. F. Kennedy, Jr. was born in Portland, Maine in 1916 and has spent\nmost of his life in this area, attending grammar school and high school\nin Portland. Mr. Kennedy has also worked as a ship chandler and a\ndrugstore clerk. A collector by nature, his favorite hobbies besides\ntreasure-hunting are bottle collecting and mineralogy.\nThe author has done extensive research on buried and sunken treasure\nlocales. Working on information furnished by Mr. Kennedy, scuba divers\nlocated three brass Revolutionary War cannons just off Portland Head\nlight. Mr. Kennedy has personally located old coins, an Indian axe circa\n1640, and other valuable artifacts, often traveling as far from Portland\nas Key West, Florida. On his days off or on his vacations, the author\ncan usually be found with his trusty metal detector scouting for more\ntreasure.\nMr. Kennedy is married, with no children.\nThe locations given in this book do not guarantee that you will find\ntreasure there, or anywhere in Casco Bay. These locations are places\nwhere history took place, maybe you will find treasure and maybe not.\nThe Author does not want to mislead you into thinking, that if you dig\nat any of these locations; you will find buried treasure.\n                     BURIED TREASURE OF CASCO BAY:\n                     A Guide For The Modern Hunter\n                        HOW TREASURE WAS BURIED\nThe word, \u201ctreasure,\u201d has excited people the world over for centuries.\nWhen we were mere children we read about hidden treasure being buried on\nlonely isles, by bands of cutthroat pirates, also the burying of caches\nof money by the outlaws and bandits of the old West.\nThe early settlers were always hiding their money from the Indians and\nbandits, and the best place to put their money was, of course, in the\nground, as they had no bank vaults in which to keep it safe.\nSo down through the years thousands of dollars in coin was hidden in\nthis fashion. Many of these caches are being discovered today in the\nback yards of rustic old houses, in old wells, along the stone walls of\ncentury-old homesteads, in fact almost anywhere around the property.\nThe many islands in Casco Bay were choice locations for the early\nsettlers; to settle on an island was one way to slow up the advance of\nIndian raiding parties. The Indians, of course, would raid some of the\nislands; but it was not convenient for them because of the trip across\nthe open water in order to reach their destination; therefore many\ntreasures that were buried on these islands still remain to be\ndiscovered by the modern day treasure hunter. A good many of these\nhidden caches were buried in old iron kettles, tough bags made of animal\nhides, old iron chests and almost anything that would keep the coins\nfrom getting too wet and corroded in the ground.\nNow for some treasure hunting locations for the modern hunter armed with\nhis metal detector. First, we will go to an old fort in Casco Bay,\nMaine, namely, \u201cFort Gorges,\u201d we will call this location number one on\nour list.\nFort Gorges is on Hog Island, Portland Harbor, Casco Bay, it is a stone\nfort in a commanding position on a reef, guarding the entrances to the\nupper harbor as well as to the ship channel. Although designed to\ncomplete the harbor defense, it was not built until much later than the\nearlier forts, Preble and Scammell. It was commenced in 1858 but was not\ncompleted until 1864 or 1865. It was built under the direction of\nCaptain Casey, of the United States Engineering Corps, and in\nbomb-proofs and barbette, was designed to receive 195 guns. Although a\nformidable looking fortress it was designed for short range guns, so the\nintroduction of modern heavy ordnance made its period of usefulness a\nbrief one. Fort Gorges may be reached by boat from Portland or Cushings\nIsland.\nThe parade ground inside the fort is a dirt one, anybody seeking buried\ntreasure there, might find such articles as buttons, shoe buckles,\ncoins, bayonets and other properties carried by the soldiers who were\nstationed there at the end of the Civil War. The buried artifacts would\nnot be too deep, maybe one or two feet for an average. This fort would\nbe one of the ideal locations for the modern treasure hunter and his\nmetal detector. I\u2019m sure your time would not be wasted in a two or three\nhour search there. If you decide to visit the old fort, do not forget to\ntake a box lunch, as the salt air will create a wonderful appetite.\nOn House Island, Casco Bay, you will find Fort Scammell. This fort was\nbuilt in 1808, under the direction of Mr. H.A.S. Dearborn, who under\nauthorization of the War Department, purchased for twelve hundred\ndollars, all the southwest part of House Island containing twelve acres\nmore or less. On the highest point of this island an octagonal\nblock-house of timber was erected, with a porthole and a gun on each\nside. The upper story projecting over the lower, two or three feet;\ncontained the battery. On the low upright center timbers of the roof,\nwas a carved wooden eagle with extended wings. Fort Scammell, like its\nsister, Fort Preble, was named for a Revolutionary officer, Colonel\nAlexander Scammell. Fort Scammell was never so extensive a fortification\nas Fort Preble.\nIt was enlarged at the time of the Civil War, until its equipment called\nfor seventy-one pieces. Fort Scammell may be reached by boat from either\nPortland or South Portland.\nThe treasure hunter, here too, will have a great time with his detector.\nThere should be, hidden out of sight, a number of old relics that could\nbe located with a good metal detector. The date of the fort being as I\nmentioned 1808, therefore the artifacts that might be found here, would\nreally have some value. Don\u2019t forget to secure permission before you\nhunt on any property. The owner will like you better for this.\nThe Island of Peaks is located in Casco Bay and is approximately three\nmiles due east from Portland. It only takes a fifteen minute boat ride\nto arrive at Peaks.\nThere are several good locations here for the treasure seeker,\nespecially if he or she is armed with a good metal detector.\nThe first location that I shall mention is located on the northerly end\nof the island. It is about three-quarters of a mile from the boat\nlanding.\nA few years ago construction of an addition to the Island school house\nwas begun; during the excavating, two silver coins were dug up. These\ncoins were identified as pieces-of-eight, or Spanish silver dollars.\nWhere they came from or who buried them, or lost them there; still\nremains a mystery. If one could secure permission to go over the\nremaining part of the yard, there is no telling what might be\ndiscovered.\nAnother spot worth checking out, is located on the back side of the\nisland at a place called \u201cPicnic Rocks\u201d or \u201cWhaleback\u201d. Here, near the\nroadway, stands; or stood; a huge elm tree. This tree was approximately\neight feet in diameter. A few years ago a fire broke out in this section\nof the island, and nobody seems to know whether or not the lonely elm\nwas burned. If it was, the huge charred stump should still be there. The\nAuthor has not checked this situation as yet; but intends to shortly.\nOn the ground surrounding this immense tree, there are several mounds,\nbelieved to be Indian graves. A real good search of the area, might be\nwell worth one\u2019s time.\nLast, but not least, the beaches on the back side of the island, (or\nnorth-easterly side) should be gone over very carefully with the metal\ndetector.\nPirates were in this area around 1726, and most anything might be buried\nalong these sandy strips. Not only buried, but who knows what might have\nbeen dropped or lost by these cutthroats of long ago. The Boston Pirate,\nEdward Low, was said to have plied these waters, in and around Casco Bay\nWho knows what beach he might have landed on, in one of his longboats?\nI most certainly would give this island a darn good check with my\ndetector, especially the beaches and the bankings leading up from them.\nOne of our next stops should include this island of Casco Bay. It is\nlocated just across the channel from Willard Beach, South Portland; in\nan easterly direction from Willard Beach.\nFirst of all, why do we wish to treasure hunt here? A little history at\nthis point might help the modern hunter, just a bit. We will go back in\nhistory to the year 1632. The first pirate ever heard of in the annals\nof piracy, was called; \u201cDixie Bull\u201d. This pirate was believed to be of\nEnglish descent. He robbed and sacked Pemaquid, Maine, in 1632; then set\nsail for Richmonds Island, which was next on his list to be robbed.\nHowever, as the story goes, a storm came up with very high winds, this\npirate galleon was just entering the channel between South Portland and\nCushing\u2019s Island, so \u201cDixie Bull\u201d decided to put into a cove on\nCushing\u2019s to wait out the storm.\nIt is said that he put ashore and buried some of the loot taken from\nPemaquid. There are several coves facing the channel. Which one was the\nexact location of his landing?\nYour guess is as good as mine, but I most certainly would go over these\ncoves, beaches, and bankings very carefully. If anything was located\nhere, you can bet it will be a real find.\nThe year 1632 was a long time ago, and any artifact uncovered here would\nbe worth its weight in gold, not only as an antique but as a real\nhistorical piece.\nAny article found here and checked as to relationship to \u201cDixie Bull\u201d\nand proved authentic; would be priceless.\nThe history of Cushing\u2019s Island dates back to the year 1623, when\nCaptain Levett came over from the old country. He was looking for a\nlikely spot to settle and Cushing\u2019s Island turned out to be that spot.\nCaptain Levett was the first white man to settle in Casco Bay. He traded\nwith the Indians and did not try to cheat them. He traded cheap jewelry\nfor beaver and otter skins and got along famously with the whole tribe.\nLevett built his house near Cellar Point.\nThe Island of Cushing\u2019s has had many names, among these being Andrews,\nPortland, Fort Island and Bangs Island. Ezekiel Cushing took the island\nover in 1762 and it has been called Cushing\u2019s Island ever since.\nIf any of you readers are skin diving enthusiasts, you might try a few\ndives in and around the channel between Cushing\u2019s Island and Willard\nBeach, South Portland, as a number of cannon were dumped overboard\nduring the War of 1812, and are probably still lying on the bottom of\nthis channel.\nAll sides of the island should receive a good going-over with your\ndetector, as this island is steeped in history of the bygone era of\nsails.\nThis cove located on the easterly end of South Portland facing Casco Bay\nis the scene of early settlers to this part of the Cape, (Elizabeth).\nToday the cove is known as Willard Beach. It was named for Captain Ben\nWillard, who was born there in 1828. Ben was a fisherman, pilot, and\nstevedore.\nThis beach was used by the early settlers, of about 1813 as a landing\nspot for their fishing boats. Many little homesteads sprung up in this\narea in the early 1800\u2019s.\nThe old houses, of course, are gone now, but who can tell what might\nstill be hidden along the beach or in the vicinity of the beach and\ncove.\nAround the old point, that is on the south side of the beach, would be a\nlikely area for the metal detector. The old fishing shacks that were\nthere have vanished now, but many a cash deal was made on this old point\nof land. There may be still, some loose coins lying around with a few\nfeet of dirt on top of them.\nA few blocks to the rear of the beach was an old tavern that the stage\ncoaches stopped at years ago. This old house is still standing. You\nprobably will not be able to secure permission to go over the property\nas the house is occupied. I told you about this old place, just to\nconvince you that this entire area is a fine one to look over.\nIf stage coaches came and went from this locality you can bet that this\nwould be an ideal location in which to hunt. Go over the beach, then try\nthe land, but for goodness sake, be sure to get permission from any\nproperty owner before you hunt on his property. We do not want you to\nget arrested and land in court.\n                        PORTLAND HEAD LIGHT AREA\nThe history book tells us that many of the old sailing vessels came to\ngrief in this area. Portland Head Light is located on the government\nreservation of Fort Williams and you definitely can not search here; but\nthe area outside of the Fort should receive your attention. If you\nproceed in a southeasterly direction along the shoreline, going away\nfrom the Fort there is no telling what you might find. The ships that\nwere wrecked in this area of the bay, carried all kinds of cargo; such\nas silks, silverware, jewelry, tools, money, tea, coffee, guns, pottery,\nglassware, etc., just to mention a few.\nMany of these articles washed ashore from the wrecked ships. It is my\nguess that there still remains, buried in the sand of the many inlets\nand coves; relics of a bygone era.\nOne of the wrecked ships in this area was the Annie C. Maguire. She came\nashore in 1886 and went to pieces on Portland Head Light Reef.\nOne of the earlier shipwrecks was that of the \u201cBohemian.\u201d She came to\ngrief on Alden\u2019s Rock; located about three miles off the Cape Elizabeth\nshore. The year was 1864. She had sailed from Liverpool, England; her\ndestination being Portland, Maine. Many of the Cape Elizabeth residents\nstill have articles in their possession that came from the \u201cBohemian\u201d.\n(The Author has a silver plated spoon from this wrecked ship, that will\nrest in the Cape Historical Society.)\nThe days that followed the disaster were busy ones for the people along\nthe shores of the mainland, as well as the islands of Casco Bay. They\nwere salvaging the bolts of silk cloth, along with many other items that\nwere washed ashore. The story goes; that the ladies of the area soon\nwere seen wearing new dresses made out of the cloth from the \u201cBohemian\u201d.\nThe location of this island will take us down the bay beyond Peaks\nIsland, and about three miles due east from Long Island.\nMany stories have been written about Cliff Island. Some were fact and\nothers were legendary. We will try to stay with the facts as close as\npossible. First a little about the geography of Cliff Island. It has\ngreat coves, low sand bars, and many lush pine groves; a nicer haven for\nthe artist, scholar, or traveler, has not been found. The Island has not\nalways been known as Cliff; for it originally was called, \u201cCrotch\u201d\nIsland, named after a curious \u201cH\u201d shaped chasm that was hewn out of the\nsolid ledge on the southeastern side of the island. On each side of the\n\u201ccrotch\u201d, are great coves which should be given your undivided\nattention, as to metal detection.\nNear Gravelly Cove, there once stood an old house, built in the early\n1700\u2019s. Its walls were constructed of hand-hewn wooden planks, stood on\nend. It was termed a \u201cpiggin\u201d, a type of dwelling very uncommon in\nMaine, there being only one other like it built at Kittery Point, about\n1630. It is said to have been erected by John Merriman, one of the\nearliest settlers.\nOne of the Indian battle grounds was the field above the old wharf at\nStrouts Point. Here many of the early settlers met their death at the\nhands of the savages.\nOn May 2, 1780, a party of Colonial soldiers camped on the island for\nseveral days, while on their way to the eastward in search of British\ncruisers.\nThere is one prominent legend of the island that the natives keep alive.\nIt concerns the notorious, \u201cCaptain Kief\u201d, who was believed to be a\nsmuggler and one-time pirate. He lived alone in a hut and during the\nstormy weather, would fasten a lighted lantern to his horse\u2019s neck;\nriding up and down the narrow stretch of the island, in the hope of\nluring passing vessels to their doom on the treacherous reefs.\nUnsuspecting pilots soon found their ships pounded to pieces and their\ncargoes salvaged and confiscated by this island ghoul. He got rich out\nof the spoils.\nToday the islanders hate to point out to the curious, the \u201cCaptain\u2019s\u201d\nown private graveyard, a pretty, grassy meadow which ever since has been\nknown as \u201cKief\u2019s Garden\u201d, and where his innocent victims are said to\nsleep their last long sleep.\nNow the reader should understand, that by reading the preceding tale,\nyou have a good location here on Cliff, for a real treasure hunt. The\nAuthor wishes you good hunting.\nHere we have one of the earliest settlements in the Casco Bay area. In\n1604, Champlain, the great explorer, landed here on Richmond\u2019s Island.\nThis was, of course, sixteen years before the landing of the Pilgrims at\nPlymouth Rock, Massachusetts. In other words, this island has a real old\nhistory in the annals of time.\nThe first trader or shop keeper to settle here was Walter Bagnall. He\ntraded with the Indians and got along fine until he started to cheat\nthem. That was his undoing, as they found it out and later killed him.\nThis island was \u201cthe\u201d trading post of the area. People came by boat and\noverland to trade here.\nRichmond\u2019s Island today is rather a deserted place compared to the old\ndays. There used to be thirty-five or forty houses here, plus two or\nthree churches.\nThe leading industry of the island was the curing and drying of salt\nfish that were caught just off shore. You can walk around the entire\nshoreline of this island in about an hour and a half. A metal detector\nshould react here to something buried long ago. The island, being a\ntrading post, should reveal some treasures of the bygone era. The island\nhas a wonderful beach on the westerly side. If you also happen to be\ninterested in shells you will find many \u201csand dollars\u201d here. A \u201csand\ndollar\u201d is a shell fish shaped like a silver dollar. They are very\ninteresting to study.\nThere is a breakwater from the mainland out to this island and you can\ncross over at low tide, but the walking is pretty rugged due to the\nlarge granite blocks used in construction. These blocks were placed at\nvarious angles so it is hard to walk over them. The best way to the\nisland is by boat, either from Breakwater Point or from Crescent Beach,\nCape Elizabeth. A small rowboat is all you need, as the inlet that you\ncross is not very wide.\nRichmond\u2019s Island is owned by a gentleman who lives on the mainland. I\nwould most certainly get his permission before landing on the island. We\ntreasure hunters want to live up to our good reputation, so don\u2019t spoil\nit by trespassing without the owner\u2019s O.K.\nThis small island was settled by Ralph Turner in 1659. He was a farmer\nwho kept his cows and garden on this island. He, however, did not live\non the island, but had a house on the mainland of the Cape. The river on\nwhich the island was located was called Casco River. It is now called\nFore River and is a part of Casco Bay, or an inlet from the Bay.\nTurner\u2019s house was located near Barbeery Creek, which now is industrial\nproperty in South Portland.\nI mention this location because of its early settlement. If this area\nwas screened carefully some mighty interesting relics could be revealed.\nTo reach this area you proceed to South Portland, then on to the\nPleasantdale area. Anyone there can tell you how to get to Turner\u2019s\nIsland. Of course the island is not an island any longer, as the gap\nbetween the island and mainland has been filled in and today the island\nappears to be part of the mainland. You can see with careful study that\nthe terrain still resembles the little island of 1659.\nThis area should have something hidden along the shoreline that would\nmake a metal detector sing.\nThe largest city in Maine offers the modern treasure seeker good hunting\ngrounds, especially the eastern side of town. This area is called the\neast-end bathing beach. The shore line here was the scene of Indian\nattacks and burning of houses back in the year 1775 when Portland was\nknown as Falmouth Neck. The British Admiral, Mowatt, attacked and\ndestroyed by shell fire the area from the Eastern Promenade to Monument\nSquare, and included the waterfront in this destruction.\nIf you think about this attack you will come to the conclusion that many\nhistorical artifacts were lost in the ruins of the fire. Some of them\nare probably still in the area, buried under three or four feet of dirt,\nor maybe deeper. Of course the shoreline is built up now, but you still\nhave a good chance of finding something along the beach, the banking\nnear the railroad tracks, and some of the surrounding area. As I have\nmentioned continually throughout this book, don\u2019t under any\ncircumstances dig without securing the property owner\u2019s permission.\nPortland was founded by George Cleeves in 1633, so you see that any\narticle found that dates back to this era would be a real find. The\nPortland area as a whole is steeped in history, the first settlers\narriving only thirteen years after the Pilgrims themselves.\nA particularly nice spot for the detector to do its work is the foot of\nFort Allen Park along the railroad tracks and shoreline at the base of\nthe hill.\nMany of the old windjammers used to anchor in the channel just off this\npoint. Therefore, the longboats or small boats from the mother ship\nwould land on the beach, while their occupants went ashore to complete\nbusiness dealings with the shopkeepers concerning cargoes, etc.\n                       CAPE ELIZABETH SHORE LINE\nWhen starting out to check this shoreline a good starting point in my\nestimation would be at the \u201cTwo Lights\u201d section of the Cape. Go along\nthe shore checking as you proceed; all spots, both among the rocks,\nsand, and higher water line. A short walk will bring you to the State of\nMaine Park. Here you will not be able to use your instruments as there\nare restrictions, but go beyond the park in a westerly direction and\nthis will lead you around the point to Crescent Beach.\nIn years past there have been a number of articles washed up on the\nbeach. Just above the beach is a salt-grass area that comes between the\nbeach and woods just beyond. I would most certainly check this section,\nthen proceed along to the field that lies about a thousand feet distant,\nalso in a westerly direction. There is no telling just what might be\nburied here. A good method to use in this area, with your detector, is\nthe \u201cgrid pattern\u201d; that is, walk up and down for awhile then reverse\ndirection and go across your own path. The design you will be making\nwill look like the plate on a waffle iron. This method is employed by\nmost of the professional treasure hunters, and is most effective.\nThe history of the Cape shoreline goes back to the year 1604, when\nChamplain, the great explorer, was in this neighborhood. He landed first\non Richmond\u2019s Island, then explored quite a bit of the mainland. He\ncould have landed or walked from Richmond\u2019s to the mainland. Maybe some\nof his belongings lie buried in this historical locality. Treasure\nseeking demands that you don\u2019t give up too easily, keep trying, and\nremember these hidden objects will not let you know where they are, you\nhave to find them. Faint heart ne\u2019er won fair lady, so get in there and\nreally search.\nMackworth\u2019s Island has an unusual and interesting background. According\nto historians, the Indian Sagamore of Casco, known as Cocawesco, made\nhis home here. On an old English chart it is called Macken\u2019s Island. The\nisland was named for Arthur Mackworth, who came to this country in 1631.\nHe died in 1657 and was buried on the island.\nThe State of Maine School for the Deaf is located on this island, which\nmay be reached from the mainland via a causeway. Please get permission\nbefore trespassing on this property. Go to the administration building\nand ask if they mind if you search along the outer shoreline. An area\nsuch as this could reveal many nice finds because of the fact that both\nour Indian chief and the first white settler here, lived on the island a\ngood many years. There seems as though there must be artifacts lying\naround hidden from view just waiting to be discovered.\nTo reach Mackworth\u2019s Island take Route 1 north from Portland, cross\nMartin Point Bridge, and you will see the island to your right as you\nare crossing this bridge. The first road to the right after leaving the\nbridge should take you to the causeway leading over to the island. You\ncould also row over to the island from the mainland as it is a very\nshort trip.\nNow here is an island that fairly reeks with legend and treasure lore.\nCertainly no island in the Bay so ideally lends itself to piratical\npractices with its deep landlocked harbor, hidden coves and thick woods\nthat even today shelter all observation from the sea. All of which lends\ncredence to staunch belief that at one time in its history it was the\nfavorite haunt of smugglers and pirates. Jewell is only a little island\nof but two hundred and twenty-one acres, one of the outer islands that\nfringe the boundaries of Casco Bay. Being out of the beaten path of\ntourist travel, it has not received the attention that its natural\nbeauties merit.\nGeorge Jewell, from whom the island is said to have taken its name, came\nfrom Saco, Maine, and is presumed to have purchased the island from the\nIndians in 1637.\nFrom earliest times it has been traditional in the history of Jewell\nIsland that a pirate\u2019s treasure lies hidden somewhere on its shores.\nJewell Island has several so-called \u201ctreasure markers.\u201d These \u201cmarkers\u201d\nare a pile of flat stones lain one on the other, until the marker\nreaches a height of about four or five feet. It is near these markers\nthat treasure was supposed to have been buried. How near, or just where,\nis a question that might be answered by your metal detector. I most\ncertainly would give the shore and beaches a good going over.\nThis island can be reached by the tourist boats that go to almost all\nthe islands in Casco Bay. If the boat does not stop at Jewell Island,\nyou can go to Cliff and cross over to Jewell by rowboat. The trip across\nthe channel is a short one.\n                         GREAT CHEBEAGUE ISLAND\nHere we have one of the largest islands in Casco Bay. The name is\npronounced \u201cShar-Big.\u201d This name in Indian language means \u201cland of many\nsprings.\u201d The Indians used this large island as a gathering place for\ntheir outings and feasts. Many Indian families would come to Chebeague\nIsland and spend the day boating, fishing and eating. The Indians were\nthe forerunners of the modern day tourist.\nOn Chebeague you will find large shell heaps still visible after\nhundreds of years. These piles of shells are the debris of countless\nfeasts held by the Indians.\nNumerous relics of these Indian days have been found, and as late as\n1935 crude implements of warfare, some household utensils, Indian\nskulls, and a curious stone pipe were unearthed.\nThe first legal document pertaining to Chebeague was a transfer of\nownership dated 1650, so this island also dates back to a period of\nseventeenth-century history. Chebeague has many large and small coves\nwhich should command your attention. When you land on Chebeague ask\nabout the old homes there. In the old days there were many homesteads on\nthis island and some of them still remain. The area surrounding these\nstructures should have a number of hidden relics buried around the yard.\nDon\u2019t forget to ask the owner for his O.K. before you start any\nexcavating.\nThe immediate shoreline would be the next location to receive a\ntreatment from your metal detector. As I have mentioned, the Indians had\ntheir outings along the beaches and shoreline. The metal detector, of\ncourse, is very valuable on a treasure hunt, but don\u2019t forget to use\nyour eyes also. Some of the artifacts you may discover will not be made\nof metal, but could be stone, wood or even leather. Articles such as\nthese, of course, would not register on your instrument, but\nnevertheless they would qualify as historical treasure.\nEven up to the present day some of these Indian relics are being found\nand preserved by local residents. The Maine Historical Society has a\nnice collection for your examination. The Society is located next to the\nLongfellow House on Congress Street, Portland. You will be most welcome;\ngo in and browse a bit. It is worth the time, as many interesting pieces\nare on display, and it will give you an idea of what you might uncover\nyourself.\nTo reach Great Chebeague Island you take a boat from Custom House Wharf,\nPortland. Most anyone can tell you how to get to the wharf. The boat\ntrip takes only a short time to reach this island of the Indian days.\nThe history of this island, located just across the channel in a\nnortherly direction from Peaks Island, dates back to the year 1635 when\na lease was given to George Cleeves and Richard Tucker by Sir Fernando\nGorges, the King of England\u2019s Representative. Diamond Island is one of\nthe earliest settled parts of our state. There is an old chart dated\n1760 that shows farm buildings on the south side of the island. One can\nstill see the remains of an old graveyard with unmarked stones. The deep\nwater near Diamond Cove was believed to be the area in which Captain\nChristopher Levett, the first white man to explore Casco Bay, anchored\nhis vessel in 1623.\nSir William Phips, the greatest treasure hunter of all time, also\nanchored at Great Diamond before going to the Louisburg campaign.\nThere is a particular area that should be examined carefully. This spot\nis almost directly across the channel from Trefethen\u2019s Landing of Peaks\nIsland. Here you will find an old abandoned ruin of a farmhouse cellar.\nThis old cellar belonged to one of the oldest farms on the island. I\nmost certainly would check this area very thoroughly, as articles of\nreal interest may still be in the vicinity. Check the old brick walls\nthen the inside area, after which proceed to go over the grounds\nsurrounding the cellar. Some of the ancient tools and implements may be\nwaiting for your metal detector to bring them to light.\nAt the beginning of this chapter I mentioned George Cleeves and Richard\nTucker. They were the founders of Portland, Maine, so this section of\nCasco Bay is a hub of the wheel of history in this bay and the state\nitself. The south shore is the side towards Peaks Island and the metal\ndetector should be used along the beaches and high ground on this side\nof the island. Don\u2019t forget to check around any large trees that stand\nalone, as the Indians liked to bury their dead in these areas. Stone\nclubs, tomahawks and grain grinding tools might be in the immediate\nvicinity.\nLooking back over the history of this island it wouldn\u2019t be too far\nfetched to imagine the landing here of pirates, maybe to take on fresh\nwater and lumber. Speaking of pirates, I would check the south-easterly\nend of the island, as this section is the closest to the open sea, a\ngood landing spot for a longboat coming from the old galleon itself\nanchored a few hundred yards from shore. It could be a locality where a\nlittle pirate loot may be buried, who knows?\nIn the vicinity of Harpswell you will find a small island that became\none of the most treasure explored islands in Casco Bay. Here we find, if\nwe check our legends of the islands, the spot of land in our island\nstudded bay that is said to be the location of the Boston Pirate Low\u2019s\nhidden treasure chest. To tell you a little about this I will go back to\nthe year 1726. At this time Pirate Low was sailing in and around Casco\nBay as he was preying on the northern shipping lanes.\nA Spanish galleon named \u201cDon Pedro Del Montclova\u201d left South America\nwith a treasure of gold and jewels bound for Spain. She sailed up from\nSouth America and reached the Florida Keys, then just as she started to\ncross the Atlantic, a British gunboat gave chase.\nThe galleon swung off her course and headed north along the Atlantic\nCoast until she finally outran the gunboat. She was now at the entrance\nof Casco Bay and her Captain thought that this would be a good location\nin which to hide among the many islands. What he did not know, however,\nwas that Pirate Low was anchored in Casco Bay and saw the Spanish\ngalleon coming around the point.\nLow boarded the galleon, killing the crew and sinking the ship. He then\nknew from talking to the Spanish crew previous to their killing, that\nthe British gunboat was on its way to the bay. Low decided to hide the\ntreasure as fast as he could. He landed on Pond Island and threw the\nchest of gold and jewels into the fresh water pond that is there. He\nknew the location of the pond because he had been there before to fill\nhis water casks.\nAfter hiding the treasure he immediately left the vicinity ahead of the\ngunboat. He was later captured and hung, so he never came back to claim\nhis hidden booty.\nMany treasure hunters have gone over this island and land surrounding\nthe old pond, but to my knowledge nobody has located this cache of gold\nand jewels. The pond itself is now dry, I understand. Maybe the treasure\nis deeper than average; instead of four or five feet deep, this one\ncould be fifteen or twenty feet deep. It is a problem in geology, just\nhow the wind and rain change the terrain in so long a time.\nI would say that a pretty sensitive detector should be used in this area\nin order to reach real depth.\nThis preceding tale is mostly legend passed down through the years, but\nwho knows whether or not it is all legend?\nI would give this island a very careful examination with my instrument\nif I were you. There\u2019s just no telling what is there.\nHere we have a fort that was started in 1808 and finished about 1812,\njust before the War of 1812. It was named for Commodore Preble,\nprominent in the Revolutionary Navy. At the time of the Civil War it was\nenlarged and had a complement of 72 guns. The early fortress was of\nwhitewashed brick ramparts which faced the channel.\nOn the site of this fort a log meeting house once stood, a gathering\nplace for the earliest settlers of this area. This location may be\nreached by going to South Portland and proceeding to the Maine\nVocational Technical Institute on Fort Road. This school now occupies\nthe Fort Preble grounds. The old fortifications are in the rear of the\ngrounds at the water\u2019s edge.\nWhen you arrive at the fort, go to the Administration Building and\nsecure permission to check the old ramparts.\nHere you will find many old gun emplacements. These should be given your\nundivided attention; use your metal detector very carefully as many\nartifacts and relics must still be lying about. Don\u2019t forget to check\nthe beach area in front of the old ramparts. The ground inside the\ngranite walls should be another interesting spot for the metal detector.\nOne of the earliest cemeteries in the entire Cape is located on this\npoint of land. It is called the \u201cThrasher\u201d burying ground. The Thrashers\nwere the early settlers of this area. They had a large farm on the point\nback in the 1600\u2019s.\nMuch trading with the Indians took place on Fort Point where Preble was\nerected, so I would definitely not miss this location on my treasure\nhunting expedition.\nAs I mentioned earlier the Civil War was in progress when the fort was\nenlarged. There are probably many articles of this period still in the\ncompounds of old Fort Preble, so go over the area and see what you can\ncome up with. I\u2019m sure your time will not be wasted.\nThis is one of the easiest locations to reach, as it is on the mainland,\nand a short ride from Portland either by bus or taxi. There is a\nrestaurant within hailing distance of the fort, so you can get a lunch\nand keep right on with your search.\nConsiderable Indian interest is attached to French\u2019s Island in the lower\nbay. An Indian skull was found under three feet of clam shells and it\nwas figured that the skull was three or four centuries old.\nFrench\u2019s Island is located between Great Chebeague and Goose Island and\nto the south of Bustin\u2019s Island. To reach this island you proceed to\nFlying Point, Freeport, then by boat to Bustin\u2019s Island, then over to\nFrench\u2019s. It is a short trip from the mainland. You will have to hire\nsomeone with a motorboat to take you across the bay. This island is\nprivately owned, so permission must be secured before you land and start\nyour treasure hunt. I believe a Portland resident owns this island. A\ncheck of the records will no doubt reveal the owner\u2019s name and address.\nThe finding of an Indian skull proves that if there were Indians on\nFrench\u2019s Island there could have been early settlers, and also pirates\non this small island. In days gone by some of the pirates preferred\nsmall islands on which to hide their ill-gotten gains.\nWhen going over this island I would give special attention to the\nbeaches. The pirates sometimes buried their treasure in a hurry, as a\ngovernment boat would be coming up fast in pursuit. It has been\nmentioned in the history books that this island was a headquarters for\nan Indian Sagamore, or Chief. Some of their trinkets and relics of the\nearly settlers may still be hidden from view awaiting your detection.\nMany of these small islands had clear fresh water springs that attracted\nthe seafarer. The longboats would put in and fill their casks with fresh\nwater for the coming voyage, so a check in this area for a spring might\npay off.\nAgain I say, please be sure to get permission from the property owners\nbefore you proceed with your expedition.\nHere history tells us that the first settlers arrived about 1743. This\nisland is one of the larger islands of Casco Bay and there are still\nmany of the old homesteads there. A definite link with this early period\nstill standing on Bailey Island is the so-called \u201cGardiner\u201d house built\nin 1818. It stands back from the road at the northern end of the island\nand in the rear is an ancient well. The timber came from the ruins of a\nlog house built by Deacon Timothy Bailey, for whom the island was named.\nAnother interesting house on the island is one called the \u201cCaptain Jot\u201d\nhomestead. As the name implies, this house belonged to a sea captain. It\ndates from 1763, an interesting location for the treasure seeker. Your\ndetector should be able to locate something of interest in this\nvicinity.\nThere are many spots to be checked on this island. A good idea is to ask\nthe natives where these old houses are.\nI have found that the inhabitants of a particular locale can tell you\nthe history of various points of interest, as most of the older folk\nhave this information at their finger tips. It usually pleases them, the\nfact that you are asking questions about their own backyard. They will\npoint out many facts and locations that the history books have\noverlooked.\nThis island may be reached from the mainland. From Portland take the\nhighway leading to Brunswick, Maine. There you will find signs directing\nyou to Bailey\u2019s Island. It is a beautiful trip to the island. The road\nis bordered by tall Maine pines, rolling meadows, streams, old farms and\nneat modern homes. To me the trip down to the island is one of lasting\nmemory.\nDuring your treasure hunting time on the island, don\u2019t forget to have\nsome tasty Maine lobster for lunch. You can purchase these delicious\nmorsels right on the island all cooked. There are tables and benches at\nwhich you may sit while enjoying one of Maine\u2019s famous lobster dinners.\nThe beaches that face the open sea should be checked carefully with your\ndetector, as many landings have taken place here from 1763 until today.\nWho knows what might be buried along these shores? This island should be\none of the finest on your check list, as it is so easy to reach. The\nauthor wishes you the best of luck here.\nOne of America\u2019s famous authors, Harriet Beecher Stowe, made this island\nstand out in the annals of Casco Bay by writing her popular story, \u201cThe\nPearl of Orr\u2019s Island.\u201d This story was published in 1862 when the island\nitself was practically isolated and unknown. The appearance of this\nstory was a literary event for thousands of Mrs. Stowe\u2019s readers.\nThe island takes its name from two brothers; namely, Clement and John\nOrr, who in 1748 bought the greater part of the island for two shillings\nan acre. The brothers originally came from the north of Ireland.\nHere on Orr\u2019s the treasure hunter will find at the north end of Long\nCove a small cove that is known as \u201cSmuggler\u2019s Cove.\u201d Orr\u2019s Island is\nprobably the best known island in Casco Bay. In the old days a rickety\nold wooden bridge was built by the settlers to connect the island with\nthe mainland, and it was really living dangerously to go over this\nancient structure. This old bridge has now been replaced by a modern\ncauseway.\nOn the Island of Orr\u2019s many Indian attacks were repulsed by the early\ninhabitants. If you are real careful when searching with your detector,\nyou should find Indian relics or artifacts that were buried by the\nsea-going population of the 1700\u2019s. Many a three- and six-masted\nschooner sailed in and out of the harbor at Orr\u2019s Island. Who knows what\npirate ship visited this area in the dark of night with maybe a\ncontraband cargo?\nIn this area I think that I would check every little cove and inlet very\ncarefully. Most anything might be found hidden along the shores and,\nalso, near some of the old dwelling sites. A good check along the\nroadway to and from the island might reveal a hidden article. Especially\ncheck both sides of the roadway and work back a ways from the edge of\nthe road about twenty or thirty feet. The old road did quite a bit of\ncurving as it wound its way to the island. These curves have been\neliminated to a great extent with the building of the new road. As I\nmentioned, if you grid the area well back from the road, you have an\nexcellent chance of discovering some by-gone article. It could be a\npewter mug, buckles from shoes, gold coins and who knows what else?\nTake your metal detector and ply the ocean side of the island. This\nsection seems most likely to have been populated by the seaman,\nsmuggler, pirate or what have you. It may be, that during trading and\nmaking business deals with each other, the seaman could have lost some\ncoins in the dirt to be buried over and lost for hundreds of years. Also\nmany of the natives, no doubt, kept their savings in the private caches\nburied from sight at the rear of their cabins.\nAnother likely area to check out would be the area where the old ferry\nused to dock. The ferry ran from Orr\u2019s Island to Bailey\u2019s Island. If you\nwanted to take the trip you signaled the ferryman by lowering the flag\nthat was flying high on the tall flagpole. The ferry would proceed\nacross the narrow passage of water known as Will\u2019s Gut. The fare was\nfifteen cents to Bailey\u2019s Island, but to return to Orr\u2019s Island, it\nwould cost you twenty-five cents.\nThe sea trip from Portland to Orr\u2019s Island by the island steamers of\nCasco Bay is a journey to remember. You, of course, can reach Orr\u2019s\nIsland by automobile via a road that swings down to Orr\u2019s from\nBrunswick, Maine. When you reach Brunswick just follow the signs and\nsoon you will be on the \u201cIsland of the Pearl.\u201d Good hunting to you.\nThis long neck of scenic beauty is a close neighbor of Orr\u2019s Island. It\nlies to the north, northwest and can be reached by auto via the rotary\ntraffic circle at Brunswick, Maine.\nMany stories and tales have been written about Harpswell, some fact and\nothers legend. Each has its own place in American literature. Located on\nthe east side of the Harpswells is the site of the Skolfield Shipyard.\nThis yard was the birthplace of many rugged sea-going vessels. Some were\nthree masted and others six. These full-rigged ships sailed into\npractically every seaport along the Atlantic Coast. A visit to this site\nwill be worth your time. The next stop on our tour of Harpswell might be\nthe old meeting house where the early settlers held their town meetings\nand discussed the Indian problem. The area near the meeting house would\nbe a good hunting ground for your detector, but please don\u2019t forget to\nsecure trespassing rights before you proceed with your search.\nOne of the phantom legends of Harpswell, and perhaps one of the best,\nwas put into poetry by one of America\u2019s best known poets; namely, John\nGreenleaf Whittier. His poem was called, \u201cThe Dead Ship of Harpswell.\u201d\nIt was written in 1866 and was inspired by the legendary tale told to\nthe younger set by their grandfathers and grandmothers. I suppose a few\ngreat-grandmothers and grandfathers also told the ghostly tale. The\npreceding words of phantom legend will give you a bit of atmosphere when\nyou arrive on Harpswell.\nAs you go down this peninsula check all coves and inlets with your\ninstrument. Leave nothing uninvestigated, as this area is one of several\nthat was abandoned in the late 1600\u2019s due to Indian uprisings.\nI would give my special attention to Pott\u2019s Point; this point is located\non the very end of the neck and a good place for pirates or smugglers to\nland and hide a chest of doubloons, pieces-of-eight or other booty taken\nfrom some poor unfortunate vessel that came into their grasp. Check the\nbeach area, then go into the interior of the \u201cPoint.\u201d Many treasures\nhave been buried under a large tree or boulder that was a thousand yards\nfrom the shore. If you see a rocky cave or large boulder check them for\nmysterious markings, such as crosses, circles, arrows and such, carved\nor cut into the rocky surface. Some of these hidden treasures have been\nlocated by following a crude direction sign left by a cut-throat on a\nrocky ledge or in a rocky cave.\nUse your probing rods as you check with the detector. The exact center\nof the location of any buried object can be determined much more easily\nwith the probe. Your camera also is a much needed piece of equipment.\nYou can record your treasure hunting progress on film for viewing by\nyour interested treasure-seeking friends. Study your movies or still\npictures with your associates. Maybe some suggestions by them would be\nof real help to you on your next treasure expedition.\n\u201cShelter Island,\u201d as you pronounce the name, it sounds almost like\n\u201cTreasure Island\u201d of Robert Louis Stevenson fame. It not only sounds\nlike it, but this island comes as close to \u201cTreasure Island\u201d as any\nisland in the entire bay. We don\u2019t seem to read or hear too much about\nthis small island in the very middle of Casco Bay. It is more or less\nhidden from the open sea and was a perfect hiding place for the smuggler\nand privateer who plied these waters while trying to escape and hide\nfrom the revenue cutters.\nWhat I have just mentioned in the preceding paragraph should make a\ntreasure hunter\u2019s ears stand up. This island was not a refuge for\nsmugglers and pirates only; it also was a refuge for the early settlers\nof Mere Point on the mainland. The settlers would be driven from the\nmainland by vicious attacks from the Indians, and they would flee to\ntheir blockhouse on Shelter Island. This blockhouse was built for this\nexact purpose, so you can imagine what you might find on this island in\nthe way of buried treasure; not only artifacts from the early settler\ndays, but also relics from the old days of smuggling and privateering.\nThe location of Shelter Island is as follows: Take the Harpswell road\nfrom Brunswick on Route 1 and proceed about half way down the Harpswell\nNeck, then go to the northern side of the shoreline. There you will see\nShelter Island just off shore. The Author has never been over to the\nisland, but has seen it from a distance. It looks very inviting as a\nspot to do some real down-to-earth treasure hunting.\nOn my trip to Harpswell, I think that I would inquire as to the\nownership of this little island, and try to include it in my tour of\ntreasure hunting locations. Here is a nice area for the metal detector\nand probe to do their work. I think, with any luck at all, you should\nlocate something of treasure value here.\nPlease check as to trespassing rights before you land here. It\u2019s better\nto be safe than sorry. I most certainly would check the coves and\nbeaches very carefully, especially any good landing place for a\nlongboat.\nOn our way down the bay we will find Long Island nestled in between\nPeaks and Great Chebeague Islands, but don\u2019t sell this island short, as\nit has a history going back to the sixteen hundreds. The first settlers\nwere here around 1640, so you see we have a background of real early\nhistory on Long Island.\nThe Indians gave special attention to Long Island because of its many\nfresh water springs. It was, and still is, a delightful place to put on\nan old fashioned shore dinner. The early settlers and Indians would join\ntogether and have a mammoth outdoor shore dinner on this island to\ncelebrate some new trading deal between each other.\nThere are several nice beaches that should receive your attention when\nchecking with the detector, but, by all means, don\u2019t forget to check the\nareas surrounding the fresh water springs. The areas leading back from\nthe beaches should be gone over with the thought in mind to watch for\nthe sunken ground locations that could have been the site of old log\ncabins or vegetable cellars. Many a treasure has been uncovered in a\nlocale such as this.\nStone walls also are a source of buried monies and household valuables.\nA small metal detector would be just the instrument to use when checking\nout cellars, walls, floors, old wells, etc. The six-inch loop detector\nwould be perfect for this type of hunting. These small detectors are\nmuch more sensitive than the larger ones when seeking small objects.\nSome of these smaller detectors also will detect through salt water\nwhere the larger detector will work only through fresh water. The larger\ndetector, of course, will give you greater depth. I have read where some\nof these larger instruments will detect a metal object that is five feet\nlong at a depth of twenty feet. This is a super job of metal detection.\nThe type of detector used, of course, has a lot to do with the size of\nthe object that you are searching for. Personally, if I were a novice at\ntreasure hunting, I would purchase a small detector and learn how to\noperate it before purchasing a larger one. Of course, if you know how to\noperate a detector, the size will make no difference whatsoever. The\nAuthor has a small detector and is now thinking about the purchase of a\nlarger model. The choice of size is strictly up to you. Happy Hunting!\nTo locate this small island we will follow Route 1 north from Portland\nuntil we reach Freeport Village. Here we will make a right turn at the\nyellow blinker light and follow the signs to Flying Point. When we reach\nFlying Point we will look offshore across the small bay and there we\nwill see Pettengill Island. There are no inhabitants on this island\nalthough I believe it is privately owned.\nThe Author rowed over to Pettengill and landed on the rocky southwest\npoint. Here I discovered an old iron cleat that had been sunk into a\nlarge boulder. The hole in the rock had been hand drilled to accommodate\nthe cleat. Whoever drilled this socket in the hard rock surely worked\nhard, as I could see it would take a person three or four hours to drill\na hole this deep with a hand drill. What type of boat was moored to this\ncleat would be anyone\u2019s guess. The cleat was checked as to age and was\nbelieved to be about a hundred years old.\nThere are several open areas in the thick pine groves that could easily\nbe locations for buried treasure. On the easterly side of the island you\nwill find a small cove and perfect beach for landing. Maybe some band of\npirates also thought that this cove was a good spot to land and hide a\nbit of loot. I would go over this cove area very carefully, and as I\nmentioned, don\u2019t forget the southwest point of the island. I still think\nyou could come up with something at either location. Your iron probe\nwould serve you in good stead, as most of the clearings are covered with\npine needles. The probe will push easily through the needles until you\nreach harder ground. Most of the islands are very rocky, so anything\nthat was buried would not be too deep due to the rocky condition,\nprobably two or three feet deep in the ground.\n                      SEBASCODEGAN or GREAT ISLAND\nThis large island lies between Orr\u2019s Island and the mainland. You will\ncross this island on your way to Orr\u2019s Island and Bailey\u2019s Island. It\nseems to be part of the mainland but actually is not. The name\n\u201cSebascodegan\u201d in Indian language means \u201cmarshy place and a place for\ngun-firing.\u201d Thus, the interpretation would mean \u201ca good place for\nhunting water fowl.\u201d\nTo reach Sebascodegan proceed the same way as though you were going to\nOrr\u2019s Island. That is, go to Brunswick and follow the signs to Orr\u2019s and\nBailey\u2019s. On the way down the neck you will notice several historic old\nchurches with the old burying ground nearby. Many of the old gravestones\nhave some really interesting epitaphs. It is worth a short stop just to\nread a few of these.\nThe first settlers to reach Sebascodegan arrived in the year 1639. The\nfirst bridge to the mainland was built in 1839, so you see, you also\nhave some real old history connected with this area of the bay.\nNear the end of the Revolutionary War several British privateers were\npreying on the shipping lanes in and around Casco Bay. One of the most\nnotorious of these sea-going bandits was a \u201cCaptain Linnacum.\u201d He was of\nScotch descent and commanded a schooner called the \u201cPicaroon.\u201d This\npirate captured many luckless coasting boats, and it is said, he buried\nseveral caches of loot in and around Sebascodegan Island. Nobody seems\nto know just where the treasures might be hidden. The many caves and\ninlets should command your attention. I also would not forget to check\nthe inland areas. In the old days this island was criss-crossed with\nIndian trails, so you see, anything might be unearthed along some of\nthese old trails. Of course, the trails have long since disappeared, but\nI would use my detector in general directions leading from the coves to\nthe forests. I would give special attention to river banks and brooks.\nThere has been many a rich find located in the vicinity of a river or\nstream.\nThe Brunswick Chamber of Commerce used to put out a regional map of the\nBrunswick area. This map was a very good job, and it showed many of the\nislands in the Brunswick area. You might stop and check at the Chamber\nof Commerce. They may still be able to help you.\nCundy\u2019s Harbor is located on the very end of this island and it would be\na likely spot for any pirate to anchor to come ashore. I would not\nforget to go over this area very carefully with my detector. You could\nask some of the natives where the schooners used to land in the old\ndays. I am sure they would be pleased to help you with some information\non the subject.\n    [Illustration: Sailing ship]\n                       TREASURE HUNTING EQUIPMENT\nSome of the treasure hunters that I know really load themselves down\nwith all sorts of equipment. They remind me of a pack mule. You do not\nhave to have a truck load of this hardware on your back. Here I will\nmention the essential articles you should take along on your next\ntreasure hunting expedition.\nFirst, I would put down on my list a metal detector, of course. Next, I\nwould take a folding Army trench shovel. These can be purchased in\nalmost all Army surplus stores. Next, I would take along my camera,\nmovie or still, and several rolls of film. A permanent record on film\ncan be enjoyed in years to come. The next article to be brought along\nshould be an iron probing bar. You could make your own or purchase one\nfrom the metal detector dealer. They are very inexpensive and very\nvaluable on a treasure hunt. If you decide to make your own, just obtain\na five-foot length of \u00bc-inch rolled steel. This may be purchased from\nany steel manufacturing plant.\nNext on the list should be old clothes. Never go on a treasure hunt with\nyour best clothes on. You may have to wade along a breakwater, cross a\nbrook, and who knows what else. I know I got caught by the in-coming\ntide one day and had to walk along a breakwater up to my hips in the\ncold Atlantic. Wear a pair of old shoes or canvas loafers. Something you\ndon\u2019t care about and then it will make no difference if they get a salt\nbath or covered with mud.\nLast, but by no means least, take along plenty of lunch, or be sure that\nthe area in which you intend to hunt contains a store or a Maine lobster\nshop. This Maine sea air will create a terrific appetite.\nBest of luck to all my readers.\n                  William Willis\u2019 History of Portland\n                        State of Maine Librarian\n\u2014Silently corrected a few typos.\n\u2014Retained publication information from the printed edition: this eBook\n  is public-domain in the country of publication.\n\u2014In the text versions only, text in italics is delimited by\n  _underscores_.\nEnd of the Project Gutenberg EBook of Buried Treasure of Casco Bay, by \nBernett Faulkner Kennedy, Jr.\n*** END OF THIS PROJECT GUTENBERG EBOOK BURIED TREASURE OF CASCO BAY ***\n***** This file should be named 58609-0.txt or 58609-0.zip *****\nThis and all associated files of various formats will be found in:\nProduced by Stephen Hutcheson and the Online Distributed\nUpdated editions will replace the previous one--the old editions will\nbe renamed.\nCreating the works from print editions not protected by U.S. copyright\nlaw means that no one owns a United States copyright in these works,\nso the Foundation (and you!) can copy and distribute it in the United\nStates without permission and without paying copyright\nroyalties. 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{"source_document": "", "creation_year": 1946, "culture": " English\n", "content": "Produced by Greg Weeks, Mary Meehan and the Online\n[Transcriber's Note: This etext was produced from Orbit volume 1 number\n2, 1953. Extensive research did not uncover any evidence that the U.S.\ncopyright on this publication was renewed.]\n[Sidenote: HER ONLY PASSION WAS BEAUTY--BEAUTY WHICH WOULD LAST FOREVER.\nAND FOR IT--SHE'D DO ANYTHING!]\n[Illustration ]\nNinon stretched. And purred, almost. There was something lazily catlike\nin her flexing; languid, yet ferally alert. The silken softness of her\ncouch yielded to her body as she rubbed against it in sensual delight.\nThere was almost the litheness of youth in her movements.\nIt was true that some of her joints seemed to have a hint of stiffness\nin them, but only _she_ knew it. And if some of the muscles beneath her\npolished skin did not respond with quite the resilience of the youth\nthey once had, only _she_ knew that, too. _But they would again_, she\ntold herself fiercely.\nShe caught herself. She had let down her guard for an instant, and a\nfrown had started. She banished it imperiously. Frowns--just one\nfrown--could start a wrinkle! And nothing was as stubborn as a wrinkle.\nOne soft, round, white, long-nailed finger touched here, and here, and\nthere--the corners of her eyes, the corners of her mouth, smoothing\nthem.\nWrinkles acknowledged only one master, the bio-knife of the facial\nsurgeons. But the bio-knife could not thrust deep enough to excise the\nstiffness in a joint; was not clever enough to remold the outlines of a\nfigure where they were beginning to blur and--sag.\nNo one else could see it--yet. But Ninon could!\nAgain the frown almost came, and again she scourged it fiercely into the\nback of her mind. Time was her enemy. But she had had other enemies, and\ndestroyed them, one way or another, cleverly or ruthlessly as\ncircumstances demanded. Time, too, could be destroyed. Or enslaved.\nNinon sorted through her meagre store of remembered reading. Some old\nphilosopher had said, \"If you can't whip 'em, join 'em!\" Crude, but apt.\nNinon wanted to smile. But smiles made wrinkles, too. She was content to\nfeel that sureness of power in her grasp--the certain knowledge that\nshe, first of all people, would turn Time on itself and destroy it. She\nwould be youthful again. She would thread through the ages to come, like\na silver needle drawing a golden filament through the layer on layer of\nthe cloth of years that would engarment her eternal youth. Ninon knew\nhow.\nHer shining, gray-green eyes strayed to the one door in her apartment\nthrough which no man had ever gone. There the exercising machines; the\nlotions; the unguents; the diets; the radioactive drugs; the records of\nendocrine transplantations, of blood transfusions. She dismissed them\ncontemptuously. Toys! The mirages of a pseudo-youth. She would leave\nthem here for someone else to use in masking the downhill years.\nThere, on the floor beside her, was the answer she had sought so long. A\nbook. \"Time in Relation to Time.\" The name of the author, his academic\nrecord in theoretical physics, the cautious, scientific wording of his\npostulates, meant nothing to her. The one thing that had meaning for her\nwas that Time could be manipulated. And she would manipulate it. For\nNinon!\nThe door chimes tinkled intimately. Ninon glanced at her watch--Robert\nwas on time. She arose from the couch, made sure that the light was\nbehind her at just the right angle so he could see the outlines of her\nfigure through the sheerness of her gown, then went to the door and\nopened it.\nA young man stood there. Young, handsome, strong, his eyes aglow with\nthe desire he felt, Ninon knew, when he saw her. He took one quick step\nforward to clasp her in his strong young arms.\n\"Ninon, my darling,\" he whispered huskily.\nNinon did not have to make her voice throaty any more, and that annoyed\nher too. Once she had had to do it deliberately. But now, through the\nyears, it had deepened.\n\"Not yet, Robert,\" she whispered. She let him feel the slight but firm\nresistance so nicely calculated to breach his own; watched the deepening\nflush of his cheeks with the clinical sureness that a thousand such\nexperiences with men had given her.\nThen, \"Come in, Robert,\" she said, moving back a step. \"I've been\nwaiting for you.\"\nShe noted, approvingly, that Robert was in his spaceman's uniform, ready\nfor the morrow's flight, as he went past her to the couch. She pushed\nthe button which closed and locked the door, then seated herself beside\nthe young spaceman on the silken couch.\nHis hands rested on her shoulders and he turned her until they faced\neach other.\n\"Ninon,\" he said, \"you are so beautiful. Let me look at you for a long\ntime--to carry your image with me through all of time and space.\"\nAgain Ninon let him feel just a hint of resistance, and risked a tiny\npout. \"If you could just take me with you, Robert....\"\nRobert's face clouded. \"If I only could!\" he said wistfully. \"If there\nwere only room. But this is an experimental flight--no more than two can\ngo.\"\nAgain his arms went around her and he leaned closer.\n\"Wait!\" Ninon said, pushing him back.\n\"Wait? Wait for what?\" Robert glanced at his watch. \"Time is running\nout. I have to be at the spaceport by dawn--three hours from now.\"\nNinon said, \"But that's three hours, Robert.\"\n\"But I haven't slept yet tonight. There's been so much to do. I should\nrest a little.\"\n\"I'll be more than rest for you.\"\n\"Yes, Ninon.... Oh, yes.\"\n\"Not yet, darling.\" Again her hands were between them. \"First, tell me\nabout the flight tomorrow.\"\nThe young spaceman's eyes were puzzled, hurt. \"But Ninon, I've told you\nbefore ... there is so much of you that I want to remember ... so little\ntime left ... and you'll be gone when I get back....\"\nNinon let her gray-green eyes narrow ever so slightly as she leaned away\nfrom him. But he blundered on.\n\"... or very old, no longer the Ninon I know ... oh, all right. But you\nknow all this already. We've had space flight for years, but only\nrocket-powered, restricting us to our own system. Now we have a new kind\nof drive. Theoretically we can travel faster than light--how many times\nfaster we don't know yet. I'll start finding out tomorrow, with the\nfirst test flight of the ship in which the new drive is installed. If it\nworks, the universe is ours--we can go anywhere.\"\n\"Will it work?\" Ninon could not keep the avid greediness out of her\nvoice.\nRobert said, hesitantly, \"We think it will. I'll know better by this\ntime tomorrow.\"\n\"What of you--of me--. What does this mean to us--to people?\"\nAgain the young spaceman hesitated. \"We ... we don't know, yet. We think\nthat time won't have the same meaning to everyone....\"\n\"... When you travel faster than light. Is that it?\"\n\"Well ... yes. Something like that.\"\n\"And I'll be--old--or dead, when you get back? If you get back?\"\nRobert leaned forward and buried his face in the silvery-blonde hair\nwhich swept down over Ninon's shoulders.\n\"Don't say it, darling,\" he murmured.\nThis time Ninon permitted herself a wrinkling smile. If she was right,\nand she knew she was, it could make no difference now. There would be no\nwrinkles--there would be only the soft flexible skin, naturally soft and\nflexible, of real youth.\nShe reached behind her, over the end of the couch, and pushed three\nbuttons. The light, already soft, dimmed slowly to the faintest of\nglows; a suave, perfumed dusk as precisely calculated as was the exact\nrate at which she let all resistance ebb from her body.\nRobert's voice was muffled through her hair. \"What were those clicks?\"\nhe asked.\nNinon's arms stole around his neck. \"The lights,\" she whispered, \"and a\nlittle automatic warning to tell you when it's time to go....\"\nThe boy did not seem to remember about the third click. Ninon was not\nquite ready to tell him, yet. But she would....\nTwo hours later a golden-voiced bell chimed, softly, musically. The\nlights slowly brightened to no more than the lambent glow which was all\nthat Ninon permitted. She ran her fingers through the young spaceman's\ntousled hair and shook him gently.\n\"It's time to go, Robert,\" she said.\nRobert fought back from the stubborn grasp of sleep. \"So soon?\" he\nmumbled.\n\"And I'm going with you,\" Ninon said.\nThis brought him fully awake. \"I'm sorry, Ninon. You can't!\" He sat up\nand yawned, stretched, the healthy stretch of resilient youth. Then he\nreached for the jacket he had tossed over on a chair.\nNinon watched him with envious eyes, waiting until he was fully alert.\n\"Robert!\" she said, and the youth paused at the sharpness of her voice.\n\"How old are you?\"\n\"I've told you before, darling--twenty-four.\"\n\"How old do you think I am?\"\nHe gazed at her in silent curiosity for a moment, then said, \"Come to\nthink of it, you've never told me. About twenty-two or -three, I'd say.\"\n\"Tomorrow is my birthday. I'll be fifty-two.\"\nHe stared at her in shocked amazement. Then, as his gaze went over the\nsmooth lines of her body, the amazement gave way to disbelief, and he\nchuckled. \"The way you said it, Ninon, almost had me believing you. You\ncan't possibly be that old, or anywhere near it. You're joking.\"\nNinon's voice was cold. She repeated it: \"I am fifty-two years old. I\nknew your father, before you were born.\"\nThis time she could see that he believed it. The horror he felt was easy\nto read on his face while he struggled to speak. \"Then ... God help\nme ... I've been making love to ... an old woman!\" His voice was low,\nbitter, accusing.\nNinon slapped him.\nHe swayed slightly, then his features froze as the red marks of her\nfingers traced across his left cheek. At last he bowed, mockingly, and\nsaid, \"Your pardon, Madame. I forgot myself. My father taught me to be\nrespectful to my elders.\"\nFor that Ninon could have killed him. As he turned to leave, her hand\nsought the tiny, feather-light beta-gun cunningly concealed in the folds\nof her gown. But the driving force of her desire made her stay her hand.\n\"Robert!\" she said in peremptory tones.\nThe youth paused at the door and glanced back, making no effort to\nconceal the loathing she had aroused in him. \"What do you want?\"\nNinon said, \"You'll never make that flight without me.... Watch!\"\nSwiftly she pushed buttons again. The room darkened, as before. Curtains\nat one end divided and rustled back, and a glowing screen sprang to life\non the wall revealed behind them. And there, in life and movement and\ncolor and sound and dimension, she--and Robert--projected themselves,\ntogether on the couch, beginning at the moment Ninon had pressed the\nthree buttons earlier. Robert's arms were around her, his face buried in\nthe hair falling over her shoulders....\nThe spaceman's voice was doubly bitter in the darkened room. \"So that's\nit,\" he said. \"A recording! Another one for your collection, I suppose.\nBut of what use is it to you? I have neither money nor power. I'll be\ngone from this Earth in an hour. And you'll be gone from it,\npermanently--at your age--before I get back. I have nothing to lose, and\nyou have nothing to gain.\"\nVenomous with triumph, Ninon's voice was harsh even to her ears. \"On the\ncontrary, my proud and impetuous young spaceman, I have much to gain,\nmore than you could ever understand. When it was announced that you were\nto be trained to command this experimental flight I made it my business\nto find out everything possible about you. One other man is going. He\ntoo has had the same training, and could take over in your place. A\nthird man has also been trained, to stand by in reserve. You are\nsupposed to have rested and slept the entire night. If the Commandant of\nSpace Research knew that you had not....\"\n\"I see. That's why you recorded my visit tonight. But I leave in less\nthan an hour. You'd never be able to tell Commander Pritchard in time to\nmake any difference, and he'd never come here to see....\"\nNinon laughed mirthlessly, and pressed buttons again. The screen\nchanged, went blank for a moment, then figures appeared again. On the\ncouch were she and a man, middle-aged, dignified in appearance,\nuniformed. Blane Pritchard, Commandant of Space Research. His arms were\naround her, and his face was buried in her hair. She let the recording\nrun for a moment, then shut it off and turned up the lights.\nTo Robert, she said, \"I think Commander Pritchard would be here in five\nminutes if I called and told him that I have information which seriously\naffects the success of the flight.\"\nThe young spaceman's face was white and stricken as he stared for long\nmoments, wordless, at Ninon. Then in defeated tones he said, \"You\nscheming witch! What do you want?\"\nThere was no time to gloat over her victory. That would come later.\nRight now minutes counted. She snatched up a cloak, pushed Robert out\nthrough the door and hurried him along the hall and out into the street\nwhere his car waited.\n\"We must hurry,\" she said breathlessly. \"We can get to the spaceship\nahead of schedule, before your flight partner arrives, and be gone from\nEarth before anyone knows what is happening. I'll be with you, in his\nplace.\"\nRobert did not offer to help her into the car, but got in first and\nwaited until she closed the door behind her, then sped away from the\ncurb and through the streets to the spaceport.\nNinon said, \"Tell me, Robert, isn't it true that if a clock recedes from\nEarth at the speed of light, and if we could watch it as it did so, it\nwould still be running but it would never show later time?\"\nThe young man said gruffly, \"Roughly so, according to theory.\"\n\"And if the clock went away from Earth faster than the speed of light,\nwouldn't it run backwards?\"\nThe answer was curtly cautious. \"It might appear to.\"\n\"Then if people travel at the speed of light they won't get any older?\"\nRobert flicked a curious glance at her. \"If you could watch them from\nEarth they appear not to. But it's a matter of relativity....\"\nNinon rushed on. She had studied that book carefully. \"And if people\ntravel faster than light, a lot faster, they'll grow younger, won't\nthey?\"\nRobert said, \"So that's what's in your mind.\" He busied himself with\nparking the car at the spaceport, then went on: \"You want to go back in\nthe past thirty years, and be a girl again. While I grow younger, too,\ninto a boy, then a child, a baby, at last nothing....\"\n\"I'll try to be sorry for you, Robert.\"\nNinon felt again for her beta-gun as he stared at her for a long minute,\nhis gaze a curious mixture of amusement and pity. Then, \"Come on,\" he\nsaid flatly, turning to lead the way to the gleaming space ship which\npoised, towering like a spire, in the center of the blast-off basin. And\nadded, \"I think I shall enjoy this trip, Madame, more than you will.\"\nThe young man's words seemed to imply a secret knowledge that Ninon did\nnot possess. A sudden chill of apprehension rippled through her, and\nalmost she turned back. But no ... there was the ship! There was youth;\nand beauty; and the admiration of men, real admiration. Suppleness in\nher muscles and joints again. No more diets. No more transfusions. No\nmore transplantations. No more the bio-knife. She could smile again, or\nfrown again. And after a few years she could make the trip again ... and\nagain....\nThe space ship stood on fiery tiptoes and leaped from Earth, high into\nthe heavens, and out and away. Past rusted Mars. Past the busy\nasteroids. Past the sleeping giants, Jupiter and Saturn. Past pale\nUranus and Neptune; and frigid, shivering Pluto. Past a senseless,\nflaming comet rushing inward towards its rendezvous with the Sun. And on\nout of the System into the steely blackness of space where the stars\nwere hard, burnished points of light, unwinking, motionless; eyes--eyes\nstaring at the ship, staring through the ports at Ninon where she lay,\nstiff and bruised and sore, in the contoured acceleration sling.\nThe yammering rockets cut off, and the ship seemed to poise on the ebon\nlip of a vast Stygian abyss.\nJoints creaking, muscles protesting, Ninon pushed herself up and out of\nthe sling against the artificial gravity of the ship. Robert was already\nseated at the controls.\n\"How fast are we going?\" she asked; and her voice was rusty and harsh.\n\"Barely crawling, astronomically,\" he said shortly. \"About forty-six\nthousand miles a minute.\"\n\"Is that as fast as the speed of light?\"\n\"Hardly, Madame,\" he said, with a condescending chuckle.\n\"Then make it go faster!\" she screamed. \"And faster and faster--hurry!\nWhat are we waiting for?\"\nThe young spaceman swivelled about in his seat. He looked haggard and\ndrawn from the strain of the long acceleration. Despite herself, Ninon\ncould feel the sagging in her own face; the sunkenness of her eyes. She\nfelt tired, hating herself for it--hating having this young man see\nher.\nHe said, \"The ship is on automatic control throughout. The course is\nplotted in advance; all operations are plotted. There is nothing we can\ndo but wait. The light drive will cut in at the planned time.\"\n\"Time! Wait! That's all I hear!\" Ninon shrieked. \"Do something!\"\nThen she heard it. A low moan, starting from below the limit of\naudibility, then climbing, up and up and up and up, until it was a\nnerve-plucking whine that tore into her brain like a white-hot tuning\nfork. And still it climbed, up beyond the range of hearing, and up and\nup still more, till it could no longer be felt. But Ninon, as she\nstumbled back into the acceleration sling, sick and shaken, knew it was\nstill there. The light drive!\nShe watched through the ports. The motionless, silent stars were moving\nnow, coming toward them, faster and faster, as the ship swept out of the\ngalaxy, shooting into her face like blazing pebbles from a giant\nslingshot.\nShe asked, \"How fast are we going now?\"\nRobert's voice sounded far off as he replied, \"We are approaching the\nspeed of light.\"\n\"Make it go faster!\" she cried. \"Faster! Faster!\"\nShe looked out the ports again; looked back behind them--and saw shining\nspecks of glittering blackness falling away to melt into the sootiness\nof space. She shuddered, and knew without asking that these were stars\ndropping behind at a rate greater than light speed.\n\"Now how fast are we going?\" she asked. She was sure that her voice was\nstronger; that strength was flowing back into her muscles and bones.\n\"Nearly twice light speed.\"\n\"Faster!\" she cried. \"We must go much faster! I must be young again.\nYouthful, and gay, and alive and happy.... Tell me, Robert, do you feel\nyounger yet?\"\nHe did not answer.\nNinon lay in the acceleration sling, gaining strength, and--she\nknew--youth. Her lost youth, coming back, to be spent all over again.\nHow wonderful! No woman in all of time and history had ever done it. She\nwould be immortal; forever young and lovely. She hardly noticed the\nstiffness in her joints when she got to her feet again--it was just from\nlying in the sling so long.\nShe made her voice light and gay. \"Are we not going very, very fast,\nnow, Robert?\"\nHe answered without turning. \"Yes. Many times the speed of light.\"\n\"I knew it ... I knew it! Already I feel much younger. Don't you feel it\ntoo?\"\nHe did not answer, and Ninon kept on talking. \"How long have we been\ngoing, Robert?\"\nHe said, \"I don't know ... depends on where you are.\"\n\"It must be hours ... days ... weeks. I should be hungry. Yes, I think I\nam hungry. I'll need food, lots of food. Young people have good\nappetites, don't they, Robert?\"\nHe pointed to the provisions locker, and she got food out and made it\nready. But she could eat but a few mouthfuls. _It's the excitement_, she\ntold herself. After all, no other woman, ever, had gone back through the\nyears to be young again....\nLong hours she rested in the sling, gaining more strength for the day\nwhen they would land back on Earth and she could step out in all the\nspringy vitality of a girl of twenty. And then as she watched through\nthe ingenious ports she saw the stars of the far galaxies beginning to\nwheel about through space, and she knew that the ship had reached the\nhalfway point and was turning to speed back through space to Earth,\nuncounted light-years behind them--or before them. And she would still\ncontinue to grow younger and younger....\nShe gazed at the slightly-blurred figure of the young spaceman on the\nfar side of the compartment, focussing her eyes with effort. \"You are\nlooking much younger, Robert,\" she said. \"Yes, I think you are becoming\nquite boyish, almost childish, in appearance.\"\nHe nodded slightly. \"You may be right,\" he said.\n\"I must have a mirror,\" she cried. \"I must see for myself how much\nyounger I have become. I'll hardly recognize myself....\"\n\"There is no mirror,\" he told her.\n\"No mirror? But how can I see....\"\n\"Non-essentials were not included in the supplies on this ship. Mirrors\nare not essential--to men.\"\nThe mocking gravity in his voice infuriated her. \"Then you shall be my\nmirror,\" she said. \"Tell me, Robert, am I not now much younger? Am I not\nbecoming more and more beautiful? Am I not in truth the most desirable\nof women?... But I forget. After all, you are only a boy, by now.\"\nHe said, \"I'm afraid our scientists will have some new and interesting\ndata on the effects of time in relation to time. Before long we'll begin\nto decelerate. It won't be easy or pleasant. I'll try to make you as\ncomfortable as possible.\"\nNinon felt her face go white and stiff with rage. \"What do you mean?\"\nRobert said, coldly brutal, \"You're looking your age, Ninon. Every year\nof your fifty-two!\"\nNinon snatched out the little beta-gun, then, leveled it and fired. And\nwatched without remorse as the hungry electrons streamed forth to strike\nthe young spaceman, turning him into a motionless, glowing figure which\nrapidly became misty and wraith-like, at last to disappear, leaving only\na swirl of sparkling haze where he had stood. This too disappeared as\nits separate particles drifted to the metallite walls of the space ship,\ndischarged their energy and ceased to sparkle, leaving only a thin film\nof dust over all.\nAfter a while Ninon got up again from the sling and made her way to the\nwall. She polished the dust away from a small area of it, trying to make\nthe spot gleam enough so that she could use it for a mirror. She\npolished a long time, until at last she could see a ghostly reflection\nof her face in the rubbed spot.\nYes, unquestionably she was younger, more beautiful. Unquestionably Time\nwas being kind to her, giving her back her youth. She was not sorry that\nRobert was gone--there would be many young men, men her own age, when\nshe got back to Earth. And that would be soon. She must rest more, and\nbe ready.\nThe light drive cut off, and the great ship slowly decelerated as it\nfound its way back into the galaxy from which it had started. Found its\nway back into the System which had borne it. Ninon watched through the\nport as it slid in past the outer planets. Had they changed? No, she\ncould not see that they had--only she had changed--until Saturn loomed\nup through the port, so close by, it looked, that she might touch it.\nBut Saturn had no rings. Here was change. She puzzled over it a moment,\nfrowning then forgot it when she recognized Jupiter again as Saturn fell\nbehind. Next would be Mars....\nBut what was this? Not Mars! Not any planet she knew, or had seen\nbefore. Yet there, ahead, was Mars! A new planet, where the asteroids\nhad been when she left! Was this the same system? Had there been a\nmistake in the calculations of the scientists and engineers who had\nplotted the course of the ship? Was something wrong?\nBut no matter--she was still Ninon. She was young and beautiful. And\nwherever she landed there would be excitement and rushing about as she\ntold her story. And men would flock to her. Young, handsome men!\nShe tottered back to the sling, sank gratefully into the comfort of it,\nclosed her eyes, and waited.\n_The ship landed automatically, lowering itself to the land on a pillar\nof rushing flame, needing no help from its passenger. Then the flame\ndied away--and the ship--and Ninon--rested, quietly, serenely, while the\nrocket tubes crackled and cooled. The people outside gathered at a safe\ndistance from it, waiting until they could come closer and greet the\nbrave passengers who had voyaged through space from no one knew where._\n_There was shouting and laughing and talking, and much speculation._\n_\"The ship is from Maris, the red planet,\" someone said._\n_And another: \"No, no! It is not of this system. See how the hull is\npitted--it has traveled from afar.\"_\n_An old man cried: \"It is a demon ship. It has come to destroy us all.\"_\n_A murmur went through the crowd, and some moved farther back for\nsafety, watching with alert curiosity._\n_Then an engineer ventured close, and said, \"The workmanship is similar\nto that in the space ship we are building, yet not the same. It is\nobviously not of our Aerth.\"_\n_And a savant said, \"Yes, not of this Aerth. But perhaps it is from a\nparallel time stream, where there is a system with planets and peoples\nlike us.\"_\n_Then a hatch opened in the towering flank of the ship, and a ramp slid\nforth and slanted to the ground. The mingled voices of the crowd\nattended it. The fearful ones backed farther away. Some stood their\nground. And the braver ones moved closer._\n_But no one appeared in the open hatch; no one came down the ramp. At\nlast the crowd surged forward again._\n_Among them were a youth and a girl who stood, hand in hand, at the foot\nof the ramp, gazing at it and the ship with shining eyes, then at each\nother._\n_She said, \"I wonder, Robin, what it would be like to travel through far\nspace on such a ship as that.\"_\n_He squeezed her hand and said, \"We'll find out, Nina. Space travel will\ncome, in our time, they've always said--and there is the proof of it.\"_\n_The girl rested her head against the young man's shoulder. \"You'll be\none of the first, won't you, Robin? And you'll take me with you?\"_\n_He slipped an arm around her. \"Of course. You know, Nina, our\nscientists say that if one could travel faster than the speed of light\none could live in reverse. So when we get old we'll go out in space,\nvery, very fast, and we'll grow young again, together!\"_\n_Then a shout went up from the two men who had gone up the ramp into the\nship to greet whoever was aboard. They came hurrying down, and Robin and\nNina crowded forward to hear what they had to report._\n_They were puffing from the rush of their excitement. \"There is no one\nalive on the ship,\" they cried. \"Only an old, withered, white-haired\nlady, lying dead ... and alone. She must have fared long and far to have\nlived so long, to be so old in death. Space travel must be pleasant,\nindeed. It made her very happy, very, very happy--for there is a smile\non her face.\"_", "source_dataset": "gutenberg", "source_dataset_detailed": "gutenberg -  Time and the Woman\n"},
{"source_document": "", "creation_year": 1946, "culture": " English\n", "content": "Produced by Chris Curnow, Joseph Cooper, Josephine Paolucci\nand the Online Distributed Proofreading Team at\nTHE POSTNATAL DEVELOPMENT OF TWO BROODS OF GREAT HORNED OWLS\n(Bubo virginianus)\nBY\nDONALD F. HOFFMEISTER AND HENRY W. SETZER\nUniversity of Kansas Publications\nMuseum of Natural History\nOctober 6, 1947\nUNIVERSITY OF KANSAS\nLAWRENCE\nUNIVERSITY OF KANSAS PUBLICATIONS, MUSEUM OF NATURAL HISTORY\nEditors: E. Raymond Hall, Chairman, Donald S. Farner, H. H. Lane,\nEdward H. Taylor\nOctober 6, 1947\nUNIVERSITY OF KANSAS\nLawrence, Kansas\nPRINTED BY\nFERD VOILAND, JR., STATE PRINTER\nTOPEKA, KANSAS\nThe Postnatal Development of Two Broods of Great Horned Owls\n(_Bubo virginianus_)\nBy\nDONALD F. HOFFMEISTER AND HENRY W. SETZER\nOpportunity regularly to observe at the nest the development of young\nGreat Horned Owls, _Bubo virginianus_ (Gmelin), under favorable\nconditions, was afforded when a pair nested and reared their three\noffspring in 1945 and one offspring in 1946 on the vine-covered north\nwall of the Museum of Natural History at the University of Kansas. The\nobservations here reported are based primarily on the three young raised\nin 1945 when daily observations were made. These have been supplemented\nby other observations made of the one nestling in 1946. Unless otherwise\nstated, observations pertain to the nest and three young in 1945.\nNEST SITE\nIn 1945 the nest was situated on a metal-covered cement ledge, two feet\nwide and 48 feet above the ground, at the northeast corner of the Museum\nBuilding. The nest was protected on the east by a stone abutment of the\nbuilding and on the south by the north wall of the building itself. Here\nthe nest could be observed at will through a laboratory window without\ndisturbing the birds. The taking of notes was begun at the time of\negg-laying and extended to the time at which the young left the nest,\nFebruary 3 through April 26, 1945. In 1946 the owls nested farther down\nthe north side of the building, behind two cement pillars, approximately\n25 feet above the ground. To examine the nest in 1946 it was necessary\nto lower an observer down the side of the building by means of a rope.\nObservations of this nest were never made more frequently than every\nother day. The adult owls were first seen at the nest on February 3,\n1946; careful examination of the nest began when the one egg hatched on\nMarch 7 and continued until April 25, shortly before the young owl left\nthe nest.\nOne large cottonwood tree, used by the parent-owls as a landing place\nwhenever they were forced from the nest, was situated approximately 110\nfeet to the north and a five-story building was located 80 feet farther\nto the north. Numerous smaller trees line the street to the east and\nthere are some on the lawns around the Museum. Also, there are about two\nacres of trees 225 feet west of the nest-site where the parent-owls took\nrefuge when forced from the cottonwood tree.\nThe nest, if it can be called a nest, was no more than a few bare\nbranches of the Virginia creeper, which covers the side of the building,\ntogether with some excrement which the owls tended to push to the\nperiphery of the nest. For most of the time the three eggs in 1945 lay\ndirectly on the metal which covered the ledge, because there was no\ndefinite floor to the nest. The single egg in 1946 lay on the cement\nshelf between the pillars and the wall of the building. This laxity in\nnest building by Great Horned Owls apparently is not uncommon (see Bent,\nPERIOD OF INCUBATION\nIncubation of the eggs probably began, in 1945, on February 5, the day\nthe first egg was laid. It has usually been assumed that, in birds of\nprey, incubation begins when the first egg is laid. The last of the\nthree eggs was laid February 7. In 1946, the single egg was being\nincubated on February 4. Since another egg had been laid two or three\ndays before this--a broken egg was found beneath the nest and there were\nremnants of the egg in the nest--incubation may have started as early as\nFebruary 1 or February 2. In comparing these dates of initial incubation\nwith other recorded dates of nesting, only those from places at, or\nnear, the latitude of Lawrence, Kansas, in the central United States,\nshould be expected to be approximately the same since the times of\negg-laying and incubation are progressively later in the year as\napproach is made toward the polar region. Baumgartner (1938:279) has\npreviously pointed this out.\nThe incubation period for the Great Horned Owl in the central United\nStates has usually been regarded as 28 to 29 days. In the nest under\nobservation in 1945, two eggs hatched on March 12 and are assumed to be\nthe first two eggs laid, with an incubation period for each of 35 and 34\ndays, respectively, and the third egg hatched on March 14 with an\nincubation period of 35 days. In 1946, the single egg hatched on the\n33rd day, assuming that incubation began on February 2, for the egg\nhatched March 7. In the period of egg-laying and also in incubation, the\nparent bird in 1945 was frequently disturbed by persons who peered at it\nthrough the window. Curious observers handled the eggs at least once and\nvigorous pounding by carpenters in the room adjacent to the nest\nfrequently flushed the adult bird but did not cause desertion of the\nnest. It may be that such disturbances prolonged the incubation period.\nHowever, in 1946, the brooding birds were undisturbed, yet the\nincubation period was nearly as long. If an observer near the nest\nexposed himself in the daytime to the incubating bird, the adult flew,\nbut exposure at 50 feet or more from the nest only caused the incubating\nbird to remain alert on the nest. When flushed, the parent usually\nreturned to the nest within 15 minutes or less after the observer\nwithdrew. On the thirty-second and thirty-third days of incubation in\n1945, the crew of carpenters demolished partitions within the building\non which the owl was nesting, and within 15 feet of the nest itself. At\nfirst the adult would fly from the nest at each outburst of hammering\nand, at one time, remained away from the nest for more than two hours.\nAfter a few hours of intermittent hammering, however, the parent bird\nremained on the nest despite all the noise produced. These observations\nbear out, rather than refute, Baumgartner's statement (1938:281) that\n\"the horned owl incubates very closely,\" for a strong stimulus was\nnecessary to keep the owl from covering the eggs.\nThe egg hatched on March 14, 1945, and approximately two days later than\nthe other two, is judged to be the one laid last. This owl, III, was\nalways 5 to 21 per cent lighter in weight than the older birds when\nweights for corresponding ages were compared. Whether this difference\nwas the result of a lack of food because of dominance of the two older\nbirds, or because of a sexual difference, we do not know. The owl that\nhatched in 1946 was likewise markedly lighter than the first two birds\nhatched in 1945 (figure 1). A series of adults from Meade County,\nsouthwestern Kansas, shows a pronounced secondary sexual difference in\nweight. In this sample the mean weight of 17 males, 1,208 grams, was 21\nper cent less than that of 25 females, 1,531 grams.\nGROWTH OF JUVENILES\nThe principal measurement of growth taken by us was the weight of the\nowls. In 1945 each of the three owls was weighed daily, with two or\nthree exceptions when a 48-hour period was interposed between weighings.\nThe young were removed from the nest to a nearby balance, weighed, and\nexamined. The owl last hatched (owl III) was weighed on the first day of\nlife and on most subsequent days. The other two owls (designated as owls\nI and II) were first weighed when they were between 53 and 60 hours\nold. On some days the birds were weighed twice, once in the morning and\nonce in the late afternoon; on most days, they were weighed only in the\nlate afternoon. The owl hatched in 1946 was weighed when seven days old\nand at irregular, but usually two day, intervals thereafter. It was\nweighed always slightly before midday.\n[Illustration: FIG. 1. Growth of four Great Horned Owls as shown by\nchanges in weight from near the time of hatching until the time of\nleaving the nest.]\nThe growth of the four owls is well shown by the changes in weight\nrecorded in figure 1. For the period during which the young owls\nremained at the nest, growth can be divided into two phases: (1) a\nrapid increase in weight during the first 3-1/2 or 4 weeks while the\nparent birds are supplying the young with ample food; and (2) a\nsubsequent period of slower growth, marked by fluctuations (actual\nlosses as well as gains) in weight resulting from the failure of the\nparent birds to provide an ample supply of food. If there is an initial\nperiod of about one week in postnatal development in which there is a\nrather slow gain in weight, as suggested by Sumner (1933:284), it was\npoorly marked in this instance. Owl IV remained at the nest until the\n50th day of age, and on the 47th and 49th days (not shown on chart, fig.\n1) weighed 1,011.4 grams and 971.4 grams, respectively. By this age, the\ngrowth curve had definitely flattened out. The fact that owl IV was\nconsistently heavier than owl III might be accounted for, in part, by\nthe fact that owl IV was always weighed in the morning when it was\ngorged with food. However, Riddle, Charles, and Cauthen (1932) have\npointed out that when there were two or more pigeons in a nest, each\ngrew less rapidly than if there was only one present.\nWithin about 12 hours after hatching, the smallest of the three owlets\n(III) weighed 48.7 grams. During the first four weeks of postnatal\ngrowth, each owl gained in weight, daily, an average of 33-1/3 grams or\nan increase of 11.1 per cent. Owl I gained an average of 36.1 grams each\nday, or a daily increase of 10.7 per cent; owl II, 37.8 grams, or 11.2\nper cent; and owl III, 26.1 grams, or 11.4 per cent. From the beginning\nof the fifth week until the time the young left the nest, the three owls\ngained on the average only 12.7 grams or approximately 1.6 per cent in\nweight daily. Individually, the daily mean increases were as follows: I,\n9.6 grams or 0.93 per cent; II, 12.7 grams or 1.86 per cent; III, 15.8\ngrams or 1.97 per cent. Prior to the twenty-sixth to twenty-eighth day\nof age, there seldom was any loss in weight from day to day, whereas\nafter this period, approximately one weight in four was less than on the\nprevious day. These data support the earlier statement that during the\nfirst 3-1/2 or 4 weeks, there is a relatively uniform and rapid increase\nin weight whereas after this period weight fluctuates.\nGrowth as measured by changes in weight in these young Great Horned Owls\nparallels growth in some other young birds. For example, nestling\nRed-tailed Hawks, as reported upon by Fitch, Swenson, and Tillotson\n(1946:215), increase in weight rapidly for about the first three weeks\nand then more gradually. Sumner's (1929b) graphs indicate the same\npattern of growth in the Barn and Great Horned owls and Red-tailed and\nCooper hawks. Pigeons, judging from the growth curves for bodily weight\nas given by Riddle, Charles, and Cauthen (1932), increase in weight\nrapidly until somewhere between the twenty-fourth and thirty-second day\nof postnatal development. However, in the Golden Eagle, the early part\nof postnatal development is not one of rapid growth, judging from\nSumner's diagram (1929a:164), but after the fourth week there is a rapid\nincrease in weight. Graphs that Sumner (1929b) gives for Sparrow Hawks,\nLong-eared Owls, and Screech Owls, indicate that in these instances also\nthe increase in weight during the first few days of postnatal\ndevelopment was not so rapid as it was after the end of the first week.\nStoner (1935) indicates that in the young Barn Swallow, increase in\nweight was most rapid between the fourth and tenth days, with the young\nremaining at the nest until the twentieth day. Much the same pattern of\nweight increase was noted by Stoner (1945) in the Cliff Swallow.\nHuggins' (1940:228) sigmoid curve for increase in weight in the House\nWren indicates that the period of rapid growth in this species does not\nbegin until the second day. Sumner (1934:284) cites other studies which\nhe believes, for altricial birds, indicate three periods of growth, an\ninitial period of rather slow gain, a period of maximum increase in\nweight, and a final period of fluctuations. As previously indicated, for\nthe Great Horned Owls under observation, and in some other species as\nindicated by published growth curves, the initial period of slow gain is\nlacking.\nThe period of a decelerated rate of growth in the young Great Horned\nOwls is correlated with the occasional lack of food. The parent birds,\nduring this latter period, remain off the nest more of the time during\nthe day, and their failure to provide the young with food may represent\nan attempt to force the young to become proficient in flight or to force\nthem away from the nest site, which amounts to the same thing. When only\nslightly more than a month old, the young began to test their wings,\nspringing into the air, and, in general, becoming more active and alert.\nSumner (1929b:110) has suggested some other possible reasons for the\nperiod of decelerated rate of growth.\nAlthough there was a daily increase in weight in the early stages of\ngrowth, there was a decided fluctuation in any twenty-four hour period.\nOn any given day, the young always were heavier in the morning than in\nthe afternoon (see figure 2); presumably they were gorged with food\nearly in the morning.\n[Illustration: FIG. 2. Morning and afternoon weights of two Great Horned\nOwls. Note that in the morning the owls weigh more than in the\nafternoon.]\nWhen the young left the nest, they were approximately three-fourths\ngrown. When owl I on the 44th day and owl II on the 45th day left the\nnest, they weighed 1,120 and 1,139 grams, respectively, or 73 and 74 per\ncent, respectively, of the average weight of 25 females (1,530.9 grams).\nOwl III weighed 943.3 grams on the 43rd day and owl IV weighed 971.4\ngrams on the 49th day, or 78 and 80 per cent, respectively, of the\naverage weight of 17 mature males (1,207.7 grams). Owl I left the nest\n18 hours before owl II did. Owl III attempted to leave when 43 days old,\nbut for it co\u00f6rdinated flight was impossible and the bird landed on the\nlawn after a 150-foot glide. When attempting to take owl IV from the\nnest on the 49th day, it sprang into the air and by gliding, aided by an\noccasional flap, sailed more than 300 feet before alighting on the\nground. After we returned the owl to the nest, it immediately sailed\nforth for even a longer distance. When attempt was made to pick up owls\nIII and IV after they had flown down to the ground, they rolled over on\ntheir backs and used both claws and beaks defensively. Such a reaction\nnever was noted at the nest; there our hands were inspected, and\nsometimes bitten by the owls as possible sources of food, but the claws\nwere rarely used offensively or defensively.\nSlightly elevated remiges and rectrices, still in the sheath, were\nvisible on the ninth day. Some remiges first ruptured the feather sheath\non the 14th day; nearly all of the primaries ruptured the sheaths by the\n19th day and the secondaries by the 20th day. The amount of eruption\nfrom the sheath for primaries, secondaries, and rectrices, as given in\ntable 1, was determined by measuring the one feather of, say, the\nsecondaries, judged to be near the mean in degree of eruption. The\nfeathers of the wing at 21 and 47 days of age are shown in figure 5. On\nthe eighth day, or slightly before, the white nestling down of the newly\nhatched bird was replaced by a downy immature plumage, which was more\nyellowish than the preceding plumage. The development of the plumage in\nthe birds under observation was much the same as that recorded by Sumner\n(1933) in _Bubo virginianus pacificus_ Cassin.\nTABLE 1.--Changes with age in certain parts of a young Great Horned Owl\nhatched in 1946.\n(Measurements are in millimeters)\nTraces of the egg-tooth were retained until the ninth day in two owls\nand until the 11th day in another. In owl IV, the egg-tooth was lost\nsometime between the 9th and 14th day. Changes in the length of the\nculmen are indicated in Table 1. The length of total culmen of owl IV\nwhen 47 days old is slightly greater than the average for three adult\nmale owls from Lawrence, Kansas (40.0 mm. as contrasted with 39.2 mm. in\nthe adults). The length of exposed culmen, without cere, in the same\nbird when 47 days old is less than the average of this measurement in\nthe three adults from Lawrence (23.7 mm. as contrasted with 26.5 mm. in\nthe adults). The femur was measured on three occasions as accurately as\npossible through the skin and flesh. The precise boundaries of the\nfemur could not be determined and the thickness of the skin and certain\nmuscle is included. These measurements are not given to indicate actual\nlength of the femur, but to indicate the relative changes in length of\nthis bone.\nRemnants of the yolk stalk were clearly evident at seven days of age\n(see fig. 5) in the owl hatched in 1946 and were still present when the\nowl was last examined (49 days of age) just before the young left the\nnest. The scablike remnant was not noted in the three young hatched in\n1945, but close inspection was not made to see if it was present.\nThe instinctive reactions of young horned owls shortly after hatching\nhave been fully described by Sumner (1934). By the third day our owls\ncould raise their heads, but when a bird was undisturbed its head lay on\nthe nest floor and the wings were slightly spread. The eyes of owls I\nand II opened at about 7-1/2 days, those of owl III on the 6th day, and\nthose of owl IV sometime between the 7th and 9th days. After the eyes\nopened, the head was held erect more of the time. The young responded\nwith \"cries\" when disturbed by handling, when stimulated by certain\nmovements of the parent, or by movements of our hands near their heads,\nwhich suggested to them the possibility of being fed. Cries were evident\nbut weak in the unhatched, pipped, egg, but soon after hatching\nincreased in intensity, and beginning at six days of age were replaced,\nin part, by the characteristic \"bill-snapping\" of more mature birds.\nThese cries of the young may serve, among other things, for recognition,\ninasmuch as they were given when the parent was inspecting the young.\nWhen the parent returned to the nest and covered the young, after having\nbeen flushed, it sometimes uttered a special note, \"hut, hut, hut,\" much\nlike the \"cluck\" note of the hen of the domestic chicken. The young\nresponded to these notes with faint cries, in contrast to the loud cries\nsignifying alarm and possibly hunger, which they gave when the parents\nwere absent from the nest.\nThe first definite evidence that the young were attempting to feed\nthemselves was obtained when they were 23 days old. Frequently\nthereafter, fresh blood was found on their beaks and claws, but as late\nas the 34th day a parent was seen feeding them. That day, after being\nflushed, a parent returned to the nest at 7 p. m., and began tearing\naway parts of a cottontail which had previously been brought to the\nnest. Bones in the hind leg of the rabbit broke readily under pressure\nof the parent's bill, and the three young crowded in close, opening\ntheir bills widely and placing them around that of the parent. Of\ncottontails, the only parts consistently uneaten were the upper cheek\nteeth and the supporting maxillae and connecting palatal bridge.\nFOOD BROUGHT TO THE NEST\nIn the 45 days that the young remained at the nest site in 1945,\nninety-one individuals of 16 different species of animals were brought\nby the parent owls (table 2). Probably a few smaller animals, of which\nwe saw no traces, were caught and eaten at night. In 1946, two\nadditional kinds of birds were brought to the nest: 1 Baldpate (_Mareca\namericana_) and 1 Pied-billed Grebe (_Podilymbus podiceps_). The large\nnumber of Rock Doves in the list can be explained by their abundance on\nthe buildings on the University campus, including the Museum building\nwhere some were nesting as close as 100 feet to the owl nest. When the\nowls were less than a week old, only small birds and mammals were\nbrought (young Rock Doves, Robins, Starlings, Grasshopper Sparrow,\nmeadow mouse, and Norway rat). The first rabbit was brought when the\nowls were eight days old.\nTABLE 2. Number of food items brought to the nest by the Great Horned\nOwls in 1945\n    Birds\n    Starling (_Sturnus vulgaris_)                      4\n    Mourning Dove (_Zenaidura macroura_)              10\n    Red-wing (_Agelaius phoeniceus_)                   1\n    Bronzed Grackle (_Quiscalus versicolor_)           1\n    Mockingbird (_Mimus polyglottos_)                  1\n    Brown Thrasher (_Toxostoma rufum_)                 1\n    Grasshopper Sparrow (_Ammodramus savannarum_)      1\n    Blue-winged Teal (_Anas discors_)                  1\n    Mammals\nAfter the 28th day, only 18 food items, or slightly less than 20 per\ncent of the total number, were brought to the nest. These last 18 food\nitems brought after the owls were 4 weeks old were no larger or bulkier\nthan those brought in the previous 20 days. The beginning of this period\nof reduced amount of food corresponds to the beginning of the second\nphase of growth characterized by marked fluctuations in weight.\nFox squirrels (_Sciurus niger_) are abundant on the University campus,\nyet there were no remains of this mammal at the nest. This may be\nexplained by the fact that fox squirrels are principally diurnal and\nGreat Horned Owls feed principally at night. Yet in early February,\n1946, when the owls were preparing the nest, they frequently flew on and\noff the nest in the early twilight of evening while one or two fox\nsquirrels fed in the periphery of trees not more than 25 feet away. Yet\nthe owls flew off to the west and left this source of food unmolested.\nWhether both owls regularly attended the young we do not know, for the\nadults were not distinctively marked. On March 17, 1945, when weighing\nthe young, one parent bird started to return to the nest but was\nfrightened away by the observer who at the same time noted the other\nparent perched in an adjacent tree. This was the first time two adults\nwere seen at the same time near the nest. In 1946, two adult owls\n(presumably both were parents) were within sight at one time when the\nyoung owl first sailed forth and landed in a wooded area some 100 yards\naway.\nSUMMARY\nGreat Horned Owls (_Bubo virginianus virginianus_) have employed as nest\nsites the protruding shelves of the stone wall of the Museum of Natural\nHistory at the University of Kansas for several years. In 1945, daily\nobservations were made on one such nest and its three young, and in 1946\nirregular observations were made on another such nest and the one young\nowl. The incubation time for the three owls, hatched in 1945, was 35\ndays for two of the young and 34 days for the third; for the one owl\nhatched in 1946, the incubation time was at least 33 days. Two owls were\nconsistently smaller; when these smaller two left the nest they were,\nrespectively, 21 and 17 per cent lighter than the other two. The smaller\ntwo were judged to be males because adult males in Kansas average\nsmaller by 21 per cent than adult females.\nGrowth of the nestling young is divisible into (1) a period of rapid\nincrease in weight during the first 25 to 28 days, and (2) a subsequent\nperiod marked by gains and losses in weight. The fluctuations in this\nlatter period are correlated with a reduction in food brought to the\nnest by the parent birds and with the development of habits of flight.\nThis second period may be considered to be a period of \"weaning.\" By\nthe forty-fifth day, the young owls are able to fly short distances and\nthus are able to leave the site of the nest permanently. At this time\nthey are about three-fourths grown.\nNinety-one individuals of 16 species of birds and mammals made up the\nfood items brought to the nest in 1945. Two factors seem to be concerned\nin the acquisition of prey: (1) its availability and (2) appropriate\nsize of the prey.\nLITERATURE CITED\nBAUMGARTNER, F. M.\n1938. Courtship and nesting of the Great Horned Owls. Wilson Bull.,\nBENT, A. C.\n1938. Life histories of North American birds of prey (Part 2), Orders\nFalconiformes and Strigiformes. U. S. Nat. Mus., Bull. 170, viii + 482\npp.\nFITCH, H. S., SWENSON, F., and TILLOTSON, D. F.\n1946. Behavior and food habits of the Red-tailed Hawk. Condor,\nHUGGINS, S. E.\n1940. Relative growth in the House Wren. Growth, 4:225-236.\nRIDDLE, O., CHARLES, D. R., and CAUTHEN, G. E.\n1932. Relative growth rates in large and small races of pigeons. Proc.\nSoc. Exp. Biol. and Med., 29:1216-1220.\nSTONER, D.\n1935. Temperature and growth studies on the Barn Swallow. Auk,\n1945. Temperature and growth studies of the Northern Cliff Swallow. Auk,\nSUMNER, E. L., JR.\n1929a. Notes on the growth and behavior of young Golden Eagles. Auk,\n1929b. Comparative studies in the growth of young raptores. Condor,\n1933. The growth of some young raptorial birds. Univ. California Publ.\n1934. The behavior of some young raptorial birds. Univ. California Publ.\n[Illustration: FIG. 3. Young Great Horned Owls in nest. Two owls are 7,\n12, 18, 32, and 36 days of age, respectively; the third owl is about 2\ndays younger in each instance.]\n[Illustration: FIG. 4. Young Great Horned Owl hatched in 1946. The two\nlower pictures show the developing facial mask. Photographs by Jo\u00e3o\nMoojen.]\n[Illustration: FIG. 5. Young Great Horned Owl hatched in 1946. Upper\nrow: Ventral views showing scar of yolk sac and ventral side of wing.\nMiddle row: Ventral (left) and dorsal view of wing at 21 days. Bottom\nrow: Ventral (left) and dorsal view of wing at 47 days. Photographs by\nJo\u00e3o Moojen.]", "source_dataset": "gutenberg", "source_dataset_detailed": "gutenberg -  The Postnatal Development of Two Broods of Great Horned Owls (Bubo virginianus)\n"},
{"source_document": "", "creation_year": 1946, "culture": " English\n", "content": "Produced by Charlene Taylor, Joseph Cooper, Christine P.\nTravers and the Online Distributed Proofreading Team at\n[Transcriber's notes: Obvious printer's errors have been corrected,\nall other inconsistencies are as in the original. The author's\nspelling has been maintained.\nCharacters enclosed in { } are superscripts.]\nSMITHSONIAN INSTITUTION\nUNITED STATES NATIONAL MUSEUM\nBULLETIN 235\nWASHINGTON, D.C.\n_Publications of the United States National Museum_\nThe scholarly publications of the United States National Museum\ninclude two series, _Proceedings of the United States National Museum_\nand _United States National Museum Bulletin_.\nIn these series are published original articles and monographs dealing\nwith the collections and work of the Museum and setting forth newly\nacquired facts in the fields of Anthropology, Biology, History,\nGeology, and Technology. Copies of each publication are distributed to\nlibraries and scientific organizations and to specialists and others\ninterested in the different subjects.\nThe _Proceedings_, begun in 1878, are intended for the publication, in\nseparate form, of shorter papers. These are gathered in volumes,\noctavo in size, with the publication date of each paper recorded in\nthe table of contents in the volume.\nIn the _Bulletin_ series, the first of which was issued in 1875,\nappear longer, separate publications consisting of monographs\n(occasionally in several parts) and volumes in which are collected\nworks on related subjects. _Bulletins_ are either octavo or quarto in\nsize, depending on the needs of the presentation. Since 1902 papers\nrelating to the botanical collections of the Museum have been\npublished in the _Bulletin_ series under the heading _Contributions\nfrom the United States National Herbarium_.\nThis work is number 235 of the _Bulletin_ series.\n                             _Director, United States National Museum_\n  For sale by the Superintendent of Documents, U.S. Government Printing\n  Office\n  Washington 25, D.C.--Price $2\n[Illustration: Shoulder-belt plate of Vermont Militia, attributed to\nEthan Allen, about 1785. In collection of Dr. John Lattimer.]\nMUSEUM OF HISTORY AND TECHNOLOGY\nAmerican Military Insignia\nJ. Duncan Campbell and Edgar M. Howell\nSMITHSONIAN INSTITUTION, WASHINGTON, D.C.\nContents\n    Organization of the Regular Army            3\n    Organization of the Militia                 6\n  Insignia of the Regular Army                  7\n    Shoulder-Belt and Waist-Belt Plates        31\n  Insignia of the Uniformed Militia            51\n    Shoulder-Belt and Waist-Belt Plates        88\nPreface\nThis catalog is a descriptive and interpretive listing of the insignia\nof the Army of the United States--other than buttons, epaulets, and\nhorse furniture--in the National Collections that were prescribed or\nworn during the period 1800-1851. The subject of early American\nmilitary buttons has been covered by L. F. Emilio in _The Emilio\nCollection of Military Buttons_ (Salem, Massachusetts: Essex\nInstitute, 1911), W. L. Calver and R. P. Bolton in _History Written\nwith Pick and Shovel_ (New York: New York Historical Society, 1950),\nand David F. Johnson in _Uniform Buttons, American Armed Forces_,\n1784-1948. (Watkins Glen, New York: Century House, 1948, 2 vols.). For\nepaulets, see Mendel L. Peterson, \"American Army Epaulets, 1814-1872,\"\n_Military Collector and Historian_ (March 1961, vol. 3, no. 1, pp.\nMost of the specimens described here are from the huge W. Stokes Kirk\nCollection acquired in 1959, supplemented by the War Department\nCollection and the numerous biographical collections of the United\nStates National Museum; in addition, a few insignia in the collections\nof J. Duncan Campbell and others are included.\nThe unique W. Stokes Kirk Collection, unmatched in scope, volume, and\nrarity, is worthy of special note. It was begun in 1878 by W. Stokes\nKirk, Sr., of Philadelphia, a dealer in U.S. Government surplus.\nStruck by the beautiful design and delicate art work in some of the\nearly insignia, Mr. Kirk put aside all old and unusual devices for his\npersonal collection. As his business expanded, so did his interest in\nmilitary rarities and curios. After each bulk purchase from government\nsources, he would have all the odd and unusual items sorted out for\nhis examination. The best of such items went into his personal\ncollection, which included rare firearms, powder flasks, insignia,\nepaulets, military caps, and the like. W. Stokes Kirk, Jr., who\nsucceeded his father and expanded the business nationally until it\nbecame almost as well known as Bannerman's Military Store in New York\nCity, maintained and enlarged the collection. After his death, in\n1946, the collection was continued by his widow, Mrs. Linnie A. Kirk\nMosler. Items in this catalog from the W. Stokes Kirk Collection are\nindicated by the letters \"S-K\" in parentheses following the United\nStates National Museum number.\nAlthough this catalog is, in more than one sense, a developmental\nhistory of American military insignia, it is not, and is not intended\nto be, a definitive study. The picture is far too incomplete. Whereas\nthe record of Regular Army devices after 1821 is fairly clear--despite\nthe fact that the uniform regulations continued sometimes to use the\ntantalizing phrase \"according to pattern\"--there remain serious gaps\nin the pre-1821 period when regulations were exceedingly vague and\nfragmentary at best; for example, the badges of the Regiment of Light\nArtillery (1812-1821). These gaps will be filled only by excavating at\nsites known to have been occupied by specific Regular units during\nparticular periods. Indeed, since this study was begun, four unique\nand significant insignia were excavated at the site of a War of 1812\ncantonment, and these greatly enrich our knowledge of the period.\nThe record of insignia of the veritable multitude of independent\nuniformed Militia companies in existence during the period under\nconsideration may never be complete. The selection presented here,\nhowever, is an excellent representative chronological cross section of\ntypical designs and variations of insignia worn by the uniformed or\n\"volunteer\" Militia, as opposed to the \"common\" or \"standing\" Militia.\nThe best sources of documentation and dating for Regular Army devices\nare the uniform regulations and ordnance regulations; these are\nsupplemented by pertinent records in the National Archives, notably\nthe letter files of the Purveyor of Public Supplies and of the\nCommissary General of Purchases. The letter files are voluminous, but\nin some cases badly mixed and in many cases incomplete. We have\nconjectured a reason for this incompleteness. The two prime\ncontractors for military insignia during the period 1812-1821 were\nGeorge Armitage and William Crumpton, both of whom had their small\nfactories in Philadelphia within a mile of the office of Callendar\nIrvine, Commissary General of Purchases. The paucity of written\ntransactions in the records in the National Archives between these\ngentlemen and Irvine tends to bear out our assumption that most of\ntheir dealings were conducted verbally in Irvine's office. This would\naccount for the lack of sketches and drawings of cap plates and belt\nplates in files of the National Archives. In cases where no specific\ndocumentary evidence is available, dating has been based on a careful\nevaluation of design development and comparison with biographical\nspecimens that can be more fairly dated through knowledge of the\nformer owner's career. Excavated insignia from datable sites have also\nreduced the problem considerably.\nFor Militia insignia worn about 1835, the best documentation is to be\nfound in _U.S. Military Magazine_, published between 1839 and 1842 by\nHuddy and Duval of Philadelphia, and in _New York Military Magazine_,\npublished by Labree and Stockton of New York during 1841. In 1939,\nFrederick P. Todd described the Huddy and Duval prints in detail\n(_Journal of the American Military Institute_, 1939, vol. 3, no. 3,\npp. 166-176). However, evaluation and consideration of over-all design\ndevelopment and comparison with dated biographical specimens of the\nearlier period, before 1835, are difficult and must be done\ncautiously, as there is no orderly pattern. One generalization does\nseem clear: during the decade after 1821, when the Regulars discarded\nlarge cap plates, the Militia almost universally adopted them and\ncontinued to wear them well into the 1840's. Very few insignia include\nthe maker's name or initials, but when they do, bracketing within a\ndefinite period is relatively easy. Similarly, when a cap plate\nappears to be original to a cap, the design of the cap and its maker's\nlabel, if included, are of great help. Finally, when there is nothing\nelse to rely on, the \"feel\" of the specimen, gained through the\nexperience of studying several thousand, has been used, although with\nreluctance.\nThe year 1800 was selected as the opening date of the study because it\nwas in that year that the first metal ornament was prescribed to\ndesignate a particular branch of service. The closing date of 1851 was\nchosen because Regular Army devices for that year and thereafter are\nwell documented in uniform regulations, manuals, and catalogs of\nmanufacturers such as William Horstmann and Sons. Militia dress after\nthat general date becomes so increasingly complex that it should be\nattempted only as a separate study.\nMost of the specimens described in this study were struck from steel\ndies; however--despite the relative wealth of knowledge on the\nstriking of coins--little is known of the exact process, especially\nprior to the appearance of the punch press in the 1830's. Several\ninsignia dies dating as early as the War of 1812 period and a number\ndating in the 1840's do exist, however. All of these examined were\nfound to be female dies, with the design in intaglio rather than in\nrelief. The design was worked into the die--the art generally termed\n\"die-sinking\"--in the same basic manner as in coin dies. The die\nsinker first softened the steel to suit his particular taste and then\nincised the design, using a succession of small chisels. The steel was\nthen retempered to withstand high impact pressures. Although there is\nno documentation on the subject, manufacturing techniques of the\nperiod indicate that the following process was probably employed: the\ndie was locked in place at the base of a drop press, similar to a\nguillotine, so that it could be struck accurately from above; a piece\nof pure lead was then affixed to the bottom of the weighted drop and\nallowed to strike the die a sufficient number of times to completely\nreceive the impression of the die and become, in effect, a male\ncounterpart; lastly, a thin sheet of brass, copper, or pewter was\nplaced on the female die and struck with the weighted lead male,\nreceiving the desired impression but without the excessive stretching\nand resultant cracking that a steel-on-steel strike might have\nproduced. Examination of finished products in the national collections\nbears out this theory of production; few if any of the specimens show\nevidence of having been struck with a steel male die.\nWith only a few exceptions, all specimens have been photographed on a\n1-inch grid. All references to right and left are made according to\nheraldic usage; the heraldic right is always on the left as viewed.\nDuring the months this work has been in progress, many people and\ninstitutions have generously assisted in many ways. It is a pleasure\nto thank them for their help.\nMr. Detmar Finke of the Office of the Chief of Military History,\nDepartment of the Army, reviewed the Regular Army portions of the\nmanuscript and made many valuable suggestions. Mr. Frederick P. Todd,\ndirector of The West Point Museum, graciously answered many questions\nrelative to both Regular Army and Militia insignia. Through the\ncourtesy of Mr. James Koping and Miss Elizabeth Ulrich of the\nPennsylvania State Library, The _U.S. Military Magazine_ of Huddy and\nDuval was made available for unlimited use.\nThanks are also given to the following, who furnished photographs of\nspecimens in their collections: Mr. Waverly P. Lewis, Devon,\nConnecticut; Mr. William E. Codd, Monkton, Maryland; The Filson Club,\nLouisville, Kentucky; The West Point Museum; The Fort Sill Museum; Old\nFort Erie Museum, Ontario, Canada; The Niagara Historical Society\nMuseum, Niagara-on-the-Lake, Ontario, Canada; The Washington County\nHistorical Society Museum, Fort Calhoun, Nebraska; the Valley Forge\nChapel Museum, and Dr. John Lattimer, New York City.\nMr. Michael Arpad of Washington, D.C., was especially helpful in\nmatters pertaining to the techniques of chasing and die sinking.\nBibliography\nThe following works have been used in gathering the material for this\nbook. They are frequently referred to in the text in shortened form.\n_American military history, 1607-1953._ (ROTC Manual 145-20,\nDepartment of the Army.) Washington, 1956.\n_American state papers, class V, military affairs._ Vol. 1.\nWashington: Gales and Seaton, 1832.\nANSELL, S. T. Legal and historical aspects of the Militia. _Yale Law\nBARNES, R. M. _Military uniforms of Britain and the Empire._ London:\nSeeley Service and Co., 1960.\nBELOTE, THEODORE T. _American and European swords in the historical\ncollections of the United States National Museum._ (U.S. National\nMuseum Bulletin 163.) Washington, 1932.\nA bit of U.S. Mint history. _American Journal of Numismatics_ (1908),\nCALVER, W. L., and BOLTON, R. P. _History written with pick and\nshovel._ New York: New York Historical Society, 1950.\nCHAMBERLAIN, GEORGIA S. Moritz Furst, die-sinker and artist. _The\nNumismatist._ (June 1954), vol. 67, no. 6, pp. 588-592.\nDAVIS, GHERARDI. _The colors of the United States Army, 1789-1912._\nNew York: Privately printed, 1912.\nEMILIO, L. F. _The Emilio collection of military buttons._ Salem,\nMassachusetts: Essex Institute, 1911.\nFINKE, DETMAR H. Insignia of rank in the Continental Army, 1775-1783.\n_Military Collector and Historian_ (fall 1956), vol. 8, no. 3, pp.\n_General regulations for the Army._ Philadelphia: M. Carey and Sons,\n_General regulations for the Army of the United States._ Washington:\nDepartment of the Army, 1835.\n_General regulations for the Army of the United States, 1847._\nWashington: J. and G. S. Gideon, 1847.\nGRONERT, T. G. The first national pastime in the Middle West. _Indiana\nMagazine of History_ (September 1933), vol. 29, no. 3, pp. 171-186.\nHistory of the organization of the United States cavalry. MS, Office\nof the Chief of Military History, Department of the Army, Washington,\nD.C.\nHOPKINS, ALFRED F. Volunteer corps hat of 1814. _Military Affairs_\nJOHNSON, DAVID F. _Uniform buttons, American armed forces, 1784-1948._\n2 vols. Watkins Glen, New York: Century House, 1948.\nJONES, WILLARD L. History of the organization of the United States\nField Artillery. MS, Office of the Chief of Military History,\nDepartment of the Army, Washington, D.C.\n_Journals of the Continental Congress, 1774-1789._ Edit. Worthington\nChauncey Ford and others. 34 vols. Washington: Carnegie Foundation,\nKIVETT, MARVIN F. Excavations at Fort Atkinson, Nebraska, a\npreliminary report. _Nebraska History_ (March 1959), vol. 40, no. 1,\nKnox papers. MSS Division, Library of Congress, Washington, D.C.\nKUHN, EDWARD C. U.S. Army colors and standards of 1808. _Military\nLEFFERTS, CHARLES W. _Uniforms of the American, British, French, and\nGerman Armies in the War of the American Revolution._ New York: New\nYork Historical Society, 1926.\nLEWIS, WAVERLY P. _U.S. military headgear, 1770-1880._ Devon,\nConnecticut: Privately printed, 1960.\nLUNDEBERG, PHILIP K. A history of the North Carolina Militia,\n1784-1848. Master's dissertation, Duke University, 1947.\nMAHON, JOHN K. The citizen soldier in national defense, 1789-1815.\nDoctor's dissertation, University of California at Los Angeles, 1950.\n----. History of the organization of the United States Infantry. (Pp.\n1-61 in vol. 2 of _The Army lineage book_, Washington: Department of\nthe Army, 1953.)\nMCBARRON, H. CHARLES. Regiment of Riflemen, winter uniform, 1812-1815.\nMilitary Collector and Historian (December 1954), vol. 6, no. 4, p.\n----. The 18th U.S. Infantry Regiment, 1814-1815. _Military Collector\nand Historian_ (summer 1955), vol. 7, no. 2, pp. 48-49.\nMCCLELLAN, E. N. Uniforms of the American Marines, 1775 to 1827.\nMimeographed in 1932 by Marine Corps Historical Section, Department of\nthe Navy, Washington, D.C.\n_The military laws of the United States._ Edit. John F. Callan.\nPhiladelphia: George W. Childes, 1863.\n_New York Military Magazine_ (1841).\n_Official Army register, corrected to October 31, 1848._ Washington,\nOfficial drawings for the U.S. Army uniform regulations of 1851.\n_Military Collector and Historian_, vol. 10, no. 1 (spring 1958), pp.\n_Old Print Shop Portfolio_ (May 1961), vol. 20, no. 9.\nPARKYN, MAJ. H. G. _Shoulder-belt plates and buttons._ Aldershot,\nHants, England: Gale and Polden, Ltd., 1956.\nPATTERSON, C. MEADE. The military rifle flasks of 1832 and 1837.\n_Military Collector and Historian_ (March 1953), vol. 5, no. 1, pp.\nPETERSON, HAROLD L. _The American sword_, New Hope, Pennsylvania: The\nRiver House, 1954.\nPETERSON, MENDEL L. American Army epaulets, 1841-1872. _Military\nCollector and Historian_ (March 1951), vol. 3, no. 1, pp. 1-14.\nPREBLE, GEORGE HENRY. _History of the flag of the United States of\nAmerica._ Boston: A. Williams and Co., 1880.\nRecords of the Adjutant General's Office. Record Group 94, National\nArchives, Washington, D.C.\n_Regulations for the government of the Ordnance Department._\nWashington: Francis P. Blair, 1834.\n_Regulations for the uniform and dress of the Army of the United\nStates, June 1851._ Philadelphia: William H. Horstmann and Sons, 1851.\nRIKER, WILLIAM H. _Soldiers of the States._ Washington: Public Affairs\nPress, 1957.\nStanding Order Book, 1st Infantry, Detroit. MSS Division, Library of\nCongress, Washington, D. C.\nSWANSON, NEIL H. _The perilous flight._ New York: Farrar and Rinehart,\nTODD, FREDERICK P. The Huddy and Duval prints. _Journal of the\nAmerican Military Institute_ (1939), vol. 3, no. 3, pp. 166-176.\n----. Notes on the dress of the Regiment of Light Artillery, U.S.A.\n_Military Collector and Historian_ (March 1950), vol. 2, no. 1, p. 10.\n----. Our National Guard: An introduction to its history. _Military\nAffairs_, vol. 5, no. 2 (summer 1941), pp. 73-86; vol. 5, no. 3 (fall\n----. The curious case of the Voltigeur uniform. _Military Collector\nand Historian_ (June 1952), vol. 4, no. 2, pp. 44-45.\n----. Notes on the organization and uniforms of South Carolina\nmilitary forces, 1860-1861. _Military Collector and Historian_\n----. Three leather cockades. _Military Collector and Historian_\nTOWNSEND, F. C., and TODD, FREDERICK P. Branch insignia of the Regular\ncavalry, 1833-1872. _Military Collector and Historian_ (spring 1956),\nUPTON, EMORY. The military policy of the United States. Senate\nDocument No. 379, 64th Congress, 1st Session. Washington: 1916.\n_U.S. Military Magazine_ (1839-1842), vols. 1-3.\nWALL, ALEXANDER J. The flag with an eagle in the canton. _New York\nHistorical Society Quarterly Bulletin_ (October 1933), vol. 17, no. 3,\nWIKE, JOHN W. Untitled MS, Office of the Chief of Military History,\nDepartment of the Army, Washington, D.C.\n_Writings of George Washington._ Edit. John G. Fitzpatrick.\nWashington: 1944.\nZIEBER, EUGENE. _Heraldry in America._ Philadelphia: Bailey, Banks,\nand Biddle, 1909.\nAmerican\nMilitary Insignia\nIntroduction\nIn almost all armies it long has been standard practice to use\ndistinctive devices of cloth and metal to distinguish between arms and\nservices, and between individual units of each arm, to enhance morale\nand develop esprit de corps. Colors of units of the British Army have\nhad ancient badges emblazoned on them since before the establishment\nof the present standing army in 1661. By the end of the first half of\nthe 18th century some of these badges had been authorized for\nplacement on horse furniture or for wear on grenadier caps. This was\nespecially true of the regiments of horse and a few of the older\nregiments of foot. The infantry regiments received numerical\ndesignations in 1751, and these numbers were worn on waist belts,\nshoulder belts, and cartridge-box plates. When the infantry units\nacquired county titles in 1782, these names often were added to the\nplates. In 1767 regimental numbers were ordered placed on the buttons\nof officers and other ranks; in practice these numbers were often\ncombined with other devices.[1]\n[Footnote 1: PARKYN'S _Shoulder-Belt Plates and Buttons_ contains a\nwealth of information on British regimental devices.]\nIn the American Army such devices have taken many forms, ranging from\ndistinctive buttons, plumes, cockades, cap plates, shoulder-belt\nplates, and waist-belt and cartridge-box plates to the well-known\nshoulder sleeve insignia and distinctive unit insignia of the present\nday. The origin of much of this insignia and many of the changes in\nits design can be tied more or less directly to the organization of\nthe Regular Army--its contractions and expansions and its changes in\narm and service designations--and to the peculiar circumstances\nsurrounding the origin and growth of the volunteer or uniformed\nMilitia. Thus, a short discussion of the organization of each is in\norder.[2]\n[Footnote 2: For history of the organization of the Army, see\n_American Military History, 1607-1953_; MAHON, \"History of the\nOrganization of the United States Infantry\"; and JONES, \"History of\nthe Organization of the United States Field Artillery.\"\nUnfortunately, there is no single, completely satisfactory source on\nthe militia system of the United States. The following works, however,\ncontain sound information and, when taken together, provide an\nexcellent background on the subject: TODD, \"Our National Guard\";\nMAHON, \"Citizen Soldier\"; LUNDEBERG, \"History of the North Carolina\nMilitia\"; ANSELL, \"Legal and Historical Aspects of the Militia\";\nGRONERT, \"First National Pastime in the Middle West\"; and RIKER,\n_Soldiers of the States_.]\nOrganization of the Regular Army\nTwo months after the War of the Revolution officially ended with the\nsigning of a peace treaty on September 3, 1783, General Washington\ndirected the Army to turn in its arms and disband.[3] Since the\nContinental Congress had made no provision for a permanent\nestablishment, Washington retained in service one infantry regiment\nand a battalion of artillery to guard military stores and take over\nposts to be evacuated by the British.[4] Early in June 1784 Congress\nordered these units disbanded except for detachments to guard stores\nat Fort Pitt and West Point; then, in order to secure the frontier\nagainst Indian unrest, it immediately authorized a regiment to be\nraised from the militia of four of the States to comprise eight\ncompanies of infantry and two of artillery.[5] This unit, called the\nFirst American Regiment, gradually turned into a regular organization.\n[Footnote 3: _Writings of George Washington_, vol. 27, p. 222.]\n[Footnote 4: Ibid., pp. 256-258; also letter dated January 3, 1784,\nfrom Henry Knox, Commander in Chief of the Army, to President of the\nContinental Congress (in Knox papers).]\n[Footnote 5: Journals of the Continental Congress, vol. 27, p. 524;\nalso, UPTON, p. 69.]\nThe failure of an expedition commanded by Col. Josiah Harmar of the\nFirst American Regiment against the Indians in 1790 awakened the\nCongress somewhat to the threat in the Northwest and resulted in the\norganization of another infantry regiment, which was designated the 2d\nInfantry Regiment; the First American Regiment was redesignated the\n\"1st\".[6] Trouble with the Indians continued, and after another severe\nreverse Congress authorized the raising of three additional infantry\nregiments and, at the same time, empowered the President to organize\nthe Army as he might see fit.[7]\n[Footnote 6: Act of March 3, 1791 (_Military Laws_, pp. 90-91).]\n[Footnote 7: Act of March 5, 1792 (_Military Laws_, pp. 92-94).]\nUnder this discretionary power, the Army was reorganized into the\nLegion of the United States. This was a field army in which the three\ncombat branches--infantry, cavalry, and artillery--were combined. The\nLegion was in turn broken down into four sublegions, with each\ncontaining infantry, cavalry, artillery, and riflemen; thus, the\nsublegions were the fore-runners of the modern combined arms team. The\n1st and 2d Infantries became the 1st and 2d Sublegions. Of the three\nadditional infantry regiments authorized, only two were organized,\nthese becoming the 3d and 4th Sublegions.[8] Under the forceful\nleadership of Gen. Anthony Wayne the Legion reversed the record on the\nfrontier and decisively defeated the Indians at the Battle of Fallen\nTimbers. The temporary peace which followed turned attention to the\nproblem of protecting the Atlantic seaboard, and in 1794 Congress\nauthorized a large increase in the artillery, assigned engineer\nofficers, and designated the new organization the Corps of\nArtillerists and Engineers.[9] The Legion was continued until it was\nreplaced in 1796 by the 1st, 2d, 3d, and 4th Infantry Regiments, which\nwere constituted from the four sublegions, two troops of light\ndragoons, and the above-mentioned Corps.[10]\n[Footnote 8: _American State Papers_, pp. 40-41.]\n[Footnote 9: Act of May 9, 1794 (_Military Laws_, p. 104).]\n[Footnote 10: Act of May 30, 1796 (_Military Laws_, p. 114).]\nThe threat of war with France in 1798 brought further expansions. In\nApril of that year an \"additional regiment\" of artillerists and\nengineers was authorized, with the Corps created in 1794 becoming the\n1st and the new unit being designated the 2d Regiment of Artillerists\nand Engineers.[11] In the following July, 12 more regiments of\ninfantry and 6 troops of light dragoons--to be combined with the two\ntroops in existence to form a regiment--were authorized; an additional\n24 regiments of infantry, plus units of other arms, authorized the\nfollowing winter made a total of 40 regiments of infantry.[12]\nActually, the greatest part of this force remained on paper. Only the\n1st and 2d Infantries ever attained their required strength, and only\n3,400 men were enlisted for the 5th through the 16th. There were no\nenlistments at all for the other regiments. Officers were assigned to\nthe six troops of light dragoons, but no enlisted personnel were\nraised and no horses were bought.[13]\n[Footnote 11: Act of April 27, 1798 (_Military Laws_, pp. 119-120).]\n[Footnote 12: Acts of July 16, 1798, and March 2, 1799 (_Military\n[Footnote 13: _American State Papers_, p. 137.]\nMore quickly than it had arisen, the threat of a war with France\nabated. Early in 1800 action was suspended under the two acts creating\nthe paper regiments, and the Army was reduced to the regular\nestablishment of four regiments of infantry, two regiments of\nartillerists and engineers, and two troops of light dragoons.[14] Two\nyears later the antipathy of the new Jefferson administration to a\nstanding army further reduced this establishment to two regiments of\ninfantry and one of artillery. The Corps of Artillerists and Engineers\nwas abolished; a Corps of Engineers was organized to be stationed at\nWest Point and \"constitute a military academy\"; and the light dragoons\nwere disbanded.[15]\n[Footnote 14: Acts of February 20 and May 14, 1800 (_Military Laws_,\npp. 139, 141); also, _American State Papers_, p. 139.]\n[Footnote 15: Act of March 16, 1802 (_Military Laws_, pp. 141-149).]\nThe Jeffersonian theories regarding a strong militia and a small\nprofessional army were rudely shaken in 1807 by the _Chesapeake-Leopard_\naffair. With war seeming imminent, Congress added to the Regular\nEstablishment, though cautiously \"for a limited time,\" five regiments of\ninfantry, one regiment of riflemen, one of light artillery, and one of\nlight dragoons. The new regiments of infantry were numbered the 3d\nthrough the 7th.[16] There was no further preparation for a fight with\nEngland until just before war was actually declared. In January 1812, 10\nregiments of infantry, two of artillery, and one regiment of light\ndragoons were added; three months later a Corps of Artificers was\norganized; and in June provision was made for eight more infantry\nregiments, making a total of 25.[17] In January 1813, following the\ndiscouragements of the early campaigns in the Northwest, Congress\nconstituted 20 more infantry regiments, bringing the total to 45, the\nlargest number in the Regular Establishment until the 20th century.[18]\nA year later three more regiments of riflemen, designated the 2d through\nthe 4th, were formed.[19]\n[Footnote 16: Act of April 12, 1808 (_Military Laws_, pp. 200-203).]\n[Footnote 17: Acts of January 11, April 23, and June 26, 1812\n[Footnote 18: Act of January 1813 (_Military Laws_, pp. 238-240).\nThere is some confusion as to just how many infantry regiments were\norganized and actually came into being. The Act of January 29, 1813,\nauthorized the President to raise such regiments of infantry as he\nshould see fit, \"not exceeding twenty.\" It seems that 19 were actually\nformed, made up partly of 1-year men and partly of 5-year men. There\nare 46 regiments listed in the Army Register for January 1, 1815, and\nit is known that several volunteer regiments were designated as units\nof the Regular Establishment and that a 47th and a 48th were\nredesignated as lower numbered units when several regiments were\nconsolidated because of low recruitment rate. Mahon (in \"History of\nthe Organization of the United States Infantry\") is not clear on this\npoint. There is an organizational chart of the Army for this period in\nthe files of the Office of the Chief of Military History, Department\nof the Army.]\n[Footnote 19: Act of February 10, 1814 (_Military Laws_, pp.\nIn March 1814 Congress reorganized both the artillery and the\ndragoons. The three artillery regiments, which had never operated as\nsuch, but rather by company or detachment, were consolidated into the\nCorps of Artillery; and the two regiments of dragoons, which had never\nbeen adequately trained and generally had given a poor account of\nthemselves, were merged into one.[20] The Regiment of Light Artillery\nremained untouched.\n[Footnote 20: Act of March 30, 1814 (_Military Laws_, pp. 252-255);\nJONES, p. 58; \"History of the Organization of the United States\nCavalry.\"]\nAlmost as soon as the war ended, Congress moved to reduce the Army[21]\nby limiting the peacetime establishment to 10,000 men, to be divided\namong infantry, artillery, and riflemen, plus the Corps of Engineers.\nThe number of wartime infantry units was reduced to eight, and the\nrifle units to one. The Corps of Artillery and the Regiment of Light\nArtillery were retained, but dragoons were eliminated.[22]\n[Footnote 21: Act of March 3, 1815 (_Military Laws_, pp. 266-267).]\n[Footnote 22: The reorganization of 1815 is treated by MAHON \"History\nof the Organization of the United States Infantry\" (pp. 11-12), JONES\n\"History of the Organization of the United States Field Artillery\"\n(pp. 59-60), and WIKE, unpublished study.]\nBy 1821 the prospects of a prolonged peace appeared so good that\nCongress felt safe in further reducing the Army. Consequently, in that\nyear the number of infantry regiments was cut to seven; the Rifle\nRegiment was disbanded; the Corps of Artillery and the Regiment of\nLight Artillery were disbanded, with four artillery regiments being\norganized in their stead; and the Ordnance Department was merged with\nthe artillery,[23] an arrangement that continued until 1832.\n[Footnote 23: Act of March 2, 1821 (_Military Laws_, pp. 303-309).]\nThe opening of the West in the decades following the War of 1812\nbrought an important change in the organization of the Army.\nExperience having shown that infantry were at a distinct disadvantage\nwhen pitted against the fleetly mounted Indians, in 1832 a battalion\nof mounted rangers was organized to quell disturbances on the\nnorthwest frontier,[24] but this loosely knit force was replaced by a\nregiment of dragoons the following year.[25] The mounted arm had come\nto stay in the Army.\n[Footnote 24: Acts of April 5 and June 15, 1832 (_Military Laws_, pp.\n[Footnote 25: Act of March 2, 1833 (_Military Laws_, pp. 329-330).]\nWhen the second Seminole War broke out in 1836, a second regiment of\ndragoons was organized.[26] And, as the war dragged through another\ninconclusive year, a reluctant Congress was forced to increase the\nsize of existing line units and to authorize an additional regiment of\ninfantry, the 8th. Meanwhile, increasing demands for surveying and\nmapping services resulted in the creation of the Corps of\nTopographical Engineers as a separate entity.[27]\n[Footnote 26: Act of May 23, 1836 (_Military Laws_, pp. 336-337).]\n[Footnote 27: Act of July 5, 1838 (_Military Laws_, pp. 341-349).]\nMeanwhile, the responsibilities of the Army in the opening of the West\ncontinued to increase, and in 1846 the Regiment of Mounted Riflemen\nwas organized to consolidate the northern route to the Pacific by\nestablishing and manning a series of posts along the Oregon Trail.[28]\nHowever, the outbreak of the War with Mexico postponed this mission.\n[Footnote 28: Act of May 19, 1846 (_Military Laws_, pp. 371-372).]\nAt the start of the War with Mexico Congress leaned heavily on\nvolunteer units, with the hard core of the Regulars remaining\nunchanged. But early in 1847 it was found necessary to add nine\nregiments of infantry and one regiment of dragoons.[29] Of the\ninfantry unit's, eight were of the conventional type; the ninth was\nformed as the Regiment of Voltigeurs and Foot Riflemen. Theoretically,\nonly half of this latter regiment was to be mounted. Each horseman was\nto be paired with a foot soldier who was to get up behind and ride\ndouble when speed was needed. In practice, however, none of the\nVoltigeurs were mounted; the entire unit fought as foot riflemen.[30]\n[Footnote 29: Act of February 11, 1847 (_Military Laws_, pp.\n[Footnote 30: MAHON, \"History of the Organization of the United States\nInfantry,\" p. 16.]\nAll of these new units proved merely creatures of the war, and the\ncoming of peace saw a reduction to the old establishment of eight\nregiments of infantry, four of artillery, two of dragoons, and one\nregiment of mounted riflemen.[31] This organization remained\nsubstantially unchanged until 1855.[32]\n[Footnote 31: Official Army Register, 1848.]\n[Footnote 32: UPTON, p. 223.]\nOrganization of the Militia\nThe \"common\" Militia was first established by the various colonies of\nall able-bodied men between roughly the ages of 16 and 60 for\nprotection against Indian attack. These militiamen were required by\nlaw to be enrolled in the unit of their township or county, furnish\ntheir own arms and equipment, and appear periodically for training.\nThey were civilian soldiers who had little or no taste for things\nmilitary, as their performance in both peace and war almost invariably\ndemonstrated. They were not uniformed and contributed little or\nnothing to the field of military dress.\nThe \"volunteer\" or \"independent\" Militia companies, on the other hand,\nwere something else again. These units, composed of men who enjoyed\nmilitary life, or rather certain aspects of it, appeared rather early\nin the Nation's history. The first of these, formed in 1638, was The\nMilitary Company of the Massachusetts, later and better known as the\nAncient and Honorable Artillery Company of Massachusetts. By 1750\nthere were a number of independent companies in existence--many of\nthem chartered--and membership in them had become a recognized part of\nthe social life of the larger urban centers.\nThe concept of volunteer Militia units was confirmed in the Uniform\nMilitia Act of 1792, which prescribed flank companies of grenadiers,\nlight infantry, or riflemen for the \"common\" Militia battalions and a\ncompany of artillery and a troop of horse for each division, to be\nformed of volunteers from the Militia at large and to be uniformed and\nequipped at the individual volunteer's expense. Thus, from within the\nnational Militia structure emerged an elite corps of amateur--as\nopposed to civilian--soldiers who enjoyed military exercise, and the\npomp and circumstance accompanying it, and who were willing to\nsacrifice both the time and the money necessary to enjoy it. Since the\nmembers were volunteers, they were ready to submit to discipline up to\na point; they trained rather frequently; many of the officers made an\neffort to educate themselves militarily; they chose their own\nofficers; and their relative permanency gave rise to an excellent\nesprit de corps. In actuality, these organizations became private\nmilitary clubs, and differed from other male social and fraternal\ngroups only in externals.\nThe great urban growth of the Nation during the period 1825-1860 was\nthe golden age of the volunteer companies, and by 1845 these units had\nall but supplanted the common Militia. It would be difficult to even\nestimate the number of volunteer companies during this period. They\nsprang up almost everywhere, more in answer to a demand by the younger\nmen of the Nation for a recreation that would meet a social and\nphysical need and by emigrant minorities for a group expression than\nfor reasons military. It was a \"gay and gaudy\" Militia, with each unit\nin its own distinctive and generally resplendent uniform. If the\n\"Raleigh Cossacks,\" the \"Hibernia Greens,\" the \"Velvet Light Infantry\nCompany,\" or the \"Teutonic Rifles\" were more \"invincible in peace\"\nthan visible in war, they were a spectacular, colorful, and exciting\nintegral of the social and military life of the first half of the 19th\ncentury.\nInsignia of the Regular Army\nUniform regulations prior to 1821 were loosely and vaguely worded, and\nthis was especially true in regard to officers' insignia. For example\nGeneral Orders of March 30, 1800, stated: \"... the swords of all\nofficers, except the generals, to be attached by a white shoulder belt\nthree inches wide, with an oval plate three inches by two and a half\nornamented with an eagle.\"[33] In 1801 the 1st Infantry Regiment\ndirected that \"the sword ... for platoon officers ... be worn with a\nwhite belt over the coat with a breast plate such as have been by the\nColonel established,\"[34] and in 1810 a regulation stated that \"those\ngentlemen who have white sword belts and plates [are] to consider them\nas uniform, but those not so provided will be permitted to wear their\nwaist belts.\"[35] As a result, the officers generally wore what they\nwished, and there was a wide variation in design. Most officer\ninsignia were the product of local jewelers and silversmiths, although\nsome known specimens are obviously the work of master craftsmen.\nQuality varied as well as design, depending on the affluence of the\nofficer concerned. Some of the plainer plates appear to have been made\nby rolling silver dollars into an oval shape.\n[Footnote 33: General Orders, March 30, 1800 (Records AGO).]\n[Footnote 34: Standing Order Book, folio 1, October 1, 1801.]\n[Footnote 35: Records AGO.]\nIn regard to enlisted men's insignia, only the descriptions of the\n1800 dragoon helmet plate and the 1814 and 1817 riflemen's cap plates\ngive us anything approaching a clear picture. \"Oblong silver plates\n... bearing the name of the corps and the number of the regiment\" for\nthe infantry in 1812, \"plates in front\" for the 1812 dragoons, and\n\"gilt plate in front\" for the 1812 light artillery are typical\nexamples. As a result, the establishment of a proper chronology for\nthese devices has depended on the careful consideration of specimens\nexcavated at posts where specific units are known to have served at\nspecific times, combined with research in pertinent records of the\nperiod in the National Archives.\nCap and Helmet Devices\nDRAGOON HELMET PLATE, 1800\n[Illustration: FIGURE 1]\nThe first known distinctive metal branch insignia authorized for the\nArmy was this helmet plate. General Order, U.S. Army, dated March 30,\n1800, prescribed for \"Cavalry ... a helmet of leather crowned with\nblack horse hair and having a brass front, with a mounted dragoon in\nthe act of charging.\"[36] This oval plate, struck in thin brass with\nlead-filled back, has a raised rim, within which is a mounted,\nhelmeted horseman in the act of charging; overhead is an eagle with a\nwreath in its beak. A double-wire fastener soldered to the back is not\ncontemporary.\n[Footnote 36: Records AGO.]\nDRAGOON HELMET PLATE, 1800, DIE SAMPLE\n[Illustration: FIGURE 2]\nAlthough from a different die, this plate, struck in thin brass,\nappears to be a die sample of the plate described above. It is also\npossible that it is a sample of the dragoon plate authorized in 1812.\n\u00b6 The 1813 uniform regulations specified for enlisted men of the\nartillery a \"black leather cockade, with points 4 inches in diameter,\na yellow button and eagle in the center, the button in uniform with\nthe coat button.\"[37] This specification gives some validity to the\nbelief that a cockade with an approximation of the artillery button\ntooled on it may also have been worn.\n[Footnote 37: General Order, Southern Department, U.S. Army, January\n24, 1813 (photostatic copy in files of division of military history,\nSmithsonian Institution); also, _American State Papers_, p. 434.]\nLEATHER COCKADE, ARTILLERY, C. 1808-1812\n[Illustration: FIGURE 3]\nThis cockade is of black leather of the size prescribed by the 1813\nregulations. Tooled into the upper fan is an eagle-on-cannon device\nwith a stack of 6 cannon balls under the trail; an arc of 15 stars\npartially surrounds the eagle device. It is believed to have been worn\non artillery _chapeaux de bras_ as early as 1808.\nThe specimen is unmarked as to maker, but from correspondence of\nCallendar Irvine, Commissary General of Purchases from 1812 to 1841,\nit seems very possible that cockades similar to this one were made by\nRobert Dingee of New York City. Dingee is first listed in New York\ndirectories as a \"saddler\" (1812); he is listed later as \"city\nweigher\" (1828) and \"inspector of green hides\" (1831). The\neagle-on-cannon design is similar to that of several Regular artillery\nbuttons worn between 1802 and 1821, but it most closely approximates a\nbutton Johnson assigns to the period 1794-1810.[38]\n[Footnote 38: Specimen no. 156 in JOHNSON, vol. 1, p. 43, vol. 2, p.\n\u00b6 The question has been raised as to whether the Regulars ever wore a\ncockade with such a device. The 1813 and 1814 uniform regulations\nmerely specified black leather cockades of 4 inches and 4-1/2 inches\nin diameter respectively. However, since the Militia generally did not\nstart adopting Regular Army devices until the 1820's it seems probable\nthat this cockade was an item of Regular Army issue, despite the lack\nof evidence of specific authorization.\nAs early as January 1799 War Office orders specified: \"All persons\nbelonging to the Army, to wear a black cockade, with a small white\neagle in the center. The cockade of noncommissioned officers,\nmusicians, and privates to be of leather with Eagles of tin.\"[39] This\nregulation was repeated in 1800.[40] By 1802 these cockade eagles had\ntaken the colors used for the buttons and lace of the different arms.\nThe Purveyor of Public Supplies in that year purchased cockade eagles\nin tin (white) for infantry and in brass (yellow) for artillery\nenlisted men at a cost of one and two cents, respectively.[41] The\ncockade eagles of infantry officers were to be of silver and those of\nartillery officers of gold. Cockades for company officers and enlisted\npersonnel were to be of leather. The loosely worded regulation of 1813\ninfers that field officers' cockades might be of silk similar to the\n\"black Ribbon\" binding specified for their hats.[42]\n[Footnote 39: TODD, \"Three Leather Cockades,\" pp. 24-25.]\n[Footnote 40: General Order, March 30, 1800 (Records AGO).]\n[Footnote 41: \"Statement of Articles of Clothing, 1802,\" in papers of\nPurveyor of Public Supplies (Records AGO).]\n[Footnote 42: General Order, Southern Department, U.S. Army, January\n24, 1813 (photostatic copy in files of division of military history,\nSmithsonian Institution); also, _American State Papers_, p. 434.]\nIt is extremely difficult to determine whether cockade eagles are of\nRegular Army or Militia origin, and to date them if the latter. They\nhave been found in a wide variety of design and size, ranging from the\nrather plain example (fig. 6) to the highly refined one on the general\nofficer's _chapeau de bras_ (fig. 4). Examination of hats worn by both\nRegulars and Militia prior to 1821 reveals that there is little to\nchoose between the eagles worn by the two components. After 1821,\nhowever, when Militia insignia tended to become more ornate and\nRegular devices more uniform, some of the Militia specimens emerge as\ndistinct types because they have no Regular counterparts. Origin of\nthe specimen, including excavations of military cantonment sites where\nthe make-up of the garrison can be determined, has been the primary\ncriterion used in assignment to either Regular Army or Militia, and to\na lesser extent in dating. Over-all design and method of manufacture\nhave also been considered in dating.\nCOCKADE EAGLE, GENERAL OFFICER, 1800-1812\n_USNM 12813. Figure 4._\n[Illustration: FIGURE 4]\nUnusually refined in design, the eagle is of gold, with head to right,\nfederal shield on breast, and olive branch in right talon. Three\narrows, with points outward, are held in left talon.\nThis cockade eagle is on a _chapeau de bras_ formerly belonging to\nPeter Gansevoort, brigadier general of the New York State Militia and\nbrigadier general, U.S. Army, 1809-1812. Although Gansevoort wore this\n_chapeau_ while serving as a Militia officer, as evidenced by a New\nYork State button attached to it, this eagle is included with Regular\nArmy devices because it is typical of those probably worn by\nhigh-ranking officers of both components.\nCOCKADE EAGLE, C. 1800-1821\n[Illustration: FIGURE 5]\nCast in pewter and gold-finished, this eagle looks to the right,\nstands on clouds, and holds three arrows (facing inward) in the right\ntalon and an upright olive branch in the left.\nThe eagle-on-clouds design is first seen on coins on the 1795 silver\ndollar.[43] It was popular during the War of 1812 period, and was not\nused in new designs by the Regular Army after 1821. Eagles of\nidentical design and size are also known in pewter without finish.\nSuch an eagle could have been worn by Militia as well as Regulars.\nSimilar specimens have been excavated at Regular Army cantonment sites\nof the period.\n[Footnote 43: Engraved by Robert Scott after a design by Gilbert\nStuart.]\nCOCKADE EAGLE, OFFICERS, 1800-1821\n_USNM 66352-M. Figure 6._\n[Illustration: FIGURE 6]\nThis cockade eagle, which is struck in thin brass and silvered, was\nexcavated on the site of a War of 1812 cantonment. Comparison with\nsimilar specimens in other collections indicates that the missing head\nwas turned to the right. This eagle is classed as an officer's device\nbecause of its silvered brass composition. The elements comprising the\narc on which the eagle stands cannot be identified because of the\nlightness of the strike.\n\u00b6 When the dragoons were disbanded in the 1802 reduction following the\ndissipation of the French scare, distinctive hat devices other than\ncockades disappeared from the service. In 1808, when the Army was\nincreased, the newly constituted regiments of light dragoons, light\nartillery, and riflemen were authorized to wear leather caps. The cap\ndevices for these units were prescribed as Roman letters, \"U.S.L.D.,\"\n\"U.S.L.A.,\" and \"U.S.R.R.,\" rather than plates. The letters were to be\nof brass, 1-1/2 inches \"in length.\"[44]\n[Footnote 44: TODD, \"Notes on the Dress,\" p. 10. Also, receipts from\nGeorge Green and Son, and letter dated August 6, 1808, from J. Smith\n(Commissary General at Washington) to Tench Coxe requesting \"brass\nletters U.S.R.R.\" (Records AGO). George Green is listed in\nPhiladelphia directories of the period as a \"brass founder and\ngilder.\"]\n[Illustration: FIGURE 7.--Specimens in Campbell collection.]\nIllustrated in figure 7 are the letters \"U\" and \"L\", of brass,\nslightly more than 1 inch \"in length\" and a letter D, of pewter, 1\ninch \"in length.\" The latter was excavated at Sackets Harbor, New\nYork, where elements of the light artillery dragoons and riflemen are\nknown to have served during 1813 and 1814. It seems obvious that\npewter letters were worn by the dragoons as consonant with their other\ntrimmings, for in July 1812 Col. James Burn of the 2d Light Dragoons\nrequested official permission to issue such.[45]\n[Footnote 45: Letter dated July 8, 1812, from J. Burn to William\nEustis (Secretary of War) and letter dated July 9, 1812, from B.\nMifflin (Deputy Commissary General of Purchases). Both letters are in\nRecords AGO.]\nWith the large increase in the Army in 1812 came a change in the\nheadgear of some corps and also a change in insignia. The light\nartillery was to wear a yoeman-crowned (i.e., wider at the crown than\nat the base) black cap with \"gilt plate in front,\" and the infantry\nplatoon officers and enlisted men were finally to have the black\ncylindrical caps (first prescribed in 1810) with \"an oblong silver\nplate in front of the cap bearing the name of the corps and number of\nthe regiment.\"[46] The rifle platoon officers and enlisted men were\nalso to wear infantry caps, but with yellow trimmings.[47] The\ndragoons were authorized \"helmets\" with \"plates\" in 1812, and the foot\nartillery regiments in the fall of the same year were ordered to wear\ncaps like the light artillery instead of the _chapeaux de bras_\npreviously worn, which would have necessitated the use of plates.\n[Footnote 46: General Orders, January 24, 1813 (Records AGO).]\n[Footnote 47: Letter dated March 30, 1812, from Coxe to Eustis\n(Records AGO); McBarron, \"Regiment of Riflemen,\" p. 100.]\nThe foot units received their new insignia almost immediately, the cap\nplates having been designed, contracted for, and delivered by late\nFebruary 1812 for the 5th, 6th, 12th, and 15th Infantry Regiments[48]\n(the latter two were new units). This rapid action in regard to the\ninfantry plates appears to be strong witness to the emphasis placed on\ndistinctive insignia as morale factors and aids to enlistment, for\nactive recruiting for the 10 new regiments did not begin until several\nmonths later. There were three different patterns of this infantry\nplate manufactured and issued, two of which are described below.\n[Footnote 48: Bill dated February 24, 1812, from William Crumpton\n(Records AGO).]\nAll arms were wearing cap plates by the middle of 1813, for there is\nrecord of such issue to the dragoons as well as record of rejection of\nill-struck specimens for infantry, artillery, and rifles.[49] These\nplates were made variously by William Crumpton and George Armitage of\nPhiladelphia, and Aaron M. Peasley of Boston.[50] Philadelphia\ndirectories list Crumpton as a button maker and silversmith between\n1811 and 1822. Armitage is first listed in Philadelphia directories,\nin 1800, as a \"silver plate worker\"; in 1801 he is listed as\n\"silverplater,\" and in 1820 as a \"silverplater and military ornament\nmaker.\" Peasley was an ornament and insignia maker in Boston during\nthe same period.[51]\n[Footnote 49: Letter dated August 31, 1812, from Eustis to Irvine;\nGeneral Order of January 24, 1813, Southern Department; letter dated\nMarch 31, 1813, from Irvine to Amasa Stetson (Deputy Commissary\nGeneral of Purchases, Boston); and letter dated July 13, 1813, from\nIrvine to M. T. Wickham. This material is in Records AGO.]\n[Footnote 50: Letter from Irvine to Wickham dated July 13, 1813, and\nbill from William Crumpton dated February 24, 1812 (both in Records\nAGO).]\n[Footnote 51: Statement of purchases for September 1813, by Stetson\n(Records AGO).]\n\u00b6 The three types of infantry cap plates issued between 1812 and 1814\nare somewhat similar, and all carry the prescribed \"name of the corps\nand number of the regiment.\" All three specimens of these types are\nground finds, two having been excavated after this work was in draft.\nThe first pictured specimen (fig. 8, left) is believed to be the\nearliest pattern issued. Infantry plates as specified in the\nregulations were contracted for with William Crumpton late in 1811 or\nearly 1812 by Tench Coxe, Purveyor of Public Supplies, and issued to\ntroop units not later than the early summer.[52] They had been in use\nbut a few months when their generally poor quality of composition\nforced several regimental commanders to complain to the new Commissary\nGeneral of Purchases, Callendar Irvine, who had just superseded Coxe,\nand to request something better. Irvine approved, and he let a\ncontract for new plates with George Armitage of Philadelphia.[53]\nIrvine's reaction to the matter of the plates is an example of his\nopinion of his predecessor, Coxe, and Coxe's work in general, which he\nhad observed while serving as Superintendent of Military Stores in\nPhiladelphia. In replying to the complaint of Colonel Simonds,\ncommanding officer of the 6th Infantry, Irvine wrote: \"The plates are\nmere tin, in some respects like the man who designed and contracted\nfor them, differing to him only as to durability ... I am contracting\nfor a plate of decent composition to issue with your next year's\nclothing.\"[54]\n[Footnote 52: Bill dated February 24, 1812, from William Crumpton\n(Records AGO).]\n[Footnote 53: Letter dated November 8, 1812, from Irvine to Colonel\nSimonds (Commanding Officer, 6th Infantry); letter dated November 3,\n1812, from Irvine to Colonel Pike (Commanding Officer, 15th Infantry);\nand letter dated November 23, 1812, from Irvine to Armitage. These\nletters are in Records AGO.]\n[Footnote 54: Letter from Irvine to Simonds cited in preceding note.]\nThe first pattern carries the \"name of the corps and the number of the\nregiment,\" the 15th Infantry, commanded by Col. Zebulon Pike who was\none of the officers who complained to Irvine about the poor quality of\ncap plates. The specimen is of tinned iron and the letters and\nnumerals have been struck with individual hand dies.\nThe two Armitage plates, very similar in over-all design (figures 8,\nright, and 9), have been designated the second and third patterns. At\nleast one of these--perhaps both--apparently was designed by, and its\ndie sunk by, Moritz Furst, well-known die sinker and designer of\nPhiladelphia. On March 6, 1813, Irvine wrote the Secretary of War:\n\"Mr. Furst executed a die for this office for striking infantry cap\nplates, designed by him, which has been admitted by judges to be\nequal, if not superior, to anything of the kind ever produced in this\ncountry.\"[55] Furst was Hungarian by birth. He studied design and die\nsinking at the mint in Vienna and came to the United States in 1807\nwith the expectation of becoming Chief Engraver at the Philadelphia\nMint, an appointment which he did not receive. He sank the dies for\nmany of the medals voted to War of 1812 leaders, did the obverse die\nwork for a number of Indian peace medals, and is believed to have\ndesigned the swords given by the State of New York to Generals Brown,\nScott, Gaines, and Macomb.[56]\n[Footnote 55: Letter in Records AGO.]\n[Footnote 56: \"A Bit of U.S. Mint History,\" pp. 45-50; and\nChamberlain, pp. 588-592.]\nCAP PLATE, INFANTRY, 1812\n_USNM 66456-M. Figure 8, right._\n[Illustration: FIGURE 8, left.]\n[Illustration: FIGURE 8, right.]\nThis is the second pattern of the infantry cap plate described in the\n1812 regulations as an \"oblong silver plate ... bearing the name of\nthe corps and the number of the regiment.\" The specimen was excavated\non the site of Smith's Cantonment at Sackets Harbor, New York, known\nto have been occupied by Regular infantry during the 1812-1815 period.\nThe piece is struck in \"white metal\" and tinned [the term \"silver\" in\nthe regulation referred only to color]. It is rectangular, with\nclipped corners, and is dominated by an eagle, with wings outspread,\ngrasping lightning bolts in the right talon and an olive branch in the\nleft talon. Below is a panoply of stacked arms, flags with 6-pointed\nstars, two drums, and a cartridge box marked \"U.S.\" The corps\ndesignation \"U.S. INFANTRY\" is above; the unit designation is blank\nwith the letters \"REGT.\" on the left. The plate is pierced with four\npairs of holes on each side for attachment.\nAnother example of this second pattern is known; it is attached to an\noriginal cap and bears the unit designation \"12 REGT.\"\nCAP PLATE, INFANTRY, 1812 (REPRODUCTION)\n[Illustration: FIGURE 9]\nThis is the third pattern of the infantry cap plate prescribed in the\n1812 regulations. Like the preceding plate, of the second pattern, the\noriginal plate from which this reproduction was made was excavated on\nthe site of Smith's Cantonment at Sackets Harbor, New York. Made of\ntin-alloy, as is the original, and rectangular with clipped corners,\nthe piece is dominated by an unusually fierce looking eagle that first\nappeared on one of the 1807 half-dollars struck at the Philadelphia\nMint. The eagle has an out-sized, curved upper beak and is grasping\nlightning bolts in the right talon and an olive branch in the left.\nBelow is a panoply of flags and muskets with drum, saber, and\ncartridge box. The corps designation \"US INFAN{Y}.\" is above, and the\nunit designation \"16 REG{T}\" is below. The \"16\" appears to have been\nadded with separate die strikes. The specimen is pierced with two\npairs of holes on each side for attachment.\nThis third pattern was also struck in brass and silvered for wear by\nofficers. Several fragments of such a plate were excavated at Sackets\nHarbor; these, although of the third pattern, are the product of a die\ndifferent from that used in striking the piece described above.\nDRAGOON CAP PLATE, 1812\n[Illustration: FIGURE 10]\nThis is an almost exact duplicate of the 1800 dragoon plate except\nthat it is struck in pewter, \"white metal,\" the color used by the\ninfantry and dragoons. It is rectangular with clipped corners that are\npierced for attachment. No detailed description of the 1812 plate has\never been found, but several identical specimens are known attached to\ndragoon helmets made by a contractor named Henry Cressman. The name\n\"Cressman\" is stamped on the lower side of the visor alongside the\ninitials of an inspector named George Flomerfelt, who is known to have\nbeen employed by the Army as an inspector in Philadelphia during the\nperiod. Henry Cressman is listed in the Philadelphia directories from\n1807 through 1817 as a shoemaker. From 1825 to 1839 he is listed as a\nmilitary cap maker.\n\u00b6 On January 12, 1814, Irvine wrote to the Secretary of War as\nfollows: \"I send herewith an infantry cap plate which, with your\npermission, I will substitute for that now in use. The advantages of\nthe former over the latter are that it is lighter, neater, and will\nnot cost half [the] price. The present plate covers the greater part\nof the front of the cap, is heavy in its appearance, and adds much to\nthe weight of the cap ...[57]\" This proposal was approved on January\n[Footnote 57: Letter in Records AGO.]\n[Footnote 58: Letter from Secretary of War to Irvine (Records AGO).]\n[Illustration: FIGURE 11.--Specimen in Campbell collection.]\n[Illustration: FIGURE 12.--Specimen in Campbell collection.]\nBut here we enter an area of some confusion and controversy. Were\nthese new plates to carry the name of the corps and/or the number of\nthe regiment? Irvine's correspondence gives us no clue, but on the\nfollowing March 28 he wrote at least two of his deputy commissary\ngenerals that he was forwarding 8,752 plates for distribution to 14\nspecifically named infantry regiments plus 851 \"blank\" plates.[59]\nFrom the total of 8,752 forwarded for specific units, it would seem\nthat these were probably plates of the new design, but then the\nvariance in the number sent for individual regiments--from a low of\n152 for the 5th Infantry to highs of 1,016 and 1,050 for the 19th and\n25th, respectively--appears odd. Specimens of the 1812 pattern are\nknown both with and without the regimental number, while no examples\nof the 1814 pattern have been found with unit designation. Two extant\nexamples of the 1814 pattern, representing two very similar but\ndistinct designs (figs. 11, 12), were excavated at Sackets Harbor, New\nYork, and Fort Atkinson, Nebraska, where Regular infantry served\nduring 1813-1816 and 1819-1821, respectively. Both plates are \"blank,\"\nand there is no appropriate place on either for the addition of the\nnumber of the unit, as in the case of the 1812 pattern.\n[Footnote 59: Letters in Records AGO.]\nAnother example of the 1814 pattern is known; it is attached to a\nbell-crowned cap of Militia origin, which indicates that the plate was\nadopted by the Militia after being discarded by the Regular\nEstablishment. A plate of the same design, but struck in pewter and\ncut in the diamond shape popular in the 1820's and 1830's, is also\nknown; it is obviously a Militia item.\nINFANTRY CAP PLATE, 1814-1821, DIE SAMPLE\n[Illustration: FIGURE 13]\nLike practically all die samples, this one is struck in brass. It is\nrectangular with unclipped corners, but is marked for clipping.\nWithin a raised oval an eagle, very similar to that on the 1812 plate,\ncarries an olive branch in its beak, three arrows in its right talon,\nand thunder bolts and lightning in its left talon; below, there is a\ntrophy of stacked muskets, drum, flag, and shield. Although this\nspecimen is struck in brass, the plate in used specimens is known only\nin silver on copper, despite the fact that there was considerable talk\nof issuing it in brass.[60]\n[Footnote 60: Letters in Records AGO: Irvine to James Calhoun (Deputy\nCommissary General of Purchases, Baltimore), January 14, 1815; Irvine\nto General Scott, January 13, 1815; Irvine to George Armitage, July\nCAP PLATE, INFANTRY OFFICER, 1814-1821\n[Illustration: FIGURE 14]\nThis plate, which is original to the hat to which it is affixed, may\nwell have been worn by a regular infantry officer during the period\n1814-1821. The cap is of the style first issued in October 1813, with\nthe front rising above the crown.[61]\n[Footnote 61: See MCBARRON, \"The 18th U.S. Infantry,\" pp. 48-49.]\nThe plate, of silver on copper, is rectangular with four scallops top\nand bottom. A floral border, 3/16 of an inch wide, that surrounds the\nwhole, strongly suggests that it was an officer's plate. Within a\ncentral oval an eagle, with wings outspread, is superimposed upon a\ntrophy of arms and flags; above, on a ribbon, are \"E PLURIBUS UNUM\"\nand 15 5-pointed stars. It is possible that this plate is a Militia\nitem, but the fact that it appears to be original on a leather cap of\nthe type worn by Regulars makes it more likely that it is another\nexample of officers' license in the matter of insignia during this\nperiod. Its attachment to the cap is a variant method: two hasp-like\nmetal loops, affixed to the plate, have been run through holes in the\nhat and a leather thong threaded through them. Most cap plates of\nthis period were pierced at the corners for attachment by threads.\n[Illustration: FIGURE 15.--Specimen in Fort Erie Museum, Ontario,\nCanada.]\n[Illustration: FIGURE 16.--Specimen in Campbell collection.]\n\u00b6 The cap plates issued to the artillery regiments (less the Regiment\nof Light Artillery) and the riflemen during the period 1812-1821 are\nknown, but only a fragment of one is represented in the national\ncollections. Illustrations of all extant are included to complete the\npicture. Two of the 1812 plates issued the 2d Regiment of Artillery\n(fig. 15) have been excavated at Fort Erie, Ontario, and are in the\ncollections of the museum there. A plate of the 3d Regiment (fig. 16)\nexcavated at Sackets Harbor, New York, is of an entirely different\ndesign. The lower third of a plate of the 1st Regiment (fig. 17),\nagain of a different design, was excavated by the authors in 1961. In\n1814, when the three regiments were consolidated into the Corps of\nArtillery, these plates were superseded by one bearing the\neagle-on-cannon device closely resembling the button of the artillery\nfor the period 1814-1821, which has the word \"Corps\" inscribed.[62]\nSpecimens of this latter plate representing two distinct though\nsimilar designs have been excavated at posts known to have been manned\nby Regular artillery in 1814 and later (figs. 18, 19). The same\ngeneral design appears also on cross-belt plates and waist-belt plates\n(see below pp. 34-35).\n[Footnote 62: See JOHNSON, vol. 1, p. 45, and vol. 2, p. 10.]\nCAP PLATE, 1ST REGIMENT ARTILLERY, 1812\n_USNM 67240-M. Figure 17._\n[Illustration: FIGURE 17]\nThe over-all design of the plate of which this brass-struck fragment\nrepresents approximately one-third can be rather accurately surmised\nby comparing it with several of the ornamented buttons issued to the\ninfantry in 1812-1815. It is probably the work of the same\ndesigner.[63] The plate is rectangular with clipped corners. Within a\nraised border is an oval surrounded by cannon, cannon balls, and a\ndrum, with the unit designation \"1 R{T} ART{Y}\". At the top of the\noval can be seen grasping claws, obviously those of an eagle (as\nsketched in by the artist) and similar to those on the buttons\nreferred to above. Single holes at the clipped corners provided means\nof attachment. It seems probable that the design of the missing\nportion also include flags and additional arms and accoutrements.\n[Footnote 63: See JOHNSON, vol. 2, specimen nos. 183, 184, 210-213.]\n\u00b6 The design of the \"yellow front plate\" authorized and issued to the\nRegiment of Light Artillery[64] in 1812 was unknown for many years. In\nMay 1961 one of the authors fortunately located this plate (fig. 20)\nin the collections of the Niagara Historical Society Museum at\nNiagara-on-the-Lake, Ontario, included in a group of British badges of\nthe War of 1812 period. There can be no doubt that the specimen is\nAmerican: the eagle's head is of the same design as that on the third\npattern 1812 infantry cap plate (fig. 9); the wreath of laurel appears\non both the 1800 and 1812 dragoon helmet plates; and the thunderbolts\nin the eagle's right talon are wholly American, as opposed to British,\nand are of the period. In the Fort Ticonderoga Museum collections\nthere is a gold signet ring (original owner unknown) that has an\nalmost identical design.\n[Footnote 64: Letter dated February 26, 1812, from Irvine to Secretary\nof War (Records AGO). In clothing returns for 1812 of light artillery\ncompanies stationed at Williamsville, N. Y., \"caps and plates\" are\nlisted as being \"on hand\" (Records AGO).]\n[Illustration: FIGURE 18.--Specimen in Campbell collection.]\nThis is one of the largest plates ever worn by the Regular\nEstablishment. It measures 4-1/4 by 5-1/4 inches, and it is not\nsurprising that it was replaced because of its size. On May 19, 1814,\nthe Commissary General of Purchases wrote Lt. Col. J. R. Fenwick,\nsecond-in-command of the light artillery, asking his opinion of a new\ndesign and stating flatly: \"The present light artillery plate is too\nlarge by one-half.\"[65] The plate illustrated as figure 21 is offered\nas a possible example of the 1814 design. A matching waist-belt plate\nis described below (p. 34).\n[Footnote 65: Letter in Records AGO.]\n[Illustration: FIGURE 19.--Specimen in U.S. Army Artillery and Missile\nCenter Museum, Fort Sill, Oklahoma.]\n[Illustration: FIGURE 20.--Specimen in Niagara Historical Society\nMuseum, Niagara-on-the-Lake, Ontario, Canada.]\n[Illustration: FIGURE 21.--Specimen in Campbell collection.]\n[Illustration: FIGURE 22.--Specimen in Campbell collection.]\n[Illustration: FIGURE 23.--Specimen in Campbell collection.]\nThere are four different patterns of riflemen's cap plates that can be\nfairly bracketed in three periods. The large (6-1/4 by 5 inches)\ndiamond-shaped brass plate with the letters \"R.R.\" (fig. 22) was\nadopted for wear in the spring of 1812 as replacement for the letters\n\"USRR\" that had been worn on the cap since the organization of the\nRegiment of Riflemen in 1808. It was excavated in the interior of one\nof the barracks comprising Smith's Cantonment at Sackets Harbor, New\nYork, where riflemen were stationed as early as August 1812. The style\nof the \"R\" is very similar to that on the 1812 Artillery cap plate,\nand the \"R.R.\" designation conforms to that on the button authorized\nfor the riflemen in 1808. The pattern of the second diamond-shaped\nplate (fig. 23), also in brass and almost identical in size, although\na ground find, is more difficult to account for, despite the fact that\nit most certainly falls in the same period. The most logical\nexplanation seems that the riflemen, who considered themselves a cut\nabove the common infantry, became disgruntled with the utter plainness\nof their plates when compared with those just issued the infantry, and\nasked for and received, possibly late in 1812, the plate with the\neagle and the designation \"U.S. Rifle Men.\" The fact that the plate\nbears the designation \"1 REG{T}\"--although there were no other rifle\nregiments from 1812 to 1814--can be explained by reference to the\n\"national color\" of the Rifle Regiment completed in 1808, which bore\nthe inscription \"1st Rifle Regt.--U.S.\" and the standard and national\ncolor of the light artillery which were inscribed \"The First Regiment\nof Light Artillery\" when there was never more than one light artillery\nunit in the Army.[66] In any case, accurate dating of the third and\nfourth patterns definitely places the second pattern in the 1812-1813\nperiod by process of elimination. It was superseded in 1814[67] very\npossibly for the same reason that the infantry plate was\nchanged--heaviness in both appearance and weight--and replaced by a\nplate with a \"design similar to that of the button ... flat yellow\nbuttons which shall exhibit a bugle surrounded by stars with the\nnumber of the regiment within the curve of the bugle.\"[68] At least\nthree specimens of this third-pattern plate are known. They all are\n3-1/4 inches in diameter, and thus are large enough for a hat\nfrontpiece and too large to be a cockade device. One of these plates\nis without a numeral (fig. 24); one has the numeral \"1,\" and one has\nthe numeral \"4\" (fig. 25). The first and second of these were found at\nFort Atkinson, but very probably were not worn as late as 1819-1821.\nPortions of specimens of this 1814 plate have also been recovered from\nan early Pawnee village site in Webster County, Nebraska, indicating\ntheir possible use as trade goods after the rifle regiment changed its\nplates in 1817.[69] The fourth pattern, with an eagle over a horn\n(fig. 26) was authorized[70] in 1817. Apparently it was worn until\n1821, since several examples of it have been found at Atkinson; other\nexamples also are known.\n[Footnote 66: See KUHN, pp. 263-267, and DAVIS, pp. 13-14 and pl. 3.]\n[Footnote 67: Act of February 10, 1814 (_Military Laws_, pp.\n[Footnote 68: Letter dated January 12, 1814, from Irvine to Secretary\nof War (Records AGO).]\n[Footnote 69: See KIVETT, p. 59.]\n[Footnote 70: A letter dated July 29, 1817, from Irvine to Secretary\nof War describes the device; a letter dated August 4, 1817, from the\nAdjutant and Inspector General (Daniel Parker) to Irvine authorizes\nthe plate but gives no description. Both letters are in Records AGO.]\n[Illustration: FIGURE 24.--Specimen in Campbell collection.]\n[Illustration: FIGURE 25]\n[Illustration: FIGURE 26.--Specimen in Campbell collection.]\n[Illustration: FIGURE 27.--Specimen in collection of Waverly P. Lewis,\nDevon, Connecticut.]\nThe cap plate for the U.S. Military Academy, c. 1815, is illustrated\n(fig. 27) because it completes the cycle for insignia of the Regular\nEstablishment for the period. Apparently it is the work of the same\ndesigner as most of the insignia of the period 1812-1815. Scratched\non its reverse side is the name George W. Frost, a Virginian who\nentered the Military Academy as a cadet in 1814 and resigned on March\nThe two plates of the U.S. Marine Corps, despite the fact that they\nare naval rather than military, are included because they fit very\nprecisely into the device design pattern of the strictly army items of\nthe period and because they are unique in their rarity.\nCAP PLATE, U.S. MARINE CORPS, C. 1807, DIE SAMPLE\n[Illustration: FIGURE 28]\nThis specimen was extremely puzzling for many years. The design is\nobviously that of the War of 1812 period, bearing strong similarity to\nboth the 1812 and 1814 infantry plates and the 1814 Artillery Corps\nplate, possibly the work of the same die sinker. The 1804 Marine Corps\nuniform regulations specified merely a \"Brass Eagle and Plate,\" but\nthe 1807 regulations called for \"Octagon plates.\"[71] Thus there was\nconsiderable reluctance to accept this die sample as the authentic\ndesign. In the summer of 1959, however, the authors, excavating at\nFort Tomkins, New York, which was known to have had a small barracks\nfor the use of naval personnel ashore, recovered parts of two brass\nplates of this identical design, and in the octagon shape--that is,\nrectangular with clipped corners (fig. 29). The design may thus be\nprecisely dated.\n[Footnote 71: See MCCLELLAN, pp. 25, 44.]\n[Illustration: FIGURE 29]\nThe specimen is struck in rectangular brass with a raised edge. The\nwhole is dominated by an eagle that is very similar to the eagles on\nthe infantry and artillery corps plates described above. The talons\ngrasp the shank of a large fouled anchor; a ribbon, held in the beak\nand streaming overhead, is embossed with the motto \"FORTITUDINE.\" The\nwhole is on a trophy of arms and flags, and below the lower raised\nedge is embossed the word \"MARINES.\" The excavated specimens vary\nslightly in size, but average 3-3/8 by 4-3/4 inches. Reproductions of\nthis die strike were made prior to its acquisition by the National\nMuseum, and specimens outside the national collections should be\nconsidered with caution.\nCAP OR SHOULDER-BELT PLATE, U.S. MARINE CORPS, 1815-1825(?)\n[Illustration: FIGURE 30]\nThis specimen is known only in die samples. Because of its similarity\nin design to the 1814 infantry plates, it cannot be dated later than\n1825. Since no naval uniformed Militia units are known for the period\n1815-1825, and since the plate is obviously not a device of the\nregular Navy, it must be assigned to the Marine Corps. In studying\nthis plate, however, we must recognize the possibility that the maker\nmay have been designing and sinking dies in the hope of having a\nsample accepted and approved for issue rather than actually executing\na contract. The plate is struck in rectangular brass, and the corners\nare marked for clipping. The design, within a wide oval with raised\nedge, consists of an eagle above a trophy of arms, flags, and a\nshield. The right talon grasps a fluke of a fouled anchor, and the\nleft talon holds the pike of a stand of colors. Reproductions of this\ndie strike were made prior to its acquisition by the National Museum,\nand specimens outside the national collections should be considered\nwith caution.\n\u00b6 The 1821 uniform regulations were significant in several respects:\ncap plates were eliminated as distinctive insignia of the various\narms; the color of certain items of dress and equipment remained the\nsole distinction; and the rules regarding nonregulation dress were\nmore precisely stated than before. The cap plates were replaced by\neagles, measuring 3 inches between wing tips, and the number of the\nregiment was cut in the shield. Regulations tersely stated that \"all\narticles of uniform or equipment, more or less, than those prescribed,\nor in any manner differing from them, are prohibited.\"[72] General and\nstaff officers were to wear black sword belts with \"yellow plates\";\nartillery officers were to wear white waist belts with a yellow oval\nplate 1-1/2 inches wide and with an eagle in the center; infantry\nofficers were to wear a similar plate that was white instead of\nyellow. Cockade eagles for _chapeau de bras_ were to be gold and\nmeasure 1-1/2 inches between wing tips. Since enlisted men were no\nlonger authorized to wear swords, they had no waist belts.\n[Footnote 72: _General Regulations_, pp. 154-162.]\nCAP AND PLATE, THIRD ARTILLERY, 1821\n_USNM 66603-M. Figure 31._\n[Illustration: FIGURE 31]\nAlthough several \"yellow\" eagles that can be attributed to the\n1821-1832 period are known, this brass specimen on the bell-crowned\ncap is the only one known to the authors that has the prescribed\nregimental number cut out of the shield. The button on the pompon\nrosette--which appears to be definitely original to the cap, as does\nthe eagle--carries the artillery \"A,\" thus the assignment to that\nbranch of the service. The eagle bears a close similarity to the\neagles on the 1812 and 1814 infantry cap plates and the 1807 Marine\nCorps cap plate, and is possibly the work of the same designer.\nCAP INSIGNIA, INFANTRY, 1822\n[Illustration: FIGURE 32]\nEarly in 1822, the Secretary of War, acting on a suggestion of\nCallendar Irvine, ordered that all metal equipment of the infantry be\nof \"white metal\" in keeping with its pompons, tassels, and lace.[73]\nThis specimen, struck in copper and silvered, is believed to have been\nissued as a result of that order.\n[Footnote 73: Letter dated January 4, 1822, from Secretary of War to\nIrvine (Records AGO).]\n\u00b6 The 1821 regulations stated that cockade eagles should measure 1-1/2\ninches between wing tips. In 1832 this wingspread was increased to\n2-1/2 inches. Thus, specimens of a relatively uniform pattern and\nmeasuring approximately 1-1/2 inches in wingspread will be considered\nas of the Regular Army, 1821-1832. Similarly, those of a relatively\nuniform pattern and measuring approximately 2-1/2 inches in wingspread\nare dated 1832-1851.\nCOCKADE EAGLE, C. 1821\n[Illustration: FIGURE 33]\nThis eagle, struck in brass, has wings extended, head to the right,\nfederal shield on breast with no stars, olive branch in right talon,\nand three arrows in left talon.\nCOCKADE EAGLE, INFANTRY, C. 1821\n_USNM 60372-M (S-K 128). Not illustrated._\nThis eagle is struck from the same die as the preceding specimen, but\nit is in white metal rather than brass.\nCOCKADE EAGLE, C. 1821\n[Illustration: FIGURE 34]\nOf silver on copper, this eagle is similar to the two preceding\nspecimens, but is struck from a variant die. It possibly was worn by\nthe Militia.\nCOCKADE EAGLE, INFANTRY, C. 1821\n[Illustration: FIGURE 35]\nThis specimen is very similar to those above, but it has 13 stars in\nthe shield on the eagle's breast.\n\u00b6 Despite the fact that it was found attached to a shako of distinct\nMilitia origin, the cap plate shown in figure 36 is believed to be\nthat prescribed for the cadets of the Military Academy in the 1821\nuniform regulations and described as \"yellow plate, diamond shape.\"\nThe letters \"U S M A\" in the angles of the diamond, the word \"CADET\"\nat the top of the oval, what appears to be the designation \"W POINT\"\nat the left top of the map, and the tools of instruction (so similar\nto those embellishing the cadet diploma, although totally different\nin rendering), make it difficult to assign this plate to any source\nother than the Academy. It is possible, of course, that this was a\nmanufacturer's sample which was never actually adopted for wear at\nWest Point. The apparent maker's name, \"CASAD,\" at the bottom of the\noval, does not appear in the city directories of any of the larger\nmanufacturing centers of the period.\n[Illustration: FIGURE 36.--Specimen in West Point Museum, West Point,\nNew York.]\nCAP INSIGNIA, 1832(?)\n[Illustration: FIGURE 37]\nDespite the facts that there was no change in cap insignia authorized\nin the 1832 uniform regulations and that this specimen is similar in\nmost respects to the 1821 eagle, its refinement of design and\nmanufacture indicates that it possibly belongs to the period of the\n1830's and 1840's. It is struck in thin brass and has three plain wire\nfasteners soldered to the reverse.\nCAP INSIGNIA, 1832(?)\n_USNM 60366-M (S-K 122). Not illustrated._\nAlthough similar to the preceding plate, this specimen measures 3-1/4\nby 2-1/4 inches, is struck from a different die, and has a much wider\nbreast shield. Of somewhat heavier brass than most such similar eagles\nand exhibiting a well-developed patina, it may have been an officer's\ndevice.\nCAP PLATE, DRAGOONS, 1833\n[Illustration: FIGURE 38]\nWhen the dragoons returned to the Army in 1833, their cap device was\ndescribed as \"a gilt star, silver eagle ... the star to be worn in\nfront.\"[74] An 8-pointed, sunburst-type star, this plate is struck in\nbrass and has a superimposed eagle that is struck in brass and\nsilvered. The eagle is basically the Napoleonic type adopted by the\nBritish after the Battle of Waterloo and altered by omitting the\nlightning in the talons and adding a wreath to the breast. Plain wire\nfasteners are soldered to the back.\n[Footnote 74: General Order No. 38, Headquarters of the Army, May 2,\n1833. (Photostatic copy in files of division of military history,\nSmithsonian Institution.)]\n\u00b6 In 1834, possibly as a result of the newly organized dragoons\nreceiving distinctive branch insignia, the infantry and artillery once\nagain were authorized devices on the dress cap designating their\nparticular arm. The gilt eagle was retained. Below the eagle was an\nopen horn with cords and tassels in silver for infantry, and cross\ncannons in \"gilt\" for artillery. The number of the regiment was added\nover the cannon or within the curve of the horn. These devices\nremained in use until the change in headgear in 1851.\nCAP INSIGNIA, INFANTRY, 1834-1851\n[Illustration: FIGURE 39]\nThis eagle is similar to the 1821 pattern, although somewhat more\ncompact in design. It is struck in brass, has wings upraised, head to\nthe right, shield on breast, olive branch in right talon, and three\narrows in left talon. The open horn, struck in brass and silvered, is\nsuspended, with bell to the right, by four twisted cords tied in a\n3-leaf-clover knot; the tassels on the four cord-ends hang below.\nCAP INSIGNIA, ARTILLERY, 1834-1851\n[Illustration: FIGURE 40]\nThis is the \"gilt ... cross cannons\" device prescribed for artillery\nin the 1834 regulations. Struck in sheet brass of medium thickness,\nthe superimposed cannon has trunnions and dolphins.\nFORAGE CAP STAR, DRAGOON OFFICER, C. 1840\n[Illustration: FIGURE 41]\nAlthough uniform regulations for the period of the 1830's and 1840's\nmake no mention of a distinctive device for the dragoon forage cap,\nphotographs in the National Archives show that officers' caps, at\nleast, carried a 6-pointed star, apparently gold-embroidered.[75] This\nspecimen is believed to be such a star. Made of gold bullion and with\nrather large sequins sewed onto a heavy paper background, the star is\nmounted on dark blue wool. The points of the star are extended with\ngold embroidery on the cloth.\n[Footnote 75: TOWNSEND AND TODD, pp. 1-2.]\nCAP INSIGNIA. CADET'S, U.S. MILITARY ACADEMY, 1842, AND ENGINEER\nSOLDIERS, 1846\n[Illustration: FIGURE 42]\nIn 1839 the cadets at the Military Academy discarded the bell-crowned\ncaps they had worn since 1821 and wore a cylindrical black shako\nsimilar to that worn by the Regular artillery and infantry. The\nartillery gilt eagle and crossed cannon replaced the diamond-shaped\nplate on the front. In 1842-1843 the crossed cannon were replaced by\nthe engineer castle as more in keeping with the original mission of\nthe Academy and the general orientation of its curriculum.\nShortly after the beginning of hostilities with Mexico in 1846, the\nCongress authorized the enlistment of a company of \"engineer soldiers\"\nthat was designated the Company of Sappers, Miners, and Pontoniers.\nThese were the first enlisted men authorized the Corps of Engineers\nsince the period of the War of 1812. The headgear for these men was\nprescribed as \"Schako--same pattern as that of the artillery, bearing\na yellow eagle over a castle like that worn by the Cadets.\"[76]\n[Footnote 76: _General Regulations for the Army of the United States,\nStruck in thin to medium brass, this plate is the familiar turreted\ncastle of the Corps of Engineers so well known today. It was worn\nbelow the eagle.\n\u00b6 To complete the branches of the Regular Establishment during the\nMexican War period, the Regiment of Voltigeurs and Foot Riflemen must\nbe mentioned, although they were apparently without any distinctive\nbranch insignia.\nThe regiment was constituted on February 11, 1847, and its uniform[77]\nwas prescribed 9 days later in the War Department's General Order\nNo. 7. However, the regiment was issued infantry woolen jackets and\ntrousers and never received what little gray issue clothing was sent\nto them in Mexico almost a year later. Uniform trimmings were to be as\nfor the infantry, with the substitution of the letter \"v\" where\nappropriate. So far as presently known, this substitution affected\nonly the button pattern--an appropriate letter \"v\" on the shield\ncentered on the eagle's breast.\n[Footnote 77: A detailed description is given in _Military Collector\nand Historian_ (June 1952), vol. 4, no. 2, p. 44.]\nThe 1851 uniform regulations radically changed almost every item of\nthe Army's dress. Most of the distinctive devices were also altered,\nalthough more in size and composition than general design. Some\ndevices were completely eliminated. While officers retained insignia\nof their arm or branch on their hats, enlisted personnel, with the\nexception of those of engineers and ordnance, had only the letter of\ntheir company, their particular arm being designated by the color of\ncollars, cuffs, bands on hats, pompons, epaulets, chevrons, and the\nlike. A newly designed sword or waist-belt plate was prescribed for\nall personnel. All items of uniform and insignia authorized in 1851\nwere included in an illustrated edition of the Regulations for the\nUniform and Dress of the Army of the United States, June 1851,\npublished by William H. Horstmann and Sons, well-known uniform and\ninsignia dealers in Philadelphia.[78]\n[Footnote 78: A partial republication of this work appears in\n_Military Collector and Historian_, vol. 10, no. 1 (spring 1958), pp.\nPOMPON EAGLE, 1851\n[Illustration: FIGURE 43]\nWorn attached to the base of the pompon by all enlisted personnel,\nthis brass eagle, similar in general design to that worn on the shako\nin the 1830's, stands with wings upraised, olive branch in right\ntalon, three arrows in left talon, and a scroll, with national motto,\nin beak. Above are stars, clouds, and bursts of sun rays. Officers\nwore an eagle of similar design of gold embroidery on cloth.\nCAP INSIGNIA, GENERAL AND STAFF OFFICERS, 1851\n[Illustration: FIGURE 44]\nThis specimen, in accord with regulations, is on dark blue cloth and\nconsists of a gold-embroidered wreath encircling Old English letters\n\"U.S.\" in silver bullion. Embroidered insignia of this period were all\nmade by hand, and they varied considerably in both detail and size.\nDuring the 1861-1865 period the same design was made about half this\nsize for wear on officers' forage caps, and the device appeared in\nvariant forms. One example is known where the numeral \"15\" is\nembroidered over the letters \"U.S.\";[79] and Miller's _Photographic\nHistory of the Civil War_ includes several photos of general officers\nwhose wreath insignia on the forage cap substitute small rank insignia\nstars for the letters.\n[Footnote 79: LEWIS, p. 64.]\nCAP INSIGNIA, OFFICER, ENGINEERS, 1851\n_USNM 300720. Figure 45._\n[Illustration: FIGURE 45]\nOn dark blue cloth, this device comprises a gold-embroidered wreath of\nlaurel and palm encircling a turreted castle in silver metal as\nprescribed in regulations. Other examples are known with the castle\nembroidered.\nHAT INSIGNIA, OFFICER, ARTILLERY, 1851\n[Illustration: FIGURE 46]\nThis specimen adheres almost exactly to the 1851 regulations, but it\nlacks the number of the regiment as called for. The number was a\nseparate insignia embroidered above the cannon. The cannon are of gold\nembroidery. The device was also made in gold metal imitation-embroidery\nin several variant designs.\nCAP INSIGNIA, OFFICER, INFANTRY, 1851\n[Illustration: FIGURE 47]\nOn dark blue cloth, this device is the well-known looped horn in gold\nembroidery with three cords and tassels. The regimental number \"4,\" in\nsilver bullion, lies within the loop of the horn. This insignia is\nalso common in metal imitation-embroidery.\nCAP AND COLLAR INSIGNIA, ENLISTED ORDNANCE, 1851\n[Illustration: FIGURE 48]\nStruck in brass, this device was worn on the caps and coat collars of\nordnance enlisted personnel. Although the shell and flame insignia\nappears in a number of variations of design, this specimen conforms\nexactly to the regulations of 1851 as published by Horstmann.\nCAP AND COLLAR INSIGNIA, ENGINEER SOLDIERS, 1851\n_USNM 61618. Figure 49._\n[Illustration: FIGURE 49]\nThe 1851 uniform regulations called for a \"castle of yellow metal one\nand five-eighths inches by one and one-fourth inches high\" on both the\ncoat collar and the hat of \"Engineer Soldiers.\" This specimen, struck\nin brass, conforms exactly to the descriptions and drawing in the\nHorstmann publication of the regulations.\nCAP INSIGNIA, DRAGOON OFFICERS, 1851\n[Illustration: FIGURE 50]\nComprising crossed sabers of gold, with edges upward, this insignia is\nsimilar to the well-known device worn by the Regular cavalry as late\n\u00b6 In 1846 the Regiment of Mounted Riflemen was organized to\nconsolidate the northern route to the Pacific by establishing and\nmanning a series of posts along the Oregon Trail.[80] The outbreak of\nthe War with Mexico postponed this mission and the unit was diverted\nto the theater of operations. Shortly after the regiment was\nconstituted it was authorized to wear a forage cap device prescribed\nas \"a gold embroidered spread eagle, with the letter R in silver, on\nthe shield.\"[81] No surviving specimen of this insignia is known, and\nthere seems some doubt that it was ever actually manufactured.[82]\n[Footnote 80: Act of May 19, 1846 (_Military Laws_, pp. 371-372).]\n[Footnote 81: General Order No. 18, June 4, 1846, War Department\n(photostatic copy in files of division of military history,\nSmithsonian Institution).]\n[Footnote 82: Insignia of the riflemen are discussed by Townsend and\nTodd, pp. 2-3.]\nCAP INSIGNIA, OFFICER, REGIMENT OF MOUNTED RIFLEMEN, 1850\n[Illustration: FIGURE 51]\nIn 1850 the regiment was given a \"trumpet\" hat device. Officers were\nto wear \"a trumpet, perpendicular, embroidered in gold, with the\nnumber of the regiment, in silver, within the bend.\"[83] This trumpet\nis also known in metal imitation-embroidery. The prescribed regimental\nnumber, which is illustrated in the Horstmann publication of the\nregulations (pl. 15), is not included on the device, probably because\nthere was but one such unit in the Regular Establishment.\n[Footnote 83: General Order No. 2, February 13, 1850, War Department\n(photostatic copy in files of division of military history,\nSmithsonian Institution).]\nCAP INSIGNIA, ENLISTED, REGIMENT OF MOUNTED RIFLEMEN, 1850\n[Illustration: FIGURE 52]\nThe same general order that gave rifle officers a gold-embroidered\ntrumpet prescribed for enlisted men a similar device to be of \"yellow\nmetal.\" This insignia lasted but one year for the men in the ranks,\nbeing unmentioned in the 1851 regulations.\nShoulder-Belt and Waist-Belt Plates\nOval shoulder-belt plates were worn by American officers during the\nWar of the Revolution, but no extant specimens are known. Highly\nornamented or engraved officers' plates for the period after 1790 are\nin several collections (fig. 53) and others are illustrated in\ncontemporary portraits (fig. 54). Just what year shoulder-belt plates\nwere issued to enlisted personnel is unknown, but their use appears to\nhave been well established by 1812. The uniform regulations for that\nyear specified swords for sergeants of infantry to be \"worn with a\nwhite cross belt 3-1/2 inches wide,\" but nothing was said about a\ndevice on the belt.[84]\n[Footnote 84: General Order, Southern Department U.S. Army, January\n24, 1813 (photostatic copy in files of division of military history,\nSmithsonian Institution).]\n[Illustration: FIGURE 53.--Specimen in Campbell collection.]\nNormally, brass or \"yellow metal\" plates were authorized for the\nartillery and silvered or \"white metal\" for the infantry and dragoons,\nas consonant with the rest of their trimmings. In actuality, however,\nwhite-metal shoulder-belt plates do not seem to have been issued to\nthe infantry prior to 1814, and brass ones were still being issued in\n1815.[85] Most of these plates were plain oval, although a few are\nknown that were struck with devices similar to those on cap plates;\nand at least one rectangular cap plate, fitted with the two studs and\nhook on the reverse normal to shoulder-belt plates, has been found. It\nseems probable that these were officers' plates. Oval brass plates\nhave been found that are identical in size and construction to the\nplain ones but with the letters \"U.S.\" embossed on them; however,\nthese are difficult to date.\n[Footnote 85: Letters from Irvine in Records AGO: To Colonel Bogardus\n(Commanding Officer, 41st Infantry), February 16, 1814; to James\nCalhoun, January 14, 1815; and to General Scott, January 31, 1815.]\n[Illustration: FIGURE 54.--Portrait in collection of The Filson Club,\nLouisville, Kentucky.]\nIt is extremely doubtful that waist-belt plates were issued to\nenlisted personnel of foot units during this period. In 1808 enlisted\ndragoons were authorized a waist-belt plate of tinned brass and, as\nfar as known, perfectly plain.[86]\n[Footnote 86: Letter to the Purveyor of Public Supplies in 1808.]\nThe 1812 regulations prescribed for the light dragoons a \"buff leather\nwaist belt, white plate in front with eagle in relief,\" and there is\nthe possibility that the light artillery had such. In actuality, there\nwas no call for a waist belt where a shoulder belt was authorized.\nNeither civilian trousers nor the few surviving military \"pantaloons\"\nof the period are fitted with belt loops, trousers being held up\neither by suspenders or by being buttoned directly to the shirt or\nwaistcoat. No example of the dragoon plate has been found. However, a\nrather tantalizing possibility exists--a fragment of a pewter belt\nplate (fig. 55) was excavated at Sackets Harbor, New York, where the\nlight dragoons are known to have served. The 1816 regulations\nspecified for artillerymen \"waist belts of white leather two inches\nwide, yellow oval plate of the same width.\" It is not made clear,\nhowever, whether this belt and plate was for officers only or for all\nranks. The unusually striking oval specimen (fig. 56) may be this\nplate, but its ornateness indicates that this particular design was\nfor officers only.\n[Illustration: FIGURE 55.--Specimen in Campbell collection.]\n[Illustration: FIGURE 56.--Specimen in Campbell collection.]\nSHOULDER-BELT PLATE, 1790(?)-1812\n_USNM 12804. Figure 57._\n[Illustration: FIGURE 57]\nThis plate was worn by Peter Gansevoort sometime during his military\ncareer, probably after 1790. Gansevoort, between 1775 and his death in\n1812, was successively major, lieutenant colonel, colonel, and\nbrigadier general of New York State Militia and brigadier general U.S.\nArmy (1809-1812). Although distinctly Militia in design, the specimen\nis included here as an example of the wide variety of such devices\nworn by officers of the 1800-1821 period.\nThis plate is octagonal, slightly convex, and has beveled edges. The\ndesign is hand engraved on copper, and the whole is gold plated.\nWithin an engraved border is the eagle-on-half-globe device of New\nYork State. Two studs and a hook soldered to the reverse are not\nbelieved to be original.\nSHOULDER-BELT PLATE, INFANTRY OFFICER, C. 1812\n[Illustration: FIGURE 58]\nThis rectangular, slightly convex plate of silver on copper has\nbeveled edges and a small slot in the center for the attachment of an\nornament. The ornament is missing, although it can be surmised that it\nwas an eagle. The reverse is fitted with two studs and a hook and\nbears the hallmark of \"W. Pinchin, Philad{a}.\" William Pinchin is\nlisted in the Philadelphia directory for 1809 as a silversmith at 326\nSassafras Street. The 1810 directory lists only \"Widow of,\" but\nanother William Pinchin (probably the son) appears in the 1820's.\nWAIST-BELT PLATE, LIGHT ARTILLERY(?), 1814-1821\n[Illustration: FIGURE 59]\nThe design of this rectangular plate, struck in rather heavy brass, is\nthe same as that offered as the 1814-pattern cap plate for the light\nartillery, although it is the product of a different and somewhat more\ncrudely sunk die. The piece is dominated by an eagle with wings\nupraised, a shield on its breast, three arrows in its right talon, and\nan olive branch in its left talon. Crossed cannon are in the\nforeground, and there is a pile of six cannon balls in the lower right\ncorner. The whole is superimposed on a trophy of colors and bayoneted\nmuskets. Above is a 5-pointed \"star of stars\" made up of 20 5-pointed\nstars.\nWAIST-BELT PLATE, OFFICER, ARTILLERY CORPS, 1814-1821\n[Illustration: FIGURE 60]\nThe rectangular plate is struck in brass on a die of the same design\nas that used in making the 1814 Artillery Corps cap plate, type I (p.\n18). Before the strike was made, a piece of thin sheet iron, slightly\nnarrower than the finished product, was applied to the reverse of the\nbrass. After the strike, which shows through clearly on the iron, the\nends of this applied metal were bent inward into tongues for\nattachments to the belt, and the remainder of the back was filled with\npewter. The edges of the obverse were then beveled to finish the\nproduct. It seems very probable that plates such as this were produced\nfor sale to officers.\nSHOULDER-BELT PLATE, OFFICER, ARTILLERY CORPS, 1814-1821\n[Illustration: FIGURE 61]\nThis is a companion piece to the Artillery Corps waist-belt plate\ndescribed above. It was struck in brass from the die of the 1814\nArtillery Corps cap plate, type I, again with a thin sheet of iron\napplied to the reverse before the strike. There is no pewter filling;\nthe beveled edges of the piece together with the adhesive effect of\nthe strike--which shows through very clearly--holds on the back. The\nplate is fitted with two simple bent-wire fasteners for attachment,\nindicating that it was intended for ornamental use only. Like its\nwaist-belt plate counterpart, this specimen must be considered an\nofficer's device.\nSHOULDER-BELT PLATE, INFANTRY, 1814-1821\n[Illustration: FIGURE 62]\nThis specimen is of the same design as the 1814 Infantry cap plate,\ntype I (p. 15). It is oval, with raised edge. Within the oval is an\neagle with an olive branch in its beak, three arrows in its right\ntalon, and thunder bolts and lightning in its left talon. Below is a\ntrophy of stacked muskets, drum, flag, and shield. The plate is silver\non copper, with sheet-iron backing and bent-wire fasteners. As in the\ncase of the Artillery Corps plate, just preceding, this must be\nconsidered an officer's plate. A similar oval plate bearing the design\nof the 1812 dragoon cap plate, and of similar construction, is known.\nSHOULDER-BELT PLATE, 1814\n[Illustration: FIGURE 63]\n[Illustration: FIGURE 64]\nExcavated on the site of Smith's Cantonment at Sackets Harbor, New\nYork, this plate is interesting in that it differs in both\nconstruction and method of attachment from similar plates of the same\nperiod in the national collections. Rather than being struck in thin\nbrass with a backing and fasteners applied to the reverse, this\nspecimen is cast in brass and the edges rather unevenly beveled, with\ntwo studs and a narrow tongue for attachment cast integrally with the\nplate and with hexagonal heads forced over the ends of the studs. This\nmeans of attachment, which indicates that the plate was intended to be\nutilitarian as well as merely ornamental, is similar to that on\nBritish plates of the period between the Revolution and the War of\n1812. The plate could have been worn by either infantry or artillery,\nfor both were issued brass plates during this period,[87] however, it\nis more probable that it was worn by the infantry, since the majority\nof the artillery in the Sackets Harbor area were stationed nearby at\neither Fort Pike or Fort Tomkins.\n[Footnote 87: Letters from Irvine in Records AGO: To Colonel Bogardus,\nFebruary 16, 1814; to James Calhoun, January 14, 1815.]\nSHOULDER-BELT PLATE, C. 1812\n[Illustration: FIGURE 65]\nThe plain, oval, slightly convex plate of brass has a raised edge. The\nface is lapped over a piece of sheet-iron backing. On the reverse is\nsoldered an early form of bent-wire fasteners. British shoulder-belt\nplates of the Revolutionary period normally had fasteners cast as\nintegral parts of the plate proper.\nSHOULDER-BELT PLATE, C. 1812\n_USNM 604312 (S-K 468). Not illustrated._\nThis plate is identical to the one described immediately above except\nthat it is struck in copper and the surface is silvered.\nSHOULDER-BELT PLATE, C. 1812\n_USNM 604314 (S-K 470). Not illustrated._\nThis plate, struck from solid brass, has a slightly beveled edge and\nbent-wire fasteners. It is slightly convex. Since it is smaller than\nthe two preceding plates, it could have been designed for the Militia.\nSHOULDER-BELT PLATE, 1815(?)-1821\n[Illustration: FIGURE 66]\nThe two specimens of this plate in the national collections are\nundocumented. Similar in size and construction to the plain oval brass\nand silvered plates, it has the raised letters \"U.S.,\" three-fourths\ninch high in the center. Definitely not later than 1832, it may well\nhave been issued soon after the end of the War of 1812. It is\nconsidered a Regular Army item since the Militia did not use the\ndesignation \"U.S.\" at this early period. In this latter connection it\nis interesting to note that an example of the 1812 Infantry cap plate,\ntype II, with the letters \"US\" crudely stamped out, is known attached\nto a cap of distinct Militia origin.\nWAIST-BELT PLATE, GENERAL OFFICER, C. 1816\n_USNM 38212. Figure 67._\n[Illustration: FIGURE 67]\nAfter the War of 1812, the State of New York presented swords to\nseveral prominent officers of the Army and Navy who had distinguished\nthemselves in actions within New York or near its borders. One of\nthese swords (USNM 10294)[88] and an unusually fine gold embroidered\nbelt (USNM 33097) with this gold belt buckle were presented to Maj.\nGen. Jacob Brown.\n[Footnote 88: Detailed descriptions of this sword are given by HAROLD\nL. PETERSON, pp. 193-194, and BELOTE, pp. 30-31.]\nChased in very fine gold, the buckle is considered by experts in the\ngoldsmithing and silversmithing fields to be one of the outstanding\npieces of American craftsmanship of its kind.[89] The central motif is\nthe New York State eagle-on-half-globe device on a wreath of the\ncolors. The head of the eagle is very similar to that on the cap\nplates of the 1807 Marine Corps, 1812 infantry, and 1814 Artillery\nCorps. The border is of a rose pattern distinctly American in feeling,\nand in each corner within the border are acanthus leaves in unusually\ndelicate Viennese baroque design.\n[Footnote 89: Mr. Michael Arpad, well known and highly regarded\nsilversmith, of Washington, D.C., has called this specimen \"an\nexquisite piece of work by a master craftsman.\"]\nThe maker of this buckle is unknown, but since it is reasonably\ncertain that the hilt of the sword was designed by Moritz Furst (see\np. 12), it is possible that the design of the buckle is his also,\nespecially in view of the Viennese touch in the acanthus leaves, his\ntraining at the mint in Vienna, and the probability that he designed\nthe 1812 infantry cap plate.\n\u00b6 Although the 1821 regulations were very specific about the\nprohibition of nonregulation items of uniform and equipment, they were\nsomewhat vague regarding specifications. General staff and engineer\nofficers were to wear black belts with a \"yellow plate,\" artillery\n\"yellow oval plates ... with an eagle in the center,\" and infantry the\nsame but \"white\" instead of yellow.[90] No oval plates meeting these\nvague descriptions are known, but the specimens described below may\nwell have been those actually approved by the Ordnance Department, and\nthus, worn.\n[Footnote 90: _General Regulations for the Army_, pp. 154-162.]\nWAIST-BELT PLATE, INFANTRY OFFICER, C. 1822\n[Illustration: FIGURE 68]\nThis plate, struck in copper and silvered, is round with an outer\nring. It is attached to a white buff belt. The plate proper contains\nan eagle with wings outspread, shield on breast, olive branch in right\ntalon, and three arrows in left talon. The whole is within a ring of\n24 5-pointed stars. The outer ring is decorated as a wreath, and the\nnarrow rectangular belt attachments are embossed with a floral\npattern. The 24 stars place this specimen between 1822 and 1836.\nSimilar buckles are known in yellow metal for either staff or\nartillery and containing 24, 26, and 28 stars, indicating that they\nprobably were worn until the rectangular eagle-wreath plate was\nprescribed in 1851.\nWAIST-BELT PLATE, INFANTRY OFFICER, 1821-1835\n[Illustration: FIGURE 69]\nThis specimen is offered as another possibility for the 1821\nregulation plate. It is identical in size and similar in design to the\npreceding plate. The plate proper contains an eagle with wings spread,\na breast shield containing the letter \"I,\" an olive branch in right\ntalon, and three arrows in left talon. There is no outer ring of\nstars. The outer ring of the buckle is decorated with a wreath, but\nthe rectangular belt attachments are plain. The 1821 regulations\ncalled for eagle buttons of \"yellow\" and \"white\" metal with the\nletters \"A\" and \"I\" (for artillery and infantry) on the eagle's\nshield, and the belt plate may have been designed to conform. There is\nalso the possibility that this plate, as well as the one described\nbelow, was designed to conform to the 1835 regulations which\nprescribed a waist belt with a \"round\" clasp.[91]\n[Footnote 91: _General Regulations for the Army of the United States_,\nWAIST-BELT PLATE, ARTILLERY OFFICER, 1821-1835\n_USNM 60455-M (S-K 211). Not illustrated._\nNearly identical to the infantry officer's plate above, this buckle,\nin brass, has the artillery \"A\" on the eagle's breast shield.\n\u00b6 Although the regulations for this period do not mention\nshoulder-belt plates for enlisted men (officers had none as they wore\ntheir swords on their waist belts), it can be assumed that they were\nworn. The two specimens described below must be dated later than\n1812-1821 because of the belt attachments. The earlier specimens had\nrudimentary bent-wire fasteners, but these, more refined, have two\nround studs and a hook soldered to the plate proper.\nSHOULDER-BELT PLATE, INFANTRY, C. 1821\n[Illustration: FIGURE 70]\n[Illustration: FIGURE 71]\nThis plate, of silver on copper, is plain oval and slightly convex.\nSHOULDER-BELT PLATE, ARTILLERY, C. 1821\n_USNM 604315 (S-K 471). Not illustrated._\nThis specimen is identical to the preceding one except that it is in\nplain brass.\n\u00b6 The 1832 uniform regulations brought some well-defined changes.\nGeneral and staff officers were to wear gilt waist-belt plates \"having\nthe letters U S and a sprig of laurel on each side in silver,\" and the\nbottom of the skirts of officers' coats were to bear distinctive\ndevices--a gold-embroidered star for general officers and officers of\nthe general staff, a shell and flame in gold embroidery for artillery\nofficers, and silver-embroidered bugles for infantry officers.\nWAIST-BELT PLATE, GENERAL AND STAFF OFFICERS, 1832\n_USNM 664. Figure 72._\n[Illustration: FIGURE 72]\nThe plate and the belt to which it is attached formerly belonged to\nCapt. Charles O. Collins, an 1824 graduate of the Military Academy.\nThe belt is of patent leather, as specified for undress wear, and is\n1-1/2 inches wide. The plate is cast in brass and has raised edges.\nRather than having \"a sprig of laurel on each side,\" it has a wreath\nof laurel enclosing the letters \"U S,\" in Old English, in silvered\nmetal affixed to the front. It is attached on the right side by a\nrectangular belt attachment with a flat hook on the left rear.\n\u00b6 The 1832 regulations specified for engineer officers a waist-belt\nplate to be \"gilt, elliptical, two inches in the shortest diameter,\nbearing the device of the button.\" Such a plate (fig. 73) is in the\ncollections of the Valley Forge Chapel Museum. It is entirely possible\nthat this plate is even earlier than 1832, for the 1821 and 1825\nregulations state that the engineer buttons were to contain \"the\ndevice and motto heretofore established.\"\n[Illustration: FIGURE 73]\nIn the collections of the West Point Museum is a button, carrying the\n\"Essayons\" device, that was excavated in the area behind the \"Long\nBarracks,\" which burned in 1825. Another such button excavated at\nSackets Harbor on the site of an 1812-1815 barracks bears a maker's\nname (Wishart) of the 1812-1816 period.\nWAIST-BELT PLATE, GENERAL AND STAFF OFFICERS, 1832(?)-1850\n[Illustration: FIGURE 74.--Specimen in Valley Forge Chapel Museum,\nValley Forge, Pennsylvania.]\nThis buckle is similar to the one (shown in fig. 73) that belonged to\nCapt. Charles O. Collins, but it is different in that the letters\n\"U.S.\" are enclosed not by a laurel wreath but by a sprig of laurel on\nthe right side and a sprig of palm on the left. The 1841 uniform\nregulations specified such a belt plate for officers of the Corps of\nEngineers, but with a \"turreted castle, raised in silver\" rather than\nthe letters \"U.S.\" This places the probable date of manufacture of\nthis specimen in the 1840's.\nCOAT-SKIRT ORNAMENT, GENERAL STAFF, 1832\n_USNM 8040. Figure 75._\n[Illustration: FIGURE 75]\nThis skirt ornament, on buff cloth, is from a coat worn by Capt.\nThomas Swords when he was assistant quartermaster general in 1838. The\ndesign consists of three 6-pointed stars of gold bullion cord: a line\nstar of twisted cord superimposed upon a larger star of closely\nstitched cord that in turn is superimposed upon a still larger star of\nsunburst type.\nCOAT-SKIRT ORNAMENT, GENERAL STAFF, 1832\n[Illustration: FIGURE 76]\nLike the preceding specimen, this ornament, on buff cloth, is\ncomprised of three stars. A star made of lines of sequins secured by\ntwo strands of twisted bullion is superimposed upon a 6-pointed star\nof gold embroidery that in turn is superimposed upon a 6-pointed star\nmade up of gold sequins secured by gold bullion cord.\nCOAT-SKIRT ORNAMENT, ARTILLERY OFFICER, 1832\n_USNM 15929. Figure 77._\n[Illustration: FIGURE 77]\nThis specimen, on red cloth, is on a coat worn by William Tecumseh\nSherman when he was a lieutenant in the 3d Artillery. The bomb is made\nof whorls of gold bullion cord, while the flames are composed of\ncurving lines of twisted bullion. The lowest flame on either side\nterminates in arrow heads.\nThere are a number of gold-embroidered shell and flame devices in the\nnational collections, all varying considerably in size and\ncomposition. Some are skirt ornaments for artillery officers, both\nRegular Army and Militia, while some are cap ornaments for ordnance\nofficers. Indeed, two coats formerly belonging to Maj. Levi Twiggs,\nU.S. Marine Corps, carry the same device.\nCOAT-SKIRT ORNAMENT, INFANTRY OFFICER, 1832\n_USNM 59861-M. Figure 78._\n[Illustration: FIGURE 78]\nThe silver coat-skirt horn ornaments of infantry officers varied\nalmost as much as the shell and flame devices, generally in relation\nto the affluence of the individual concerned. Unlike such ornaments of\nthe other services, the horns were paired in rights and lefts on the\ncoat.\nThis specimen, of silver bullion cord, is on a coat that once belonged\nto Lt. William Williams Mather, an 1828 graduate of the Military\nAcademy who left the service in 1836. The horn is looped, and it is\nsuspended by twisted bullion from a simple 3-leaf-clover knot. The\nwhole is backed on blue cloth.\nCOAT-SKIRT ORNAMENT, INFANTRY OFFICER, 1832\n_USNM 1056. Figure 79._\n[Illustration: FIGURE 79]\nThis rather elaborate specimen is on a coat worn by John Porter Hatch\nwhen he was a lieutenant of infantry in 1845. The body of the\nhorn--which is merely curved rather than looped--is made of silver\nlam\u00e9 encircled by three ornamented bands of bullion. The mouthpiece\nand bell are of bullion. The whole is suspended by a rather ornate\n3-leaf-clover knot of bands of edged bullion and is backed on blue\ncloth.\nCOAT-SKIRT ORNAMENT, CORPS OF TOPOGRAPHICAL ENGINEERS, 1839(?)\n_USNM 22702. Figure 80._\n[Illustration: FIGURE 80]\nThe uniform regulations for the period 1832-1846 carry no mention of\ncoat-skirt ornaments for the Corps of Topographical Engineers, rather\nonly prescribing the \"slashed skirt flaps to be embroidered in gold,\nwith oak leaves and acorns\" like the collar and cuffs. There is in the\nnational collections, however, a uniform for the Corps that\ncorresponds with 1839 regulations in every way except that the coat\nskirts carry this ornament--a shield within a wreath of oak leaves--of\ngold embroidery. The device appears to be of the same vintage as the\nother embroidery on the coat.\n\u00b6 Although the 1832 uniform regulations make no mention of swords for\nnoncommissioned officers, in 1833 the Ames Manufacturing Company of\nChicopee, Massachusetts, began the manufacture of a new sword for the\nRegular artillery. Based on a European pattern, this weapon was the\npopular conception of the short Roman stabbing sword, or _gladius_. In\n1834 this weapon was also authorized for infantry noncommissioned\nofficers.[92]\n[Footnote 92: _Regulations for the Government of the Ordnance\nDepartment_, p. 64; and HAROLD L. PETERSON, pp. 42-43.]\nWAIST-BELT PLATE, ARTILLERY NONCOMMISSIONED OFFICER, 1833\n[Illustration: FIGURE 81]\nThis is the belt-plate assembly designed for carrying the short \"Roman\npattern\" NCO sword. The plate is of two round pieces joined by an\nS-hook that is open on one end for unbuckling. Each round piece has a\nflat loop for attachment to the white buff belt. The right-hand round\npiece has an eagle with head to the left, wings drooping, three arrows\nin the right talon, and an olive branch in the left talon. The\nleft-hand piece has crossed cannons and the letters \"U.S.\" The whole\nis cast in rough bronze.\nAssemblies of this type were popularly known as \"Dingee\" belts,\nbecause one of the primary contractors for them was Robert Dingee of\nNew York City. The eagle on this plate is very similar to the one on\nDingee's contract rifle flasks of 1832.[93]\n[Footnote 93: See PATTERSON, p. 8.]\nWAIST-BELT PLATE, INFANTRY NONCOMMISSIONED OFFICER, 1834\n[Illustration: FIGURE 82]\nThis plate and belt are identical to the artillery specimen above\nexcept that the left-hand round portion exhibits three stacked muskets\nand a drum instead of crossed cannon.\n[Illustration: FIGURE 83.--Specimen in collection of William E. Codd,\nTowson, Maryland.]\n\u00b6 NCO belt plates similar to the two above also appeared in what might\nbe called a staff or branch immaterial pattern, with the crossed\ncannon and/or stacked muskets and drum replaced by the letters \"US\"\nalone (fig. 83). This pattern apparently was intended for wear by\nNCO's other than those assigned to the infantry, artillery, or\ndragoons.\nWAIST-BELT PLATE, DRAGOON OFFICER, 1833\n_USNM 5664. Figure 84._\n[Illustration: FIGURE 84]\nThis plate, which formerly belonged to Gen. William S. Harney when he\ncommanded the 2d Dragoons in 1836, is identical to the general and\nstaff officers' plate of the 1832 regulations except that the letters\n\"U.S.\" have been replaced by the letter \"D\" in Old English, as\nprescribed.[94]\n[Footnote 94: General Order No. 38, Headquarters of the Army, May 2,\n1833 (photostatic copy in files of the division of military history,\nSmithsonian Institution).]\nWAIST-BELT PLATE, NONCOMMISSIONED OFFICER, 1836\n[Illustration: FIGURE 85]\nThe 1835 uniform regulations replaced the rather impractical S-hook\nNCO belt plate with a \"round clasp\" on which the branch designation\nwas replaced with the raised letters \"U S.\" Similar in over-all design\nto the 1821 officers' plate, round with outer ring, these plates were\nrough cast in brass and had a stippled surface.\nWAIST-BELT PLATE, NONCOMMISSIONED OFFICER, 1836\n_USNM 604114 (S-K 270). Not illustrated._\nThis specimen is very similar to the preceding plate, but it is of a\ndefinitely different casting and is generally heavier in over-all\nappearance, the inner ring is much more convex, and the letters \"U S\"\nare raised only slightly and spread farther apart.\nSHOULDER-BELT PLATE, OFFICERS, 1839\n_USNM 40886. Figure 86._\n[Illustration: FIGURE 86]\nThe 1839 uniform regulations specified a shoulder belt (rather than a\nwaist belt) for carrying the sword, with a \"breast plate according to\nthe pattern to be furnished by the Ordnance Department.\" This plate,\nwhich was worn by Capt. Erastus Capron, 1st Artillery, an 1833\ngraduate of the Military Academy, is believed to be that\nspecified.[95] The specimen is rectangular with beveled edges, cast in\nbrass, and has the lines of a modified sunburst radiating outward. In\nthe center, within a wreath of laurel, are the letters \"U S\" in Old\nEnglish. Both the wreath and letters are of silvered copper and are\napplied. The plate is attached by three broad hooks rather than two\nstuds and a hook.\n[Footnote 95: _U.S. Military Magazine_ (April 1841), illustrations for\n\"United States Infantry, Full Dress\" and \"United States Artillery\n(Captain).\"]\nSHOULDER-BELT PLATE, OFFICERS, 1839\n_USNM 604330 (S-K 486). Not illustrated._\nThis plate is almost identical to the Capron specimen above except\nthat the letters \"U S,\" instead of being in Old English, are formed of\noak leaves.\nWAIST-BELT PLATE, CORPS OF TOPOGRAPHICAL ENGINEERS, 1839\n_USNM 22702. Figure 87._\n[Illustration: FIGURE 87]\nThe 1839 uniform regulations prescribed this plate for the Corps of\nTopographical Engineers. The oval inner plate, which contains the\nprescribed eagle, shield, and the letters \"U S\" in Old English, is\nstruck in medium weight copper and gilded. This inner plate is\nsoldered to a cast-bronze and gilded tongue which in turn is brazed to\na cast-bronze belt attachment. The oval outer ring, bearing the\nprescribed \"CORPS OF TOPOGRAPHICAL ENGINEERS\" in Roman capitals, is\ncast in brass and gilded. To the inner edge of this outer ring are\nbrazed two curved seats for the inner oval. The whole is brazed to the\nbelt attachment, also cast in brass and gilded.\n\u00b6 In view of the large and somewhat elaborate cap plates as well as\nshoulder-belt plates adopted by both the Regulars and Militia early in\nthe 19th century, it is somewhat surprising that apparently neither\ncomponent had ornamentation on its cartridge boxes until the Ordnance\nRegulations of 1834 prescribed a very ornate design embossed on the\nleather flap.[96] Certainly there was precedent for such, for both the\nBritish and German mercenary troops of the Revolution and the British\nand Canadian troops of the War of 1812 wore metal ornaments on their\ncartridge boxes. At least partial explanation for this omission may\nlie in one of Callender Irvine's reasons for rejecting brass cartridge\nboxes in favor of leather ones: \"The leather ... affords no mark for\nthe enemy to sight at. The brass ... would afford a central object, as\nregards the body of the Soldier, and one which would be seen at a\ngreat distance to fire at.\"[97] Why Irvine did not object equally to\nthe large white and yellow metal cap and shoulder-belt plates as\ntargets is unknown. In any case--with a possible few Militia\nexceptions such as a Militia cartridge box with a plate bearing the\nlikeness of Washington in silver, both about 1835--the 1839 model oval\nplates were the first to be worn.\n[Footnote 96: _See Military Collector and Historian_ (June 1950), vol.\n[Footnote 97: Letter dated June 29, 1813, from Irvine to Secretary of\nWar (Records AGO).]\nThe ordnance regulations of 1839 and the ordnance manual of 1841\nbrought in two distinctly new types of plates, the familiar brass oval\nwaist-belt and cartridge-box plates with the letters \"U. S.\" and the\nround shoulder-belt plate with the eagle. The oval plates fall into\ntwo general sizes, 3.5 inches by 2.2 inches (for plates on the\ninfantry's cartridge box and the cavalry's waist belts)[98] and 2.8\ninches by 1.6 inches (for plates on the infantry's waist belts and the\ncavalry's carbine cartridge boxes and pistol cartridge boxes). The use\nof each plate is determined by the type of fastener. These plates were\nstruck in thin brass and the backs generally leaded, although some\nwere used without such backing, probably to save both weight and\nmaterial. Cartridge boxes were also embossed with the outline of this\noval plate in lieu of the plate itself. It is interesting to note that\nthe larger plates with lead backs weighed about 5-1/2 ounces and the\nsmaller ones just over 2 ounces.\n[Footnote 98: The cavalry waist-belt plate is actually specified to be\n3.6 inches by 2.2 inches.]\nWAIST-BELT PLATE, CAVALRY, 1839\n[Illustration: FIGURE 88]\n[Illustration: FIGURE 89]\nThe specimen is oval, slightly convex, and struck in thin brass. The\nface has a raised edge and the letters \"U S.\" The reverse is leaded,\ncarries two studs and a hook (indicating its use), and is stamped with\nthe maker's name, \"W. H. Smith, Brooklyn.\" Smith is listed in New York\nCity directories of the Civil War period as a contractor for metal and\nleather supplies.\nCARTRIDGE-BOX PLATE, INFANTRY, 1839\n[Illustration: FIGURE 90]\nThis plate is identical to the preceding one except that it is leaded\nand fitted with two looped-wire fasteners. The reverse is stamped with\nthe name of the maker, \"J. L. Pittman,\" who, like Smith, was a\ncontractor in the New York City area in the Civil War period.\nCARTRIDGE-BOX PLATE, CAVALRY, 1839\n_USNM 604395 (S-K 542). Not illustrated._\nThis is the oval \"US\" plate of the smaller size (2-3/4 by 1-1/8 in.),\notherwise identical to the larger plate. It is fitted with two\nlooped-wire fasteners.\nWAIST-BELT PLATE, INFANTRY, 1839\n[Illustration: FIGURE 91]\nThis specimen is identical to the preceding plate except that it is\nfitted with two brass hooks for attachment to the belt and the reverse\nis stamped with the maker's name, \"Boyd & Sons.\" No trace of a\nmanufacturer of such products by the name of Boyd has been found. It\nis probable that he worked during the Civil War period when there were\nmany such contractors.\nWAIST-BELT PLATE, INFANTRY, 1839\n_USNM 604399 (S-K 546). Not illustrated._\nThis plate is identical to those above except that the reverse is\nstamped with the maker's name. \"H. A. Dingee.\"\nWAIST-BELT PLATE, INFANTRY, 1839\n[Illustration: FIGURE 92]\nThe reverse side of this plate is fitted with the rather rudimentary\nwire fasteners similar to those on shoulder-belt plates of the\n1812-1821 period. In other respects the specimen is identical to the\npreceding ones of 1839.\n\u00b6 The 1839 regulations specified a bayonet-belt plate \"round, brass,\nwith eagle.\" The 1841 ordnance manual was more exact, specifying the\nplate to be \"brass, circular, 2.5 in. diameter, with an Eagle,\" and\nthen stating: \"The bayonet belt is about to be discontinued ...\"\nAlthough not so authorized at the time, this plate, so familiar during\nthe Civil War period, was switched over to the shoulder belt\nsupporting the cartridge box. Such plates were manufactured in great\nquantities and in many variations of the original design by a dozen or\nmore contractors during the period 1861-1865.\nCARTRIDGE-BOX-BELT PLATE, 1839\n[Illustration: FIGURE 93]\nThis circular plate, with raised rim, is dominated by an eagle of\nrefined design that is very similar to the eagles appearing on the War\nof 1812 plates. The eagle has its wings drooped, head to the left,\nthree arrows in the right talon, and an olive branch in the left\ntalon. This specimen can be dated with the earliest cartridge-box\nplates because of its backing and the type of fasteners. Whereas the\nbacks of the later models were lead-filled, this plate was struck in\nthin brass over tin and the edges of the obverse crimped to retain the\nbacking. The fasteners are of the bent-wire type typical of the\n1812-1832 period and are not the \"2 eyes of iron wire\" called for in\nthe ordnance manual of 1850. None of the later examples of this design\nevidence any of the refinement of the original. At least eight\nvariations are represented in the national collections.\nCARTRIDGE-BOX-BELT PLATE, 1839, DIE SAMPLE\n_USNM 60339-M (S-K 95). Not illustrated._\nThis is a die sample, struck in copper, of the plate described above.\nSWORD-BELT PLATE, 1851\n[Illustration: FIGURE 94]\n[Illustration: FIGURE 95]\nThe 1851 regulations prescribed this plate for all officers and\nenlisted men. It was specified to be \"gilt, rectangular, two inches\nwide, with a raised bright rim; a silver wreath of laurel encircling\nthe 'Arms of the United States'; eagle, scroll, edge of cloud and rays\nbright. The motto, 'E Pluribus Unum,' in silver letters upon the\nscroll; stars also of silver; according to pattern.\"[99]\n[Footnote 99: _Regulations for the Uniform and Dress_, pl. 21.]\nThis plate has had a longer history than any other similar Army\ndevice. It was authorized for all personnel until 1881 when it was\ndropped as an item of enlisted equipment. It was retained for\nofficers, first for general wear, then for dress only. It was worn\nwith officers' dress blue uniforms until 1941, but was not revived\nwhen blues reappeared after World War II. A plate of the same general\nsize and pattern, although gilt in its entirety, was prescribed for\nsenior NCO's of the Marine Corps until about 1950 or 1951.\nThe buckle appears in many variations of design, at least 12 being\nrepresented in the national collections. Many of these variations are\nthe result of the plate being produced in great numbers by many\ndifferent contractors during the Civil War. The original design itself\nis interesting. The 1851 description called for an \"edge of cloud and\nrays\" and the official, full size drawing in _Regulations for the\nUniform and Dress of the Army_ includes the \"edge of cloud\" and\npictures the eagle with its head to the heraldic left. At least 50 of\nthese plates were examined by the authors, but only this specimen had\nthe \"edge of cloud,\" silver letters and stars, and the eagle with its\nhead to the left. In most specimens the plate proper is bronze, in one\npiece, and with the wreath silvered or left plain; in a few specimens\nthe wreath is in white metal and has been applied after casting. This\nparticular specimen is of an early issue. It is cast in heavy brass,\nwith the wreath applied, and has the narrow brass tongue for\nattachment on the reverse (fig. 95), typical of the early types.\nSWORD-BELT PLATE, 1851, DIE SAMPLE\n[Illustration: FIGURE 96]\nThis is a sample struck from a die which apparently was not approved\nfor the 1851 pattern plate. The eagle has wings upraised (2 inches tip\nto tip), head to right, shield on breast, scroll with \"E Pluribus\nUnum\" in beak, three arrows in right talon, and an olive branch in\nleft talon. Stars are intermixed with \"edge of cloud\" and rays.\nThe specimen leads to the interesting speculation as to the weight\ngiven to correct heraldic usage at this period. The significance of\nthe clouds, or lack of them, is unknown, but it should be noted that\nin all but the earliest specimens the eagle's head is turned to the\nright, or the side of honor, and the olive branch is placed in the\nright talon, indicating peaceful national motives as opposed to the\nthree arrows, signs of belligerency, in the left talon. In this\nrespect, it is interesting to note that until 1945 the eagle on the\nPresident's seal and flag carried its head turned to the heraldic\nleft.\n_Insignia of the Uniformed Militia_\nCap and Helmet Devices\nHAT ORNAMENT, INDEPENDENT DRAGOONS(?), c. 1800\n_USNM 14978. Figure 97._\n[Illustration: FIGURE 97]\nThis silver ornament is one of the most unusual pieces of military\ninsignia in the national collections. Obviously military, it is just\nas obviously of Militia origin. Although hardly artistic in design, it\nhas a rather attractive simplicity and has been made with considerable\ncare. The eagle is of the \"frogleg\" design that first appeared on\nbuttons of the post-Revolutionary Army and, later on, of the Legion.\nIn its right talon the eagle is grasping what appear to be rather\nstylized thunderbolts, and in its left, arrows. The arc above the\neagle's head is comprised of sunrays, an edge of clouds, and 16\n6-pointed stars. If the number of stars is of significance, the piece\nwould date prior to November 1802 when the 17th state, Ohio, was\nadmitted to the union. The \"frog-legged\" aspect of the design would\ntend to confirm such dating, and the thunderbolts in the right talon,\nsymbolic of a belligerent attitude, could be attributed to the\nnational temper during the \"quasi war\" with France, 1798-1800. The\n\"ID,\" in delicate floriated script on the eagle's breast, quite out of\nconsonance with the design and execution of the piece proper and\nobviously the work of a talented engraver, is interpreted as\n\"Independent Dragoons.\" Too small for a hat frontpiece, it was\nprobably worn as a side ornament on a dragoon helmet.\nLEATHER FAN COCKADE, C. 1810\n[Illustration: FIGURE 98]\nThe leather fan cockade became a part of the uniform in the late 18th\ncentury, having evolved from the cloth cockade adopted early in the\nRevolution.[100] Enlisted men's cockades of the early 19th century\nwere of leather, as were those of line officers.[101] This cockade, of\nblack tooled leather with painted gold fan tips, was a common form of\nthe period and was worn with an eagle in the center or possibly on the\nupper fan. It is assigned to the Militia because of the gold\nornamentation.\n[Footnote 100: FINKE, pp. 71-73.]\n[Footnote 101: TODD, \"Three Leather Cockades,\" pp. 24-25.]\nCAP PLATE, C. 1810\n[Illustration: FIGURE 99]\nThis grenadier-type plate, which is untrimmed and thus may be a die\nsample, is a rare example of the use of coiled snakes as a military\ndevice after 1800. A familiar motif of the Revolution, coiled snakes\nwere not revived as a popular military symbol during the War of 1812.\nThis specimen is struck in brass and is believed to have been made for\na specific independent Militia organization, designation unknown, for\nwear prior to 1812.\nCOCKADE EAGLE, 1812-1815\n[Illustration: FIGURE 100]\nThe eagle-on-clouds design, which first appeared on coins on the 1795\nsilver dollar, was popular on insignia during the period 1812-1821.\nThe heraldic significance of the clouds, if any, is unknown. Somewhat\nlarger than most cockade devices, this eagle is struck in brass and\nsilvered and has two simple wire fasteners soldered to the reverse. A\nvery similar badge is shown by Rembrandt Peale in an oil portrait of\nCol. Joseph O. Bogart of the 3d Flying Artillery.[102]\n[Footnote 102: Reproduced in _Antiques_ (July 1947), vol. 52, no. 7,\nCOCKADE EAGLE, C. 1814\n[Illustration: FIGURE 101]\nThis eagle, of the general design first seen on the 1807 half-dollar,\nis very similar to the one on buttons ascribed to staff officers,\n1814-1821.[103] The eagle, struck in brass, has wings upraised and the\nfamiliar hooked beak; it stands on a wreath of the colors. The wire\nfasteners on the reverse are of a somewhat unusual type and may not be\ncontemporary.\n[Footnote 103: JOHNSON, specimen nos. 101-105.]\n\u00b6 Die work for cap, shoulder-belt, and waist-belt plates was\nexpensive, and many Militia organizations found it expedient to\npurchase devices \"ready made\" from existing dies. By varying the\ntrimming and adding borders of various designs, the same dies could be\nused to strike all three types of plates. Such badges are called\n\"common\" plates.\nThe common plates that follow were very popular during the period\n1812-1835 and, although relatively rare today, were made in\nconsiderable quantity and in many die variations for the Militia in\nevery part of the country. They are known in brass, copper, and\nsilver-on-copper. It is possible that specimens such as these may have\nbeen worn by some officers of the Regular Establishment between 1814\n[Illustration: FIGURE 102]\nThis is a typical example of the common plates of the 1814-1835\nperiod. The piece is struck in brass and has an edged and stippled\nborder. The design is dominated by an eagle with wings outspread, head\nto left, arrows in right talon, olive branch in left talon, and with\nthe national motto on a ribbon overhead. The whole is superimposed on\na trophy of arms and colors with an arc of 13 6-pointed stars above. A\nplume socket, apparently original, is soldered to the reverse, as are\ntwo looped-wire fasteners. The fasteners are of a later period.\n[Illustration: FIGURE 103]\nStruck in copper and silvered, this piece is a die variant of the\npreceding plate. A floral border replaces the plain border, and the\noverhead arc has 5-pointed rather than 6-pointed stars. The floral\nborder marks it as probably an officer's device.\n[Illustration: FIGURE 104]\nA die variant of the preceding plate, this device has an unusually\nwide floral border. As in so many of the common pieces of this period,\nthe center device was purposely designed small so that the die could\nbe used to strike matching waist-belt plates. Examples of waist-belt\nplates struck from dies of this particular design are known. Struck in\ncopper, there is a plume socket soldered to the reverse along with two\nlooped-wire fasteners. The fasteners are not contemporary.\n[Illustration: FIGURE 105]\nThis is a die variant of the three plates immediately preceding.\nHowever, the center device lacks the fineness of detail of the others,\na fact that suggests that several makers working with different die\nsinkers produced this basic pattern. The plate is struck in copper,\nand originally it had a plume socket attached to the reverse. The\npresent looped-wire fasteners are not original.\n[Illustration: FIGURE 106]\nThis plate, which is of brass, is of a less common design than its\npredecessors. However, since there is another such plate, but of\nsilver-on-copper, in the national collections, it can be surmised that\npieces of this same pattern were made for use by several different\nunits.\nA floral-bordered shield is topped by an out-sized sunburst with 13\nstars, clouds, and the motto \"Unity is Strength.\" In the center of\nthe shield is the eagle, with wings widely outspread and with\nlightning bolts in the right talon and an olive branch in the left\ntalon. The lightning bolt device, obvious sign of belligerency, first\nappeared about 1800 and is not seen in plates designed after 1821. The\nmotto and the date 1776 are far more typical of Militia than Regular\nArmy usage.\n\u00b6 In 1821 the Regular Army discarded all its large cap plates and\nadopted the bell-crown leather cap. Militia organizations lost no time\nin adopting a similar cap and, conversely, placing on it--and on the\ntall beaver which followed in the 1830's--the largest plates it could\naccommodate, using variations of discarded Regular Army patterns as\nwell as original designs.\nFrom 1821 until well into the 1840's large cap plates were\nmass-produced by manufacturers in Boston, New York, Philadelphia, and\nperhaps other cities of the New England metal manufacturing area. The\nfew early platemakers, such as Crumpton and Armitage of Philadelphia\nand Peasley of Boston, were joined by a number of others. Prominent\namong these were Charles John Joullain, who made plates in New York\nduring the 1820's, and William Pinchin of Philadelphia. Joullain is\nfirst listed in New York directories, in 1817, as a \"gilder,\" and so\ncontinues through 1828. Sometimes his given name is listed as Charles,\nsometimes as James, and finally as Charles James. From 1820 to 1828\nhis address is the same, 32 Spring Street. There is a William Pinchin\n(Pinchon) listed in the Philadelphia directories as a silverplater or\nsilversmith almost continuously from 1785 through 1863, indicating the\npossibility of a family occupation.\nIt is believed that some of the New England makers of uniform buttons\nalso manufactured plates. Among such buttonmakers of the 1820's and\n1830's were R. and W. Robinson, D. Evans and Co., Leavenworth and Co.,\nBenedict and Coe, and others in Connecticut and Massachusetts.\nButtonmakers often stamped their names or easily recognizable\nhallmarks on the back of their products.\nIn most cases it is virtually impossible to ascertain the precise\nunits for which these different plates were first designed, and the\nproblem is further complicated because the maker would sell a specific\nplate design to several different units. Those designs that\nincorporate all or part of a state's seal were originally made for\nMilitia organizations of the particular state, but in several\ninstances these plates were sold--altered or not--to units in other\nparts of the country. Militia organizations that were widely separated\ngeographically purchased cap plates from distant manufacturers who had\nperhaps a dozen or more stock patterns to offer at a cost much lower\nthan that involved in making a new die from which to strike\ncustom-made ornaments. It made no difference to the Savannah Greys, in\nGeorgia, that their new cap plates were the same as those worn by\norganizations in Pennsylvania and Massachusetts. Toward the end of\nthis period of large cap plates, manufacturers came out with two-piece\nornaments. After 1833, when the Regiment of United States Dragoons was\nauthorized its large sunburst plate with separate eagle ornament in\nthe center, insignia makers introduced a veritable rash of full\nsunburst, three-quarter sunburst, and half-sunburst cap plates with\ninterchangeable centers. And for the first time small Militia units\ncould afford their own distinctive devices at little extra cost.\nShoulder-belt and waist-belt plates underwent the same evolution, and\nby the late 1830's such plates had become a mixture of either single\ndie stampings or composite plates made of several parts soldered or\notherwise held onto a rectangular or oval background.\nStudy of cap plates and other insignia in the Huddy and Duval prints\nin _U.S. Military Magazine_ points to the years between 1833 and\nperhaps 1837 or 1838 as the transition period from single to composite\nornaments, years during which there was also tremendous growth in the\npopularity and number of independent Militia units. In contrast to the\n1820's when the Militia often waited until the Regulars discarded a\ndevice before adopting it, in 1840 there were no less than five\norganizations, mounted and dismounted, wearing the 1833 dragoon plate\nin full form while it was still in use by the Regulars. _U.S. Military\nMagazine_ illustrates such plates for the Richmond Light Infantry\nBlues, the Georgia Hussars, the Macon Volunteers, the Jackson Rifle\nCorps of Lancaster, Pa., the Montgomery Light Guard, and the Harrison\nGuards of Allentown, Pa. The plate of the Harrison Guards is an\nexample of the license sometimes practiced by Huddy and Duval in the\npreparation of their military prints. The color bearer in this print\nis depicted wearing a full sunburst plate, while the description of\nthe uniform called for \"a semi-circular plate or _gloria_.\"[104]\n[Footnote 104: _U.S. Military Magazine_ (March 1839), p. 4.]\nIn the following descriptions of plates, the term \"stock pattern\" is\nused because the insignia are known to have been worn by more than one\norganization, because their basic designs are so elementary that it\nappears obvious that they were made for wide distribution, or because\nthey are known to have been made both in silver and in gilt metals.\nCAP PLATE, ARTILLERY, C. 1825\n[Illustration: FIGURE 107]\nOn the raised center of this shield-shaped plate is the\neagle-on-cannon device within an oval floral border; the Federal\nshield is below. The whole is superimposed on a trophy of arms and\ncolors with portions of a modified sunburst appearing on the sides.\nThe plate is struck in brass. The eagle-on-cannon first appeared on\nRegular artillery buttons in 1802. About 1808 it was used as an\nembossed device on the leather fan cockade, and in 1814 it became the\nprincipal design element of the cap plate for Regulars. This plate is\nthought to be one of the earliest of the post-1821 series of Militia\ncap plates incorporating the discarded design of the Regular\nartillery.\nUNIDENTIFIED ORNAMENT, PROBABLY CAP PLATE, C. 1821\n[Illustration: FIGURE 108]\nThis silver-on-copper plate is unique in size, shape, and over-all\ndesign. It is one of the most unusual Militia insignia in the national\ncollections. The standing eagle of the 1807 mint design with Federal\nshield, the panoply of arms and colors, and the rayed background all\nsuggest that this plate was made not later than the early 1820's.\nQuite possibly it is a cap plate of the War of 1812 period, but\npositive dating is impossible. Three simple wire fasteners are affixed\nto the reverse.\nCAP PLATE, ARTILLERY, C. 1825\n[Illustration: FIGURE 109]\nAlthough the Regular riflemen wore a diamond-shaped plate from 1812 to\n1814, this shape does not appear on Militia caps until the mid-1820's.\nIt was a common form through the 1830's, but since it was always made\nas a one-piece die-struck plate it became out-dated in the late 1830's\nwhen the composite plates came into vogue.\nThis plate, struck in brass and bearing the eagle-on-cannon device,\nmust be considered a stock pattern available to many organizations.\nInsignia struck from the same die could have been easily made into\nshoulder-belt plates as well.\nCAP PLATE AND PLUME HOLDER, C. 1825\n[Illustration: FIGURE 110]\nThis brass plate is similar in many respects to the regular infantry\ncap plate, type I, 1814-1821. It is attached to a bell-crowned shako\nof distinctly Militia origin and is cut in the diamond shape popular\nwith the Militia in the 1820's and 1830's. The design lies within a\nraised oval dominated by an eagle similar to ones used on War of 1812\ninsignia. Below the eagle is a Federal shield and a trophy of stacked\nmuskets, a drum surmounted by a dragoon helmet, a gun on a truck\ncarriage, and colors--one the National Colors with 16 stars in the\ncanton.\nThe plume holder attached to the cap above the plate is an unusually\ninteresting and distinctive device. It is a hemisphere of thin brass\nwith a round plume socket at the top. The hemisphere has an eagle on a\nshield and a superimposed wreath device in silver. The blazonry of the\nshield cannot be identified with any particular state or locality.\nCAP PLATE, C. 1821\n[Illustration: FIGURE 111]\nThe familiar hooked-beak eagle dominates the center of this brass,\nscalloped-edge plate. The arrows of belligerency, however, are held in\nthe left talon. Surrounding the eagle is a three-quarter wreath of\nolive with the national motto above and the date 1776 below. While\nthere is a possibility that this plate may fall into the period\n1814-1821 because of its outline shape, it lacks the panoply of arms\nassociated with that era. It is much more probable that this is one of\nthe earliest plates made for Militia during the years 1821-1830. Since\nthis plate is also known in silver-on-copper, it is considered a stock\npattern.\nCAP PLATE, MILITIA, ARTILLERY(?), C. 1821\n[Illustration: FIGURE 112]\nThis oval, brass-struck plate framed within a large wreath of laurel\nis one of the finest in the national collections, comprising as it\ndoes a number of devices of excellent design and considerable detail\nstanding in high relief. The curving line of 21 stars above the motto,\ndecreasing in size laterally, is an interesting detail, and the eagle\nand panoply of arms is reminiscent of those on the plate ascribed to\nthe Regiment of Light Artillery, 1814-1821, and on several of the\ncommon Militia plates of the same period. It is assigned to the\nartillery because of its \"yellow metal\" composition. It has simple\nwire fasteners, applied to the reverse, and carries no plume socket.\nCAP PLATE, NEW YORK, C. 1825\n[Illustration: FIGURE 113]\nThis unusually large, shield-shaped plate, struck in brass, is\ndominated by an eagle--within a smaller shield with raised\nedge--standing on a half globe and wreath of the colors, both of which\nare superimposed on a trophy of arms and flags; clouds and sun rays\nare above. The specimen represents one of the large cap plate patterns\nadopted by the Militia for wear on the bell-crown cap soon after it\ncame into general use in the early 1820's. While a stock pattern in a\nsense, its use was most likely confined to New York State Militia\nbecause its principal device, the eagle-on-half-globe, is taken\ndirectly from that state's seal. These large plates were widely worn\nuntil the middle or late 1830's when newer styles began to replace\nthem. The plume socket affixed to the reverse appears to be\ncontemporary, but has been resoldered.\nCAP PLATE, NEW YORK, C. 1825\n[Illustration: FIGURE 114]\nThis is a variant of the preceding plate and well illustrates how an\ninsignia-maker could adapt a single die for several products. The\neagle-on-half-globe, with a portion of the trophy of arms and colors,\nand the clouds and sunburst above have merely been cut out from the\nplate proper for use alone. The plate is struck in brass.\nAnother specimen, of silver-on-copper, is known, indicating that this\ninsignia was made for wear by infantry as well as by other branches of\nthe service; consequently, it may be termed a stock pattern.\nCAP PLATE, NEW YORK, C. 1825\n[Illustration: FIGURE 115]\nIllustrating fine craftsmanship, this elaborate brass cap plate\ncomprises perhaps the most ornate and intricately detailed design ever\nattempted by a military ornament die sinker. The strike itself has\nbeen so well executed that the most minute details are even today\nreadily discernible, even after very apparent use. Made for New York\nMilitia, its central theme is the eagle-on-half-globe superimposed on\na trophy of arms and flags.\nMany of the facets of detail are of particular interest. Almost every\nray of the aura of sunlight can still be clearly seen; the North Pole\nis well marked with a vertical arrow; the Arctic Circle, Tropic of\nCapricorn, and the Equator are included on the half-globe, as are the\nmeridians of longitude and the parallels of latitude; both North\nAmerica and South America are shown, and that portion of North America\neast of the Mississippi basin is clearly denominated \"UNITED STATES.\"\nAn unusual feature of the design is the way the arrows are held in the\neagle's left talon--some of the arrow heads point inward, some\noutward. What appears to have been a contemporary plume socket has\nbeen resoldered to the reverse.\nAlthough this plate is unmarked as to maker, another plate of a\nsimilar design but of silver-on-copper has the maker's mark \"J.\nJOULLAIN, MAKER, N. YORK.\" Since two distinct but similar designs are\nknown, and the finished product is found in both brass and\nsilver-on-copper, it seems probable that this plate was produced by\nmore than one maker, and for all arms of the service. It is therefore\ndeemed a stock pattern.\nCAP PLATE, RIFLEMEN, C. 1825\n[Illustration: FIGURE 116]\nAlmost immediately after the last Regular rifle regiment was disbanded\nin 1821, Militia riflemen adopted the large open horn with loops and\ntassels that the Regulars had worn from 1817 to 1821. The basic device\nwas altered slightly by showing an eagle in flight and the horn\nsuspended much lower on its cords. The illustrated brass plate is one\nof four die variants, and more than a dozen similar to it have been\nexamined. It is significant that all are of brass, for these were made\nand worn during the period when the trimmings for infantry were silver\nor \"white metal.\"\nThis plate differs from the others examined in that it has 17\n6-pointed stars along the upper and lower parts of the shield inside\nthe border. The number of stars cannot be significant in dating for\nthe plate was obviously made long after 1812 when the 18th state,\nLouisiana, was admitted to the Union. A plume socket affixed to the\nreverse appears to be original.\nUndoubtedly made as a stock pattern by several manufacturers, these\nplates continued in use for at least 15 years after they first\nappeared about 1825. Although _U.S. Military Magazine_ illustrates\nmany large cap plates for the period 1839-1841, none has a shield\noutline. This may indicate a decline in the popularity of the design,\nbut it must be remembered that Huddy and Duval presented the uniforms\nof only a small cross-section of the Militia of the period.\nCAP PLATE, RIFLEMEN, C. 1825\n[Illustration: FIGURE 117]\nThis is a second form of Militia riflemen's plates. Struck in brass,\nit differs from the preceding primarily in the placement of 17\n5-pointed stars along the upper half of the shield, between the\nborders. Other small differences show that the basic die was not that\nused for the preceding specimen. The most obvious difference is the\nlegend \"E PLURIBUS UNUM\" carried on the ribbon behind the knotted cord\nof the horn, an element not present in the other.\nA third form, not illustrated, substitutes a floral border for the\nplain border around the edge of the shield and contains no stars as\npart of the design. Still a fourth form, also not illustrated, has the\nsame center device of eagle and open horn placed in a longer and\nnarrower shield, with 23 6-pointed stars between the borders.\n\u00b6 These various combinations of devices give a good clue as to the\nmethod of manufacture of stock patterns, and indicate the use of\nseveral different dies and hand punches. The blank metal was first\nstruck by a die that formed the plain or floral border and cut the\noutline of the plate. Next, a smaller die containing the center device\nof eagle and horn was used. Then the stars, and sometimes elements of\nthe floral border, were added by individual striking with a hand\npunch. This latter method is clearly revealed by the comparison of\nseveral \"identical\" plates in which the stars or elements of the\nborder are irregularly and differently spaced.\nCAP PLATE, RIFLEMAN PATTERN, C. 1825\n[Illustration: FIGURE 118]\nThis plate is called \"rifleman pattern\" because it is silver-on-copper\nand is the only known example of this type of insignia made for wear\nby infantry, or possibly for Militia riflemen whose trimmings were,\nincorrectly, silver.\nThere are several conjectures about this cut-out device made from a\ndie of the preceding series of shield plates. It may have been made\nafter 1834, when the open horn with cord and tassels was adopted by\nthe Regular infantry as a branch device. It is equally possible that\nit was submitted to a Militia infantry organization by some maker as a\nsample during the 1820's and when selected was silvered to conform\nwith other trimmings. In either case, it illustrates how a single die\ncould serve to make many different variations from a basic design.\nCAP PLATE, RIFLEMEN, C. 1825\n[Illustration: FIGURE 119]\nThe very unusual construction of this brass plate for riflemen\nindicates that it is possibly one of the earliest of the composite\nplates. Within a wreath of crossed laurel boughs is a small center\ncircle with raised edge to which has been soldered the eagle and horn\ndevice struck in convex form.\nCAP PLATE, RIFLEMEN, C. 1830\n[Illustration: FIGURE 120]\nThe diamond-shaped plate was in vogue with Militia units during the\nlate 1820's and the 1830's. Examples of such plates for the Washington\nGrays (Philadelphia) and the Philadelphia Grays are recorded in _U.S.\nMilitary Magazine_.[105] This brass plate, possibly made for a\nparticular unit from stock dies, is a typical example of the endless\nvariety possible with the use of a few dies. The blank was struck with\na die for the center device of eagle and horn, but the irregularity of\nthe spacing of the stars shows that they were added later by hand.\nSimilar plates may be found with essentially this same device, but\nplaced on small shields or backgrounds of other shapes.\nCAP PLATE, C. 1835\n[Illustration: FIGURE 121]\nThe eagle and horn devices were sometimes separated by the\nmanufacturer to produce this type ornament open with cord and tassels.\nStruck in brass, it differs in form and detail from the silver horn\nadopted by the Regular infantry in 1834 as a cap plate.\nSeveral Militia units of the late 1830's and 1840's used a horn as an\nadditional ornament on the rear of the cap, notably the State\nFencibles (Philadelphia) and the National Guard (Philadelphia). On the\nrear of the leather cap of the State Fencibles were \"two broad rich\nstripes of silver lace, starting from the same point at the top and\nrunning down, forming an angle, in the center of which is a bugle\nornament....\"[106] The cap of the National Guard has been described as\nbeing \"of blue cloth ... and in the rear a plated bugle\nornament.\"[107]\n[Footnote 106: _U.S. Military Magazine_ (March 1839), p. 3 and pl. 2.]\n[Footnote 107: _U.S. Military Magazine_ (October 1841), p. 32.]\n\u00b6 In the following series of rather similar plates, four different\ndies are used for the center ornament, perhaps made by as many\ndifferent die sinkers. The relatively large number of these plates\nstill in existence suggests that they were worn very extensively.\nThose with silver finish were used by infantry; the gilt or copper\nones by artillery and perhaps by staff officers. All specimens are\ncurrently fitted with plain wire fasteners and plume sockets, both of\nwhich may or may not be original.\nCAP PLATE, INFANTRY, C. 1825\n[Illustration: FIGURE 122]\nThe floral-bordered shield outline of this silver-on-copper infantry\nplate is known to have been used also with the rifleman's eagle-horn\ndevice in the center. The panoply of arms and flags used as a\nbackground for the center device, which is characterized by the long\nneck of the eagle swung far to the right, links it closely to the\nplate of similar type worn during the period 1814-1821. Because of its\nlarge size, it is assigned to the post-1821 era of the bell-crown cap,\ncontemporary with the riflemen's large plates. The 13 5-pointed stars\nwere added with a hand punch.\nCAP PLATE, C. 1825\n[Illustration: FIGURE 123]\nThis brass plate is a duplicate of the preceding, lacking only the\nhand-applied stars. The crispness of detail indicates that it was one\nof the very early products of the die.\nCAP PLATE, C. 1825\n[Illustration: FIGURE 124]\nThe second variation of the series is a product of perhaps the best\nexecuted die of the group, with unusually fine detail in the eagle's\nwings and with neatly stacked cannon balls at the bottom of the center\ndevice. It includes other excellent detail not found in other dies: an\neagle-head pommel on one sword, a star pattern made of smaller stars\nin the cantons of the flags, and crossed cannon, rammer, and worm\nbehind the Federal shield. It is struck in brass.\nCAP PLATE, C. 1825\n[Illustration: FIGURE 125]\nA tall, slender, rather graceless eagle with broad wings and erect\nhead reminiscent of the Napoleonic eagle is the outstanding difference\nin this third example of the series. The floral border lacks a\nfinished look because the plate, which is of brass, was apparently\nhand trimmed.\nCAP PLATE, C. 1825\n[Illustration: FIGURE 126]\nThis fourth variation, of silver-on-copper, bears an eagle with very\nsmall legs (somewhat out of proportion), an erect head, a fierce mien,\nand a heavy round breast. The design is struck on a shield-plate with\nthe exact measurements as on one of the riflemen series.\nCAP PLATE, MUSICIAN, C. 1825\n[Illustration: FIGURE 127]\nThe oldest known plate made expressly for musicians, this\nsilver-on-copper, floral-bordered shield bears an eagle similar to one\nfor riflemen of the same period (see fig. 116). Among the early\nmusical instruments easily identifiable in the design are the tambor,\nthe serpent, the French horn, and the rack of bells. Such a plate was\nundoubtedly a stock pattern, available in either gilt or silver\nfinish, and was probably sold well into the 1840's. The reverse is\nfitted with what appears to be a contemporary plume socket, although\nresoldered, and two simple wire fasteners.\nCAP PLATE, MUSICIAN, C. 1835\n[Illustration: FIGURE 128]\nThis gilded brass plate, while not as old as the preceding one, is of\nan unusual pattern. Made for New York State Militia, it carries the\neagle-on-half-globe device at the top. The central design includes a\nFrench horn, a serpent, and a straight horn, all intertwined about an\nopen roll of sheet music. It is probably a stock pattern. The reverse\nis fitted with three simple bent-wire fasteners.\nCAP PLATE, C. 1830\n[Illustration: FIGURE 129]\nThe design on this brass plate, reminiscent of that on the regular\ninfantry cap plate, 1814-1821, was adopted for wear by the Militia\nafter being discarded by the Regular Establishment. The ornate floral\nborder and diamond shape place it in the late 1820's and the 1830's,\nalthough the lightning in the eagle's left talon and the arrows in its\nright talon are usually associated with plates designed prior to 1821.\nIt has been suggested that this is the plate worn by the West Point\ncadets after 1821, but such seems doubtful.\n\u00b6 No Militia plates enjoyed wider use or longer life than those\npatterned after the plate that disappeared from the Regular\nEstablishment with the disbanding of the dragoons in 1815. More than a\ndozen die variants are known, several worn by more than one Militia\nunit. Although size and shape may vary, any plate exhibiting a mounted\ntrooper with upraised saber can safely be assigned to mounted Militia.\nHowever, the dating of such plates is a real problem because they are\nknown to have been in use as late as 1861.\nA Huddy and Duval print of the Washington Cavalry of Philadelphia\nCounty shows that unit wearing a plate similar to the one used by the\nRegulars, differing only in its brass composition, as opposed to the\noriginal pewter of the 1812 regulations.[108] A cap in the collections\nof the Valley Forge Museum that was worn by a member of this unit in\nthe period 1835-1845 is very similar to the one shown in the Huddy and\nDuval print. The cap is a copy of the 1812 Regular Army pattern, with\nsomewhat more ornate brass bindings in place of the iron strips. A\nsimilar cap, carrying the label \"Canfield and Bro., Baltimore,\" is\nowned by Lexington, Virginia, descendants of a member of the\nRockbridge [Virginia] Dragoons. That unit is said to have worn such a\ncap upon first entering Confederate service in 1861.\n[Footnote 108: See _U.S. Military Magazine_ (February 1840), pl. 29.]\nIn the national collections there is a dragoon cap (USNM 604767, S-K\n912) carrying a plate of this design struck on a massive\ndiamond-shaped piece with concave sides. There are additional\nvariations in several private collections and at the Fort Ticonderoga\nMuseum. The mounted horseman device was also struck on heart-shaped\nmartingale ornaments.\nCAP PLATE, DRAGOONS, C. 1830\n[Illustration: FIGURE 130]\nThe horseman on this brass plate, designed with a rather crude,\nchildlike simplicity, is garbed quite differently than the Regular\ndragoon on the 1812 pewter specimen. The plate is assigned to the\ngeneral 1830 period to fit the era of the diamond-shaped plates, but\nits use doubtless continued on into the 1840's. By nature of its\ndesign it would have been a manufacturer's stock pattern.\nCAP PLATE, ARTILLERY(?), C. 1830\n[Illustration: FIGURE 131]\nThe eagle on this brass plate is similar to the ones on the preceding\nshield plates, but the Federal shield on which he stands is ornamented\nwith three star devices composed of smaller stars. An unusual feature\nof this plate is the addition of the flaming portion of a grenade\nrising from the eagle's head, a device not a part of any other known\ncap plate. This symbol suggests artillery, and the plate is of the\nproper color. Although an unusual over-all design, the lack of any\ncomponents of state arms or crests indicate that it may have been a\nstock pattern. The reverse is fitted with two simple bent-wire\nfasteners.\nCAP PLATE, MASSACHUSETTS INFANTRY, C. 1830\n[Illustration: FIGURE 132]\nThis silver-on-copper plate bears the familiar elements of the\nMassachusetts seal: Indian, in hunting shirt, with bow in right hand,\narrow with point downward in left hand, and star above right shoulder.\nThe crest--an arm grasping a broad sword on a wreath of the colors--is\nsuperimposed on a burst of sun rays above. The State's motto is\nwritten around the shield. The earlier plates containing elements of\nstate arms were for the most part confined to the States of\nMassachusetts, Connecticut, and New York. No large plates bearing\nPennsylvania State symbols that can be dated prior to 1835 are known.\nThis seal was not authorized by law until 1885. However, the devices\nand the motto were elements of the seal of the Commonwealth of\nMassachusetts ordered prepared by the state legislature in 1780 and,\nalthough apparently never formally approved, used as such for many\nyears. It differs considerably in detail from the seal in use from\n[Footnote 109: See ZIEBER, pp. 141-144.]\nCAP PLATE, MASSACHUSETTS INFANTRY, C. 1835\n[Illustration: FIGURE 133]\nThis scalloped plate, which is struck in thin iron metal and silvered,\nbears elements of the Massachusetts seal, minus the motto, and the\nlegend \"MASSACHUSETTS MILITIA.\" Its silver color assigns it to the\ninfantry. The form of the specimen indicates that it was probably\ndesigned prior to 1839. In consideration of its over-all design and\nthe use of the word \"MILITIA,\" it was probably made as a stock pattern\nand sold to several different organizations. A plume holder, which has\nbeen resoldered to the reverse, appears to be of the same metal as the\nplate proper. It is pierced at the sides for attachment.\n\u00b6 Painted cap fronts were worn during the War of the Revolution by\nseveral units of the Continental Army--including the Light Infantry\nCompany of the Canadian Regiment, Haslet's Delaware Regiment, and the\nRhode Island Train of Artillery[110]--and it is probable that the\npractice continued among some volunteer corps up to the War of 1812.\nTheir use in the uniformed Militia units generally declined after the\nintroduction of die-struck metal cap plates. Two notable exceptions\nare a cap plate of the Morris Rangers that is attached to a\ncivilian-type round hat of the 1812-1814 period[111] and the cap front\ndescribed below (fig. 137).\n[Footnote 110: Illustrated in LEFFERTS, pls. 4, 7, 21.]\n[Footnote 111: In the collections of the Morristown National\nHistorical Park. The Morris Rangers was one of three uniformed Militia\nunits in Morris County, New Jersey, at the outbreak of the War of\n1812; it saw service at Paulus Hook in 1814 (HOPKINS, pp. 271-272).]\nAlthough discarded by the more elite volunteer corps, painted metal\nhat fronts in the \"tombstone\" shape similar to that of the Morris\nRangers continued to be used, to some extent, by the common Militia.\nEasily attached to the ordinary civilian hat of the period, they\nprovided the common Militia a quick and inexpensive transformation\nfrom civilian to military dress at their infrequent musters perhaps as\nlate as 1840. There are several contemporary sketches of these musters\nand in one, dated 1829 (fig. 134), these \"tombstone\" plates can be\nidentified.\n[Illustration: FIGURE 134.--From Library of Congress print.]\nA total of perhaps a dozen of these hat fronts are known. Most are of\nConnecticut origin, although at least two containing New York State\ndevices are extant. The most elaborate of these devices bears, oddly\nenough, elements of the Connecticut State seal, the motto _Qui Trans.\nSust._, and the crest of the Massachusetts coat of arms--an arm\ngrasping a broad-sword (fig. 135). The elaborate detail of this plate\nindicates that it was probably an officer's. The fact that unit\ndesignations on other such known hat fronts run as high as the \"23d\nRegt.\" is definite proof that these were devices of the common Militia\nas opposed to the volunteer corps.\n[Illustration: FIGURE 135.--Specimen in Campbell collection.]\nPAINTED CAP FRONT, CONNECTICUT, C. 1821\n[Illustration: FIGURE 136]\nThis painted front, of leather rather than metal, forms an integral\npart of the cap itself. Edged in gold, it has the unit designation\n\"LIGHT INFANTRY: 2d COMP.\" in gold at the top; a shield in the center\ncontains elements of the Connecticut State seal, and below it is the\nstate motto \"QUI TRANS SUST\" (\"He who brought us over here will\nsustains us\").\nCAP FRONT, C. 1830\n[Illustration: FIGURE 137]\nA majority of these hat fronts are very similar in design, size, and\nshape, and are painted over a black background on thin precut sheets\nof tinned iron. This specimen carries a gold eagle with the Federal\nshield on its breast and a ribbon in its beak. The unit designation,\n\"2d COMP{Y}. 23d REG{T}.\", also in gold, is below. The artwork,\nalthough somewhat unartistically executed, has an attractive\nsimplicity. Other such hat fronts in the national collections are of\nthe 2d Company, 6th Regiment; 3d Company, 6th Regiment; and 1st\nCompany, 8th Regiment. The plate shown here has metal loops soldered\nto the reverse close to the edge midway between top and bottom for\nattachment to a civilian type hat by means of a ribbon or strip of\ncloth. Other such plates have hole for attachment with string.\nCAP PLATE, SOUTH CAROLINA, c. 1835-1850\n[Illustration: FIGURE 138]\nThis crescent-shaped, silver-on-copper plate bears an eagle that is\nvery similar in design to the one adopted by the Regular Army in 1821.\nSometimes mistakenly identified as a gorget because of its shape, the\ncrescent form of the specimen is an old South Carolina State heraldic\ndevice. A cap worn by the Charleston Light Dragoons after the Civil\nWar, and probably before, carries a similar crescent-shaped plate,\nwith the familiar palmetto tree device substituted for the eagle.[112]\nThe design of the eagle, however, places this piece in the 1835-1850\nperiod. A silvered ornament, it may have been made originally for\neither infantry or dragoons, and must be considered a manufacturer's\nstock pattern.\n[Footnote 112: Illustrated in _Military Collector and Historian_\nCAP PLATE, WASHINGTON GRAYS, C. 1835\n[Illustration: FIGURE 139]\nThis brass, diamond-shaped plate was worn by the Washington Grays, a\nlight artillery outfit of Philadelphia. Within a raised oval are a\nprofile of Washington--with his shoulders draped in a toga, a\ntypically neoclassic touch--and, below, the unit designation \"GRAYS\"\nin raised letters. A matching oval shoulder-belt plate struck from the\nsame die is known.[113]\n[Footnote 113: See _U.S. Military Magazine_ (April 1839), pl. 5.]\nMany Militia units named themselves after prominent military\npersonalities. There were Washington Guards, Washington Rifles,\nJackson Artillerists, and so forth.\nCAP PLATE, NATIONAL GREYS, C. 1835\n[Illustration: FIGURE 140]\nAn illustration in _U.S. Military Magazine_[114] shows this plate\nbeing worn by the National Greys; however, with such a nondistinctive\ncenter ornament as the rosette of six petals, it must surely have been\na stock pattern sold to many different organizations. The sunburst\nproper is struck in brass, as is the rosette, and each of the rays is\npierced at the end for attachment. The rosette is affixed with a brass\nbolt, also for attachment, which must have extended through the front\nof the cap.\n[Footnote 114: May 1839, pl. 7.]\nCAP PLATE, ARTILLERY, C. 1840-1850\n[Illustration: FIGURE 141]\nThis plate is struck in very thin brass. The combination of devices in\nthe design, especially of the cannon and cannon balls, indicates that\nit was probably made for Militia artillery. Its shape suggests that it\nmay have been worn high on the cap front, with the sunburst serving an\nadded function as a cockade of sorts. It was very probably a stock\npattern.\nCAP PLATE, MOUNTED TROOPS, C. 1836\n[Illustration: FIGURE 142]\nFrom the size of this brass plate it can be assumed that it was worn\nwithout other ornament on the front of the round leather cap\nassociated with mounted troops. The upper portion of the shield bears\n8-pointed stars, an unusual feature. The arrows in the eagle's left\ntalon point inward, a characteristic of eagle representation between\n1832 and 1836. The plate is known both in brass and with silver\nfinish. It was probably a stock pattern issued to both cavalry and\nmounted artillery.\nCAP EAGLE, C. 1836\n[Illustration: FIGURE 143]\nThis brass eagle was worn in combination with backgrounds of full-,\nhalf-, and three-quarter sunbursts and as a single ornament on the cap\nfront. The inward-pointed arrows in the left talon place it in the\n1832-1836 period. Known in both brass and silver-on-copper, it was a\npopular stock pattern sold to many units.\nCAP PLATE, C. 1836\n[Illustration: FIGURE 144]\nStruck in copper, and silvered, this eagle, which is very similar in\ndesign to that prescribed for the Regular Establishment in both 1821\nand 1832, was made for Militia infantry from about 1836 to perhaps as\nlate as 1851. Specimens struck in brass are also known, and the same\neagle is found on half-sunburst backgrounds. It is quite possible that\nthis is the eagle illustrated in the Huddy and Duval prints as being\nworn by both the Washington Blues of Philadelphia and the U.S. Marine\nCorps.[115]\n[Footnote 115: _U.S. Military Magazine_ (February 1840), pl. 28;\n(November 1840), unnumbered plate.]\nCHAPEAU ORNAMENT, C. 1836\n[Illustration: FIGURE 145]\nThis brass ornament is a die sample or unfinished badge. After the\ncircular device was trimmed from the brass square, it would have been\nworn as an officer's chapeau ornament or as a side ornament on the\nround leather dragoon cap of the period. The four arrows in the\neagle's left talon are unusual.\nCHAPEAU COCKADE, GENERAL OFFICER, C. 1840\n[Illustration: FIGURE 146]\nThis large, round chapeau cockade with its gold embroidery and sequins\non black-ribbed silk and its ring of 24 silver-metal stars appears to\nbe identical to cockades that have been shown as being worn around\n1839 by Gen. Edmund P. Gaines and Gen. Winfield Scott[116] but without\nthe added center eagle. Close examination of this cockade shows it to\nbe complete, with no traces of a center eagle ever having been added.\nThe 24 stars would have been appropriate at any time between 1821 and\n[Footnote 116: _U.S. Military Magazine_ (May 1841), unnumbered plate;\n(March 1841), unnumbered plate.]\nCAP AND CAP PLATE, JACKSON ARTILLERISTS, C. 1836\n[Illustration: FIGURE 147]\nThe Jackson Artillerists of Philadelphia, after the appearance of the\nregular dragoon cap plate in 1833 and the large crossed cannon of the\nregular artillery one year later, lost no time in combining these two\ndevices to make their distinctive cap device.[117] It seems probable,\nhowever, that the plate was adopted by other artillery units and\neventually became more or less of a stock pattern.\n[Footnote 117: Illustrated in _U.S. Military Magazine_ (January 1840),\nCAP PLATE, WASHINGTON GRAYS(?), C. 1836\n[Illustration: FIGURE 148]\nThe Washington Grays of Philadelphia wore a diamond-shaped plate with\na likeness of George Washington in the center (see fig. 139), but\nthis plate, for some other \"Washington\" unit, bears his likeness in\nsilver metal on a brass sunburst background. This silver outline of\nthe head of Washington is also known on cartridge-box flaps of the\nperiod.\nCAP PLATE, ARTILLERY, DIE SAMPLE, C. 1836\n[Illustration: FIGURE 149]\nThis uncut, brass cap plate may have been a manufacturer's die strike\nsent out as a sample, with others, so that a distant Militia\norganization could select a pattern. The finished plate is known on a\nbell-crown cap of the pattern of the 1820's, but its design indicates\nthat it probably should be dated after 1834 when the Regular artillery\nfirst adopted the crossed-cannon device. The eagle is distinctly\nsimilar to the one adopted by the Regulars in lieu of cap plates in\n1821, and the modified sunburst background probably was taken from the\n1833 dragoon device.\nCAP PLATE, C. 1836\n[Illustration: FIGURE 150]\nThis cap plate is a somewhat wider variation of the 1833 dragoon\ndevice than most of the Militia plates of that type popular in the\nlate 1830's and the 1840's. While the brass sunburst has the usual\n8-pointed form, the eagle, applied to the center, is unusually small\n(1-3/8 by 1 in.) and gives every indication of having been originally\ndesigned as a cockade eagle at a somewhat earlier period.\nCAP PLATE, C. 1836\n[Illustration: FIGURE 151]\nThis pattern of the 1833 dragoon eagle on a half-sunburst, struck in\nbrass and silvered, was worn by the Washington [D.C.] Light Infantry\n[118] and possibly by other units of the period. Both the eagle and\nthe half-sunburst were obviously stock items.\n[Footnote 118: Illustrated in _U.S. Military Magazine_ (August 1839),\nCAP PLATE, REPUBLICAN BLUES, C. 1836\n[Illustration: FIGURE 152]\nThis silver-metal plate can be accurately identified by reading its\ndevices. The center device is from the seal of the State of Georgia.\nDuring the period that the plate was worn, one of the best known of\nthe State's Militia organizations was the Republican Blues--the \"RB\"\non the plate--of Savannah.[119] The silver color of the plate also\nagrees with the other trimmings of the uniform of that unit.\n[Footnote 119: A volunteer Militia company known as the Republican\nBlues was organized in Savannah in 1808. From notes filed under\n\"Georgia National Guard\" in Organizational History and Honors Branch,\nOffice of the Chief of Military History, Department of the Army,\nWashington, D.C.]\nCAP PLATE, IRISH DRAGOONS, C. 1840\n[Illustration: FIGURE 153]\nThis three-quarter-sunburst plate with the monogram \"I D\" applied in\nsilver is identical to one on a brass-bound dragoon cap in the\nnational collections carrying in its crown the label \"Irish Dragoons,\nBrooklyn, N.Y.\" (USNM 604691, S-K 837). It is typical of the two-piece\nsunburst-type plates and was probably worn until the 1850's. The plate\nwas attached by means of two looped-wire fasteners that were run\nthrough holes in the helmet and secured by leather thongs.\nCAP AND PLATE, LANCER TYPE, C. 1840\n[Illustration: FIGURE 154]\nWith no regulations but their own to restrain them, Militia\norganizations designed their uniforms to suit their fancies, although\ngenerally following the regulations for the Regulars. This often led\nto odd and unusual cap shapes and trimmings and bindings on clothing,\nand to somewhat garish horse furniture in in some mounted units.\nThe illustrated cap and plate is very similar to the ones worn by the\nBoston Light Infantry[120] about 1839-1840 except that the upper or\n\"mortar board\" portion is beige instead of red and the plate is a full\ninstead of a three-quarter sunburst. The mortar board form is that\nintroduced by the Polish lancers in Europe in the early years of the\n19th century and worn by most European lancer regiments of the same\nperiod. Lancer units in the British Army adopted this type cap in 1816\nwhen they were first converted from light dragoons.[121] The large,\nbrass, eagle-on-sunburst plate was obviously patterned after the one\nprescribed for the Regular dragoons in 1833.\n[Footnote 120: Depicted in _U.S. Military Magazine_ (November 1839),\n[Footnote 121: BARNES, p. 106 and pl. 2(14).]\nCOCKADE EAGLE, INFANTRY, C. 1836\n[Illustration: FIGURE 155]\nAs an example of more than a dozen known variants of the eagle, this\nsilver-on-copper specimen is illustrated to show the general form and\nsize of Militia cockade eagles that became distinct types in the\n1830's and continued until about 1851. All such eagles were obviously\nstock patterns.\nCOCKADE EAGLE, C. 1836\n[Illustration: FIGURE 156]\nThis gold-embroidered cockade eagle with a wreath of silver lam\u00e9 about\nits breast appears to have been patterned directly after the eagle on\nthe 1833 Regular dragoon cap plate (see fig. 38). It possibly is one\nof a type worn by general officers of Militia. On this specimen, both\nthe eye and mouth of the eagle are indicated with red thread.\nCOCKADE EAGLE, C. 1836\n[Illustration: FIGURE 157]\nThis gold-embroidered eagle, with wings and tail of gold embroidery\nand gold sequins, was worn by staff and field officers, and possibly\ngeneral officers, of Militia. A duplicate on an original chapeau is in\nthe collections of the Maryland Historical Society in Baltimore,\nMaryland. Eagle ornaments such as this were generally centered on a\nround cloth cockade about 6 inches in diameter. The eagle's mouth is\nindicated by embroidery with red thread. Similar eagles of a smaller\nsize are known on epaulets of the same period.\nCAP PLATE, C. 1840\n[Illustration: FIGURE 158]\nThe flaming grenade, adopted by the Regulars in 1832 after long usage\nby the British and other foreign armies, was quickly adopted by the\nMilitia. This specimen, of silver-on-copper, was worn as a cap plate\neither in conjunction with another device below it on the cap front or\nas a lone distinctive ornament. It cannot precisely be identified as\nan artillery plate, but since some Militia artillery units are\ndefinitely known to have worn silver buttons of the artillery pattern,\nsuch is highly probable. Also known in brass and in smaller sizes, it\nis a stock pattern.\nCAP PLATE, C. 1840\n[Illustration: FIGURE 159]\nAlthough this plate appears to be of possible French or British\norigin, close examination indicates that it is probably an American\nMilitia device of the 1840's. Its looped-wire fasteners indicate that\nit is a cap plate. The design of the modified Napoleonic-type eagle is\nalmost exactly that used in the 1833 Regular dragoon cap plate and\nother Militia plates; and the period of apparent manufacture coincides\nwith the early use of the flaming grenade as an American device.\nIncorporating two devices common to the period, it would have been a\nstock pattern.\nCAP PLATE, ARTILLERY, C. 1840\n[Illustration: FIGURE 160]\nThe 1840 button for the Ordnance Corps bears a flaming grenade over\ncrossed cannon, devices that date from 1832 and 1834 respectively.\nConsequently, it seems likely that this combination emerged as a stock\npattern for Militia artillery early in the 1840's. This specimen,\nstruck from a single piece of brass, is a copy of the French artillery\ndevice of the same period, and, while it is believed to be American,\nit may be a foreign insignia. Confusion arises in the case of foreign\ndesigns, for die sinkers often used as a model either an actual\nimported badge or a scale drawing of one.\nCAP PLATE, ARTILLERY, C. 1840\n[Illustration: FIGURE 161]\nThis is a variation of the pattern of the preceding specimen in which\nsilver-metal devices have been placed on a small, gilt, half-sunburst\nplate. This was probably a stock pattern available to any Militia\norganization beginning about 1840 and worn for the next 20 or 30\nyears.\nCAP PLATE, SOUTH CAROLINA, C. 1840\n[Illustration: FIGURE 162]\nThe palmetto of South Carolina in outline form first appeared as a\nlarge cap ornament about 1840, after having been worn in smaller size\nas a cockade ornament and on the side of dragoon caps. A Huddy and\nDuval print shows it on the caps of the DeKalb Rifle Guards of Camden,\nSouth Carolina.[122] The illustrated specimen was worn into the\n1850's, and it is highly probable that some South Carolina troops wore\nplates such as this in the early days of the Civil War.\n[Footnote 122: _U.S. Military Magazine_ (August 1841), unnumbered\nplate].\nThe palmetto was adopted as the principal heraldic device of South\nCarolina in commemoration of the defeat of Admiral Sir Peter Parker's\nfleet by the garrison of Sullivan's Island under Col. William Moultrie\nin June 1776. The defenses of the island were constructed primarily of\npalmetto logs. The devices comprising this brass plate are all taken\nfrom the state seal, including the mottos _Animis Opibusque Parati_\nand _Dum Spiro Spero Spes_. The date \"1776\" alludes to the year of\nMoultrie's victory and not to the organization date of any particular\nunit.\nCAP PLATE, SOUTH CAROLINA, C. 1840\n[Illustration: FIGURE 163]\nStruck from a different die, with broader fronds and a wider base,\nthis brass plate is of the same period as the preceding one.\nCAP PLATE, C. 1840\n[Illustration: FIGURE 164]\nThis grenadier-type plate, struck in brass, is one of the most\nbeautiful examples of the die maker's art in the national collections.\nOn a sunburst-over-clouds background is an eagle grasping the top of\nthe Federal shield superimposed on panoply of arms and colors. The\nnational motto is on a ribbon below. Certainly not from a stock\npattern, this plate obviously was made for a specific Militia unit of\nconsiderable affluence. Three simple wire fasteners soldered to the\nreverse provide means of attachment.\nThis specimen is one of the scarce examples of military plates bearing\nthe maker's name \"BALE,\" which may be seen just above the raised lower\nedge and below the \"UNUM.\" This was probably Thomas Bale of New York\nwho is first listed in New York directories, in 1832, as an engraver\nat 68 Nassau Street. The 1842 directory lists him as a die sinker at\nthe same address in partnership with a Frederick B. Smith. He is last\nlisted in 1851.\nCAP AND CAP PLATE, 1ST ARTILLERY, PENNSYLVANIA, C. 1840\n[Illustration: FIGURE 165]\nThe plate on this cap uses only the shield of the Pennsylvania seal\nwithout crest or supporters. It is surrounded at the sides and bottom\nwith a wreath carrying a ribbon with the unit designation \"first\nartily.\" Equally interesting and unusual is the small separate\ninsignia at the pompon socket. It is based on the 1840 flaming grenade\nordnance device with crossed cannon superimposed.\nCOCKADE EAGLE, C. 1840\n[Illustration: FIGURE 166]\nThis eagle is of a rather odd design, and the five arrows in its left\ntalon is an even more unusual variation. It is believed to be a\ncockade eagle because of its form and size, but it may well have been\nused elsewhere on the person as a piece of uniform insignia.\nCHAPEAU COCKADE, STATE FENCIBLES (PENNSYLVANIA), C. 1840\n[Illustration: FIGURE 167]\nThe State Fencibles of Philadelphia were originally organized as \"Sea\nFencibles\" in 1812 for duty at the port of Philadelphia. This cockade,\nwith brass eagle, was first worn about 1840 and it continued in use\nfor many years thereafter. Dates incorporated as parts of devices are\ngenerally the original organizational dates of the units concerned--as\nis the case in this instance--and bear no necessary relation to the\nage of the badges. Some Militia cap plates bear the date \"1776,\" and\nthere are waist-belt plates bearing organization dates of 100 years\nearlier than the dates at which the plates were made.\n\u00b6 The transition to composite plates in the late 1830's was a\ntremendous step forward in the field of military ornament. Handsome\ninsignia could be manufactured less expensively and individual units\nwere able to have plates distinctive to themselves at relatively low\ncost; however, only gold and silver colors could be used. In the\nmid-1840's there was introduced a new manufacturing technique which\nopened this field even wider. In this innovation, various stock\npatterns were struck with a round center as a part of the design. In\neither the initial strike, or a second, this round center was punched\nout, leaving a hole. Then pieces of colored leather or painted tin,\ncarrying distinctive numerals, letters, monograms, or other devices\nwere affixed to the reverse of the plate, in effect filling the hole.\nAlthough this added a step in manufacture, it permitted the\nincorporation of bright colors, which added zest and sparkle to the\nfinished product. Such plates remained popular until the 1890's, and a\nfew are still worn on the full-dress caps of some units. This type of\ninsignia came into use at the time when many of the independent\ncompanies of the larger states, such as New York and Pennsylvania,\nwere starting to become elements of regiments and brigades within the\nover-all Militia structure of the state, thus the use of distinctive\nnumbers and/or letters on the badges. Many of these units, however,\nretained their original designation[123] and continued to wear\ninsignia distinctive to themselves on full-dress uniforms.\n[Footnote 123: _New York Military Magazine_ (June 26, 1841), vol. 1,\nCAP PLATE, 1845-1850\n[Illustration: FIGURE 168]\nThe first of the stock patterns, with basic wreath and 8-pointed\nstarlike sunburst, has the numeral \"1\" on black leather as a center\ndevice. Other specimens in the national collections have single\nnumerals, single letters, branch of service devices, and state coats\nof arms. This plate, and those following, were worn through the 1850's\non the dress cap copied after the pattern adopted for the Regular\nEstablishment in 1851. It is struck in brass.\nCAP PLATE, 1845-1850\n[Illustration: FIGURE 169]\nThis stock pattern, in brass, is very definitely military in\ncomposition, employing cannon and flag-staff spearheads radiating from\na beaded center and superimposed on a sunburst background. The metal\nletter \"1\" is backed with black leather.\nCAP AND CAP PLATE, ALBANY BURGESSES CORPS, C. 1851\n[Illustration: FIGURE 170]\nThis unusually ornate and distinctive plate is that of the Albany [New\nYork] Burgesses Corps that was founded, as stated on the plate itself,\nOctober 8, 1833. The arms and the motto \"ASSIDUITY\", appearing above\nthe ribbon with the letters \"A B C,\" are those of the city of Albany.\nCAP AND CAP PLATE, RIFLES, C. 1851\n[Illustration: FIGURE 171]\nThe original buttons on the sides of this cap have the eagle with the\nletter \"R\" (used by both Regulars and Militia) on the shield. The\nbrass plate proper, however, includes no device indicative of any\nparticular branch of service; combining flags and a Federal shield\nsurmounted by an eagle, it may well have been a stock pattern.\nCAP PLATE, C. 1850(?)\n[Illustration: FIGURE 172]\nThe type and form of this eagle plate give no clue to its age, or to\nthe identity of the unit that wore it other than the numeral \"1\" in\nthe eagle's beak and the letter \"E\" in the shield. It is a type more\napt to have been made about 1850 than later. The eagle is struck in\nbrass, and the stippled inner portion of the shield, product of a\nseparate strike, is soldered in place; thus, the plate proper must be\nconsidered a stock pattern.\nCAP PLATE, C. 1850(?)\n[Illustration: FIGURE 173]\nA companion piece to the preceding plate, this specimen differs in\nthat the letters \"R G\" and their stippled background are struck\nintegrally with the plate proper--indicating that two dies were\ncombined for a single strike--and in that the shield, ribbon, and\nnumeral \"1\" have been silvered.\nCAP PLATE, 10TH REGIMENT, MASSACHUSETTS VOLUNTEER MILITIA, C. 1850\n[Illustration: FIGURE 174]\nThis plate is of a type form worn on Militia dress caps prior to the\nCivil War. There is little doubt that plates such as this continued in\nuse for several decades after their initial appearance. This brass\nspecimen, surmounted by elements of the Massachusetts seal, is struck\nas a stock pattern for Massachusetts troops with the center left\nblank. The numeral \"10\" is applied to a black-painted metal disk\naffixed with simple wire fasteners.\nCAP PLATE, GEORGIA, C. 1850\n[Illustration: FIGURE 175]\nThis plate and the one following are of Militia types worn on caps in\nthe 1850's and perhaps earlier. Such plates are known to have been in\nuse with little or no change almost to the present day on military\nschool dress shakos and dress caps worn by some National Guard units.\nThe plate proper, which is of brass, is the well-known half-sunburst\ndevice so popular in the 1830's and 1840's. The Georgia state seal,\nalso in brass, is applied with wire fasteners. The plate is dated\nlater than a similar one of the Republican Blues (fig. 152) because of\nthe \"feel\" of the piece and the fact that it cannot be ascribed to a\nparticular unit whose existence can be dated.\nCAP PLATE, VIRGINIA, C. 1850\n[Illustration: FIGURE 176]\nThis plate differs from the preceding one only in that it substitutes\nthe coat of arms of Virginia for that of Georgia. The backgrounds,\nalthough very similar, are products of different dies.\nShoulder-Belt and Waist-Belt Plates\nWAIST-BELT PLATE, 1ST MARINE ARTILLERY, 1813\n[Illustration: FIGURE 177]\nUndoubtedly one of the most interesting of all the Militia plates of\nthe War of 1812 period is this rectangular one worn by John S. Stiles\nof (as indicated by the engraving) the \"First Marine Artillery of the\nUnion.\" Engraved in brass, it bears an unusual combination of military\nand naval devices--the familiar eagle-on-cannon of the Regular\nartillery and the eagle with oval shield that appears on naval\nofficers' buttons of the period.[124] Actually, the devices befit the\ncharacter of the organization. The following quotation from _Niles\nWeekly Register_ of Baltimore, June 26, 1813, tells something of the\nunit:\n     The First Marine Artillery of the Union, an association of the\n     masters and mates of vessels in Baltimore, about 170 strong all\n     told, assembled on Sunday last and proceeded to the Rev. Mr.\n     Glendy's church in full uniform, where they received an address\n     suited to the occasion; which, as usual, done honor to the head\n     and heart to the reverend orator. We cannot pass over this\n     pleasant incident without observing that the members of this\n     invaluable corps are they who, of all other classes of society,\n     feel the burthens and privations of the war.\n[Footnote 124: JOHNSON, vol. 1, pp. 40, 74.]\nObviously, this organization was one of the state fencible units\nenlisted for defense only, but little else is known about it. In 1814\nthere was in Baltimore, a Corps of Marine Artillery commanded by a\nCapt. George Stiles. The roster of this unit, however, does not\ninclude the name John S. Stiles. Other records do indicate that a Lt.\nJohn S. Stiles commanded a section of the Baltimore Union Artillery at\nthe Battle of North Point in 1814.[125] It is probable that John\nStiles, originally a member of the 1st Marine Artillery of the Union\nhad transferred his commission to the Baltimore Union Artillery.\n[Footnote 125: SWANSON, pp. 253, 382.]\n\u00b6 An example of Militia officers' shoulder-belt plates of the period\n1812-1816 is a solid silver oval plate (fig. 178) engraved with an\neagle and elements of the arms of Massachusetts within a shield\nsuspended from the eagle's neck. Being silver, the plate probably was\nworn by infantry or possibly dragoons. Many such plates were locally\nmade, as was this one, and examination of a number of specimens gives\nreason to believe that many were made by rolling out large silver\ncoins into thin ovals, which were then engraved and fitted with\nfasteners on the reverse. The fasteners on all pieces studied indicate\nthat the plates were intended to be ornamental rather than functional.\n[Illustration: FIGURE 178.--Specimen in Campbell collection.]\nIn the Pennsylvania State Museum there is a similar oval plate that\nwas worn by Col. Philip Spengler of that State's Militia in 1812-1816.\nOrnamented with an eagle, with the initials \"PS\" within an oval below,\nit generally follows the construction of the illustrated plate,\ndiffering only slightly in size. Since plates of this general type\nwere made locally by hand, each is unique in itself. Identification\nmust depend upon an interpretation of the devices engraved on the\nface. The initials of the officer for whom the plate was made are\noften included.\nSHOULDER-BELT PLATE, C. 1812\n[Illustration: FIGURE 179]\nA second example of a Militia officer's plate is this engraved brass\nspecimen with the design placed along the longer axis of the oval.\nSince there probably were many \"Volunteer Rifle Companies,\" it is\nimpossible to determine precisely which one wore this plate. The\ninitials of the officer may be read either \"I. B.\" or \"J. B.,\" for\nmany of the early-19th-century engravers used the forms of the letters\n\"I\" and \"J\" interchangeably. The two small hooks on the reverse\nindicate that the plate was for a shoulder belt rather than for a\nwaist belt, and that it was ornamental rather than functional.\nSHOULDER-BELT BUCKLE, C. 1812(?)\n[Illustration: FIGURE 180]\nThis brass buckle, obviously made for a sword hanger, has an eagle in\nflight above, a 13-star flag below, and four 5-pointed stars on either\nside. The spearhead on the pike of the flag is definitely of military\ndesign, and, in the absence of nautical devices in the engraving, the\nbuckle must be considered an army item.\nORNAMENTED WAIST-BELT PLATE, 1812-1825(?)\n[Illustration: FIGURE 181]\nCast in silver and then carefully finished, this rectangular plate\nwith beveled edge is one of the most ornate and beautiful known. In\nthe center is an officer's marquee with an eagle, wings spread,\nperched on top. In front of the marquee are a field piece with bombs,\ncannon balls, and drum; the whole on grassy ground and superimposed on\na trophy of colors and bayonetted muskets. The canton of one color\nhas, instead of stars, an eagle with a shield on its breast and a\nribbon in its beak. It has been suggested that the eagle-in-canton\nflag would tend to date the piece after 1820 when many Militia units\nhad the design in its colors;[126] however, flags of such design are\nknown to have been used as early as the last year of the\nRevolution.[127] In addition, the \"feel\" of the specimen is early, and\nit is included here as a possible Militia dragoon officer's plate\nsince the dragoons of the War of 1812 period generally wore their\nswords attached to a waist belt rather than to a shoulder belt.\n[Footnote 126: The national collections contain several such Militia\ncolors.]\n[Footnote 127: See WALL.]\nWAIST-BELT PLATE, INFANTRY, 1814-1825(?)\n[Illustration: FIGURE 182]\nThis plate is typical of the early waist-belt plates, which generally\nwere more square than rectangular. It bears the over-all design of the\n1814-1821 series of \"common\" cap plates. Struck in copper and\nsilvered, it would have been appropriate for either infantry or\ndragoons, as both wore \"white metal\" trimmings during this period.\nThere are as many die variations known for this type belt plate as for\nthe matching cap plates.\nThe wide latitude allowed officers in selecting their own insignia\nmakes it quite possible that this design was worn by some officers of\nthe Regular Establishment, particularly those in the high-numbered\nregiments, which were organized during the course of the War of 1812.\nA third use of this basic design is indicated by a museum specimen at\nFort Ticonderoga, N.Y.: cut into its outline form, it was worn on the\nside of Militia dragoon caps.\nWAIST-BELT PLATE, INFANTRY, 1814-1825(?)\n[Illustration: FIGURE 183]\nThis brass plate is one of several similar examples made of both brass\nand silvered copper that differ only in small die variations and the\nuse of either 5-pointed or 6-pointed stars. The arc of 17 stars in\nthis specimen may or may not be significant, because there were 17\nstates in the Union from 1802 until 1812 when Louisiana was admitted.\nNot until 1816 did the 19th state, Indiana, come into the Union. After\nthinking in terms of and working with 17 stars for a 10-year period,\ndie sinkers may well have overlooked the inclusion of a star for\nLouisiana. Buttons for the Regular rifles made after 1812 but before\n1821 show an arc of 17 stars.[128] As in the case of the preceding\nplate, there is a good possibility that this one was worn by Regular\nofficers in 1814-1821. It is also probable that the pattern was made\nand sold to Militia for many years after 1821.\n[Footnote 128: JOHNSON, vol. 1, pp. 61.]\nWAIST-BELT PLATE, MILITIA ARTILLERY, C. 1821-1840(?)\n[Illustration: FIGURE 184]\nWhile this plate could have been worn by an officer of the Regular\nartillery in the period 1814-1821 when uniform regulations were vague\nand seldom enforced, it is more probable that it was a Militia item of\nabout 1821-1835. The reason for this is that the eagle-on-cannon\ndevice was adopted quickly by Militia units when it was discarded by\nthe Regulars in 1821, and the over-all design of the plate itself\nfollows the pattern adopted by the Regulars in 1821 (see fig. 68).\nSeveral artillery organizations of the Massachusetts Militia wore the\ndiscarded button pattern (eagle-on-cannon with the word \"CORPS\" below)\nuntil the 1840's,[129] and this plate would have been an ideal match.\n[Footnote 129: JOHNSON, vol. 1, pp. 161, 162.]\nThe whole is cast in brass, the inner ring rather crudely so. The\nouter ring is embossed with zig-zag fretwork enclosing a circle of\n5-pointed stars; the rectangular belt attachments have a floral\ndesign.\nWAIST-BELT PLATE, MAINE, C. 1821\n[Illustration: FIGURE 185]\nThis plate, struck in copper, contains the basic devices of the State\nof Maine seal enclosed by a curled ribbon border embellished with\n5-pointed stars. The specimen is more square than rectangular, a\ncharacteristic of waist-belt plates of the early 1800's. It was\nprobably worn by Maine Militia no later than the 1820's, possibly a\nfew years earlier. The method of attachment also is indicative of this\nearly period: the heavy vertical wire is brazed to one end of the\nreverse, and the L-shaped tongue to the other. This plate obviously\nwas a stock pattern.\nWAIST-BELT PLATE, C. 1830\n[Illustration: FIGURE 186]\nThis plate, cast in brass, is typical of the small plates, both round\nand rectangular, that were worn with light-weight, full-dress staff\nswords. It is an example of the early, hand-made, bench-assembled\ntypes. The outer ring carries the wreath typical of the period, while\nthe inner ring carries the eagle with its head to the right, shield on\nbreast, arrows in left talon, and olive branch in right talon. The\nwhole lies within a ring of 13 5-pointed stars; the uppermost five\nstars are mixed with a sunburst rising from the eagle's wings.\nWAIST-BELT PLATE, C. 1821(?)-1830\n[Illustration: FIGURE 187]\nThis brass, bench-assembled plate is similar to the Regular artillery\nbelt plate of 1816 (fig. 56) in that the design on the inner ring is\nstruck with a series of separate hand-held dies on a piece of blank\nround stock. The floral design on the belt attachments is cast. In\nmany of the early bench-made plates, the final assemblyman marked the\nmatching pairs so that they could readily be re-paired after buffing\nand plating. In this specimen, each ring bears the numeral XXVIII.\nWAIST-BELT PLATE, NEW YORK, C. 1830\n[Illustration: FIGURE 188]\nThis plate, with the center ring struck in medium brass and the belt\nattachment cast, was worn by Militia of New York State, as indicated\nby the eagle-on-half-globe device taken from that state's seal. Of\nbrass, it is assigned to the artillery. The quality of the belt to\nwhich it is attached and the ornateness of the plate itself indicate\nthat it was made for an officer. The left-hand belt attachment is\nmissing.\nWAIST-BELT PLATE, C. 1830\n[Illustration: FIGURE 189]\nThis small, cast-brass plate is another example of the plates made for\nsocial or full-dress wear with the light-weight staff sword. The\ndesign on the inner ring is unusual in that the eagle, with upraised\nwings, is standing on the Federal shield. The plate is a bench-made\nproduct, with the inner and outer rings bearing the numeral VII. It\nwas very probably a stock pattern for officers.\nWAIST-BELT PLATE, C. 1836\n[Illustration: FIGURE 190]\nRather unusual in construction, this small silver-on-copper\nrectangular plate was struck in thin metal. Two broad tongues, for\nattachment to a belt, are inserted in the rear; and the reverse is\nfilled with lead to imbed the fasteners. The eagle design is very\nsimilar to the one prescribed for the caps of the Regular\nEstablishment in 1821, although somewhat reduced in size. The general\nlack of finish and polish in construction indicates that the specimen\nwas probably the product of an inexperienced and small-scale\nmanufacturer.\nOFFICER'S WAIST-BELT PLATE, C. 1837\n[Illustration: FIGURE 191]\nThis unusually large plate, which is struck in medium brass and with\nthe edges crimped over a heavier piece of brass backing, is believed\nto be an officer's plate because of its size, gilt finish, and\nover-all ornate design. Within a floral and star pattern border, the\nspecimen is dominated by an eagle, on a sunburst background, that\nholds in its left talon five arrows with points inward; above are 25\nstars and an edge of clouds above. Arrows held with points inward are\nusually considered indicative of the general period 1832-1836. If the\nnumber of stars is of any significance, such dating would be correct,\nas the canton of the National Colors contained 25 stars from 1836 to\n1837. The central design used without the border is also known in\nsmaller, more standard sized plates. The design is a stock pattern.\nThis type plate is also known in both brass and silver.\nSHOULDER-BELT PLATE, WASHINGTON GRAYS, C. 1835\n[Illustration: FIGURE 192]\nThis may well be a companion piece to the diamond-shaped cap plate\nascribed to the Washington Greys[130] of Philadelphia (see fig. 139).\nIn any case, the two appear to have been struck from the same die. It\nmay also have been worn by the Washington Greys of Reading,\nPennsylvania, or by another company of the same designation. The\nspecimen is struck in thin brass with a tin backing applied before the\nstrike and the edges crimped over the reverse. Three soldered\ncopper-wire staples provide means of attachment.\n[Footnote 130: The spelling of \"Grays\" may or may not be significant.\nA Huddy and Duval print of the Washington Greys in _U.S. Military\nMagazine_ (April 1839, pl. 5) used \"Greys\" in the title and \"Grays\" on\nan ammunition box in the same print.]\n\u00b6 Militia organizations generally modeled their uniforms rather\nclosely on those of the Regular Establishment; of course, there were\ncertain exceptions, notably the flamboyant Zouave units. However, the\nMilitia often added additional trimmings that gave the \"gay and gaudy\"\ntouch for which they were noted. Following the example of the\nRegulars, the Militia adopted coat-skirt ornaments almost immediately\nafter their appearance in 1832. They used the regulation flaming\ngrenades, open and looped horns, and 5-and 6-pointed stars, but in\nboth gold and silver on varicolored backgrounds and in a wide variety\nof sizes. They also used a number of peculiarly Militia forms, such as\ncrossed-cannon, elements of state seals, and devices peculiar to\nspecific units.\nCOAT-SKIRT ORNAMENT, ARTILLERY, C. 1836\n[Illustration: FIGURE 193]\nTypical of Militia coat-skirt ornaments is this pair of crossed cannon\ndevices for Militia artillery. They are of gold embroidery on a\nbackground of black velvet. Similar pairs in the national collections\nare embroidered in silver. The Regular artillery never wore the\ncrossed cannon device on the skirt of the coat; so used, it was\nexclusively a Militia ornament.\nCOAT-SKIRT ORNAMENT, SOUTH CAROLINA, C. 1836\n[Illustration: FIGURE 194]\nAnother coat-skirt ornament with an even more distinctly Militia touch\nis this small palmetto tree of gold embroidery, with sequins, on\nblack wool cloth. As the palmetto tree is the basic device of the\nSouth Carolina seal (see pp. 81 and 83), this specimen must be\nattributed to the Militia of that state.\n\u00b6 Most Militia cartridge-box plates made in the decade after 1841 were\noval, following the pattern of the Regulars. While a few of these\nvaried from the prescribed sizes, most were almost identical in both\nsize and shape to those of the Regular Establishment, but with\nstrictly Militia ornamentation. The exact years in which these plates\nwere produced cannot be determined, but it is reasonably sure that\nthey were supplied to Militia for some years prior to the opening of\nthe Civil War. Not included here are similar types known to have been\nmade for units born of the war as the Pennsylvania Fire Zouaves,\nPennsylvania Home Guard, Pennsylvania Reserve Brigade, and the Ohio\nVolunteer Militia. Cartridge-box and waist-belt plates often are\nidentical except for the methods of attachment. The plates for\ncartridge boxes have two wire loops imbedded in the backing (see fig.\n90), while those for waist belts have one or two round, or sometimes\narrowheaded, prongs on one side of the reverse, and with a narrow\ntongue on the opposite side bent parallel to the plane of the plate\n(see fig. 91).\nCARTRIDGE-BOX PLATE, C. 1841\n[Illustration: FIGURE 195]\nThis brass, oval cartridge-box plate, with its eagle on a panoply of\narms and colors, closely matches in size the 1841 Regular cavalry's\nplates for carbine cartridge boxes and the infantry's waist belts.\nAlthough plates of this design were worn as waist-belt plates, the two\nlooped-wire fasteners on the reverse of this specimen clearly indicate\nits use on a cartridge box. This was undoubtedly a stock pattern. An\noil painting of Capt. George Bumm, Pennsylvania State Artillery, c.\n1840, shows the subject wearing a waist-belt plate of this same\ndesign.[131]\n[Footnote 131: _Old Print Shop Folio_, p. 216.]\nCARTRIDGE-BOX PLATE, C. 1841\n[Illustration: FIGURE 196]\nSlightly smaller than the preceding specimen, this brass plate bears\nthe eagle design popular from 1821 to 1851. Fitted with looped-wire\nfasteners, it would have been a stock pattern for cartridge boxes.\nCARTRIDGE-BOX PLATE, MAINE, C. 1850\n[Illustration: FIGURE 197]\nA frequently misidentified plate is this brass-struck, lead-filled\noval with the raised letters \"VMM\" for Volunteer Maine Militia. It is\nalso known in a smaller size. The reverse is fitted with the two\nlooped-wire fasteners normal to such plates.\nOther prewar oval plates bearing raised letters are known for the\nAlabama Volunteer Corps (AVC), North Carolina (NC), South Carolina\n(SC), State of New York (SNY), and New Hampshire State Militia (NHSM).\nMany such plates recently have been reproduced for sale, and more\nprobably will be made if a market is created. Thus, all plates of\nthis general type should be cautiously considered.\nWAIST-BELT PLATE, DIE SAMPLE, C. 1840\n[Illustration: FIGURE 198]\nOne of the more unusual forms of the militant eagle used on ornaments\nis shown on this brass die sample for a waist-belt plate. The eagle,\nwith fierce mien and wings outspread, stands high on a craggy ledge.\nAn example of an untold number of odd and unusual pieces of insignia,\nthis specimen is unidentified as to unit or area of intended use. It\nmay well have been designed for use as a stock pattern.\nWAIST-BELT PLATE, RIFLEMEN, C. 1840\n[Illustration: FIGURE 199]\nA stock pattern, this plate is struck in brass with the open-horn\ndevice of riflemen, which has been previously discussed. Wire\nfasteners are on the reverse. Although the outer ring of the plate is\nmissing, it was probably decorated with a wreath, a common form in the\nWAIST-BELT PLATE, CHARLESTOWN ARTILLERY, C. 1840\n[Illustration: FIGURE 200]\nThis 2-piece, brass-cast plate was worn by members of a Charlestown,\nMassachusetts, unit. The date \"1786,\" as on nearly all dated pieces\nof insignia, refers to the date of original organization of the unit.\nThe design of the plate is typical of early- to mid-Victorian taste.\nWAIST-BELT PLATE, MASSACHUSETTS, C. 1840\n[Illustration: FIGURE 201]\nBearing elements of the seal of the State of Massachusetts, this plate\nlikely was a stock pattern sold to many officers. In construction, it\nis a composite piece similar to the plate for officers of the Corps of\nTopographical Engineers (see fig. 87 and p. 45) with the device\napplied to the inner oval. Because of its unusually striking\nappearance, it would have been a most appropriate type for staff and\nfield officers, and possibly general officers.\nWAIST-BELT PLATE, NEW YORK, C. 1840\n[Illustration: FIGURE 202]\nThis plate, struck in poor-quality, medium-weight brass, is of a stock\npattern bearing the eagle-on-half-globe device and the motto\n\"Excelsior\" from the New York State seal superimposed on a panoply of\narms and colors. This type of belt plate, with the device on the inner\npanel and a wreath between the inner and outer borders, is most\ncharacteristic of the 1840's. More than ten different plates are known\nthat vary only as to the design of the inner panel; some contain New\nYork State heraldic devices, and others contain variants of the usual\neagle design of the period.\nWAIST-BELT PLATE, PHILADELPHIA, C. 1840\n[Illustration: FIGURE 203]\nThe devices on this cast-brass plate comprise the arms of the City of\nPhiladelphia, and its form and pattern, especially the floral design\nof the outer ring, place it in the 1840's. The piece is bench-made and\ncarries on the reverse many marks of the file used in its final\nassembly. It must be considered a stock pattern.\nWAIST-BELT PLATE, SOUTH CAROLINA, C. 1840\n[Illustration: FIGURE 204]\nSomewhat larger than many plates of the period, this brass specimen\ncarries the South Carolina palmetto device. Such plates also were\nstruck in copper and silver plated. It obviously was a stock pattern\nsold to several different units. The rectangular plate with the\nvine-patterned border was a stock pattern in itself, with many\ndifferent devices being added in the center as ordered. This is one of\nthe many pieces of insignia too often called Confederate but which\nante-date the Civil War by almost two decades.\nWAIST-BELT PLATE, C. 1840\n[Illustration: FIGURE 205]\nThe eagle device on this silver-on-copper specimen closely resembles\nthat on the cap plate of the First Troop Philadelphia City Cavalry\n(USNM 604964-M) and may possibly be the matching belt-plate worn by\nthat organization. Such an eagle, however, would have been a stock\npattern of the manufacturer, and sold to many different units. A very\nunusual aspect of this particular eagle are the three arrows held in\nthe left talon: two of them point inward, the third outward.\nWAIST-BELT PLATE, ARTILLERY, C. 1840\n[Illustration: FIGURE 206]\nAlthough members of the artillery of the Regular Establishment wore\nthe crossed-cannon device on their shakos, they never wore it on\nwaist- or shoulder-belt plates. Thus, this cast-brass plate must have\nbeen a stock pattern sold to many Militia units. The outer ring is\nmissing.\nWAIST-BELT PLATE, C. 1840\n[Illustration: FIGURE 207]\nThis specimen, roughly cast in brass and gilded, is unusual because\nthe Militia rarely used the letters \"U S\" on any of its equipment. The\npattern does not conform to anything prescribed for Regulars and the\nquality does not come up to standards required by the Regular\nEstablishment; hence it must have been worn by Militia. It would have\nbeen a stock pattern. There is the possibility that it might have been\nworn by diplomatic personnel, but its poor quality makes this\nunlikely.\nWAIST-BELT PLATE, C. 1850\n[Illustration: FIGURE 208]\nThe over-all design of this plate, which is cast roughly in brass and\ngilded, reflects the growing ornateness of the Victorian era.\nObviously a stock pattern, it would have suited the fancy of several\nunits and cannot be identified further than \"for Militia.\" The design\nof the eagle is unusual in that three arrows are carried in the right\ntalon--although it is possible that this is intended to reflect the\nbelligerency inherent in the period of the War with Mexico--and there\nis a single large star in the canton of the Federal shield.\nWAIST-BELT PLATE, C. 1840\n[Illustration: FIGURE 209]\nThe generalities that apply to all \"stock pattern\" insignia are\nequally valid in referring to this brass-struck plate with a 5-pointed\nstar as its sole ornament. Dating its period of design poses no\ndifficulty, for it contains the panel with wreath inside an edging\nborder characteristic of the 1840's. The star device would have been\nappropriate for Militia units of Maine (\"North Star\"), Texas (\"Lone\nStar\"), or for dragoon units that took the star as a distinctive\ninsignia. Although it may have been worn by Texans, it is doubtful\nthat it was made originally for them. The design enjoyed a long life,\nand plates of this general pattern were struck well into the 1880's.\nThe major difference between earlier and later specimens is that the\nearly ones were struck on rather heavy sheets of copper-colored brass,\nwith fasteners consisting of a tongue and heavy wire loops brazed to\nthe reverse. The later plates have a bright brassy color, are struck\non thin brass, and have the loop and tongue soldered rather than\nbrazed.\nWAIST-BELT PLATE, C. 1840\n[Illustration: FIGURE 210]\nThe lack of a mane on the beast on this plate marks it as a tiger. The\nbest known and most affluent Militia organization with the nickname\n\"Tigers\" was the Boston Light Infantry, although a number of others\nalso were so-called. The craftsmanship and general elegance of this\ngold-plated brass specimen suggests that it was worn by an officer,\nthough an occasional volunteer company was so richly endowed that all\nits members, officers and enlisted men alike, wore expensive devices.\nThe bench-assembled manufacturing technique, gaudy embellishment, and\nlack of a distinct Victorian touch date the piece about 1840. The\ntiger's head is applied.\nWAIST-BELT PLATE, C. 1840\n[Illustration: FIGURE 211]\nThe full-flowing mane on the beast on this plate identifies it as a\nlion. The device would have been appropriate for wear by the Albany\nBurgesses Corps, which, when founded in 1833, almost immediately\nadopted the lion's head as its distinctive insignia. The unit\ncontinued to wear this plate for about half a century. While that\nunit's cap plate (fig. 170) is much more formal and is without a\nlion's head, its buttons contain the lion--with head turned to\nhalf-right--as a principal ornament. While it is probable that the\noriginal die for this cast-brass plate was sunk for the Albany\norganization, the manufacturer would not have hesitated to offer it\nfor sale to any interested Militia unit.\nWAIST-BELT PLATE, C. 1840\n[Illustration: FIGURE 212]\nThe raised letters \"W G\" on this cast-brass and gilded plate would\nhave been suitable for many Militia units of the period. We can only\nsuggest that it may have been worn by members of a \"Washington Greys\"\nor \"Washington Guard\" from Pennsylvania or New York. A round plate\nwith an outer wreath would have been more appropriate for officers\nthan for enlisted personnel.\nWAIST-BELT PLATE, WASHINGTON GREYS, C. 1850\n[Illustration: FIGURE 213]\nThe waist-belt plates shown in the _U.S. Military Magazine_[132] for\nthe Washington Greys of Philadelphia and Reading, Pennsylvania, while\nindistinct, are definitely not of this pattern. Thus, this brass plate\nwith its sunken letters filled with black enamel must have been worn\nby yet a third unit with such a name. Additional specimens in the\nnational collections have the company letters \"G\" and \"K.\"\nWAIST-BELT PLATE, C. 1840\n[Illustration: FIGURE 214]\nThis oval, convex, brass plate, with two studs and a hook soldered to\nthe reverse for attachment, very probably was originally a\nshoulder-belt plate. The letters \"W L G\" incised on the obverse are\nvery patently the added work of an engraver of no great talent. The\nletters doubtless stand for Washington Light Guard, and, since there\nwere several Militia units of that designation, it seems possible that\none of the less affluent units bought the plates and had them engraved\nlocally.\nWAIST-BELT PLATE, CITY GUARDS, C. 1840\n[Illustration: FIGURE 215]\nThere were City Guards in Charleston, South Carolina, New York City,\nPhiladelphia, and possibly in other places. Thus it is impossible to\ndetermine just which of these units wore this cast-brass plate. The\nornamented outer oval is typical of the 1840's.\nWAIST-BELT PLATE, NATIONAL GUARD, C. 1850\n_USNM 60206-M. Figure 216._\n[Illustration: FIGURE 216]\nA number of Militia units carried the designation \"National Guard.\"\nThe unit that used this particular plate was from New Jersey, for\nscratched on the reverse is \"Sergeant O. Clinton, October 9th, 1851,\n1st Reg Hudson Brigade, NJSM\"; However, the adjutant general, State of\nNew Jersey, was unable to give any information on such an\norganization. The specimen is cut from rolled brass with sunken\nletters filled with black enamel.\n\u00b6 Shoulder-belt plates underwent the same transition as cap plates did\nbeginning about 1837-1838, with the single die strike plate yielding\nto the composite plate, and applied devices being attached to oval,\nrectangular, or rectangular \"clipped corner\" plates. While some single\ndie plates were made and worn after 1840, no composite types that\npredate 1835 are known. The following group of shoulder-belt plates\nare typical of those that first appeared about 1840. Of these, several\ncontinued unchanged through the Civil War and into the 1870's and\nSHOULDER-BELT PLATE, C. 1840\n[Illustration: FIGURE 217]\nThis unusually large, oval, brass plate with the letters \"C G\" in\nsilver applied with wire fasteners is another of that sizable group of\nlettered insignia that cannot be attributed definitely to a particular\norganization. The \"C G\" may stand variously for City Guard, Cleveland\nGreys, Charleston Guard, or some other organization. With a stock of\noval and rectangular blanks and a set of lettering and number-cutting\ndies, an almost limitless combination of plates could be turned out by\na single manufacturer.\nSHOULDER-BELT PLATE, NEW YORK, C. 1840\n[Illustration: FIGURE 218]\nThe basic form of this brass plate--with one of the many variations of\nthe seal of the State of New York[133] applied with wire fasteners--is\na copy, with minor changes, of the bevelled plate prescribed for the\nRegular Establishment in 1839. Distinctly an officer's plate, it would\nhave been appropriate for artillery or staff.\n[Footnote 133: ZIEBER, p. 166.]\nSHOULDER-BELT PLATE, C. 1840\n[Illustration: FIGURE 219]\nThis composite plate, struck in brass, has a bevelled, rectangular\nbase almost identical to the base of the 1839 regulation plate (see\nfig. 86). The design consists of a silvered center ornament comprising\na trophy of flags, a sword, and a liberty pole surmounted by a wreath\nof laurel inclosing fasces and a Federal shield with 26 stars in its\ncanton. This silver ornament is applied with four simple wire\nfasteners rather than soldered. Since the sun rays in the background\nradiate outward not from the center but from the edge of a circle\nabout 1-1/2 inches in diameter, almost any desired center ornament\ncould have been added to the basic strike, or the plate could be\nstruck a second time to add a device integral to it. Thus the\nbackground portion of the specimen must be considered a stock pattern.\nA print of the National Guards of Philadelphia in _U.S. Military\nMagazine_ for October 1841 shows an officer wearing a similar plate.\nIf the stars are significant, the plate can be dated between 1837 and\nSHOULDER-BELT PLATE, C. 1840\n[Illustration: FIGURE 220]\nIn this plate, the center ornament used in the preceding specimen has\nbeen struck directly in a rectangular, bevelled background. However,\nthe background of this plate has a stippled surface rather than a\nsunburst. An interesting feature is that there are four slots punched\nthrough the plate for the attachment of an additional device over the\nwreath and shield. This is another of the many examples of how a unit\nmight have an insignia distinctive to itself at little extra cost.\nThis plate is obviously of a stock pattern. The national collections\nalso contain a die sample of this particular plate.\nSHOULDER-BELT PLATE, C. 1840\n[Illustration: FIGURE 221]\nAnother example of the rectangular, bevelled-edged, shoulder-belt\nplate for officers is this brass-cast copy of the 1839 Regular Army\npattern with the wire-fastened letters \"S V G\" substituted for \"U. S.\"\nThe specimen bears a touchmark \"W. Pinchin Philad\" on the reverse (see\np. 33). The unit for which this plate was made is unidentified.\nSHOULDER-BELT(?) PLATE, C. 1840\n[Illustration: FIGURE 222]\nThe silver letters \"S F\" applied with wire fasteners to the small\nbrass plate are most appropriate for the State Fencibles of\nPhiladelphia, and it is believed to have possibly been worn by that\nunit in the 1840's. A print in the _U.S. Military Magazine_[134]\nportraying this unit shows an officer wearing a plate of an entirely\ndifferent design, but since a plate in this simple form would most\nprobably have been worn by enlisted personnel, and the soldier in the\nprint is to be seen only from the rear, such identification as to unit\nmay be correct.\n[Footnote 134: March 1839, pl. 2.]\nSHOULDER-BELT PLATE, BOSTON LIGHT INFANTRY, C. 1840\n[Illustration: FIGURE 223]\nThis unusually large silver-on-copper plate with its brass letters \"B\nL I\", \"1798\", and brass tiger's head is attributed to the Boston Light\nInfantry. The applied devices are attached with simple wire fasteners.\nThe date 1798 is believed to be the year of the original organization\nof the unit, but the adjutant general of the Commonwealth of\nMassachusetts was unable to verify this.\nSHOULDER-BELT PLATE, NEW YORK LIGHT GUARD, C. 1840\n[Illustration: FIGURE 224]\nThe _New York Military Magazine_ provides us with a strong clue in\nidentifying this clipped-corner, bevelled-edged brass plate with a\nsilver-on-copper tiger's head applied. In a sketch of the Light Guard\nof New York it is related that, following a visit in 1836 to the\nBoston Light Infantry, members of the company \"adopted, as part of\ntheir uniform, a silver tiger's head, to be placed on the breast\nplate, as a further memento of the spirited and elegant corps whose\nguests they had been.\"[135] This specimen is in agreement with that\ndescription.\n[Footnote 135: _New York Military Magazine_ (1841), vol. 1, p. 118.]\nSHOULDER-BELT PLATE, DRAGOONS, C. 1840\n[Illustration: FIGURE 225]\nAn unusual manufacturing technique was used in making this plate. It\nwas struck in very heavy brass about 1/16 inch thick and the whole\ntinned; then, all the tin on the obverse, except that on the crested\nhelmet device, was buffed away, giving the center ornament the\nappearance of having been silvered. The specimen obviously was made\nfor a particular mounted unit, designation unknown. An interesting\ndetail is the letter \"A\" on the half-sunburst plate of the dragoon\nhelmet device.\nSHOULDER-BELT PLATE, C. 1840\n[Illustration: FIGURE 226]\nThis plate, which is of brass with a cast, white-metal likeness of\nWashington applied with wire fasteners, may well have belonged to\neither the Washington Greys of Philadelphia or the unit of the same\ndesignation of Reading, Pennsylvania. Prints of these two\norganizations in _U.S. Military Magazine_[136] show profiles on the\nshoulder-belts plates, although the plate of the Reading unit is\ndepicted as being oval.\nSHOULDER-BELT PLATE, C. 1840\n[Illustration: FIGURE 227]\nThis brass plate with its wire-applied devices obviously belonged to\nan Irish-group Militia unit. The Huddy and Duval print of the Hibernia\nGreens of Philadelphia[137] definitely depicts an Irish harp on both\nthe shoulder-belt plate and the cap plate, but the motto \"ERIN GO\nBRAGH\" is not included. The specimen would have been suitable for\nseveral Militia organizations, such as the Irish Jasper Greens of\nSavannah, Georgia, and the Montgomery Hibernia Greens. Its devices are\nwire-applied, and it possibly was a stock pattern.\n[Footnote 137: _U.S. Military Magazine_ (January 1840), pl. 27.]\nSHOULDER-BELT PLATE, C. 1840\n[Illustration: FIGURE 228]\nThis plain brass plate, having wire-applied pewter letters \"S L I\" is\nbelieved to have been worn by the Salem Light Infantry of\nMassachusetts.\nSHOULDER-BELT PLATE, NEW ENGLAND GUARDS, C. 1840\n[Illustration: FIGURE 229]\nLetters signifying the New England Guards are embossed on a shield of\nwhite metal that is attached to this brass plate, which has scalloped\ncorners. Although the officer depicted in the Huddy and Duval print of\nthe New England Guards[138] wears a waist belt rather than a shoulder\nbelt for his sword, the soldier standing in the background is shown\nwith crossed shoulder belts. Thus, this plate may have been an item of\nequipment for enlisted personnel rather than for officers.\n[Footnote 138: _U.S. Military Magazine_ (November 1839), pl. 21.]\nSHOULDER-BELT PLATE, MASSACHUSETTS, C. 1840\n[Illustration: FIGURE 230]\nAlthough the white-metal arm and sword on wreath device wired to this\nlarge brass plate immediately identifies the origin of the specimen as\nMassachusetts, the considerable heraldic license taken by this\ninsignia-maker is only too evident. When the Massachusetts State seal\nwas first adopted in 1780, the blazonry of the crest was given as\nfollows: \"On a Wreath a dexter Arm cloathed and ruffled proper,\ngrasping a Broad Sword....\"[139] The designer has placed the arm in\narmor and replaced the \"broad sword\" with a scimiter-like, edged\nweapon. The use of the crest of a state seal or coat of arms to\nindicate the state was common usage, with the eagle-on-half-globe of\nNew York providing an excellent example. This plate would have been\nappropriate for wear by any Massachusetts unit, and is thus considered\nto have been a stock pattern.\n[Footnote 139: ZIEBER, pp. 143-144.]\nSHOULDER-BELT PLATE, SOUTH CAROLINA, C. 1840\n[Illustration: FIGURE 231]\nThe silver palmetto tree identifies this as a South Carolina plate.\nThe letters \"L\" and \"A\" are subject to several interpretations, the\nmore probable being \"Light Artillery.\" The devices are attached with\nsimple wire fasteners, and the basic brass plate can be considered to\nhave been a stock item adaptable to any number of units.\nSHOULDER-BELT PLATE, C. 1845\n[Illustration: FIGURE 232]\nThis brass, lead-backed badge bears no devices that would assist in\nidentifying it as to unit, and its general composition would have made\nit appealing to more than one Militia organization. It is considered a\nstock pattern. The stars-on-belt motif, forming the border of the\noval, is very unusual, as are the 14 arrows in the eagle's left talon\nand the star beneath its beak. The center eagle device is applied with\nsimple wire fasteners.\n\u00b6 Following the War with Mexico, many State Militia, especially those\nin the south, began using their state coats of arms as the principal\ndevices on their waist-belt plates. The plates for officers followed\nthe earlier pattern for Regulars, a round device clasped within an\nouter ring. Plates of enlisted personnel more often were rectangular,\nbut there were many exceptions. The following series includes examples\nof both types.\nWAIST-BELT PLATE, ALABAMA C. 1850\n[Illustration: FIGURE 233]\nThe old Alabama State seal with a representation of a map of the State\nhung from a tree trunk, as depicted on the inner ring of this\ncast-brass waist-belt plate, became obsolete after the Civil War when\nthe \"reconstruction\" government changed the device to that of an eagle\nresting on a Federal shield. Some years later, however, the original\nseal, in somewhat modified form, was readopted. Although made in the\nearly 1850's, plates of this type were worn by personnel of the\nConfederate States Army throughout the Civil War. Many plates of this\nsame basic pattern were made in England and run through the blockade.\nWAIST-BELT PLATE, CALIFORNIA, C. 1850\n[Illustration: FIGURE 234]\nThe 31 six-pointed stars in the outer ring of this cast-brass plate\nbearing the central elements of the California State seal indicate\nthat it was made after statehood was granted in 1850 but before 1858\nwhen Minnesota became the 32d State. Actually, this design for the\narms of the State was adopted in anticipation of admission to the\nUnion, on October 2, 1849.[140] The ornate design of this plate is\nmore characteristic of the 1840's than later, indicating that it was\nmade very early in the 1850's.\n[Footnote 140: ZIEBER, p. 114.]\nWAIST-BELT PLATE, FLORIDA, C. 1850\n[Illustration: FIGURE 235]\nThe palm tree, standing alone, although sometimes mistaken for the\npalmetto of South Carolina, is representative of the State of Florida.\nThus, this plate is ascribed to Florida Militia, about 1850. The late\nRichard D. Steuart, of Baltimore, Maryland, an outstanding authority\non Confederate equipment and accoutrements, was firm in asserting that\nthis pattern should be ascribed to Florida.\nWAIST-BELT PLATE, MASSACHUSETTS, C. 1850\n[Illustration: FIGURE 236]\nWhile cast-brass plates of this type were first made in the early\n1850's, their use continued for 20 years or more after that decade.\nThe principal device on this specimen is taken from the arms of the\nCommonwealth of Massachusetts. The form of the plate is identical to\nthe pattern of the eagle-wreath plate adopted by the Regulars in 1851.\nWAIST-BELT PLATE, C. 1845\n[Illustration: FIGURE 237]\nThe star device was used by the Militia of both Texas and Maine, as\nwell as by volunteer units located in other states; thus, this plate\ncannot be ascribed to any particular geographical area. Plates such as\nthis, with the silver wreath of laurel and palm, are patterned\ndirectly after the basic plate prescribed for officers of the Corps of\nEngineers in 1841. They would have been stock items for general sale.\nWAIST-BELT PLATE, C. 1850\n[Illustration: FIGURE 238]\nThis cast-brass officer's plate, a pre-Civil War product of American\nmanufacture, would have been appropriate for wear by Texas Militia.\nObviously a stock pattern, it would also have been sold to Militia\norganizations in other parts of the country. As in the case of most\nround plates, the outer ring is of a standard design; variation in\npattern would occur on the inner ring.\nWAIST-BELT PLATE, NEW YORK, C. 1850\n[Illustration: FIGURE 239]\nThis brass-struck rectangular plate carries the arms of the State of\nNew York[141] with its familiar eagle-on-half-globe device. The whole\nis superimposed on a sunburst background. The plate originally was\nmade for Militia, but it is conceivable that such a plate may have\nbeen worn by early uniformed police.\n[Footnote 141: For the variations in the arms of New York see ZIEBER,\nWAIST-BELT PLATE, NEW YORK, C. 1850\n[Illustration: FIGURE 240]\nThis brass-cast plate with its letters \"S N Y\" for State of New York\nis copied directly from the 1836 plate for noncommissioned officers of\nthe Regular Establishment. The example is the oldest known use of the\nletters \"S N Y\" for New York Militia. In later patterns, the letters\n\"S N Y\" and \"N Y\" were placed on rectangular plates and on oval plates\nworn on the waist belt and on cartridge boxes just prior to and during\nthe Civil War. Small square plates with silver, Old English letters\n\"NY\" are included in the 1900 catalog of the Warnock Uniform Co. of\nNew York as regulation pattern that year for National Guard officers.\nWAIST-BELT PLATE, NEW YORK CITY, C. 1850\n[Illustration: FIGURE 241]\nThis cast-brass plate bears the arms of the city of New York\nsuperimposed on an almost full sunburst. The surrounding wreath of\nlaurel is taken directly from the plate authorized for general and\nstaff officers of the Regular Establishment in 1832. While this is\nthought to be the plate for the New York City Guards, for whom a\nmatching shoulder-belt plate is known, there is the possibility that\nit was also worn by uniformed police of the 1850's.\nWAIST-BELT PLATE, C. 1850\n[Illustration: FIGURE 242]\nA stock pattern, this cast-brass and gilded plate would have been\nappropriate for any of the several organizations called \"National\nGuards\" or \"National Greys\" that existed in a number of states. The\nletters \"N G\" do not connote the National Guard as we know it today.\nWAIST-BELT PLATE, OHIO, C. 1850\n[Illustration: FIGURE 243]\nThe center piece applied to this cast-brass plate with wire fasteners\nbears an early form of the arms of the State of Ohio.[142] The plate\nproper has holes in it other than those needed to apply the present\ndevice, which indicates that it was a stock part, or possibly that the\npresent center device is not original to the plate.\n[Footnote 142: For an interesting discussion of the evolution of the\narms of Ohio see PREBLE, pp. 639-642.]\nWAIST-BELT PLATE, OHIO, C. 1850\n[Illustration: FIGURE 244]\nThis plate bears another variation of the Ohio State arms. Here, the\narms lie within a wreath as prescribed for Regular general and staff\nofficers in 1832. The entire specimen is cast in brass; the wreath,\nsun, arrows, canal wall, and hull of keelboat are silvered.\nWAIST-BELT PLATE, PENNSYLVANIA, C. 1850\n[Illustration: FIGURE 245]\nOfficers of the Pennsylvania Volunteer Militia wore plates of this\ntype in the 1850's, although most were discarded in 1861 when\nPennsylvania troops went into active Federal service. The outer ring,\nwith floral wreath design, has been modified to give the appearance of\na solid rectangle. Another plate in the national collections bears the\nletters \"P V M\" with the conventional outer ring.\nWAIST-BELT PLATE, C. 1850\n[Illustration: FIGURE 246]\nJust prior to 1850 there were two Militia units in Philadelphia using\nthe letters \"P G\" to indicate organizational designation--the\nPhiladelphia Guards and the Philadelphia City Greys. This brass-cast\nplate is believed to have been worn by the Philadelphia Guards, whose\nbuttons were marked \"P G.\" The buttons worn by the Philadelphia City\nGreys carried the three letters \"P C G.\"[143]\n[Footnote 143: JOHNSON, vol. 1, p. 145, vol. 2, pl. 63.]\nWAIST-BELT PLATE, PROVIDENCE MARINE CORPS ARTILLERY C. 1850\n[Illustration: FIGURE 247]\nThe letters and device on this rather unusual brass plate make its\nidentification easy. The letters stand for the Providence [R.I.]\nMarine Corps Artillery; the date 1801 is the unit's original\norganization date. The crossed cannon indicate Militia artillery. The\nletters and numerals are of white metal and brazed to the plate. The\nbrass crossed cannon are affixed with wire fasteners. The reverse is\nfitted with a broad tongue and two wire hooks for attachment.\nWAIST-BELT PLATE, SOUTH CAROLINA, C. 1850\n[Illustration: FIGURE 248]\nAlthough this specimen is not so old as the similar South Carolina\nplate described previously (fig. 162), it is believed to date about\n1850. The plate proper is of rolled brass, and the applied device,\nwhich comprises well-known elements of the arms of South Carolina, is\nstruck in brass and attached by means of two wire staples and leather\nthongs.\nWAIST-BELT PLATE, VIRGINIA, C. 1850\n[Illustration: FIGURE 249]\nThis plate, carrying the Virginia seal, was made about 1850 for wear by\nofficers. Similar plates made by British manufacturers during the Civil\nWar to be run through the blockade are generally distinguishable by\ntheir unusually sharp, clean die work. The center device of this\nspecimen is struck in brass and brazed in place; the remainder of the\nplate is brass-cast.\nWAIST-BELT PLATE, GRAY GUARDS, C. 1850\n[Illustration: FIGURE 250]\nThe unit for which this plate was made cannot be precisely identified.\nIt is reasonable to assume that there were several Militia\norganizations called \"Gray Guards.\" The central \"G\" probably indicates\n\"Company G.\" The whole is cast brass.\nWAIST-BELT PLATE, C. 1850\n[Illustration: FIGURE 251]\nThis plain brass plate of unusually fine manufacture is very\ndefinitely a stock pattern which could have been sold without ornament\nor, as was more likely, with a center device added by soldering or\nbrazing. The plate was cast in three pieces, with the round center\nbrazed to the belt attachment. It was bench-fitted, as indicated by\nthe numbers on the reverse of the inner and outer rings.\nWASTE-BELT PLATE, C. 1850\n[Illustration: FIGURE 252]\nThis is a typical stock pattern with the company designation \"E.\"\nOther specimens in the national collections have the letters \"D,\" \"F,\"\n\"K,\" and \"R.\" Although rather crudely cast in brass, this piece has\nbeen bench-fitted and then gilded.\nWAIST-BELT PLATE, C. 1850\n[Illustration: FIGURE 253]\nThis is another stock pattern with company designation. In this case,\nthe numeral \"1\" has been applied with wire fasteners rather than cast\nintegrally with the two portions of the plate. The national\ncollections also contain similar plates with the numerals \"2,\" \"26,\"\nWAIST-BELT PLATE, C. 1850\n[Illustration: FIGURE 254]\nThis is another typical stock pattern with the eagle-on-shield device\nsurrounded by 13 5-pointed stars as the center ornament. It is cast in\nbrass in two pieces. An example of this plate, on a belt, formed part\nof a cased Sharps rifle outfit displayed at the 1960 National Rifle\nAssociation meeting in Washington, D.C.\nWAIST-BELT PLATE, MUSICIAN, C. 1850\n[Illustration: FIGURE 255]\nThe musician's lyre has never been strictly a military ornament, being\nwidely worn by civilian bands; thus, this plate cannot precisely be\nidentified as military or nonmilitary. Unlike most plates of this type\nand period, the entire piece is struck in brass rather than cast.\nWAIST-BELT PLATE, C. 1850\n[Illustration: FIGURE 256]\nThe letters \"T C B\" on this brass-cast plate open wide the doors of\nconjecture as to interpretation. Possible combinations range from\nTrenton City Blues (if such a Militia organization ever existed) to\nTroy Cornet Band, a nonmilitary unit. Plates such as this can seldom\nbe positively identified.\nWAIST-BELT PLATE, C. 1850\n[Illustration: FIGURE 257]\nAs in the case of the preceding plate, the letters \"H R\" on this\nspecimen cannot be specifically identified. Similar unidentified\nplates in the national collections have the letters \"S O I\" and \"P B.\"\nWAIST-BELT PLATE, C. 1850\n[Illustration: FIGURE 258]\nThis plate is known both in heavy metal stamping and in thin, cheap\nbrass. Examples of the latter type appear to have been struck in the\nperiod of the 1890's from a die then 50 years old. A plate similar to\nthis one has been excavated from a Civil War battlefield site. A stock\npattern, the design was obsolete for issue to Militia before the\nCivil War, but it is known to have been continued almost to the end of\nthe century for use by groups such as secondary school cadet corps.\n\u00b6 The shoulder-belt plates worn in the 1850's were little changed from\nthose of the preceding decade. In the Regular Establishment the\nshoulder belt and plate for officers had been discarded in favor of\nthe waist belt for carrying the sword, but Militia officers--bound by\nno regulations--continued to wear the shoulder belt. Enlisted\npersonnel wore at least one shoulder belt, and in many cases used two\nbelts, which crossed, one belt carrying the cartridge box and the\nother the bayonet and scabbard. Mounted Militia sometimes wore the\nsaber on a waist belt and the carbine cartridge box on a shoulder\nbelt. It is interesting to note that the custom of using elements of\nstate seals on waist-belt plates was not followed to any great extent\nin the embellishment of shoulder-belt plates except in the Southern\nStates.\nCARTRIDGE-BOX-BELT PLATE, SOUTH CAROLINA, C. 1845(?)\n[Illustration: FIGURE 259]\nIn size and pattern this plate is exactly like that prescribed for the\nRegular Establishment in 1841, substituting the arms of South Carolina\nfor the eagle. It possibly may date as early as 1845. Made for South\nCarolina Militia, plates similar to this were worn during the Civil\nWar and several have been recovered from battlefield sites. The\nspecimen is struck in brass and the reverse filled with lead. It has\nthree bent-wire fasteners imbedded in the reverse, which indicates\nthat it was decorative rather than functional. A similar plate with\nelements of the Virginia State seal is known. Modern reproductions of\nboth are being sold.\nSHOULDER-BELT PLATE, C. 1850\n[Illustration: FIGURE 260]\nA popular stock pattern of the 1850's, this design with the silver\nnumeral \"1\" on a rectangle of rolled brass was worn for at least half\na century after it first appeared. Similar plates are known with all\nnumerals through 9 and a few higher numbers. Other plates of the same\ngeneral type are known with company letters \"A\" through \"M.\" The plate\nproper is fitted with two brass wire hooks and a medium width tongue,\nindicating a functional use. The numeral is attached by means of two\nstaples with leather thongs reeved through on the reverse of the\nplate.\nSHOULDER-BELT PLATE, C. 1850\n[Illustration: FIGURE 261]\nThis rolled-brass plate with its silver \"TC\" monogram is presently\nunidentified. In the national collections there is a Militia helmet\nwith the same device used as part of the cap plate; also known is\nanother insignia, comprising the monogram alone, that was used as a\ncartridge-box device. _New York Military Magazine_ for July 17, 1841,\nrefers to the elegant armory of the Troy [N.Y.] Corps where the Light\nGuard of New York had been visitors. This plate may have been an\ninsignia of that organization. The monogram is affixed with staples\nand leather thongs, and the plate proper carries a large safety pin\nsoldered to the reverse for purely decorative attachment. It is\nunknown whether the safety pin fasteners are contemporary with the\nplates to which they are attached. Rudimentary safety pins were known\nin Egypt before Christ, but they apparently did not appear in America\nuntil the 1830's and 1840's. Walter Hunt patented the first American\nsafety pin in 1849.[144]\n[Footnote 144: U.S. Patent 6281 (April 10, 1849).]\nSHOULDER-BELT PLATE, C. 1850\n[Illustration: FIGURE 262]\nSeveral Militia organizations of the 1840's and 1850's were called\n\"Republican Guards,\" and this silver \"RG\" monogram on a rolled-brass\nrectangle would have been appropriate on shoulder belts of so-named\nunits. The monogram is affixed with wire fasteners, but the means of\nattachment for the plate proper are missing.\nSHOULDER-BELT PLATE, C. 1850\n[Illustration: FIGURE 263]\nThe silver letters \"GG\" on this rolled-brass plate present several\npossibilities for identification. Among the uniformed Militia units\nof the 1840's and 1850's were Garibaldi Guards, German Guards, and\nGray Guards. This piece could have been the device of any of the\nthree. The letters are affixed with wire fasteners, and a safety pin\nis soldered to the rear of the plate proper for decorative attachment.\nSHOULDER-BELT PLATE, C. 1850\n[Illustration: FIGURE 264]\nThis oval brass plate with the wire-affixed silver-on-copper letters\n\"AG\" is unidentified, but it might well have been worn by the American\nGuards, or by a uniformed company from some city as Atlanta or Albany,\nwith the letter \"G\" representing \"Grays,\" \"Guards,\" \"Grenadiers,\" or\nthe like. It was attached to the belt with three simple wire\nfasteners.\nSHOULDER-BELT PLATE, C. 1850\n[Illustration: FIGURE 265]\nThe white-metal device on this brass plate comprises elements of the\narms of \"New Amsterdam\" topped by the crest of the arms of New York\nState with supporting figures representing the original Indian owner\nof Manhattan Island and the mariner who became the first white\nsettler. The specimen is believed to have been worn by the New York\nCity Guard. The device is affixed with three staples originally\nintended to be reeved through with leather thongs, although now bent\nover. The means of attachment of the plate proper are missing.\nSHOULDER-BELT PLATE, C. 1850\n[Illustration: FIGURE 266]\nThe letters \"K L G\" forming the white-metal monogram on this brass\nplate indicate that it could well have been worn by the Kentish Light\nGuard of Rhode Island. The monogram is attached by means of two\nstaples with thongs reeved through, and the plate proper is fitted\nwith four similar staples. The reverse bears the hallmark of William\nH. Horstmann and Sons, well-known military outfitters of Philadelphia.\nSHOULDER-BELT PLATE, C. 1850\n[Illustration: FIGURE 267]\nThe white-metal letters \"SG\" on this brass plate lend themselves to so\nmany interpretations that no identification is attempted. The applied\ndevice has two staples for attachment, and the plate proper is fitted\nwith a safety pin on the reverse.\nSHOULDER-BELT PLATE, C. 1850\n[Illustration: FIGURE 268]\nMany volunteer companies used the designation \"Rifle Guards,\" and this\nplate with the initials \"C R G\" probably falls into such a category.\nThe \"C,\" of course, cannot be identified. The monogram is of pewter\nand has three round lugs fitted through holes in the plate proper for\nattachment with pins. The plate itself has a safety pin soldered to\nthe reverse for attachment.\nSHOULDER-BELT PLATE, SCOTT LEGION(?), C. 1850\n[Illustration: FIGURE 269]\nAlthough this plate bearing the profile of Gen. Winfield Scott is very\nsimilar in design and construction to several bearing the head of\nWashington and dated much earlier, it is believed to postdate the War\nwith Mexico when Scott's popularity was at its zenith. There were\nseveral volunteer units called \"Scott Legion\" during this period. The\npiece was struck, with a tin backing applied, and the edges of the\nobverse were then crimped over. It is fitted with three wire staples\nfor attachment.\nSHOULDER-BELT PLATE, C. 1850\n[Illustration: FIGURE 270]\nThis is a stock pattern in cast brass. It is oval with raised edges\nand has a white-metal \"F\" applied with simple wire fasteners. Although\nthe piece has the appearance of a waist-belt plate or cartridge-box\nplate, the wire fasteners on the reverse indicate that it was intended\nfor shoulder-belt wear. In the national collections is a similar plate\nwith the letter \"I,\" indicating that the letters designate companies\nof larger units rather than a unit itself.\nSHOULDER-BELT PLATE, ARTILLERY, C. 1850\n[Illustration: FIGURE 271]\nThis rolled-brass plate with a wire-applied silvered \"A\" and pile of\ncannon balls topped by the hand die-struck motto \"ALWAYS READY\" is\nunidentified beyond the fact that it was worn by a member of Company A\nof a Militia unit using a popular motto. Similar specimens in the\nnational collections have center letters \"B,\" \"D,\" and \"E.\" The plate\nwas attached to the shoulder belt by means of two flat brass fasteners\nsoldered to the reverse. The fasteners are almost as wide as the plate\nitself.\nBALDRIC DEVICE, C. 1850\n[Illustration: FIGURE 272]\nThe baldric is a highly ornamented wide sash normally worn by drum\nmajors and sometimes by band leaders. During at least part of the\nCivil War, baldrics were worn by some aides-de-camp, and the 1902\nuniform regulations specified them for Signal Corps officers. This\nspecimen and the one that follows are the earlier of several examples\nin the national collections; they fall in the early 1850's. The\nshield, suspended from a lion's mouth by small chains, carries an\neagle with a shield on its breast. The stars and edge of clouds,\nabove, are somewhat similar to those on the 1851 regulation\nwaist-belt plate. The whole is superimposed on a three-quarter\nsunburst. Both the lion's head and the shield are fitted with simple\nwire fasteners for attachment.\nBALDRIC DEVICE AND BALDRIC, C. 1850\n_USNM 66622-M. Figure 273._\n[Illustration: FIGURE 273]\nThe device is attached to a red, gold-edged-embroidered baldric worn\nby the drum major of the 72d New York Militia during the Civil War but\nbelieved to ante-date 1861. The brass shield, with ebony drum sticks,\nis suspended from an eagle of the 1834 Regular Army pattern for wear\nas a cap device. The shield, convex with beveled edges, is very\nsimilar to waist-belt and shoulder-belt plates of about 1850.\n\u00b6 Few Militia gorgets are known, and this scarcity leads us to believe\nthat few were made and worn, despite the Militia's love for the \"gay\nand gaudy.\" Still, some units did adopt them, and officers of the\nPortland [Maine] Rifle Corps were still wearing them in the late\n1850's.[145] As a military symbol for officers, the gorget passed its\nzenith in the late 18th century. Gorgets were worn during the War of\nthe Revolution by both American and British officers, and the British\nalso gave them to Indian chiefs as marks of authority. Officers in at\nleast one regiment of the Regular Establishment wore them as part of\ntheir regulation dress about the turn of the 19th century, but they\nwere not a part of the prescribed uniform during or after the War of\n[Footnote 145: In the national collections are a uniform jacket,\nchapeau, and gorget once owned by Frederick Forsyth, a member of the\nPortland Rifle Corps in 1857.]\n[Illustration: FIGURE 274]\nThis gorget, of gilded brass, is of 2-piece construction. The\neagle-on-clouds, very similar to cockade eagles worn in 1808-1821, is\nattached by four wire fasteners rather than brazed. The engraved\nedging on the gorget proper is rather crudely done. Although composite\ninsignia did not come into general use until the mid-1830's, it seems\nreasonable to assume that this particular design of the eagle device\napplied to the chapeau might equally have been applied to a gorget. A\nsimilar specimen in the national collections has a silver-on-copper\neagle instead of a brass one.\n[Illustration: FIGURE 275]\nThis gorget is of 3-piece construction, the specimen proper being of\nbrass and the wreath and eagle of gilded brass applied with wire\nfasteners. Although the eagle is of the early \"on-clouds\" design, the\nfeel of the piece is later, and this, together with the rather wide\ncrescent indicate that it belongs to the period of the 1830's and\nGORGET, STATE FENCIBLES, NEW YORK, C. 1840-1850\n[Illustration: FIGURE 276]\nThis brass gorget, with wreath and letters in applied silver, is an\nexample of one of the later types worn by Militia. The letters \"S F\"\nare interpreted as \"State Fencibles,\" and the \"Excelsior\" buttons on\nthe ends of the crescent identify the origin of the unit as New York\nState. Fencibles were basically troop units organized for home defense\nonly. There was a volunteer Militia company called the \"State\nFencibles\" in New York City as early as 1800. It apparently lost its\nidentity as such in 1847 or 1848 when the organization split, half\nentering the 8th Regiment and half entering the 9th Regiment of New\nYork State Militia.[146]\n[Footnote 146: Personal communication from Frederick P. Todd, July 6,\n1960. Mr. Todd is the foremost authority on New York Militia units.]\nU.S. Government Printing Office: 1963", "source_dataset": "gutenberg", "source_dataset_detailed": "gutenberg -  American Military Insignia, 1800-1851\n"},
{"source_document": "", "creation_year": 1946, "culture": " English\n", "content": "Produced by Stephen Hutcheson and the Online Distributed\nProofreading Team at https://www.pgdp.net\n[Illustration: DENVER, COLORADO]\n  _But from these immense prairies may arise one great advantage to the\n  United States, viz., the restriction of our population to some certain\n  limits, and thereby a continuation of the union. Our citizens being so\n  prone to rambling, and extending themselves on the frontiers, will,\n  through necessity, be constrained to limit their extent on the west to\n  the borders of the Missouri and the Mississippi, while they leave the\n  prairies, incapable of cultivation, to the wandering and uncivilized\n  Aborigines of the country.\n  Exploratory Travels Through The Western Territories of North America\n  comprising a voyage from St. Louis, on the Mississippi, to the source\n  of that river, and a journey through the interior of Louisiana and the\n  north-eastern provinces of New Spain. Performed in the years 1805,\n  1806, and 1807, by order of the Government of the United States. By\n  Zebulon Montgomery Pike. Published by Paternoster-Row, London, 1811:\n  W. H. Lawrence and Company, Denver, 1889. Quotation from pages\n_A nontechnical description of the origin and evolution of the landscape\n                    GEOLOGICAL SURVEY BULLETIN 1493\n                UNITED STATES DEPARTMENT OF THE INTERIOR\n                      CECIL D. ANDRUS, _Secretary_\n                     H. William Menard, _Director_\n[Illustration: U. S. DEPARTMENT OF THE INTERIOR \u00b7 March 3, 1849]\n       UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON: 1980\n  Library of Congress Cataloging in Publication Data\n  Trimble, Donald E.\n  The geologic story of the Great Plains.\n  (U.S. Geological Survey Bulletin 1493)\n  Bibliography: p. 50\n  Includes index.\n  I. Geology\u2014Great Plains. I. Title.\n  II. Series: United States Geological Survey Bulletin 1493.\n For sale by the Superintendent of Documents, U.S. Government Printing\n  Landforms of today\u2014The surface features of the Great Plains          19\n  FRONTISPIECE. Aerial photograph of Denver.\n  2-3. Maps showing:\n      2. Physical divisions of the United States and maximum extent\n      3. The Great Plains province and its sections                     8\n  4. Photograph of Mescalero escarpment and southern High Plains        9\n  6-8. Maps showing:\n      6. Paleogeography of U.S. in Late Cretaceous                     14\n      7. Structural setting of the Great Plains                        14\n      8. Progressive southward expansion of areas of deposition        17\n  9. Photograph of Big Horn strip mine at Acme, Wyo.                   18\n  11-16. Photographs showing:\n      11. Weathering of granite at Sylvan Lake in the Black Hills      22\n      12. Capulin Mountain National Monument, N. Mex.                  24\n      16. Scotts Bluff National Monument, Nebr.                        28\n  17. Aerial photograph of the Nebraska Sand Hills                     30\n  19-30. Photographs showing:\n      20. Ground moraine on the Coteau du Missouri in North Dakota     34\n      21. Slump blocks in North Unit of Theodore Roosevelt National\n      23. Devils Tower National Monument, Wyo.                         38\n      24. Glaciated valley in Crazy Mountains, Mont.                   39\n      25. Powder River Basin in vicinity of Tongue River               40\n      27. Badlands of Little Missouri River in South Unit of\n            Theodore Roosevelt National Memorial Park, N. Dak.         42\n      28. Hogback ridges along the Front Range, Colo.                  43\n  1. Generalized chart of rocks of the Great Plains                    15\nThe Great Plains! The words alone create a sense of space and a feeling\nof destiny\u2014a challenge. But what exactly is this special part of Western\nAmerica that contains so much of our history? How did it come to be? Why\nis it different?\nGeographically, the Great Plains is an immense sweep of country; it\nreaches from Mexico far north into Canada and spreads out east of the\nRocky Mountains like a huge welcome mat. So often maligned as a drab,\nfeatureless area, the Great Plains is in fact a land of marked contrasts\nand limitless variety: canyons carved into solid rock of an arid land by\nthe waters of the Pecos and the Rio Grande; the seemingly endless\ngrainfields of Kansas; the desolation of the Badlands; the beauty of the\nBlack Hills.\nBefore it was broken by the plow, most of the Great Plains from the\nTexas panhandle northward was treeless grassland. Trees grew only along\nthe floodplains of streams and on the few mountain masses of the\nnorthern Great Plains. These lush prairies once were the grazing ground\nfor immense herds of bison, and the land provided a bountiful life for\nthose Indians who followed the herds. South of the grasslands, in Texas,\nshrubs mixed with the grasses: creosote bush along the valley of the\nPecos River; mesquite, oak, and juniper to the east.\nThe general lack of trees suggests that this is a land of little\nmoisture, as indeed it is. Nearly all of the Great Plains receives less\nthan 24 inches of rainfall a year, and most of it receives less than 16\ninches. This dryness and the strength of sunshine in this area, which\nlies mostly between 2,000 and 6,000 feet above sea level, create the\nsemiarid environment that typifies the Great Plains. But it was not\nalways so. When the last continental glacier stood near its maximum\nextent, some 12,000-14,000 years ago, spruce forest reached southward as\nfar as Kansas, and the Great Plains farther south was covered by\ndeciduous forest. The trees retreated northward as the ice front\nreceded, and the Great Plains has been a treeless grassland for the last\nFor more than half a century after Lewis and Clark crossed the country\nin 1805-6, the Great Plains was the testing ground of frontier\nAmerica\u2014here America grew to maturity (fig. 1). In 1805-7, explorer\nZebulon Pike crossed the south-central Great Plains, following the\nArkansas River from near Great Bend, Kans., to the Rocky Mountains. In\nlater years, Santa Fe traders, lured by the wealth of New Mexican trade,\nfollowed Pike\u2019s path as far as Bents Fort, Colo., where they turned\nsouthwestward away from the river route. Those pioneers who later\ncrossed the plains on the Oregon Trail reached the Platte River near the\nplace that would become Kearney, Nebr., by a nearly direct route from\nIndependence, Mo., and followed the Platte across the central part of\nthe Great Plains.\nAlthough these routes may have seemed long and tedious to those dusty\ntravelers, they provided relatively easy access to the Rocky Mountains\nand had a continuous supply of fresh water, an absolute necessity in\nthese plains. The minds of those frontiersmen surely were occupied with\nthe dangers and demands of the moment\u2014and with dreams\u2014but the time\nafforded by the slow pace of travel also gave them ample opportunity for\nthought about the origins of their surroundings.\nToday\u2019s traveler, who has less time for contemplation, races past a\nchanging kaleidoscope of landscape. The increased awareness created by\nthis rapidity of change perhaps is even more likely to stimulate\nquestions about the origin of this landscape.\nLewis and Clark and the Santa Fe and Oregon Trails._]\nFor instance, the westbound traveler on Interstate Highway 70 traverses\nnearly a thousand miles of low, rounded hills after leaving the\nAppalachians; the rolling landscape is broken only by a few flat areas\nwhere glacial ice or small lakes once stood. Suddenly, near Salina,\nKans., the observant traveler senses a difference in the landscape.\nInstead of rounded hills, widely or closely spaced, he sees on the\nskyline flat surfaces, or remnants of flat surfaces. As he climbs gently\nwestward these broken horizontal lines stand etched against the sky.\nAbout 35 miles west of Salina he finds himself on a broad, flat plateau,\nwhere seemingly he can see forever. True, in places he descends into\nstream valleys, but only briefly, for he soon climbs back onto the flat\nsurface.\nThis plateau surface continues for 300 miles to the west\u2014to within 100\nmiles of the abrupt front of the Rocky Mountains. East-flowing streams,\nsuch as the Smoky Hill, the Saline, the Solomon, and the Republican\nRivers and their tributary branches, have cut their valleys into this\nsurface, but these valleys become increasingly shallow and disappear\nentirely near the western rim of the plateau in eastern Colorado.\nThe distant peaks of the Rockies are seen for the first time as the\ntraveler approaches the escarpment that forms the western edge of this\ngreat plateau. After crossing the escarpment near Limon, Colo., he\nbegins the long gentle descent to Denver, on the South Platte River near\nthe foot of the mountains that loom so awesomely ahead. He has crossed\nthe Great Plains. The distances have been great, but the contrasts have\nbeen marked.\nHad our traveler selected a different route, either to the north or\nsouth, he would have found even greater contrasts, for the Great Plains\nhas many parts, each with its own distinctive aspect. Why should such\ndiverse landscapes be considered parts of the Great Plains? What are\ntheir unifying features? And what created this landscape? Has it always\nbeen this way? If not, when was it formed? How was it formed?\nWe will look here at some of the answers to those questions. The history\nof events that produced the landscape of the Great Plains is interpreted\nboth from the materials that compose the landforms and from the\nlandforms themselves. As we will see, all landforms are the result of\ngeologic processes in action. These processes determine not only the\nsize and shape of the landforms, but also the materials of which they\nare made. These geologic processes, which form and shape our Earth\u2019s\nsurface, are simply the inevitable actions of the restless interior of\nthe Earth and of the air, water, and carbon dioxide of the atmosphere,\naided by gravity and solar heating (or lack of it). They all have helped\nsculpture the fascinating diversity of the part of our land we call the\nGreat Plains.\n                       WHAT IS THE GREAT PLAINS?\nThe United States has been subdivided into physiographic regions that,\nalthough they have great diversity within themselves, are distinctly\ndifferent from each other (fig. 2).\nFrom the Rocky Mountains on the west to the Appalachians on the east,\nthe interior of our country is a vast lowland (see cover) known as the\nInterior Plains. These plains are bounded on the south by a region of\nInterior Highlands, consisting of the Ozark Plateaus and the Ouachita\nprovince, and by the Coastal Plain. In the Great Lakes region, the\nInterior Plains laps onto the most ancient part of the continent, the\nSuperior Upland. West of the Great Lakes it extends far to the north\ninto Canada. Certainly the Rocky Mountains are distinctly different from\nthe region to the east, which is the Great Plains. The Great Plains,\nthen, is the western part of the great Interior Plains. The Rocky\nMountains form its western margin. But what determines its eastern\nmargin?\nDuring the Pleistocene Epoch or Great Ice Age, huge glaciers formed in\nCanada and advanced southward into the great, central, low-lying\nInterior Plains of the United States. (See figure 2.) These glaciers and\ntheir deposits modified the surface of the land they covered, mostly\nbetween the Missouri and the Ohio Rivers; they smoothed the contours and\ngave the land a more subdued aspect than it had before they came. This\nglacially smoothed and modified land is called the Central Lowland.\nAlthough the ice sheets lapped onto the northern part, the Great Plains\nis the largely unglaciated region that extends from the Gulf Coastal\nPlain in Texas northward into Canada between the Central Lowland and the\nfoot of the Rocky Mountains. Its eastern margin in Texas and Oklahoma is\nmarked by a prominent escarpment, the Caprock escarpment. Its southern\nmargin, where it abuts the Coastal Plain in Texas, is at another abrupt\nrise or scarp along the Balcones fault zone.\n[Illustration: _Figure 2.\u2014Physical divisions of the United States and\nmaximum extent of the continental ice sheets during the Great Ice Age._]\n                       THE GREAT PLAINS\u2014ITS PARTS\nWithin the Great Plains are many large areas that differ greatly from\nadjoining areas (fig. 3). The Black Hills stands out distinctively from\nthe surrounding lower land, and its dark, forested prominence can be\nseen for scores of miles from any direction. At the southern end of the\nGreat Plains is another, less imposing, forested prominence\u2014the Central\nTexas Uplift. Most impressive, perhaps, is the huge, nearly flat plateau\nknown as the High Plains, which extends southward from the northern\nborder of Nebraska through the Panhandle of Texas, and which forms the\ncentral part of the Great Plains. The east and west rims of the southern\nHigh Plains are at high, cliffed, erosional escarpments\u2014the Caprock\nescarpment on the east and the Mescalero escarpment on the west. The\nnorth edge of the High Plains is defined by another escarpment, the Pine\nRidge escarpment, which separates the High Plains from a region that has\nbeen greatly dissected by the Missouri River and its tributaries. There,\nseveral levels of rolling upland are surmounted by small mountainous\nmasses and flat-topped buttes and are entrenched by streams. This region\nis the Missouri Plateau. The continental glacier lapped onto the\nnortheastern part of the Missouri Plateau and altered its surface.\nThe South Platte and Arkansas Rivers and their tributaries have\nsimilarly dissected an area along the mountain front that is called the\nColorado Piedmont, and the Pecos River has excavated a broad valley\ntrending southward from the Sangre de Cristo Mountains in New Mexico\ninto Texas. The Mescalero escarpment separates the Pecos Valley from the\nsouthern High Plains (fig. 4). South and east of the Pecos Valley,\nextending to the Rio Grande and the Coastal Plain, is a broad plateau of\nbare, stripped, flat-lying limestone layers bearing little but cactus\nthat is called the Edwards Plateau. Green, crop-filled valleys with\ngently sloping valley walls and rounded stream divides trend eastward\nfrom the High Plains of western Kansas and characterize a Plains Border\nsection. And finally, between the Colorado Piedmont on the north and the\nPecos Valley on the south, volcanic vents, cinder cones, and lava fields\nform another distinctive terrain in the part of the Great Plains called\nthe Raton section.\n[Illustration: _Figure 3.\u2014The Great Plains province and its sections._]\n[Illustration: _Figure 4.\u2014Mescalero escarpment and the southern High\nPlains (Llano Estacado) south of Tucumcari, N. Mex., Photograph by C. D.\nMiller, U. S. Geological Survey._]\nCan such diverse parts of our land have a sufficiently common origin to\njustify their being considered part of one unified whole\u2014the Great\nPlains? Probably so, but to understand why, we must examine some of the\nearlier geologic history of the Great Plains as well as subsequent\nevents revealed in the present landforms. We will find that all parts of\nthis region we call the Great Plains have a similar early history, and\nthat the differences we see are the results of local dominance of\ncertain processes in the ultimate shaping of the landscape, mostly\nduring the last few million years. The distinctive character of the\nlandscape in each section is determined in part by both the early events\nand the later shaping processes.\nThe Interior Plains, of which the Great Plains is the western, mostly\nunglaciated part (fig. 2), is the least complicated part of our\ncontinent geologically except for the Coastal Plain. For most of the\nhalf billion years from 570 million (fig. 5) until about 70 million\nyears ago, shallow seas lay across the interior of our continent (fig. 6\n). A thick sequence of layered sediments, mostly between 5,000 and\n10,000 feet thick, but more in places, was deposited onto the subsiding\nfloor of the interior ocean (table 1). These sediments, now consolidated\ninto rock, rest on a floor of very old rocks that are much like the\nancient rocks of the Superior Upland.\nAbout 70 million years ago the seas were displaced from the continental\ninterior by slow uplift of the continent, and the landscape that\nappeared was simply the extensive, nearly flat floor of the former sea.\n                     WARPING AND STREAM DEPOSITION\nMost of these rocks of marine origin lie at considerable depth beneath\nthe land surface, concealed by an overlying thick, layered sequence of\nrocks laid down by streams, wind, and glaciers. Nevertheless, their\ngeologic character, position, and form are exceptionally well known from\ninformation gained from thousands of wells that have been drilled for\noil. The initial, nearly horizontal position of the layers of rock\nbeneath the Interior Plains has been little disturbed except where\nmountains like the Black Hills were uplifted about 70 million years ago.\nAt those places, which are all in the northern and southern parts of the\nGreat Plains, the sedimentary layers have been warped up and locally\nbroken by the rise of hot molten rock from depth. Elsewhere in the\nInterior Plains, however, earth forces of about the same period caused\nonly a reemphasis of gentle undulations in the Earth\u2019s crust.\nThese undulations affected both the older basement rocks and the\noverlying sedimentary rocks, and they take the form of gentle basins and\narches that in some places span several States. (See sketch map, figure\n7.) A series of narrow basins lies along the mountain front on the west\nside of the Great Plains. A broad, discontinuous arch extends southwest\nfrom the Superior Upland to the Rocky Mountain front to form a buried\ndivide that separates the large Williston basin on the north from the\nAnadarko basin to the south.\nWhile the flat-lying layers of the Interior Plains were being only\ngently warped, vastly different earth movements were taking place\nfarther west, in the area of the present Rocky Mountains. Along a\nrelatively narrow north-trending belt, extending from Mexico to Alaska,\nthe land was being uplifted at a great rate. The layers of sedimentary\nrock deposited in the inland sea were stripped from the crest of the\nrising mountainous belt by erosion and transported to its flanks as the\ngravel, sand, and mud of streams and rivers. This transported sediment\nwas deposited on the plains to form the rocks of the Cretaceous Hell\nCreek, Lance, Laramie, Vermejo, and Raton Formations. Vegetation thrived\non this alluvial plain, and thick accumulations of woody debris were\nburied to ultimately become coal. This lush vegetation provided ample\nfood for the hordes of three-horned dinosaurs (_Triceratops_) that\nroamed these plains. Their fossilized remains are found from Canada to\nNew Mexico.\n[Illustration: _Figure 5.\u2014Geologic time chart and the progression of\nlife forms. Note Cretaceous_ Triceratops, _Oligocene_ Titanotheres, _and\nMiocene_ Moropus.]\n  The Earth is very old\u20144.5 billion years or more according to recent\n  estimates. Most of the evidence for an ancient Earth is contained in\n  the rocks that form the Earth\u2019s crust. The rock layers themselves\u2014like\n  pages in a long and complicated history\u2014record the surface-shaping\n  events of the past, and buried within them are traces of life\u2014the\n  plants and animals that evolved from organic structures that existed\n  perhaps 3 billion years ago.\n  Also contained in rocks once molten are radioactive elements whose\n  isotopes provide Earth scientists with an atomic clock. Within these\n  rocks, \u201cparent\u201d isotopes decay at a predictable rate to form\n  \u201cdaughter\u201d isotopes. By determining the relative amounts of parent and\n  daughter isotopes, the age of these rocks can be calculated.\n  Thus, the results of studies of rock layers (stratigraphy), and of\n  fossils (paleontology), coupled with the ages of certain rocks as\n  measured by atomic clocks (geochronology), attest to a very old Earth!\n[Illustration: _Figure 6.\u2014Generalized paleogeographic map of the United\nStates in Late Cretaceous time (65 to 80 million years ago), when most\nof the Great Plains was beneath the sea._]\n[Illustration: _Figure 7.\u2014Structural setting of the Great Plains.\nWilliston basin and Anadarko basin are separated by a midcontinental\narch._]\n[Illustration: Table 1.\u2014Generalized chart of rocks of the Great Plains]\n   Geologic age        Missouri        High Plains\u2014Plains         Pecos\n    Millions of       Plateau\u2014Black      Border\u2014Colorado      Valley\u2014Edwards\n     years ago            Hills              Piedmont         Plateau\u2014Central\n  Quaternary\n     Pleistocene  Glacial deposits,   Alluvium, sand       Piedmont, terrace,\n                    alluvium, and       dunes, and loess     and bolson\n                2 erosional surface\n  Tertiary\n     Pliocene     EROSION\n                5 Flaxville Gravel    Ogallala formation\n     Miocene      Arikaree Formation  Arikaree Formation\n            22-24 erosional surface\n     Oligocene    White River Group   White River Group    Mostly missing\n            37-38 erosional surface\n     Eocene       Wasatch and Golden\n                    Valley Formations\n     Paleocene    Fort Union          Denver, Poison\n                    Formation           Canyon, and Raton\n  Cretaceous      Hell Creek and      Vermejo and Laramie\n                    Lance Formations    Formations\n                  Fox Hills Sandstone Trinidad and Fox\n                  Shales, sandstones, and limestones\n                    deposited in Late Cretaceous sea\n                  Dakota Sandstone    Dakota Sandstone\n  Jurassic        Sundance            Morrison Formation   Jurassic rocks not\n                    Unkpapa Sandstone\n  Triassic        Dominantly red rocks\n  PALEOZOIC       Paleozoic rocks, undivided\n  PRECAMBRIAN     Precambrian rocks, undivided\nAs the mountains continued to rise, the eroding streams cut into the old\ncore rocks of the mountains, and that debris too was carried to the\nflanks and onto the adjoining plains. The mountainous belt continued to\nrise intermittently, and volcanoes began to appear about 50 million\nyears ago. Together, the mountains and volcanoes provided huge\nquantities of sediment, which the streams transported to the plains and\ndeposited. The areas nearest the mountains were covered by sediments of\nLate Cretaceous and Paleocene age (table 1)\u2014the Poison Canyon Formation\nto the south, the Dawson and Denver Formations in the Denver area, and\nthe Fort Union Formation to the north (fig. 8). Vegetation continued to\nflourish, especially in the northern part of the Great Plains, and was\nburied to form the thick lignite and subbituminous coal beds of the Fort\nUnion Formation (fig. 9). The earliest mammals, most of whose remains\ncome from the Paleocene Fort Union Formation, have few modern survivors.\nBeginning about 45 million years ago, in Eocene time, there was a long\nperiod of stability lasting perhaps 10 million years, when there was\nlittle uplift of the mountains and, therefore, little deposition on the\nplains. A widespread and strongly developed soil formed over much of the\nGreat Plains during this period of stability. With renewed uplift and\nvolcanism in the mountains at the end of this period, great quantities\nof sediment again were carried to the plains by streams and spread over\nthe northern Great Plains and southeastward to the arch or divide\nseparating the Williston and Anadarko basins (fig. 8). Those sediments\nform the White River Group, in which the South Dakota Badlands are\ncarved. In addition to the _Titanotheres_, huge beasts with large, long\nhorns on their snouts who lived only during the Oligocene (37 to 22\nmillion years ago), vast herds of camels, rhinoceroses, horses, and\ntapirs\u2014animals now found native only on other continents\u2014grazed those\nOligocene semiarid grassland plains.\n[Illustration: _Figure 8.\u2014Progressive southeastward expansion of areas\ncovered by Paleocene, Oligocene, and Miocene-Pliocene sedimentary\ndeposits._]\n  Powder River basin\n  Denver basin\n  Raton basin\n  PLAINS\n    Margin of Oligocene deposition\n    Margin of Miocene-Pliocene deposition\n[Illustration: _Figure 9.\u2014Big Horn coal strip mine in Fort Union\nFormation at Acme, Wyo. Photograph by F. W. Osterwald, U.S. Geological\nSurvey._]\nSometime between 20 and 30 million years ago the streams began\ndepositing sand and gravel beyond the divide, and, for another 10\nmillion years or more, stream sediments of the Arikaree and Ogallala\nFormations spread over the entire Great Plains from Canada to Texas,\nexcept where mountainous areas such as the Black Hills stood above the\nplains. Between 5 and 10 million years ago, then, the entire Great\nPlains was an eastward-sloping depositional plain surmounted only by a\nfew mountain masses. Horses, camels, rhinoceroses, and a strange\nhorselike creature with clawed feet (called _Moropus_) lived on this\nplain.\nSometime between 5 and 10 million years ago, however, a great change\ntook place, apparently as a result of regional uplift of the entire\nwestern part of the continent. While before, the streams had been\ndepositing sediment on the plains for more than 60 million years,\nbuilding up a huge thickness of sedimentary rock layers, now the streams\nwere forced to cut down into and excavate the sediments they had\nformerly deposited. As uplift continued\u2014and it may still be\ncontinuing\u2014the streams cut deeper and deeper into the layered stack and\ndeveloped tributary systems that excavated broad areas. High divides\nwere left between streams in some places, and broad plateaus were formed\nand remain in other places. The great central area was essentially\nuntouched by erosion and remained standing above the dissected areas\nsurrounding it as the escarpment-rimmed plateau that is the High Plains.\nThis downcutting and excavation by streams, then, which began between 5\nand 10 million years ago, roughed out the landscape of the Great Plains\nand created the sections we call the Missouri Plateau, the Colorado\nPiedmont, the Pecos Valley, the Edwards Plateau, and the Plains Border\nSection. Nearly all the individual landforms that now attract the eye\nhave been created by geologic processes during the last 2 million years.\nIt truly is a young landscape.\n      LANDFORMS OF TODAY\u2014The surface features of the Great Plains\nThe mountainous sections of the Great Plains were formed long before the\nremaining areas were outlined by erosion. Uplift of the Black Hills and\nthe Central Texas Uplift began as the continental interior was raised\nand the last Cretaceous sea was displaced, 65 to 70 million years ago.\nThey stood well above the surrounding plains long before any sediments\nfrom the distant Rocky Mountains began to accumulate at their bases. In\nsouthern Colorado and northern New Mexico, molten rock invaded the\nsedimentary layers between 22 and 26 million years ago. The Spanish\nPeaks were formed at this time from hot magma that domed up the surface\nlayers but did not break through; the magma has since cooled and\nsolidified and has been exposed by erosion. Elsewhere the magma reached\nthe surface, forming volcanoes, fissures, and basalt flows. A great\nthickness of basalt flows accumulated at Raton Mesa and Mesa de Maya\nbetween 8 and 2 million years ago. Volcanism has continued\nintermittently, and the huge cinder cone of Capulin Mountain was created\nby explosive eruption only 10,000 to 4,000 years ago. Most of these\nvolcanic masses were formed before major downcutting by the streams\nbegan. Other igneous intrusions and volcanic areas in the northern Great\nPlains similarly were formed before the streams were incised.\nTo examine the origin of the present landscape and of the landforms\ntypical of the various sections of the Great Plains, it is convenient to\nbegin with the Black Hills, the Central Texas Uplift, and the Raton\nsection simply because they were formed first\u2014they existed before the\nother sections were outlined.\nThe Black Hills is a huge, elliptically domed area in northwestern South\nDakota and northeastern Wyoming, about 125 miles long and 65 miles wide\n(fig. 10). Rapid City, S. Dak., is on the Missouri Plateau at the east\nedge of the Black Hills. Uplift caused erosion to remove the overlying\ncover of marine sedimentary rocks and expose the granite and metamorphic\nrocks that form the core of the dome. The peaks of the central part of\nthe Black Hills presently are 3,000 to 4,000 feet above the surrounding\nplains. Harney Peak, with an altitude of 7,242 feet, is the highest\npoint in South Dakota. These central spires and peaks all are carved\nfrom granite and other igneous and metamorphic rocks that form the core\nof the uplift. The heads of four of our great Presidents are sculpted\nfrom this granite at Mount Rushmore National Memorial. Joints in the\nrocks have controlled weathering processes that influenced the final\nshaping of many of these landforms. Closely spaced joints have produced\nthe spires of the Needles area, and widely spaced joints have produced\nthe rounded forms of granite that are seen near Sylvan Lake (fig. 11).\nMarine sedimentary rocks surrounding the old core rocks form\nwell-defined belts. Lying against the old core rocks and completely\nsurrounding them are Paleozoic limestones that form the Limestone\nPlateau (fig. 10). These tilted layers have steep erosional scarps\nfacing the central part of the Black Hills. Wind Cave and Jewel Cave\nwere produced by ground water dissolving these limestones along joints.\nThese caves are sufficiently impressive to be designated as a national\npark and a national monument, respectively. Encircling the Limestone\nPlateau is a continuous valley cut in soft Triassic shale. This valley\nhas been called \u201cthe Racetrack,\u201d because of its continuity, and the Red\nValley, because of its color. Surrounding the Red Valley is an outer\nhogback ridge formed by the tilted layers of the Dakota Sandstone, which\nare quite hard and resistant to erosion. Streams that flow from the\ncentral part of the Black Hills pass through the Dakota hogback in\nnarrow gaps.\n[Illustration: _Figure 10.\u2014Diagram of the Black Hills uplift by A. N.\nStrahler (Strahler and Strahler, 1978). Used by permission._]\n  Dakota Sandstone hogback\n  Limestone plateau\n  Belle Fourche River\n  Spearfish\n  Bear Butte\n  Sundance\n  Red Valley\n  Rapid City\n  Red Valley\n  Hot Springs\n  Cheyenne River\n  Edgemont\n  Mt. Rushmore National Monument\n  Jewel Cave National Monument\n  Wind Cave National Park\n[Illustration: _Figure 11.\u2014Jointed granite rounded by weathering at\nSylvan Lake, in the central part of the Black Hills, S. Dak._]\nThe Black Hills, then, is an uplifted area that has been carved deeply\nbut differentially by streams to produce its major outlines. Those\noutlines have been modified mainly by weathering of the ancient core\nrocks and solution of the limestone of the Limestone Plateau.\nThe domed rocks of the Central Texas Uplift form a topography different\nfrom that of the Black Hills. Erosion of a broad, uplifted dome here has\nexposed a core of old granites, gneisses, and schists, as in the Black\nHills, but in the Central Texas Uplift, erosion has produced a\ntopographic basin, rather than high peaks and spires, on the old rocks\nof the central area. A low plateau surface dissected into rounded ridges\nand narrow valleys slopes gently eastward from the edge of the central\narea to an escarpment at the Balcones fault zone, which determines the\neastern edge of the Great Plains here. Northwest of the central basin\nthe Colorado River flows in a broad lowland about 100 miles long, but\nthe northern edge of the uplift, forming a divide between the Brazos and\nthe Colorado Rivers, is a series of mesas formed of more resistant\nsandstone and limestone.\nThe cutting action of streams, modified or controlled in part by\ndifferences in hardness of the rock layers, has been responsible for the\nlandforms of the Central Texas Uplift. Weathering of the old core rocks\nhas softened them sufficiently to permit deeper erosion of the central\narea, and solution of limestone by ground water has formed such features\nas Longhorn Caverns, 11 miles southwest of Burnet, Tex.\nVolcanism characterizes the Raton section. The volcanic rocks, which\nform peaks, mesas, and cones, have armored the older sedimentary rocks\nand protected them from the erosion that has cut deeply into the\nadjoining Colorado Piedmont to the north and Pecos Valley to the south.\nThe south edge of the Raton section is marked by a spectacular\nsouth-facing escarpment cut on the nearly flat-lying Dakota Sandstone.\nThis escarpment is the Canadian escarpment, north of the Canadian River.\nNorthward for about 100 miles, the landscape is that of a nearly flat\nplateau cut on Cretaceous rock surmounted here and there by young\nvolcanic vents, cones, and lava fields. Capulin Mountain is a cinder\ncone only 10,000 to 4,000 years old (fig. 12). Near the New\nMexico-Colorado border, huge piles of lava were erupted 8 to 2 million\nyears ago onto an older, higher surface on top of either the Ogallala\nFormation of Miocene age or the Poison Canyon Formation of Paleocene\nage. (See table 1.) These lava flows formed a resistant cap, which\nprotected the underlying rock from erosion while all the surrounding\nrock washed away. The result is the high, flat-topped mesas, such as\nRaton Mesa and Mesa de Maya (fig. 13), that now form the divide between\nthe Arkansas and Canadian Rivers. At Fishers Peak, on the west end of\nRaton Mesa, about 800 feet of basalt flows rest on the Poison Canyon\nFormation at about 8,800 feet in altitude. Farther east, on Mesa de\nMaya, about 400 feet of basalt flows overlie the Ogallala Formation at\naltitudes ranging from about 6,500 feet at the west end to about 5,200\nfeet at the east end, some 35 miles to the east. The Ogallala here rests\non Cretaceous Dakota Sandstone and Purgatoire Formation, for the Poison\nCanyon Formation was removed by erosion along the crest of a local\nuplift before the Ogallala was deposited.\n[Illustration: _Figure 12.\u2014Capulin Mountain National Monument in\nnortheastern New Mexico. This huge cinder cone, which erupted between\n4,000 and 10,000 years ago, rises more than 1,000 feet above its base.\nPhotograph by R. D. Miller, U.S. Geological Survey._]\nEast of the belt of upturned sedimentary layers that form the hogback\nridges at the front of the Rocky Mountains, the layered rocks in the\nRaton Basin have been intruded in many places by igneous bodies, the two\nlargest of which form the Spanish Peaks (fig. 14), southwest of\nWalsenburg, Colo. These two peaks are formed by igneous bodies that were\nintruded 26 to 22 million years ago and have since been exposed by\nremoval of the overlying sedimentary rock layers by erosion. Radiating\nfrom the Spanish Peaks are hundreds of dikes, nearly vertical slabs of\nigneous rock that filled fractures radiating from the centers of\nintrusion. Erosion of the sedimentary layers has left many of these\ndikes as conspicuous vertical walls of igneous rock that project high\nabove the surrounding land surface. Some of these dikes north of\nTrinidad, Colo. extend eastward for about 25 miles, almost to the\nPurgatoire River.\n[Illustration: _Figure 13.\u2014Lava-capped Mesa de Maya, east of Trinidad,\nColo. Spanish Peaks in left distance. Mesa rises about 1,000 feet above\nsurrounding area. Photograph by R. B. Taylor, U.S. Geological Survey._]\nThe northern boundary of the Raton section is placed somewhat\nindefinitely at the northern limit of the area injected by igneous\ndikes. The eastern boundary of the Raton section is at the eastern\nmargin of the lavas of Mesa de Maya and adjoining mesas, where\nlava-capped outliers of Ogallala Formation are separated from the\nOgallala of the High Plains only by the canyon of Carrizo Creek.\nAt the end of Ogallala deposition, some 5 million years ago, the Great\nPlains, with the exception of the uplifted and the volcanic areas, was a\nvast, gently sloping plain that extended from the mountain front\neastward to beyond the present Missouri River in some places. Regional\nuplift of the western part of the continent forced the streams to cut\ndownward; land near the mountains was stripped away by the Missouri, the\nPlatte, the Arkansas, and the Pecos Rivers, and the eastern border of\nthe plains was gnawed away by lesser streams. A large central area of\nthe plain is preserved, however, essentially untouched and unaffected by\nthe streams, as a little-modified remnant of the depositional surface of\n5 million years ago. This Ogallala-capped preserved remnant of that\nupraised surface is the High Plains. In only one place does that old\nsurface still extend to the mountains\u2014at the so-called \u201cGangplank\u201d west\nof Cheyenne, Wyo. (fig. 15). In places, as at Scotts Bluff National\nMonument, Nebr. (fig. 16), small fragments of this surface have been\nisolated from the High Plains by erosion and now stand above the\nsurrounding area as buttes.\n[Illustration: _Figure 14.\u2014Spanish Peaks, southwest of Walsenburg, Colo.\nIgneous rocks and many radiating dikes exposed by erosion. Photograph by\nR. B. Taylor, U.S. Geological Survey._]\n[Illustration: _Figure 15.\u2014Looking east toward Cheyenne at \u201cthe\nGangplank.\u201d Interstate Highway 80 and the Union Pacific Railroad follow\nthe Gangplank from the High Plains in the distance onto the Precambrian\nrocks (older than 570 m.y.) of the Laramie Mountains in the foreground.\nPhotograph by R. D. Miller, U.S. Geological Survey._]\n[Illustration: _Figure 16.\u2014Aerial view of Scotts Bluff National\nMonument, Nebr. Buttes on the south side of the valley of the North\nPlatte River isolated by erosion from High Plains in the background.\nHighest butte stands about 800 feet above valley floor._]\nThe High Plains extends southward from the Pine Ridge escarpment, near\nthe South Dakota-Nebraska border (fig. 3), to the Edwards Plateau in\nTexas. The Platte, the Arkansas, and the Canadian Rivers have cut\nthrough the High Plains. That part of the High Plains south of the\nCanadian River is called the Southern High Plains, or the Llano Estacado\n(staked plain). The origin of this name is uncertain, but it has been\nsuggested that the term Llano Estacado was applied by early travelers\nbecause this part of the High Plains is so nearly flat and devoid of\nlandmarks that it was necessary for those pioneers to set lines of\nstakes to permit them to retrace their routes.\nThe Llano Estacado is bounded on the west by the Mescalero escarpment\n(fig. 4) and on the east by the Caprock escarpment. The southern margin\nwith the Edwards Plateau is less well defined, but King Mountain, north\nof McCamey, Tex., is a scarp-bounded southern promontory of the High\nPlains. The remarkably flat surface of the Llano Estacado is abundantly\npitted by sinks and depressions in the surface of the Ogallala\nFormation; these were formed by solution of the limestone by rainwater\nand blowing away or deflation by wind of the remaining insoluble\nparticles. Many of these solution-deflation depressions are aligned like\nstrings of beads, suggesting that their location is controlled by some\nkind of underlying structure, such as intersections of joints in the\nOgallala Formation.\nThe solution-deflation depressions are less abundant north of the\nCanadian River, but occur on the High Plains surface northward to the\nArkansas River and along the eastern part of the High Plains north of\nthe Arkansas to the South Fork of the Republican River.\nCovering much of the northern High Plains, however, are sand dunes and\nwindblown silt deposits (loess) that mantle the Ogallala Formation and\nconceal any solution-deflation depressions that might have formed. The\nNebraska Sand Hills (fig. 17), the largest area of sand dunes in the\nwestern hemisphere, is a huge area of stabilized sand dunes that extends\nfrom the White River in South Dakota southward beyond the Platte River\nalmost to the Republican River in western Nebraska but only to the Loup\nRiver in the northeast part of the High Plains (fig. 18). Loess covers\nthe western High Plains southward from the sand dunes almost to the\nArkansas River, and to the South Fork of the Republican in the eastern\npart. This extensive cover of loess has created a fertile land that\nmakes it an important part of America\u2019s wheatlands (fig. 19).\n[Illustration: _Figure 17.\u2014Aerial view, looking northwest, of the\nNebraska Sand Hills west of Ashby, Nebr._]\nOther, smaller areas of sand dunes lie south of the Arkansas River\nvalley. The only large areas of sand dunes on the Llano Estacado, or\nSouthern High Plains, are along the southwestern margin near Monahans,\nsouthwest of Odessa, Tex.\nOil and gas are present in the Paleozoic rocks that underlie the High\nPlains at depth. Gas fields are ubiquitous in much of the eastern part\nof the High Plains between the Arkansas and Canadian Rivers. Just south\nof the Canadian River, at the northeast corner of the Southern High\nPlains, a huge oil and gas field has been developed near Pampa, Tex. Oil\nand gas fields also are abundant in the southwestern part of the\nSouthern High Plains, south of Littlefield, Tex.\n[Illustration: _Figure 18.\u2014The Sand Hills region of Nebraska. Arrows\nshow inferred direction of dune-forming winds. Map from Wright (1970),\nused by permission._]\n  WYOMING\n    Badlands National Monument\n    Missouri River Valley\n  JAMES RIVER LOBE\n  MINNESOTA\n  IOWA\n  SOUTH DAKOTA\n  NEBRASKA\n    Rosebud\n    Valentine\n  DES MOINES LOBE\n  NEBRASKA\n    Ashby\n  SANDHILLS\n    Platte River Valley\n  IOWA\n  MISSOURI\n  NEBRASKA\n  KANSAS\n  COLORADO\n    Muscotah\n  TOPEKA\n  EXPLANATION\n    Transverse dunes\n    Longitudinal dunes\n    Wind-blown sand\n    Loess thickness (in feet)\n[Illustration: _Figure 19.\u2014Little-modified loess plain in southeastern\nNebraska. Photograph by Judy Miller._]\nThe surface of the High Plains, then, has been little modified by\nstreams since the end of Ogallala deposition. It has been raised by\nregional uplift and pitted by solution and deflation, and large parts of\nit have been covered by wind-blown sand and silt. It has been drilled\nfor oil and gas and extensively farmed, but it is still a geological\nrarity\u2014a preserved land surface that is 5 million years old.\nBeginning about 5 million years ago, regional uplift of the western part\nof the continent forced streams, which for 30 million years had been\ndepositing sediment nearly continuously on the Great Plains, to change\ntheir behavior and begin to cut into the layers of sediment they so long\nhad been depositing. The predecessor of the Missouri River ate headward\ninto the northern Great Plains and developed a tributary system that\nexcavated deeply into the accumulated deposits near the mountain front\nand carried away huge volumes of sediment from the Great Plains to\nHudson Bay. By 2 million years ago, the streams had cut downward to\nwithin a few hundred feet of their present level. This region that has\nbeen so thoroughly dissected by the Missouri River and its tributaries\nis called the Missouri Plateau.\nAbout 2 million years ago, after much downcutting had already taken\nplace and river channels had been firmly established, great ice sheets\nadvanced southward from Canada into the United States. (See figure 2.)\nThese continental glaciers formed, advanced, and retreated several times\nduring the last 2 million years. At the north and east margins of the\nMissouri Plateau they lapped onto a high area, leaving a mantle of\nglacial deposits covering the bedrock surface and forcing streams to\nadopt new courses along the margin of ice. The part of the Missouri\nPlateau covered by the continental glaciers now is referred to as the\nGlaciated Missouri Plateau. South of the part once covered by ice is the\nUnglaciated Missouri Plateau.\n    Preglacial Drainage\nBefore the initial advance of the continental ice sheets, the Missouri\nRiver flowed northeastward into Canada and to Hudson Bay. Its major\ntributaries, the Yellowstone and the Little Missouri joined the Missouri\nin northwestern North Dakota. The east-flowing Knife, Heart, and\nCannonball Rivers in North Dakota also joined a stream that flowed\nnorthward to Hudson Bay.\n    Glaciated Missouri Plateau\nWhen the continental ice sheets spread southward into northern Montana\nand the Dakotas, a few isolated areas in Montana stood above the\nsurrounding plain. These are mostly areas that were uplifted by the\nintrusion of igneous bodies long before the streams began downcutting\nand carving the land. The northernmost of these isolated mountains, the\nSweetgrass Hills, were surrounded by ice and became nunataks, or islands\nof land, in the sea of advancing ice, which pushed southward up against\nthe Highwood Mountains, near Great Falls, the Bearpaws south of Havre,\nand the Little Rockies to the east.\nMuch of the northern part of Montana is a plain of little relief that is\nthe surface of a nearly continuous cover of glacial deposits, generally\nless than 50 feet thick. This plain has been incised by the east-flowing\npostglacial Teton, Marias, and Milk Rivers.\nIn North Dakota, a high area on the east side of the Williston basin\nacted as a barrier to the advance of the ice, most of which was diverted\nsoutheastward. The margin of the ice sheet, however, lapped onto the\nbedrock high, where it stagnated. Earlier advances moved farthest south;\nthe later advances stopped north of the present course of the Missouri\nRiver\u2014their maximum position marked by ridges of unsorted, glacially\ntransported rock debris (till) called terminal moraines. North of the\nterminal moraines is a distinctive landscape characterized by a rolling,\nhummocky, or hilly surface with thousands of closed depressions between\nthe hills and hummocks, most of them occupied by lakes. This is the\ndeposit left by the stagnant or dead ice, and it is called dead-ice\nmoraine. The rolling upland in North Dakota that is covered by dead-ice\nmoraine and ridges of terminal moraines from the last glacial advances\nis called the Coteau du Missouri (fig. 20). A gently sloping scarp,\nseveral hundred feet high and mostly covered by glacial deposits\n(referred to collectively as drift), separates the Coteau du Missouri\nfrom the lower, nearly flat, drift-covered plains of the Central Lowland\nto the east. This escarpment, which is called the Missouri escarpment,\nis virtually continuous across the State of North Dakota southward into\nSouth Dakota. The base of the Missouri escarpment is the eastern\nboundary of the Great Plains in these northern states.\n[Illustration: _Figure 20.\u2014Ground moraine on the Coteau du Missouri,\nnorthwestern North Dakota. Photograph by R. M. Lindvall, U. S.\nGeological Survey._]\nThe advancing ice front blocked one after another of the\nnorthward-flowing streams of the region, diverting them eastward along\nthe ice front. Shonkin Sag, north of the Highwood Mountains near Great\nFalls, Mont., is an abandoned diversion channel of the Missouri River,\noccupied when the ice front stood close to the north slopes of the\nHighwoods. Much of the present course of the Missouri River from Great\nFalls, Mont., to Kansas City, Mo., was established as an ice-marginal\nchannel, and the east-flowing part of the Little Missouri River in North\nDakota was formed in the same way. These valleys were cut during the\nlast 2 million years.\nThe north-flowing part of the Little Missouri River and the east-flowing\ncourses of the Knife, Heart, and Cannonball Rivers in North Dakota are\nfor the most part older, preglacial courses. The Little Missouri was\ndammed by the ice, and its waters impounded to form a huge lake during\nthe maximum stand of the ice, but the deposits of this glacial lake are\nfew and make no imprint on the landscape.\nThe valley of the east-flowing, glacially diverted part of the Little\nMissouri River, however, is markedly different from that of the\nnorth-flowing preglacial river. It is much narrower and has steeper\nwalls than the old valley. Because it is younger, it is little modified,\nexcept by huge landslides that have affected both walls of the valley.\nTremendous rotated landslide blocks in the North Unit of Theodore\nRoosevelt National Memorial Park are some of the best examples of the\nslump type of landslide to be seen anywhere (fig. 21).\nMelting ice at the front of the glaciers provided large volumes of\nmeltwater that flowed across the till-mantled surface in front of the\nglacier as it melted back toward Canada. This meltwater took many\ncourses to join the glacially diverted Missouri River, and these sinuous\nmeltwater channels wind across the dead-ice moraine and the older, less\nhummocky ground moraine between the Coteau du Missouri and the Missouri\nRiver. Locally the sediment carried by the meltwater streams was banked\nagainst a wall of ice to form a small hill of stratified drift that is\ncalled a kame. Streams flowing in tunnels beneath the ice formed\nsinuous, ridgelike deposits called eskers, and in places the meltwater\ndeposits form broad flat areas called outwash plains.\n[Illustration: _Figure 21.\u2014Rotated slump blocks in huge landslide, North\nUnit of Theodore Roosevelt National Memorial Park, N. Dak. Note that\nlayering of Fort Union Formation in cliffs on skyline, where landslide\noriginated, is horizontal._]\nThis rather limited variety of landforms, then, characterizes the\nlandscape of the Glaciated Missouri Plateau. The landforms themselves\nare testimony to their glacial origin and to the great advances of the\ncontinental ice sheets. This is a stream-carved terrain that has been\nmodified by continental glaciers and almost completely covered by a\nthick blanket of glacially transported and deposited rock debris,\nlocally hundreds of feet thick. Subsequent stream action has not altered\nthe landscape greatly.\n    Unglaciated Missouri Plateau\nBeyond the limits reached by the ice of the continental glaciers, the\nUnglaciated Missouri Plateau displays the greatest variety of landforms\nof any section of the Great Plains. In western Montana, many small\nmountain masses rise above the general level of the plateau, including\nthe Highwood, Bearpaw, and Little Rocky Mountains near the margin of the\nglaciated area, and the Judith, Big Snowy, Big Belt, Little Belt,\nCastle, and Crazy Mountains farther south (fig. 22). Many of these, such\nas the Crazy, Castle, Judith, and Big Snowy Mountains, are areas\nuplifted by large, deeply rooted, intrusive igneous bodies called\nstocks, which have been exposed by subsequent erosion of the arched\noverlying sedimentary rock layers. Some, such as the Highwood and\nBearpaw Mountains, are predominantly piles of lava flows, although in\nthe Bearpaws the related intrusive bodies of igneous rock form a part of\nthe mountains. The Big and Little Belt Mountains were formed by\nmushroom-shaped intrusive igneous bodies called laccoliths, which have\nspread out and domed between layers of sedimentary rocks. A number of\nigneous bodies also intrude the rocks of the Missouri Plateau around the\nperiphery of the Black Hills. Devils Tower, the first feature to be\ndesignated a National Monument, is the best known of these igneous rock\nfeatures (fig. 23).\n[Illustration: _Figure 22.\u2014The Highwood Mountains seen from the Little\nBelt Mountains, Mont. Photograph by I. J. Witkind, U. S. Geological\nSurvey._]\nThe uplift and volcanism that formed these mountains took place before\nthe streams began to cut downward and segment the Great Plains. The\nmountains had been greatly dissected before the advent of the Great Ice\nAge, when alpine glaciers formed on the Castle and the Crazy Mountains\nand flowed down some of the stream-cut valleys. Alpine glacial features\nsuch as cirques, in the high parts of the mountains, and glacially\nmodified U-shaped valleys (fig. 24) are impressive evidence of this\nglaciation.\n[Illustration: _Figure 23.\u2014Devils Tower National Monument, Wyo. An\nigneous intrusive body exposed by erosion. Photograph by F. W.\nOsterwald, U. S. Geological Survey._]\nThe Missouri River and its tributaries\u2014the Sun, Smith, Judith,\nMusselshell, and Yellowstone Rivers in Montana and the Little Missouri\nRiver in North Dakota\u2014have cut down into the Missouri Plateau, cut broad\nupland surfaces at many levels, and established confined valleys with\nvalley floors flanked by terrace remnants of older floodplains. Locally,\nhigh buttes that are remnants of former interstream divides rise above\nthe uplands. Large lakes also were formed in most of these tributary\nvalleys because of damming by the continental ice sheets.\n[Illustration: _Figure 24.\u2014U-shaped, glaciated valley of Big Timber\nCreek, Crazy Mountains, Mont. Photograph by W. C. Alden, 1921, U. S.\nGeological Survey._]\nWest of the Black Hills, in Wyoming, the Tongue River and the Powder\nRiver have excavated the Powder River Basin and produced similar\nfeatures (fig. 25). The east-flowing tributaries of the Missouri\nRiver\u2014the Knife, Heart, and Cannonball Rivers in North Dakota and the\nGrand, Moreau, Belle Fourche, Cheyenne, Bad, and White Rivers in South\nDakota\u2014similarly have shaped the landscape.\nMost of these rivers flow in broad, old valleys, established more than 2\nmillion years ago, before the first advance of the continental ice\nsheets. Some of these valleys have been widened by recession of the\nvalley walls by badland development. Badlands are formed by the cutting\naction of rivulets and rills flowing down over a steeply sloping face of\nsoft, fine-grained material composed mainly of clay and silt. The\nintricate carving by thousands of small streams of water produces the\ndistinctive rounded and gullied terrain we call badlands. Badlands\nNational Monument in South Dakota (fig. 26) has been established in the\nremarkable badlands terrain cut into the White River Group along the\nnorth valley wall of the White River, and the South Unit of Theodore\nRoosevelt National Memorial Park is in the colorful badlands of the\nLittle Missouri River, formed on the Fort Union Formation (fig. 27).\nThe White River also has cut a steep scarp along its southern wall that\nis called the Pine Ridge escarpment. This escarpment defines the\nboundary between the Missouri Plateau and the High Plains here.\n[Illustration: _Figure 25.\u2014View northeast across the Deckers coal mine\nand the Tongue River in the Powder River Basin, southeastern Montana.\nTypical terrain of unglaciated Missouri Plateau. Small mesas with\ncliffed escarpments on capping layer of resistant sandstone, such as\nthose in the foreground, are common. Coal mine is about 1 mile across.\nPhotograph by R. B. Taylor, U. S. Geological Survey._]\nThe landscape of the Unglaciated Missouri Plateau has been determined\nlargely by the action of streams, but in some areas igneous intrusions\nand volcanoes have produced small mountain masses that interrupt the\nplain, and valley glaciers have modified the valleys in some of these\nmountains.\n[Illustration: _Figure 26.\u2014Badlands in Badlands National Monument, S.\nDak. Photograph by W. H. Raymond, III, U. S. Geological Survey._]\n[Illustration: _Figure 27.\u2014Badlands of the Little Missouri River in\nSouth Unit of Theodore Roosevelt National Memorial Park, N. Dak. View\nlooking northwest from Painted Canyon Overlook along Interstate Highway\n94, west of Belfield._]\n                         THE COLORADO PIEDMONT\nThe Colorado Piedmont lies at the eastern foot of the Rockies, (fig. 1)\nlargely between the South Platte River and the Arkansas River. The South\nPlatte on the north and the Arkansas River on the south, after leaving\nthe mountains, have excavated deeply into the Tertiary (65- to\n2-million-year-old) sedimentary rock layers of the Great Plains in\nColorado and removed great volumes of sediment. At Denver, the South\nPlatte River has cut downward 1,500 to 2,000 feet to its present level.\nThree well-formed terrace levels flank the river\u2019s floodplain, and\nremnants of a number of well-formed higher land surfaces are preserved\nbetween the river and the mountains. Along the western margin of the\nColorado Piedmont, the layers of older sedimentary rock have been\nsharply upturned by the rise of the mountains. The eroded edges of these\nupturned layers have been eroded differentially, so that the hard\nsandstone and limestone layers form conspicuous and continuous hogback\nridges (fig. 28). North of the South Platte River, near the Wyoming\nborder, a scarp that has been cut on the rocks of the High Plains marks\nthe northern boundary of the Colorado Piedmont. Pawnee Buttes (fig. 29)\nare two of many butte outliers of the High Plains rocks near that scarp,\nseparated from the High Plains by erosion as is Scotts Bluff, farther\nnorth in Nebraska. To the east, about 10 miles northwest of Limon,\nColo., Cedar Point forms a west-jutting prow of the High Plains.\nThe Arkansas River similarly has excavated much of the Tertiary piedmont\ndeposits and cut deeply into the older Cretaceous marine rocks between\nCanon City and the Kansas border. The upturned layers along the mountain\nfront, marked by hogback ridges and intervening valleys, continue nearly\nuninterrupted around the south end of the Front Range into the embayment\nin the mountains at Canon City. Skyline Drive, a scenic drive at Canon\nCity, follows the crest of the Dakota hogback for a short distance and\nprovides a fine panorama of the Canon City embayment.\n[Illustration: _Figure 28.\u2014Hogback ridges along the Front Range west of\nDenver, Colo. South Platte River emerges from the mountains and cuts\nthrough hogbacks in middle distance. Photograph courtesy of Eugene\nShearer, Intrasearch, Inc._]\nExtending eastward from the mountain front at Palmer Lake, a high divide\nseparates the drainage of the South Platte River from that of the\nArkansas River. The crest of the divide north of Colorado Springs is\ngenerally between 7,400 and 7,600 feet in altitude, but Interstate\nHighway 25 crosses it at about 7,350 feet, nearly 1,500 feet higher than\nColorado Springs and more than 2,000 feet higher than Denver. From the\ncrest of the divide to north of Castle Rock, resistant Oligocene Castle\nRock Conglomerate (which is equivalent to part of the White River Group\nof the High Plains) is preserved in many places and forms a protective\ncaprock on mesas and buttes. This picturesque part of the Colorado\nPiedmont looks quite different from the excavated valleys of the South\nPlatte and Arkansas Rivers.\nMuch of the terrain in the two river valleys has been smoothed by a\nnearly continuous mantle of windblown sand and silt. Northwesterly\nwinds, which frequently blow with near-hurricane velocities, have\nwhipped fine material from the floodplains of the streams and spread it\neastward and southeastward over much of the Colorado Piedmont.\nWell-formed dunes are not common, but alined gentle ridges of sand and\nsilt and abundant shallow blowout depressions inform us of the windblown\norigin of this cover.\n[Illustration: _Figure 29.\u2014Pawnee Buttes in northeastern Colorado.\nButtes isolated by erosion from High Plains in the background. Ogallala\nFormation caps top of Buttes. White River Group forms lower part. The\ntop of the highest butte is about 240 feet above the saddle between the\ntwo buttes. Photograph by R. D. Miller, U. S. Geological Survey._]\nIn the Colorado Piedmont, then, the erosional effects of streams are the\nmost conspicuous features of the landscape, but these are enhanced by\nthe steep tilting of the layered rocks along the western margin as a\nresult of earth movement and modified by the nearly ubiquitous products\nof wind action, which have softened the landscape with a widespread\ncover of windblown sand and silt.\nSouth of the land of volcanic rocks that is the Raton section, the Pecos\nRiver has cut a broad valley from the Sangre de Cristo Mountains, in New\nMexico, southward to the Rio Grande, and has removed the piedmont cover\nof Ogallala Formation and cut deeply into the underlying rocks. The\nOgallala Formation capping the High Plains to the east forms a rimrock\nat the top of the sharp Mescalero escarpment, which is the eastern\nboundary of the Pecos Valley. (See figure 4.) The western boundary of\nthe Pecos Valley is the eastern base of discontinuous mountain ranges.\nThe great thickness of Tertiary deposits that formed on the northern\nGreat Plains did not accumulate here, and the Pecos River has cut its\nvalley into the older marine sedimentary rocks. The rocks underlying the\nsurface of much of the Pecos Valley are upper Paleozoic limestones.\nThe soluble nature of limestone is responsible for some of the most\nspectacular features of the landscape in the Pecos Valley. For about 10\nmiles north and 50 miles south of Vaughn, N. Mex., collapsed solution\ncaverns in upper Paleozoic limestones have produced an unusual type of\ntopography called karst. Karst topography is typified by numerous\nclosely spaced sinks or closed depressions, some of which are very deep\nholes, caused by the collapse of the roof of a cave or solution cavity\ninto the underground void, leaving hills, spines, or hummocks at the top\nof the intervening walls or ribs separating the depressions.\nAlthough the karst in the vicinity of Vaughn is perhaps the most\nconspicuous solution phenomenon, sinks and caves are common throughout\nthe Pecos Valley. At Bottomless Lakes State Park east of Roswell, N.\nMex., seven lakes occupy large sinkholes caused by the solution of salt\nand gypsum in underlying rocks.\nThe most spectacular example of solution of limestone by ground water is\nCarlsbad Caverns, N. Mex., one of the most beautiful caves in the world.\nThis celebrated solution cavity is preserved in a national park.\nThe Pecos River along much of its present course flows in a\nvertical-walled canyon with limestone rims. The Canadian River, flowing\neastward from the Sangre de Cristo Mountains, has cut a deep canyon\nalong the northern part of the Pecos Valley section. The sharp rims of\nthe Dakota Sandstone at the Canadian escarpment, north of the Canadian\nRiver, form the northern boundary of the Pecos Valley section.\nThe sharp, northeast-trending broken flexure called the Border Hills\nthat is crossed by U. S. Highway 70-380 about 20 miles west of Roswell\nis a unique landform of the Pecos Valley. This markedly linear upfolded\n(anticlinal) structure forms a ridge more than 30 miles long and about\n200 feet high.\nAs in the Colorado Plateau, windblown sand and silt mantle the landscape\nin many places, but the greatest accumulations are along the base of the\nMescalero escarpment at the northeast and southeast corners of the Pecos\nValley section.\nEast of the Pecos River, in the southeast part of the Pecos Valley, the\nunderlying rocks have yielded much oil and potash. Oil fields are common\neast of Artesia and Carlsbad, and potash is mined east of Carlsbad.\nThe Pecos and Canadian Rivers and their tributaries have created the\ngeneral outline of the landscape of the Pecos Valley, but underground\nsolution of limestone by ground water and the collapse of roofs of these\ncavities have contributed much detail to the surface that characterizes\nthe Pecos Valley today.\nSouth of the Pecos Valley section, the Pecos River continues its journey\nto the Rio Grande in a steep-walled canyon cut 400 to 500 feet below the\nlevel of a plateau surface of Cretaceous limestone from which little has\nbeen stripped except a thin Tertiary cover of Ogallala Formation (fig.\n30). To the east, the plateau has been similarly incised by the Devils\nRiver and the West Nueces and Nueces Rivers. East of the Nueces to the\nescarpment formed by the Balcones fault zone, the southern part of the\nEdwards Plateau has been intricately dissected by the Frio, Sabinal,\nMedina, Guadalupe, and Pedernales Rivers and their tributary systems.\nSan Antonio and Austin, Tex., are located on the Coastal Plain at the\nedge of the Balcones fault zone.\n[Illustration: _Figure 30.\u2014Rio Grande and the flat-lying limestone\nlayers of the Edwards Plateau downstream from the mouth of the Pecos\nRiver. Mexico on the left side of picture. Photograph by V. L. Freeman,\nU. S. Geological Survey._]\nThe Pecos River, and to a lesser extent the Devils and Nueces Rivers,\nparticularly in their lower courses, have entrenched themselves deeply\nin the plateau in remarkable meandering courses of a type that is\nusually found only in broad, low-lying floodplains. These stream courses\nreflect the stream environment prior to regional uplift.\nSinkholes pit the relatively undissected limestone plateau surface in\nthe northeast part of the Edwards Plateau, and some underground solution\ncavities in the limestone are well-known caves, such as the Caverns of\nSonora, southwest of Sonora, Tex.\nOil and gas fields are widely developed in the northern part of the\nEdwards Plateau, but only cattle ranches are found in the bare southern\npart.\nAncient oceans deposited the limestones that now cap the Edwards\nPlateau; streams planed off the surface of the flat-lying limestone\nlayers and entrenched themselves in steep-walled valleys; and ground\nwater dissolved the limestone and created the solution cavities that are\nthe caves and sinks of the Edwards Plateau. Water has created this\nlandscape.\n                         PLAINS BORDER SECTION\nThe Missouri Plateau, the Colorado Piedmont, the Pecos Valley, and the\nEdwards Plateau all were outlined by streams that flowed from the\nmountains. On the eastern border of the Great Plains, however, headward\ncutting by streams that have their source areas in the High Plains has\ndissected a large area, mainly in Kansas. This Plains Border Section\ncomprises a number of east-trending river valleys\u2014of the Republican,\nSolomon, Saline, Smoky Hill, Arkansas, Medicine Lodge, Cimarron, and\nNorth Canadian Rivers\u2014and interstream divides, most of which are\nintricately dissected.\nNorth of the Arkansas River, the east-flowing Republican, Solomon,\nSaline, and Smoky Hill Rivers have incised themselves a few hundred feet\nbelow the Tertiary High Plains surface and have developed systems of\nclosely spaced tributary draws. The interstream divides are narrow, and\nthe tributary heads nearly meet at the divides. This intricately\ndissected part of the Plains Border section is called the Smoky Hills.\nSome isolated buttes of Cretaceous rocks left in the upper valley of the\nSmoky Hill River are called the Monument Rocks. A large area of rounded\nboulders exposed by erosion south of the Solomon River, southwest of\nMinneapolis, Kans., is called \u201cRock City.\u201d These boulders originated as\nresistant nodules (concretions) within the Cretaceous rocks that\ncontained them.\nSouth of the Arkansas River is a broad, nearly flat upland sometimes\nreferred to as the Great Bend Plains. The Medicine Lodge River has cut\nheadward into the southeastern part of the Great Bend Plains and created\na thoroughly dissected topography in Triassic red rocks that is locally\ncalled the Red Hills. In a few places, badlands have formed in the Red\nHills.\nSome large sinks or collapse depressions have formed because of solution\nof salt and gypsum at depth by ground water. Big and Little Basins, in\nClark County in south-central Kansas, were formed in this way.\nSand dunes have accumulated in places, especially near stream valleys.\nDunes are common, for example, along the north side of the North\nCanadian River.\nOil and gas fields are widely developed in the southeast part of the\nPlains Border section\u2014in the Smoky Hills, the Great Bend Plains, and the\nRed Hills.\nThe Plains Border section, like the Missouri Plateau, the Colorado\nPiedmont, and the Pecos Valley, is primarily a product of stream\ndissection. The differences in the outstanding landforms of the section\nare mainly the result of differences in the hardness of the eroded\nrocks.\nThe Great Plains, as we have seen, is many things. It contains thick\nlayers of rock that formed in oceans, and younger layers of rocks\ndeposited by streams. These rocks have been affected by earth movements\nand injected by hot molten rock, some of which reached the surface as\nvolcanic rock. The rocks have been carved by streams, dissolved by\nground water, partly covered by glaciers, and blown by winds. All of\nthese agents have played important roles in determining the landscape\nand the landforms of the Great Plains. But the streams were the master\nagent. They formed the great depositional plain that was to become the\nGreat Plains, and then began to destroy it\u2014leaving only the High Plains\nto remind us of what it was. Those long miles we travel across the High\nPlains are a journey through history\u2014geologic history.\nThis narrative history of geologic and biologic events in the Great\nPlains had its origin in a study intended to identify potential National\nNatural Landmarks in the Great Plains, commissioned by the National Park\nService. William A. Cobban, G. Edward Lewis, and Reuben J. Ross of the\nU. S. Geological Survey were collaborators in that study, and some of\ntheir contributions to the history of life on the Great Plains have been\nincorporated into this narrative, which was undertaken at the urging of\nWallace R. Hansen.\nThe photographic illustrations, other than those obtained from the film\nlibrary of the U. S. Geological Survey, were provided by the interest\nand effort of my friends and colleagues of the Geological\nSurvey\u2014including C. R. Dunrud, V. L. Freeman, C. D. Miller, R. D.\nMiller, F. W. Osterwald, R. L. Parker, W. H. Raymond, III, Kenneth\nShaver, and R. B. Taylor\u2014and by Eugene Shearer, Intrasearch, Inc.,\nDenver, Colo. Without their help this publication would not have been\npossible.\n                         SOME SOURCE REFERENCES\nAlden, W. C., 1932, Physiography and glacial geology of eastern Montana\n    and adjacent areas: U. S. Geological Survey Professional Paper 174,\nBluemle, J. P., 1977, The face of North Dakota\u2014the geologic story: North\n    Dakota Geological Survey Education Series 11, 73 p.\nColton, R. B., Lemke, R. W., and Lindvall, R. M., 1961, Glacial map of\n    Montana east of the Rocky Mountains: U. S. Geological Survey\n    Miscellaneous Geologic Investigations Map I-327.\nColton, R. B., Lemke, R. W., and Lindvall, R. M., 1963, Preliminary\n    glacial map of North Dakota: U. S. Geological Survey Miscellaneous\n    Geologic Investigations Map I-331.\nCurtis, B. F., ed., 1975, Cenozoic history of the southern Rocky\n    Mountains\u2014Papers deriving from a symposium presented at the Rocky\n    Mountain Section meeting of the Geological Society of America,\n    Boulder, Colorado, 1973: Geological Society of America Memoir 144,\nDarton, N. H., 1905, Preliminary report on the geology and underground\n    water resources of the central Great Plains: U. S. Geological Survey\n    Professional Paper 32, 433 p.\nFlint, R. F., 1955, Pleistocene geology of eastern South Dakota: U. S.\n    Geological Survey Professional Paper 262, 173 p.\nFrye, J. C., and Leonard, A. B., 1965, Quaternary of the southern Great\n    Plains, _in_ Wright, H. E., Jr., and Frey, D. G., eds., The\n    Quaternary of the United States\u2014A review volume for the 7th Congress\n    of the International Association for Quaternary Research: Princeton\n    University Press, p. 203-216.\nHoward, A. D., 1958, Drainage evolution in northeastern Montana and\n    northwestern North Dakota: Geological Society of America Bulletin,\nJohnson, R. B., 1961, Patterns and origin of radial dike swarms\n    associated with West Spanish Peak and Dike Mountain, south-central\n    Colorado: Geological Society of America Bulletin, v. 72, no. 4, p.\nJudson, S. S., Jr., 1950, Depressions of the northern portion of the\n    southern High Plains of eastern New Mexico: Geological Society of\n    America Bulletin, v. 61, no. 3, p. 253-274.\nKeech, C. F., and Bentall, Ray, 1971, Dunes on the plains\u2014The Sand Hills\n    region of Nebraska: Nebraska University Conservation and Survey\n    Division Resources Report 4, 18 p.\nLemke, R. W., Laird, W. M., Tipton, M. J., and Lindvall, R. M., 1965,\n    Quaternary geology of northern Great Plains, _in_ Wright, H. E.,\n    Jr., and Frey, D. G., eds., The Quaternary of the United States\u2014A\n    review volume for the 7th Congress of the International Association\n    for Quaternary Research: Princeton University Press, p. 15-27.\nMansfield, G. R., 1907, Glaciation in the Crazy Mountains of Montana:\n    Geological Society of America Bulletin, v. 19, p. 558-567.\nPettyjohn, W. A., 1966, Eocene paleosol in the northern Great Plains,\n    _in_ Geological Survey research 1966: U. S. Geological Survey\n    Professional Paper 550-C, p. C61-C65.\nRobinson, C. S., 1956, Geology of Devils Tower National Monument,\n    Wyoming: U. S. Geological Survey Bulletin 1021-I, p. 289-302.\nSmith, H. T. U., 1965, Dune morphology and chronology in central and\n    western Nebraska: Journal of Geology, v. 73, no. 4, p. 557-578.\nStormer, J. C., Jr., 1972, Ages and nature of volcanic activity on the\n    southern High Plains, New Mexico and Colorado: Geological Society of\nStrahler, A. N., and Strahler, A. H., 1978, Modern physical geography:\n    New York, John Wiley & Sons, 502 p.\nThornbury, W. D., 1965, Regional geomorphology of the United States: New\n    York, John Wiley, 609 p.\nWright, H. E., Jr., 1970, Vegetational history of the Central Plains,\n    _in_ Pleistocene and recent environments of the central Great\n    Plains: Kansas University Department of Geology Special Publication\n            [Italic page numbers indicate major references]\n  Page\n  Theodore Roosevelt National Memorial Park                        35, 40\n  [Illustration: U. S. DEPARTMENT OF THE INTERIOR \u2022 March 3, 1849]\n--Retained publication information from the printed edition: this eBook\n  is public-domain in the country of publication.\n--In the text versions only, text in italics is delimited by\n  _underscores_.\nEnd of the Project Gutenberg EBook of The Geologic Story of the Great Plains, by \nDonald E. 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{"language": "eng", "scanningcenter": "capitolhill", "contributor": "The Library of Congress", "date": "1946", "subject": ["Torpedoes", "Acoustic emission", "Underwater acoustics", "Fire control (Naval gunnery)", "Naval research", "Torpedoes -- Automatic control", "Naval research -- United States"], "title": "Acoustic torpedoes", "creator": ["Albers, Vernon Martin, 1902-", "United States. Office of Scientific Research and Development. National Defense Research Committee, issuing body"], "lccn": "2015460884", "collection": ["library_of_congress", "americana"], "shiptracking": "ST005578", "call_number": "18881370", "identifier_bib": "00434111821", "boxid": "00434111821", "volume": "22", "possible-copyright-status": "The Library of Congress is unaware of any copyright restrictions for this item.", "description": ["Title on half-title page: Summary technical report of the National Defense Research Committee", "\"Manuscript and illustrations for this volume were prepared for publication by the Summary Reports Group of the Columbia University Division of War Research under contract OEMsr-1131 with the Office of Scientific Research and Development. This volume was printed and bound by the Columbia University Press\"--Unnumbered page ii", "In a set of declassified documents held as a collection by the Library of Congress", "LC Science, Business & Technology copy no. 238", "\"Copy no. 136.\"", "Includes bibliographical references (pages 163-166)", "Introduction / by W.V. Houston -- Echo-ranging torpedo control systems / by Vernon M. Albers", "xi, 172 pages : 28 cm"], "mediatype": "texts", "repub_state": "4", "page-progression": "lr", "publicdate": "2016-04-13 14:50:41", "updatedate": "2016-04-13 15:55:37", "updater": "associate-mike-saelee@archive.org", "identifier": "acoustictorpedoe22albe", "uploader": "associate-mike-saelee@archive.org", "addeddate": "2016-04-13 15:55:39", "scanner": "scribe3.capitolhill.archive.org", "operator": "associate-mike-saelee@archive.org", "imagecount": "194", "scandate": "20160506143116", "ppi": "300", "foldoutcount": "0", "identifier-access": "http://archive.org/details/acoustictorpedoe22albe", "identifier-ark": "ark:/13960/t1qg3cp1j", "scanfee": "100", "invoice": "1263", "curation": "[curator]associate-annie-coates@archive.org[/curator][date]20160510111943[/date][state]approved[/state][comment]199[/comment]", "sponsordate": "20160531", "backup_location": "ia906105_26", "fadgi": "true", "republisher_operator": "associate-mike-saelee@archive.org", "republisher_date": "20160509144052", "republisher_time": "643", "external-identifier": "urn:oclc:record:1038747267", "publisher": "Washington, D.C. : National Defense Research Committee", "oclc-id": "19119285", "associated-names": "Albers, Vernon Martin, 1902-; United States. Office of Scientific Research and Development. National Defense Research Committee, issuing body", "ocr_module_version": "0.0.21", "ocr_converted": "abbyy-to-hocr 1.1.37", "page_number_confidence": "100", "page_number_module_version": "1.0.3", "creation_year": 1946, "content": "/Return  To \nLibrary  oi  Congress \n-ssa*ss\u00abjE0 \nof \nn SEP  7 iseo \nu B^ut7^r^UgU8t  1960 \nF CONORE ss \nLCJIEGULATION:  BEFORE  SERVICING \nOR  REPRODUCING  ANY  PART  OF  THIS \nDOCUMENT,  ALL  CLASSIFICATION \nMARKINGS  MUST  BE  CANCELLED: \ndefense \nLlBBAl lx  on  t \nOF \nCo*GBESS \nSUMMARY  TECHNICAL  REPORT \nOF  THE \nNATIONAL  DEFENSE  RESEARCH  COMMITTEE \nThis  document  contains  information  affecting  the  national  defense  of  the  United \nStates  within  the  meaning  of  the  Espionage  Act,  50  U.S.C.,  31  and  32,  as \namended.  Its  transmission  or  the  revelation  of  its  contents  in  any  manner  to \nan  unauthorized  person  is  prohibited  by  law. \nThis  volume  is  \"classified  in  accordance  with  security  regulations  of \nthe  War  and  Navy  Departments  because  certain  chapters  contain  material \nwhich  was  SECRET  at  the  date  of  printing.  Other  chapters  may  have  had \na lower  classification  or  none.  The  reader  is  advised  to  consult  the  War  and \n[Navy agencies listed on the reverse of this page for the current classification of any material.\n\nManuscript and illustrations for this volume were prepared for publication by the Summary Reports Group of the Columbia University Division of War Research, under contract OEMsr-1131 with the Office of Scientific Research and Development. This volume was printed and bound by the Columbia University Press.\n\nDistribution of the Summary Technical Report of NDRC has been made by the War and Navy Departments. Inquiries concerning the availability and distribution of the Summary Technical Report volumes and microfilmed and other reference material should be addressed to the War Department Library, Room 1A-522, The Pentagon, Washington 25, D.C., or to the Office of Naval Research, Navy Department, Attention: Reports and Documents.]\nSUMMARY TECHNICAL REPORT OF DIVISION 6, NDRC\nVOLUME 22\nACOUSTIC TORPEDOES\n\nOFFICE OF SCIENTIFIC RESEARCH AND DEVELOPMENT\nVANNEVAR BUSH, DIRECTOR\nNATIONAL DEFENSE RESEARCH COMMITTEE\nJames B. Conant, Chairman\nRichard C. Tolman, Vice Chairman\nRoger Adams, Army Representative\nFrank B. Jewett, Navy Representative\nKarl T. Compton, Commissioner of Patents\nIrvin Stewart, Executive Secretary\n\nArmy representatives in order of service:\nMaj. Gen. [names redacted]\nBrig. Gen. G. V. Strong\nR. C. Moore\nC. C. Williams\nW. A. Wood, Jr.\nCol. E. [name redacted]\nCol. L. A. Denson\nCol. P. R. Faymonville\nBrig. Gen. E. A. Regnier\nCol. M. M. Irvine\nA. Routheau\n\nNavy representatives in order of service:\nRear Adm. H. G. Bowen\nRear Adm. J. A. Furer\nCapt. Lybrand P. Smith\nRear Adm. A. H. Van Keuren\nCommodore H. A. Schade\n\nCommissioners of Patents in order of service:\nConway P. Coe\nCasper W. Ooms\n\nNOTES ON THE ORGANIZATION OF NDRC\nThe duties of the National Defense Research Committee were:\n1. To recommend to the Director of OSRD suitable projects and research programs on the instrumentalities of warfare, along with contract facilities for carrying out these projects and programs.\n2. To administer the technical and scientific work of the contracts.\n\nMore specifically, NDRC functioned by initiating research projects on requests from the Army or the Navy, or from an allied government through the Liaison Office of OSRD, or on its own considered initiative as a result of the experience of its members. Proposals prepared by the Division, Panel, or Committee for research contracts for performance of the work involved in such projects were first reviewed by NDRC, and if approved, recommended to the Director of OSRD. Upon approval of a proposal by the Director of OSRD, a contract was issued.\nDirector,  a contract  permitting  maximum  flexibility  of \nscientific  effort  was  arranged.  The  business  aspects  of  the \ncontract,  including  such  matters  as  materials,  clearances, \nvouchers,  patents,  priorities,  legal  matters,  and  administra- \ntion of  patent  matters  were  handled  by  the  Executive  Sec- \nretary of  OSRD. \nOriginally  NDRC  administered  its  work  through  five \ndivisions,  each  headed  by  one  of  the  NDRC  members. \nThese  were: \nDivision  A \u2014 Armor  and  Ordnance \nDivision  B \u2014 Bombs,  Fuels,  Gases,  & Chemical  Problems \nDivision  C \u2014 Communication  and  Transportation \nDivision  D \u2014 Detection,  Controls,  and  Instruments \nDivision  E \u2014 Patents  arid  Inventions \nIn  a reorganization  in  the  fall  of  1942,  twenty-three  ad- \nministrative divisions,  panels,  or  committees  were  created, \neach  with  a chief  selected  on  the  basis  of  his  outstanding \nwork  in  the  particular  field.  The  NDRC  members  then  be- \nA reviewing and advisory group came to the Director of OSRD with the following organizations:\n\nDivision 1 \u2014 Ballistic Research\nDivision 2 \u2014 Effects of Impact and Explosion\nDivision 3 \u2014 Rocket Ordnance\nDivision 4 \u2014 Ordnance Accessories\nDivision 5 \u2014 New Missiles\nDivision 6 \u2014 Sub-Surface Warfare\nDivision 7 \u2014 Fire Control\nDivision 8 \u2014 Explosives\nDivision 9 \u2014 Chemistry\nDivision 10 \u2014 Absorbents and Aerosols\nDivision 11 \u2014 Chemical Engineering\nDivision 12 \u2014 Transportation\nDivision 13 \u2014 Electrical Communication\nDivision 14 \u2014 Radar\nDivision 15 \u2014 Radio Coordination\nDivision 16 \u2014 Optics and Camouflage\nDivision 17 \u2014 Physics\nDivision 18 \u2014 War Metallurgy\nDivision 19 \u2014 Miscellaneous\nApplied Mathematics Panel\nApplied Psychology Panel\nCommittee on Propagation\nTropical Deterioration Administrative Committee\n\nAs events of the years preceding 1940 revealed:\n\nLibrary of Congress\nNDRC FOREWORD\nThe seriousness of the world situation led more and more scientists in this country to recognize the need for organizing scientific research for national emergency service. Their recommendations to the White House received careful and sympathetic attention, resulting in the formation of the National Defense Research Committee (NDRC) by executive order of the President in the summer of 1940. NDRC members, appointed by the President, were instructed to supplement the work of the Army and Navy in the development of war instrumentalities. A year later, upon the establishment of the Office of Scientific Research and Development (OSRD), NDRC became one of its units. The Summary Technical Report of NDRC is a conscientious effort to summarize and evaluate its work and present it.\nThe useful and permanent form comprises seventy volumes, broken into groups corresponding to the NDRC Divisions, Panels, and Committees. Each group's report contains a summary stating the problems presented, the philosophy of attacking them, and summarizing the results of research, development, and training activities. Some volumes may be \"state of the art\" treatises covering subjects to which various research groups contributed information. Others may contain descriptions of devices developed in the laboratories. A master index of all divisional, panel, and committee reports which together constitute the Summary Technical Report of NDRC is contained in one volume.\nSome declassified NDRC-sponsored research of sufficient popular interest was reported in monograph form, such as the series on radar by Division 14 and the monograph on sampling inspection by the Applied Mathematics Panel. Since the material in these monographs is not duplicated in the Summary Technical Report of NDRC, they are an important part of the story of these aspects of NDRC research.\n\nIn contrast, information on subsurface warfare is largely classified and of general interest to a more restricted audience.\nA restricted group. Consequently, Division 6's report is found almost entirely in its Summary Technical Report, which runs to over twenty volumes. The extent of a Division's work cannot therefore be judged solely by the number of volumes devoted to it in the Summary Technical Report of NDRC. Account must be taken of the monographs and available reports published elsewhere. Any great cooperative endeavor must stand or fall with the will and integrity of the men engaged in it. This fact held true for NDRC from its inception, and for Division 6 under the leadership of Dr. John T. Tate. To Dr. Tate and the men who worked with him \u2013 some as members of Division 6, some as representatives of the Division\u2019s contractors \u2013 belongs the sincere gratitude of the Nation for a difficult and often dangerous job well done. Their efforts.\nContributed significantly to the outcome of our naval operations during the war and richly deserved the warm response they received from the Navy. In addition, their contributions to the knowledge of the ocean and to the art of oceanographic research will assuredly speed peacetime investigations in this field and bring rich benefits to all mankind.\n\nThe Summary Technical Report of Division 6, prepared under the direction of the Division Chief and authorized by him for publication, presents the methods and results of widely varied research and development programs. It is essentially a record of the unstinted loyal cooperation of able men linked in a common effort to contribute to the defense of their Nation.\n\nTo all of them we extend our deep appreciation.\n\nVannevar Bush, Director\nOffice of Scientific Research and Development\nJ. B. Conant, Chairman\nThe National Defense Research Committee's Division 6 conducted substantial research and development on acoustic homing control for torpedoes and mines. This work led to the design and production of homing devices that saw important Service use. The British undertook similar research and development, but the results appeared to have limited Service application. Additionally, the enemy developed an acoustic homing torpedo, but effective counter-measures became available promptly. When plans were made a year ago for the Division 6 summary report series, a proposal was made.\nThis volume contains material relating to actual structures. Due to the pressure of their other duties, it has not been possible for competent persons to summarize the vast amount of involved material for this task. All of this material has, however, been made available to interested Service technical personnel. Since the Division 6 report series was planned, the Office of Research and Inventions requested a comprehensive study and report on torpedoes. As part of this project, a report on guided torpedoes was furnished to that office, and presumably, this is also available to interested Service personnel. This report will therefore be somewhat restricted in scope. It includes, however, as Part I, a general analysis of the problem presented, Principles and Applications of Acoustic Homing Control to Torpedoes.\nPrepared by Dr. W. V. Houston and as part of \"Echo-Ranging Torpedo Control Systems,\" report by Dr. V. M. Albers. This report is particularly relevant as it covers the less highly developed method of acoustic control, which may hold considerable future promise. In the bibliography appears a list of the more pertinent reports prepared by Division 6.\n\nJohn T. Tate\nChief, Division 6\nE. H. Colpitts\nChief, Section 6.1\n\nVII\n\nPREFACE\n\nThis report was prepared by the Columbia University Special Studies Group as part of the studies made in connection with Projects NO-94, NO-149, NO-157, and NO-181. It covers the theoretical studies associated with the application of acoustic control to various kinds of torpedoes. Although some of the theoretical work was done directly by the Special Studies Group, much of this was done in collaboration with other organizations.\nThis is a compilation of experimental results and theoretical developments carried out by various groups. Some attempt has been made to give credit to these groups for their work, but this was not possible in all cases. A major part of the report is concerned with torpedo self-noise and its influence on control systems. Torpedo self-noise is the dominating factor that limits the use of such control systems, so methods for its control must constitute the principal objective of future research in this area. This report contains references to specific developments only insofar as they are useful in illustrating theoretical principles. Detailed descriptions of the various systems that were tried and their success will be found elsewhere.\n\nW. V. Houston\n\nPart II\n\nThis report is intended to cover, as far as possible, the following topics: self-noise in torpedoes and its impact on control systems; methods for controlling self-noise; and the potential application of advanced control theories to torpedo guidance. The report will also discuss the experimental results and theoretical developments related to these topics, as well as the implications for future research.\nThe work which has been done in the development of echo-ranging control for torpedoes. It is assumed that the reader is familiar with conventional electronic circuits. The emphasis, in discussing the various systems, is on their functional behavior and the details of circuit design which are unconventional. It is important for the reader to bear in mind the fact that all of the systems described, except the General Electric system, are still in the research stage, and the General Electric system is, at the time of preparation of this report, just in the pre-production stage. The chapters covering the various British systems are necessarily very brief since relatively little material is available about them. The report is divided into four main parts. The first, which is essentially introductory, covers a review of the general principles of echo-ranging and the requirements for an effective echo-ranging system. The second part describes the design and operation of the British Admiralty system. The third part deals with the design and operation of the Marconi-Elliot system. The fourth part describes the design and operation of the General Electric system.\nView of terminology in underwater sound, the nature of the problem of echo-ranging torpedo control, and a general description of the major components involved in all echo-ranging control systems. The second and third covers, respectively, discuss the systems developed for anti-submarine and anti-surface-ship service, with a separate chapter devoted to each. The fourth division contains an attempt at evaluation of the work that has been done up to the time of preparation of this report.\n\nIn discussing each system, a general description is first given with a block diagram to indicate the general principles utilized in the device. This is followed, in all cases where the information is available, by a detailed discussion of the major components of the system with individual circuit diagrams of each functional component.\nThis report is confined chiefly to the descriptions of the electronic gear used in echo-ranging torpedoes. Only those physical characteristics determining the behavior of a torpedo under echo-ranging control are noted.\n\nVernon M. Albers\n\nCONTENTS\nPART I\nINTRODUCTION\n1. Objectives of Homing Control\n2. Properties of Acoustic Homing Systems\n3. General Observations on Torpedo Self-Noise\n4. Cavitation and Cavitation Noise\n5. Machinery and Other Noise\n6. Hydrophone Discrimination and Isolation\n7. Total Torpedo Noise\n8. Transformation of Acoustic Signal into a DC Voltage\n9. Torpedo Dynamics and Stability\n10. Miscellaneous Problems\n11. Signal and Noise Levels\n12. Identification of the Echo\nPART II\n\nEcho-Ranging Torpedo Control Systems\nBy Vernon M. Albers\n\n15 Introduction\n16 Major Components\n17 Nature of the Control Problem\n18 General Electric NO 181 System\n19 Harvard Underwater Sound Laboratory N0181 System\n20 The British Dealer System\n21 Ordnance Research Laboratory Project 4 System\n22 Bell Telephone Laboratories 157B and 157C S Systems\n23 Geier Torpedo Control System\n24 British Trumper System\n25 British Bowler System\n26 Evaluation\n\nGlossary\nBibliography\nContract Numbers\nService Project Numbers\n\nPART I\n\nINTRODUCTION\nChapter 1\n\nObjectives of Homing Control\n\nThe modern naval torpedo is a highly effective weapon by means of which a large explosive charge is detonated near the underwater part of the enemy ship. Its success depends largely on the accuracy with which it is directed to its target. The torpedo's homing control system must provide the necessary guidance to ensure that the torpedo hits the target in the most effective manner. This paper discusses the various echo-ranging torpedo control systems that have been developed to meet this objective.\nThe enemy ship's hull is distinguishable from a mine due to its self-propelled nature and ability to be directed towards a selected target. Traditionally, the torpedo is a weapon of stealth, capable of being launched several miles from the target and traveling underwater along a predetermined course. In many cases, the explosion provides the first indication of imminent danger, and it is often difficult to determine whether the ship has been struck by a torpedo or has struck a mine. However, the surprise element of a torpedo attack is sacrificed when torpedoes are launched from aircraft. In such cases, the target ship can usually detect the torpedo launch and take appropriate evasive action. Even in the case of a submarine-launched torpedo, the wake produced by the ordinary steam-driven weapon and the noise cause potential detection.\nA torpedo's approach can be detected by the driving mechanism, allowing for evasive action. This action typically involves turning towards or away from the oncoming torpedo, reducing the probability of a hit due to the narrow target presented. Since a torpedo's speed is not much greater than that of the ship, almost any turn can disrupt the calculations used to aim the torpedo.\n\nA simple torpedo follows a preset course at a specified depth, and the accuracy with which it does so measures the effectiveness of the control mechanism. To determine the course, it is necessary for the torpedo to know which direction to set.\nAn officer needs to determine a target ship's speed, course, bearing, and range. The speed and course are difficult to ascertain, particularly from a submarine's periscope view. Consequently, many torpedoes miss their targets even without evasive action. This is widely acknowledged, leading to the practice of firing torpedo salvos with up to four torpedoes on slightly varying courses to account for potential aiming errors and serve as a countermeasure against evasive action. The purpose of a homing device is to enable a lethal hit despite evasive actions and errors in the torpedo's initial course.\nA homing device is intended to minimize the effect of aiming errors and evasive action taken by the target. Such a device makes use of some characteristic property of the target, so that when the torpedo comes within homing range, it no longer follows the preset course but is directed toward the target. In such a case, the torpedo will eventually strike the target and explode, unless the target's speed permits it to escape. A homing device can be associated with various types of search procedures. One extreme is illustrated by the ExF42 mine and the ExFF3 torpedo. In these cases, the torpedo is launched from the air or from a submarine and follows a circular path at the set depth.\nThe torpedo requires only information necessary for placing it within operating range of the target for launch. This is feasible in cases of a torpedo launched from an airplane against a submarine sighted on the surface, and possibly in some cases for a torpedo launched from a submarine against an attacking surface vessel. In most cases, the effective homing range will be much smaller than the running range, and a preset course must be used to direct the torpedo into the target's neighborhood. In this latter case, the torpedo is aimed in the usual way, and the homing mechanism corrects the course if necessary near the end of the run. The homing device's effect can be described as an enlargement.\nThe effectiveness of homing control objectives depends on the specific properties of each homing mechanism. The effectiveness of a homing torpedo relies primarily on two features.\n\n1. The effective homing range should be as great as possible and not be limited to the direction straight ahead. Homing range straight ahead holds limited value, as the torpedo will strike what is directly ahead without any homing mechanism. Conversely, excessive homing sensitivity to the side may make the torpedo susceptible to certain interferences.\nTypes of decoy. It seems desirable to have a long homing range uniformly distributed ahead of the torpedo.\n\n1. A torpedo should have a sufficiently short turning radius. The turning radius should be shorter than the homing range for the torpedo to get around and approach the target. However, a turning radius that is too short leads to instability along the course and difficulties in automatic steering. The torpedo must be maneuverable enough to keep pointed at the target, but it must also be steady on the desired course.\n\nThe advantages of homing devices are fairly obvious, but it must not be forgotten that there are also disadvantages. Among them may be mentioned the following six.\n\n1. The homing mechanism occupies space and weight that must be taken from either the explosive charge.\nCharging or discharging from the fuel supply requires careful consideration of all facts, with particular emphasis on the targets against which the weapon is likely to be used.\n\n1. The homing mechanism introduces increased complications in manufacture and maintenance. The techniques involved in the homing devices may be quite different from those normally associated with torpedoes, so a completely new type of training may be necessary for adequate maintenance and operation. In large-scale planning, this may be a very significant factor.\n\n2. To gain an adequate homing range, it may be necessary to operate at a lower torpedo speed than would otherwise be possible. In the case of acoustic homing, it is the self-noise of the torpedo that usually sets the limit to the homing range, and this noise in-\n\n(Assuming the text is cut off and the intended meaning is about the limitations of the acoustic homing range due to the self-noise of the torpedo)\n\nThe limitations of the acoustic homing range depend on the self-noise of the torpedo.\nThe torpedo's creases rapidly as its speed increases. It is necessary to determine if the required decrease in speed justifies the advantages of the homing property. This decision requires knowledge of the speed of expected target ships, as using a torpedo too slow to reach the target is useless.\n\nFour. Different homing systems sometimes cause the torpedo to strike various parts of the ship. An acoustic torpedo that operates by listening tends to end its course in a stern chase and strike near the propellers. An echo-ranging torpedo may, under some circumstances, strike near the bow. These points of impact may not always be satisfactory since, although a hit on the propellers may be disabling, it may not be correct to assume that the ship will always sink.\n\nFive. Most homing devices are subject to some form of inaccuracy.\nOf more or less effective countermeasures, which, if used, may make the torpedo less likely to hit the target than if the homing device had not been present.\n\nLimitations of homing devices:\n1. Some homing devices may make it less likely for multiple torpedoes to hit the same target without interference. This is particularly true of acoustic listening torpedoes with considerable homing ranges on each other.\n2. In spite of these limitations, homing devices now known are an advantage to the group using them, as the number of torpedoes required to make a hit is markedly reduced.\n\nChapter 2\nProperties of Acoustic Homing Systems\n\nVarious types of homing control have been suggested. Radio control would be convenient due to the extensive development of radio techniques. However, no radio waves of usable frequency for homing exist.\nTorpedoes that can penetrate water more than a short distance require an antenna projecting out of the water. Such an appendage would seriously hamper the motion and steering of the torpedo and does not seem very practicable. However, torpedoes have been built with such antennas to enable radio-controlled guidance from a launching plane. Yet, they have not been extensively used. Magnetic control has been suggested and may be practicable, but the magnetic disturbance intensity due to a target ship falls off so rapidly with distance that it seems very doubtful if homing ranges as great as 100 yards could be obtained. However, if countermeasures against acoustic homing devices prove highly effective, the development of magnetic homing may be justified.\nIt has been suggested that following a ship's wake could be used to produce a homing control. Such a device might operate satisfactorily, but its tactical usefulness would be limited. It would have to be fired to come in contact with the wake at some point not too far behind the ship and could not be used against a stationary ship. Moreover, in the case of a maneuvering target, the wake might be such a complicated affair that it would be difficult to follow. Nevertheless, such a homing device may have its uses, although it has not been developed sufficiently for the results of extensive field tests to be available.\n\nThe most promising type of homing control and the one that has been the object of extensive study and development during the past four years is acoustic.\nTic. Sound travels in water without much attenuation as long as the frequency is below some 60,000 c. Although the ocean is not a homogeneous medium, and the sound traveling in it may be reflected, refracted, and scattered, sound signals can be sent for appreciable distances. For about thirty years, sonic methods have been used for locating submarines, for communicating between submarines, and for communicating between submarines and surface ships. In this connection, much has been learned about the propagation of sound in sea water, and during the last few years, this study, and the study of acoustic homing devices, has been carried to such an extent that it is possible to lay down in a general way the possibilities and the limitations of acoustic homing devices for subsurface use. This is not to say that no more research is needed, but the lines along which research should be conducted are clear.\nResearch on methods for sonic location of a target can be well laid down. Methods for sonic location can be divided into two classes, and homing devices based on each have been built.\n\n1. Echo ranging: This is a method of determining the direction and distance of a reflecting body by the echo it sends back in response to a sound signal. The homing device must respond to the echo in such a way as to direct the torpedo toward it.\n2. Listening: In this method, the sound travels in one direction only. To operate a listening method of homing control, the target must produce noise. This noise is then picked up by the homing device, which determines the direction from which the signal is coming and directs itself toward the target.\n\nBoth of the above methods have been tried for homing torpedoes and have been shown to work successfully.\nThe listening method is simpler, not only in its acoustic and electronic gear, but also in the application to torpedo controls of the received information. However, it requires the target ship to make some noise in the adopted frequency range, making it ineffective against a ship at rest and quiet. Regarding torpedoes for use against submarines, a submarine at considerable depth makes practically no noise, as cavitation of its propellers is suppressed and it may be very quiet in the frequency ranges normally used. A listening device can be countered by the operation of a strong source of noise at a distance from the target ship. Such a decoy can be built to simulate a ship's noise very closely. The echo ranging type of homing control is effective.\nThe acoustic homing torpedo is effective against both stationary and moving targets, and would be effective against a deeply submerged submarine. To counter it requires some method of producing false echoes, such as an echo repeater. However, it is more complicated in construction, and the exact extent of its effectiveness has not yet been determined in operational use.\n\nThe operation of either type of acoustic homing torpedo is limited by the conditions of the water. For the ranges normally under consideration, 100 to 1,000 yards, this is only serious under the worst conditions. Nevertheless, such regions as Chesapeake Bay in the summer are so bad that echo-ranging operation over as much as 500 yards is improbable. Although both types of homing control are limited by sound refraction in the water, the echo-ranging system is particularly affected.\nThe ranging type is seriously handicapped by reverberation and false echoes. Echoes from the bottom are so serious that satisfactory operation in shallow water is unlikely, and even reflections from the surface may occasionally be troublesome. The operating range of any acoustic torpedo is most seriously limited by the torpedo self-noise. This noise may be generated in the water due to cavitation of the propellers, cavitation on various parts of the body, and other causes, or it may be the noise made by the torpedo machinery. The noise due to cavitation can be reduced or eliminated by running the torpedo at a sufficiently great depth of submergence. If the torpedo is to be used as an antisubmarine weapon, this is no additional complication. But if it is to be used against surface ships, the necessity is to maintain a greater degree of underwater silence.\nThe problem of arranging a torpedo to rise properly and strike a target introduces numerous issues. In any case, a torpedo's self-noise increases with its speed, and it is probably safe to assert that the acoustic operating range of a high-speed torpedo can never be made as great as that of a slower torpedo. Nevertheless, it may still be great enough to be useful. A high-speed torpedo is needed only when the target is a high-speed vessel. The high speed of the target produces more noise than a lower-speed vessel and, to some extent, counteracts the increased self-noise of the torpedo. This advantage does not accrue in the case of an echo-ranging control where the range is not increased by an increase in target noise. The study of torpedo self-noise and means for reducing it constitutes the principal line of effort in torpedo development.\nThe improvement of acoustic homing torpedoes involves two lines of attack. One is the reduction of noise at its source. This includes a study of propeller design and the overall shape with the objective of eliminating cavitation and reducing other types of water noise. It also involves the reduction of internal machinery noise due to gears, flow of high-pressure air, and motion of high-speed parts. The other line of attack is the attempt to reduce the hydrophone response to the noise that exists. This involves the selection of hydrophones whose directivity pattern is such that there is very little response to cavitation and other noise produced in the water. It also involves mounting the hydrophone in such a way that vibrations are not picked up from the body of the torpedo itself. In addition, it may be necessary to use sound-absorbing materials to further reduce the noise produced by the torpedo.\nUseful to modify the torpedo structure at various points to reduce sound transmission to the shell and through it to the hydrophones. Much work has already been done along these lines, but much more remains to be done before the best practical acoustic homing torpedo can be built.\n\nThe importance of torpedo speed in reaching the target and self-noise in reducing homing range suggests that the ideal torpedo would have at least two, and possibly three, speeds. The maximum speed would be used for attacking fastest ships. The self-noise of the torpedo would be fairly high, but the high noise of the target ship would override this in a listening torpedo, and in an echo-ranging torpedo, some reduction in range would have to be accepted since the torpedo must have enough speed to catch the target.\nAgainst lower-speed targets, a lower torpedo speed could be used. The speed-changing mechanism would also increase the acoustic sensitivity to make use of the reduced self-noise and keep the effective acoustic range from being seriously reduced by the reduction in target noise. It seems possible that careful selection of various speeds and the best utilization of them might lead to the specification of an almost universal torpedo for use from submarines and possibly another for use from aircraft.\n\nChapter 3\n\nGENERAL OBSERVATIONS ON TORPEDO SELF-NOISE\n\nTo operate properly, an acoustic torpedo must distinguish between the signal on which it is expected to steer and other noises that may be present. These other noises may be in the surrounding water or they may be in the torpedo itself. Careful measurements, made by the Bell Telephone Laboratories.\nFive measurements in deep water indicate that far from the shore, the water background noise is primarily due to surface disturbances such as whitecaps. It was found that when no whitecaps were present, the noise level at 25 kc was as low as -74 dB, while with many whitecaps it was as high as -50 dB. Heavy swells seemed to have no effect in producing noise. Water noises provide a limit below which no acoustic torpedo can be expected to operate. However, if the water noise is isotropic, i.e., if it comes equally from all directions, a directional hydrophone will respond to it very much less than to a plane wave coming along the direction of maximum sensitivity. The difference in response to these two types of sound is just the directivity index of the hydrophone. Because directional hydrophones are normally used.\n3.1 Importance of Self Noise\n\nThis noise of the torpedo itself, which affects the hydrophones in the torpedo, is normally the most important limiting factor in the operation of an acoustic torpedo. This is quite clear in the case of a torpedo that listens to the noise of the target ship. A torpedo has most of the characteristics of a ship, especially a submarine, on a small scale. It is unlikely that any significant difference in quality will exist between the noise of the target and the noise of the torpedo. Hence, discrimination must be made on the basis of intensity alone. When this is done, it is a fair general statement to say that acoustic control can be expected only when the root mean square self-noise level is significantly lower than the target noise level.\nThe abbreviation \"dbs\" signifies decibel spectrum level and refers to the intensity of noise in a 1 c wide frequency band. The reference intensity is that corresponding to a root mean square pressure of 1 dyne per sq cm. For a discussion of terminology and reference levels in sound measurements, see Division 6, Volume 10, Calibration Methods, Chapter 4, \"Types of Acoustic Measurements.\"\n\nThe [rms] value of the target noise is equal to or greater than the [rms] response of the hydrophone to the torpedo self-noise. Sometimes it is possible, by special arrangements, to recognize a slightly lower signal. However, operation is considered reliable only when the signal is somewhat above the self-noise. Nevertheless, the above statement is a satisfactory rough criterion for estimating the acoustic operating range of any listening control.\nA possible exception to the general statement is when the target noise is strongly modulated with the propeller blade frequency. Since the top of a large ship propeller is closer to the surface of the water than the bottom, each blade may have its maximum cavitation as it passes through the top position. Since such propellers usually have a much smaller rate of rotation, the modulation frequency is lower, and the target noise may be identified at a slightly lower level than indicated. With an echo-ranging control, the problem appears to be different at first. It may be possible to impose a character on the emitted signal that can be detected in the presence of noise. However, the advantage to be gained by this method is distinctly limited because the target is rarely a plane.\nThe surface is typically composed of multiple surfaces, and the combined effect tends to distort the incident ping and make it more akin to noise. For effective acoustic control, it can be approximated as a general rule that the rms response of hydrophones to torpedo self-noise must be less than or equal to the rms response to the signal from the target. In a listening torpedo, the signal strength is fixed by the nature of the target, and in an echo-ranging type, it is not practical to increase the signal strength indefinitely. Therefore, attention must be given to reducing the hydrophones' response to torpedo self-noise. The condition is stated this way because it can be achieved by reducing:\n\n1. self-noise.\nThe level of noise generated and the sensitivity of hydrophones to predominant sources are key issues. There's a possibility that characteristic modulations of noise may provide added discrimination.\n\nGeneral observations on torpedo self-noise: It's essential to identify noise sources and study how the noise is transmitted to hydrophones.\n\n3.2 External Measurements of Torpedo Noise\n\nThe simplest way to obtain a preliminary estimate of torpedo noise is by measuring it with a hydrophone in the water as the torpedo passes. The primary challenge lies in determining the distance between the hydrophone and the torpedo corresponding to measured noise levels with sufficient accuracy.\nMeasurements made in this way serve as a starting point for the general study of the problem, and in fact, observations of different observers show a remarkable amount of agreement. Figure 1 displays a series of curves based on the measurements of several observers.1 Frequency in kC\n\nFigure 1. Noise level measurements on various torpedoes at a distance of 6 meters. These curves represent averages of several observers.\n\nAlthough the observers differ somewhat among themselves, and in all probability, the conditions of measurements were not identical, there is sufficient agreement among them to permit drawing the rough average curves shown in the figure. From these curves, several conclusions can be drawn.\n\n1. Individual differences between different kinds of torpedoes seem relatively insignificant. In particular, the Mark 18 electric torpedo is no quieter.\nThe Mark 13 turbine-driven torpedo is surpassed by: it is possible to plot a curve of torpedo noise as a function of speed at a given depth. Figure 2 displays the noise level, at 25 kc, as a function of speed for torpedoes running 12 to 15 ft deep.\n\nSPEED IN KNOTS\n\nFigure 2. A curve of noise level at 25 kc as a function of speed for an \"ideal\" torpedo. The points indicated were taken from the curves in Figure 1. A smooth curve drawn through these points may then be regarded as the noise-speed curve of an idealized torpedo. This lumping of all torpedoes together must be viewed with caution. The observations used refer to British, American, and one German torpedo only, and it may be incorrect to extend the generalization to others.\nForeign torpedoes. It is possible that the British and American trends of development have led to torpedoes with very similar noise characteristics above 10 kc. Figure 3 displays the curve of Figure 2 with a large number of individual observations indicated. This shows that the dispersion of measurements on any one type of torpedo is at least as great as any possible differences between different torpedoes. It is clear that the curve drawn in Figure 3 is not the one that would be drawn through the points if they were all given equal weight. However, if the observations for the same type of torpedo are first grouped together as in Figure 2, the fit is fairly good.\n\nBritish Marks 3ZH1 and IX\n\u00a9 British Mark XV\n+ US Mark 13\n\u25a1 US Mark 14\n\u00a9US Mi\n\u00a9 British 0 GERMi\nH Mark X\nWELECTR i\nIC(G7E)\nA A m V A f\nSPEED  IN  KNOTS \nFigure  3.  This  curve  is  the  same  as  in  Figure  2 but \nthe  points  represent  a number  of  individual  observa- \ntions. The  distribution  of  these  points  gives  an  idea \nof  the  extent  of  agreement  between  different  observers. \nThe  curve  is  not  intended  to  be  the  best  curve  through \nthe  points  but  is  based  on  illustrative  assumptions  used \nin  Chapter  9. \n3.  This  ideal  curve  of  noise  at  25  kc  seems  to  rise \nrather  rapidly  between  20  and  30  knots  and  there- \nafter to  rise  more  slowly.  As  will  be  indicated  in  the \nnext  chapters  this  rapid  rise  probably  represents  the \ndevelopment  of  propeller  and  other  cavitation,  which \nis  the  dominant  source  of  noise  in  this  region.  Above \n30  knots  the  machinery  noise  becomes  dominant \nagain  and  continues  to  rise,  while  the  cavitation \nnoise  remains  constant  or  even  falls  off  a little.  Below \nIt is probable that individual differences between torpedoes make it more difficult to make the same kinds of generalizations. At lower frequencies, the individual characteristics of torpedoes are more significant. The noise level of all torpedoes falls off roughly 6 db per octave above 10 kc. This indicates that the noise is inversely proportional to the square of the frequency. From this point of view, there is probably no advantage in selecting one frequency rather than another. Although the self-noise falls off as the frequency is increased, the target noise for a listening torpedo falls off at about the same rate. Two other factors, however, need consideration: one is the hydrophone discrimination to be discussed.\nChapter 6 likely increases as the frequency rises, so the use of a higher frequency may produce an improvement in signal-to-noise ratio. On the contrary, attenuation increases rapidly with frequency, starting around 4 dB per kilometer near 25 kc and rising to around 14 dB per kilometer near 60 kc. The question of the best frequency to use has not been thoroughly investigated. In the following discussion of self-noise, attention will be centered on the 25-kc region, as most work has been done there.\n\nChapter 4\n\nCAVITATION AND CAVITATION NOISE\n\n4.1 THE NATURE OF CAVITATION\n\nThe phenomenon of cavitation derives its name from the fact that actual cavities form in the water. There may be a few large cavities or a large number of very small cavities, either attached to the surface of moving bodies or free in the water.\nCavitation occurs at points in a liquid where the pressure would become negative in a perfect incompressible fluid. In reality, it's only necessary for the pressure to fall below the vapor pressure of the liquid, causing the liquid to form small cavities filled with vapor. Cavitation is a phenomenon essential to liquids, occurring where pressure falls below the vapor pressure, resulting in the formation of cavities filled with vapor.\nIf cavitation does not occur in gases. An attempt to reduce the pressure of a gas below zero causes the gas to expand and fill the entire available space. Water, on the contrary, does not expand much when the pressure is reduced but instead evaporates to fill the available volume with water vapor. In many cases, the pressure of water vapor is insignificant compared to other pressures involved. In such cases, the vapor pressure may be neglected, and it may be considered that an attempt to reduce the pressure of a liquid below zero results merely in the creation of vacuums.\n\n4.1.1 A Simple Case of Cavitation\nA simple case of cavitation occurs when water flows through a tube of diminishing cross section. It is true that under suitable conditions, liquids such as water can cavitate.\nUnder the circumstances considered, water's ability to support tension can be ignored. Since the water is not particularly pure and solid surfaces are moving through it, a reduction of pressure to the vapor pressure of water or below will always result in cavities. The cross section diminishing, the velocity of the water increases and, according to Bernoulli's theorem, V + \u03c1v\u00b2 = constant. (1) The pressure must decrease as the cross section diminishes because the pressure must decrease as the velocity increases. In equation (1), the pressure is measured in pounds per square foot, the density in slugs per cubic foot, and the velocity in feet per second. In these units, the density of water is approximately 62.4.\nApproximately 2,500 psf corresponds to a reduction of pressure when the velocity is 50 fps. This is more than an atmosphere. If the pressure is one atmosphere where the water has a negligible velocity, cavitation will occur down the stream where the velocity approaches 50 fps.\n\n4.1.2 Vortex Cavitation\n\nCavitation can also occur in situations associated with rotational motion of the water and the accompanying centrifugal force. As an illustration of the kind of thing that can occur, consider a simple vortex at the center of which pressure will be a minimum. This can be understood by considering an idealized vortex consisting of the rotation of a cylindrical volume of water with radius R, at a constant angular velocity \u03c9. The velocity at any point inside the cylinder is then given by:\n\nv = \u03c9r\nOutside of this cylinder, the motion is \"irrotational,\" even though the water is moving around the central cylindrical core. This is possible if the velocity is inversely proportional to r. These two motions give the same velocities at radius R, if the constants are properly selected. Let us assume that for r < R, the velocity is given by i, and for r > R, it is given by k. The significant measure of the strength of this vortex is the quantity K that is called the circulation.\n\nII\n\nOutside the central cylinder of radius R, the motion is \"irrotational,\" and Bernoulli's theorem can be used to determine the pressure in terms of the pressure at great distances from the vortex. This leads to:\n\nFor r < R, the analysis shows that\n\nwhence V = P / (2 * r^2)\n\nAt the center of the core, the pressure is\n\nThis pressure depends both on K and R. It depends on the constant K through the circulation, and on R through the radius of the cylinder.\nboth  on  the  strength  of  the  vortex  K and  the  extent \nof  the  vortex  R.  For  a given  value  of  K,  the  pressure \nbecomes  lower  if  R is  made  smaller.  It  is  clear  from \nthis  form  of  expression  that  it  is  quite  possible  for  the \npressure  po  at  the  center  of  the  vortex  to  become \nnegative,  and  hence  for  these  equations  to  fail  to \ndescribe  the  physical  situation.  Under  such  condi- \ntions, a cavity  will  open  up  at  the  center,  and  cavita- \ntion will  occur.  Figure  1 shows  the  way  in  which  the \nFigure  1.  Speed  of  the  water  and  the  pressure  plotted \nas  a function  of  the  distance  from  the  center  for  an  ideal- \nized vortex  of  a simple  type. \npressure  and  the  velocity  depend  on  the  distance \nfrom  the  center  of  a simple  vortex  of  this  kind. \nThe  importance  of  cavitation  in  a vortex,  when \nconsidering  the  self  noise  of  a torpedo,  comes  from \nThe fact that a trailing vortex is left behind the tip of a propeller driving a torpedo through water. If the circulation around this vortex is great enough, or if the vortex is concentrated enough (R small enough), cavitation will occur and will be a serious source of noise. Since the magnitude of the propeller thrust is associated with the circulation K, the only way to avoid cavitation and maintain thrust is to shape the propeller blade so that the vortex is not shed in a concentrated form but is spread out over a considerable volume. This means that the vortex will have very little similarity to the simple type of vortex described here, but will be much more complex. Nevertheless, the principle involved is that illustrated; since vorticity cannot be reduced without reducing thrust, efforts to reduce it will be ineffective.\nThe cavitation of the propeller must be directed towards getting the vorticity to occupy a volume greater than some minimum volume. A thorough study of this problem has been conducted at the Harvard Underwater Sound Laboratory (HUSL).22 Figure 2 depicts a test propeller in a water tunnel at the David Taylor Model Basin (DTMB). The cavitating vortices from the propeller tips are clearly visible extending in helices downstream.\n\n4.1.3 Body Cavitation\nWhen a solid body moves through water with velocity V, the speed of the water with respect to the body has a variety of values at various points, and at some places is considerably higher than V. At such points, the pressure is lower than in the free water and may become low enough to initiate cavitation.\nThe phenomenon of cavitation. Cavitation can occur in the neighborhood of a torpedo moving through the water quite apart from the cavitation that may exist in the propeller tip vortices. For illustration, consider the case of a sphere. This is simple enough that the flow of a perfect fluid around it can be calculated. If the sphere is considered at rest and the fluid to be moving past it with a velocity V, the velocity at a point in the fluid outside the sphere is given by:\n\nr = R + V*sin(\u03b8)\nv = V*cos(\u03b8)\n\nWhere r and \u03b8 are polar coordinates based on the center of the sphere as the origin and the direction of flow as the polar axis. R is the radius of the sphere. It follows from these equations that the point of maximum velocity is at the surface of the sphere. Then, according to Bernoulli's theorem, the pressure at this point is lower than the ambient pressure, potentially leading to the formation of vapor bubbles and cavitation.\nThis text provides the pressure around the equator of the sphere in terms of velocity V, given that the water motion is described by the above expression. When the velocity is large enough for p to equal the vapor pressure of water, or approximately zero, cavitation occurs around the equator of the sphere. If the velocity is increased further, cavitation spreads over more and more of the sphere, and the equation ceases to give the correct description of the water velocity in the cavitation region. The type of calculation indicated often serves to indicate the velocity at which cavitation will set in but does not describe the further development of the phenomenon and the enlargement of the cavity.\n\n4.1.4 Cavitation Coefficient\nIf Vc is the velocity at which cavitation just occurs.\nThe cavitation properties of a body can be described by a cavitation coefficient Kc. From equation (4) describing the pressure around a sphere, this value of Kc = 1.25 can be considered a statement of the susceptibility of the equator of the sphere to cavitation. It is important to note that Vc is the velocity of the whole water stream with reference to the sphere and not the velocity of the water at the point where cavitation begins.\n\nCalculations of this type have been worked out to give the critical values of Kc for a number of different shapes. For ellipsoids of revolution whose major and minor axes are a and b, the following values were found:\n\na | Kc\n--|-----\nb\n\nIn addition, the value for a simple, \"half streamline\" body is 0.33. These results indicate that in general, cavitation occurs more readily around the regions of high pressure gradient, specifically at the stagnation points or the points of separation of the flow, where the pressure is lowest.\nThe body of a propeller is blunter than that of a somewhat pointed one., 4.1.5 Propeller Blade Cavitation\n\nA similar type of cavitation may also occur on a propeller's blades since these blades move through the water with a velocity considerably higher than the forward motion of a torpedo itself. A propeller blade is essentially a short hydrofoil moving through the water at a certain angle of attack, thus pressure is increased on its face and decreased on its back. As the speed increases, this decrease of pressure becomes greater and greater and may eventually produce a pressure as low as the vapor pressure or lower. Under these circumstances, cavitation sets in as usual. This type of cavitation has been known for some time in connection with propellers, as it seriously reduces their efficiency. The pressure of the water at some distance from the propeller blades causes this phenomenon.\nA propeller blade sets a limit to the pressure reduction on its back surface. Reaching this limit at one point on the propeller surface results in less additional thrust from further increases in propeller speed. Calculating pressure distribution over simple hydrofoils is not difficult, but making the calculation for an actual propeller is more complex. After a propeller is built, it can be tested for cavitation and the conditions under which it occurs can be observed.\n\nCavitation is significant in ordinary propellers due to its effect on propeller efficiency. However, it is far more crucial in the case of acoustic torpedoes because of the noise it produces. This has led to increased interest in studying this phenomenon.\nAnd methods for reducing it. However, to eliminate the noise, it seems necessary to essentially eliminate cavitation, not merely reduce its amount.\n\n4.2 Observations of Cavitation\nFigure 2 demonstrates the way in which propeller tip cavitation can be observed in a water tunnel. If cavitation does not appear under normal operating conditions, it can usually be brought about by increasing the propeller loading or reducing the water pressure.\n\nExtensive observations of body cavitation have been made in the High Speed Water Tunnel at the California Institute of Technology [CIT]. A small body of the shape to be studied was placed in the water stream and observed visually. Both the velocity of the water and its pressure could be varied.\n\nFigure 2. Photographs of a propeller in a water tunnel\nat the David Taylor Model Basin, cavitating vortices trailed from the propeller tips. A cavitation coefficient Kc, as defined above, could be attributed to various points on the body and would describe the conditions under which cavitation would appear. In a slightly different sense, a cavitation parameter can be used to describe the conditions under which a body is moving or the conditions in the water tunnel. In this case, the velocity is just the existing velocity. It can then be said that cavitation begins at a certain point on the body when the cavitation parameter is decreased below the value of the cavitation coefficient at that point. Observations on a sphere gave K = 1.2 as the point at which cavitation first set in. This is in adequate agreement with the calculated value of 1.25. On a cylindrical body with a hemispherical nose, cavitation observations were made.\nThe observation was made for a torpedo with a cavitation coefficient of approximately 0.75. This observed value of 0.75 indicates that a torpedo of this shape, running 15 ft deep where the pressure is approximately 3,000 psf, would begin to cavitate at a speed around 68.9 fps, or approximately 38 knots. Since it may be desired to run acoustic torpedoes at speeds greater than 38 knots and possibly at depths less than 15 ft, it is important to have nose shapes that do not cavitate easily. The following are the results from testing various shapes in the Water Tunnel:\n\nNose length (ft) Body diameter (cal) Kc\nHemisphere  Ogive, 1.125-cal radius\nOgive, 2.0-cal radius\nEllipsoid  Ellipsoid\nHalf streamline with quartic transition curve\n\nNote: These values of the cavitation coefficient apply only when the torpedo is traveling in the direction of its axis, i.e., when the pitch angle is zero.\nAnd yaw are zero. At other values of pitch and yaw, cavitation tends to set in earlier. The elongated noses, in particular, are especially sensitive to yaw angles. Furthermore, other points on the torpedo show more pronounced tendencies to cavitate than the nose. In particular, the fins of the Mark 13 torpedo show a critical value of Kc = 0.93 at zero yaw, and Kc = 1.6 at 4 degrees yaw. Hence, the problem of designing a torpedo to travel at high speeds without cavitation presents numerous difficulties. The torpedo will nearly always yaw and pitch to some extent, and it will certainly travel with a yaw angle if it is expected to turn in a small circle. Those shapes that tend to postpone cavitation to high speeds when traveling in a straight line also tend to produce cavitation easily when moving at an angle to their axes.\nObservations were made at the High Speed Water Tunnel concerning cavitation on an airfoil section. They show quite clearly the dependence of the critical cavitation parameter on the angle of attack and hence on the thrust exerted by a propeller. Studies have also been made by HUSL of propeller cavitation in a model tunnel. This work showed that the incidence of cavitation could be described in terms of a cavitation parameter in the same way as cavitation about a torpedo nose.\n\nThere are various cavitation parameters that might be used in connection with a propeller. One of these uses the propeller tip speed as the significant velocity. However, it is true that those parts of the propeller blade close to the axis do not have so high a speed as the tips and hence the speed of the closest parts to the axis is not considered in this parameter.\nThe hydrofoil section is not always the same as tip speed. Another method is to use the forward speed of the propeller through the water. At least, this is the same for all parts of the propeller and is roughly proportional to the propeller tip speed. It is probably of little importance which cavitation parameter is used, as long as its significance is recognized. If the forward speed through the water is used, cavitation will occur at rather large values of the cavitation parameter because the propeller tips will be moving at a considerably higher speed than the speed used in the parameter.\n\nThe HUSL observations indicated that propeller tip cavitation usually sets in first, and that later cavitation on the blades could be observed. Similar observations have been made at the DTMB propeller tunnel.\n\n4.3 Noise due to cavitation.\nThe principal importance of cavitation in the design of acoustic torpedoes is due to the noise produced. It is now quite clear that cavitation, even barely incipient cavitation, is a major source of noise. However, the detailed mechanism of its production is not at all clear, and much work remains to be done before quantitative relationships can be established between the intensity and character of the noise and the properties of the cavitation.\n\nWhen underwater sound work was first initiated in the University of California laboratory at Point Loma, some preliminary exploratory work was started at Berkeley. It was hoped in this way to get some general indication as to the way noises are produced under water. The general conclusion was that the noise associated with breaking the surface of the water or with cavitation was greater.\nThe noise produced by moving rough surfaces through water was negligible compared to that due to any kind of surface disturbance. This is in conformity with the general observation that ambient noise in the sea increases sharply as white-caps appear. In an effort to study the relationship between cavitation and noise, a hydrophone was installed in the High Speed Water Tunnel at CIT. With this hydrophone, observations were made of the noise level as a function of the cavitation parameter for a number of torpedo and bomb models. This work is described in detail in a report from this laboratory. One of the major difficulties in using a water tunnel for noise measurements of this kind is the large amount of noise produced by the tunnel itself.\nThe pumping machinery is noisy, and this noise is easily transmitted to the working section. The background noise also varies with the speed and pressure of the water. However, it was confirmed that the noise produced by cavitation on the model outweighs other noises and can be clearly recognized.\n\nAnother difficulty is the fact that the cross section of the tunnel in the working region is rather small. Measuring sound intensity in such a space is difficult due to interference phenomena and reflection from the walls. The intensity measured is strongly dependent on the exact position and orientation of the hydrophone. It is practically impossible to get a significant measure of absolute sound intensity under these conditions, but it is possible to get a qualitative idea of the way the sound levels vary.\nnoise sets in sharply with the incidence of cavitation, rises to a maximum, and then falls off as cavitation builds up. To produce cavitation easily, a model was used with a flat nose. This was produced by cutting off a hemispherical nose at about three-quarters of its radius. Under these conditions, cavitation set in at A = 2.6. Figure 3 gives an idealized curve for this case. As the velocity of the water is increased, or the pressure is reduced, so that K passes through the value 2.5, the sound intensity increases sharply by over 20 db. It then continues to rise more slowly but finally reaches a maximum.\n\nDespite the difficulties indicated above, there may be a good deal of question as to the validity of detailed conclusions from this type of work. Nevertheless, several points stand out. It is most striking that cavitation sets in more easily with a flat nose and occurs at a lower velocity or higher vacuum than with a rounded nose. The sound intensity increases significantly when cavitation occurs and reaches a maximum before decreasing as cavitation builds up further.\nThe increase in noise level is coincident with the onset of cavitation. In other curves given in the report, the increase is not so sharp, and it may be that the sharpness of this rise is associated with the shape of the body. However, the principal conclusion is clear: cavitation produces noise, and cavitation noise in torpedoes sets in rather sharply as cavitation begins.\n\nAnother point indicated in Figure 3 is that further decrease of the cavitation parameter is associated with a decrease in the intensity of the noise, rather than a continued building up. This seems to be the case.\n\nVelocity in ft/sec at 15 ft depth\nCavitation parameter\n\nFigure 3. Idealized curve of cavitation noise as a function of the cavitation parameter for the case of a flat-nosed projectile. The sound levels are in decibels above the background.\nserved quite generally in work with models and other experiments designed to study the noise due to cavitation. Various suggestions have been made to explain it, but none of them are yet supported by adequate experimental evidence. These suggestions include (1) the idea that the increasing cavitation tends to absorb the noise and prevent its reaching the hydrophone; (2) the idea that the noise is produced against the surface of the body itself rather than throughout the entire volume of the cavitation; and (3) the idea that the noise is produced downstream where bubbles collapse, and that this distance is greater for highly developed cavitation than at the beginning.\n\nSome indications from work in the High Speed Water Tunnel point to the possibility that the noise is not a function of the cavitation parameter alone,\nThe uncertainty of the evidence makes it best to consider cavitation noise as a single-valued function of the cavitation parameter. Figure 4 displays sound levels in the propeller tunnel of the David Taylor Model Basin, illustrating the effect of a small nick in the propeller.\n\nFigure 4 depicts observations from the propeller tunnel at DTMB. For this study, the pressure was kept constant while the speed of water past the propeller and the propeller RPM were both varied. The hydrophone in the water tunnel exhibited a distinct rise in noise level at a fairly definite velocity, which coincided with the onset of cavitation. The difference between a good propeller and one with a nick in the blade is clearly demonstrated.\nIn this figure, cavitation could be observed at the blade defect at a rather low speed. The noise was very loud when it was observed. In the work carried out by HUSL, noise measurements could be made only at very low speeds. However, under these circumstances, the noise increased very rapidly just before tip cavitation could be seen.\n\n4.4 Cavitation Noise in Torpedoes\nA good illustration of the character of cavitation noise is given by a series of observations made on the ExF42 mine at DTMB. In this work, the mine was attached to the strut supporting it from the high-speed carriage. The motor in the mine was then driven at such a speed as to furnish the power necessary for the propulsion of the mine, while the carriage itself provided the power to drag the strut through the water.\nA hydrophone was placed in the towing channel so that the mine passed over it at a few feet distance. The maximum reading of sound intensity at the hydrophone was taken as a measure of the noise produced by the mine and its propeller. The noise increased little up to a speed of almost 15 knots. But at this speed, it rose almost discontinuously through a considerable range. This was observed with the mine submerged 4 ft under the surface of the water, so the cavitation parameter is about 3.8.\n\nA principal characteristic of cavitation and the noise associated with it is its combined dependence on pressure and speed. If it can be established that cavitation on a given object sets in at a certain value of the cavitation parameter, it can be readily determined what speed corresponds to this.\nCavitation parameter for any given depth of submergence. Figure 5 demonstrates the relationship between speed in knots at various depths corresponding to several values of the cavitation parameter. The cavitation speed and depth of submergence in feet for three values of the cavitation parameter are presented in the figure. Since the ExF42 mine began cavitating at 15 knots when 4 ft deep, it follows from the lower of the three curves that at 120 ft deep, it could be driven at over 30 knots before cavitation sets in. The other two curves in the figure represent other possible situations in which the critical cavitation parameter is somewhat lower than that for the ExF42 mine. However, it must be remembered that this conclusion is valid only if the speed of all parts of the torpedo are proportionally increased.\nIt is assumed that the propeller turns twice as fast to give 30 knots as to give 15 knots. This is not strictly true, as propeller efficiency depends on the speed. Cavitation noise can be identified by the way it varies with depth. If cavitation noise is present, the noise level will decrease at greater depths. In fact, if the principal noise of a torpedo is due to cavitation, this noise can always be eliminated by operating at sufficient depth.\n\nThe procedure for analyzing torpedo self-noise consists in making a series of runs at different speeds and at different depths. Changes with depth at a constant speed can be attributed to changes in the noise caused by cavitation, while changes with speed at constant depth must be attributed to changes in both cavitation and machinery noise.\n\nPresumably, machinery noise is independent of depth.\nIn the study leading to the development of acoustic torpedoes, various measurements have been made showing the presence of cavitation noise. A set of measurements made by Bell Telephone Laboratories (BTL) for the ExS13 mine is given in Table 1. The mine was operated at speeds of 12, 16, and 20 knots and at depths ranging from 10 to 80 ft. The data indicated are plotted against the cavitation parameter in Figure 6, where they fall on a smooth curve within the following limits:\n\nCavitation noise in torpedoes\n\nFigure 6. Self noise of the ExS13 mine plotted as a function of the cavitation parameter.\nTable 1.7: Measurements of the self-noise of an ExSl3 mine in a band near 24 kc. Level measurements are in dB above 1 dyne per sq cm.\n\nSpeed (knots ft per sec) Depth (feet) Cavitation parameter K Noise level (db) of experimental error\n\nAt depths less than 50 ft, the ExS13 mine, running at 20 knots, was producing essentially cavitation noise. Numerous other examples of measurements showing the presence of cavitation noise are given in Chapter 10.\n\nChapter 5: Machinery and Other Noise\n\nIn addition to cavitation, the machinery in a torpedo is an important source of noise. At first\n\nIn addition to cavitation, the machinery in a torpedo is an important source of noise.\nThe machinery might be expected to be the principal source of noise for a torpedo running out of the water, which sounds like a tractor. In fact, in high-speed torpedoes, the engine and gear noise may dominate the cavitation. However, for torpedoes operating between 20 and 30 knots, cavitation and machinery noise are of nearly the same order of magnitude. This has made the problem of identifying the source of the noise especially difficult. Cavitation noise can be reduced by going to greater depths, but if cavitation and machinery noise are approximately equal in magnitude, reducing one does not greatly reduce the total. The only way to identify machinery noise is to eliminate it. This requires a slow process of trying one thing after another until some method of sound isolation is effective.\nIsolation significantly reduces total noise, and this must be done after cavitation noise has been effectively eliminated at an adequate depth. Extensive studies on this topic have been conducted by the Harvard Underwater Sound Laboratory (HUSL) and some studies on motor isolation have been conducted by the Bell Telephone Laboratories (BTL). This work provides general indications regarding machinery noise but is far from providing complete information on the subject, and much important work remains to be done.\n\n5.1 Gear Noise\n\nMeshing gears are a troublesome source of noise in all torpedoes containing them. In the standard torpedo with counter-rotating propellers, the main reversing gears appear to be the dominant source of noise. Of the weapons with a single propeller, the reduction of gear noise is particularly important.\nThe Ex20F contains no important gear trains, but in the ExFF3 and the ExF42 mines, the rudders are driven by high-speed motors through a train of reducing gears. Indications from noise measurements suggest that the steering motors and gears fix the background level at around 57 dB in the neighborhood of 24 kc. This low value is only achieved by careful equipment selection, and levels will frequently be much higher when an acoustic test is not used for gear inspection.\n\nExtensive studies of the main reversing gear problem have been conducted by HUSL 8. These studies clearly show that much noise is due to this source. They investigated various gear forms and materials and were able to produce some reduction in noise. The most effective procedure, however, was an isolation of the gear system from the shell.\nTwo  effective  methods  seemed  to  be  (1)  an  isolated \ngear  housing  and  (2)  an  isolated  idler  gear. \nThe  gear  housing  encloses  the  gears  and  keeps \nthem  away  from  the  water.  The  housing  is  then \nisolated  from  the  shell  by  a thick  layer  of  Fairprene. \nThe  isolated  idler  gear  is  a much  simpler  arrange- \nment in  which  the  idler  gear  shaft  is  not  mounted \ndirectly  on  the  shell  but  is  isolated  from  it  by  a thick \nblock  of  Fairprene.  Figure  1 shows  schematically \nhow  this  is  done,  and  shows  the  simplicity  of  such  a \nmodification  for  the  Mark  18  torpedo. \nThe  work  on  these  gears  has  been  done  principally \non  the  Mark  18  torpedo.  This  appeared  to  be  a par- \nticularly promising  object  of  study  for  the  following \nreasons. \n1.  It  was  at  first  expected  that  an  electric  motor \nwould  be  a quieter  mode  of  propulsion  than  a steam \nturbine  but  the  measurements  mentioned  in  Sec- \nThe third experiment 3.2 did not support this assumption. It might be suspected that the gears were dominating at least the machinery noise.\n\nThe gears in the Mark 18 are open to the sea water and fairly independent of the power plant. This makes their modification a relatively simple problem and permits a study of the wide variety of suggestions necessary in this kind of work.\n\nThe measurements made by HUSL indicated that at a depth of 50 ft, where presumably the cavitation was suppressed and the gear noise was dominant, the isolated idler reduced the effective noise level at 25 kc from -29 to approximately -44 dB. This is a very significant reduction and makes the Mark 18, at this depth, suitable for acoustic control.\n\nSince the reversing gears appear to be such an important source of noise, one might think it better to:\nA single propeller and no gears are used for torpedoes running at speeds below 20 knots. However, for torpedoes running at speeds much above 20 knots, it is almost essential to use two counter-rotating propellers. This is true for two reasons.\n\n1. Balancing the torque of a single propeller in a cylindrical torpedo is very difficult. While it is possible to put some elements off-center to create a stabilizing moment, there is a limit to the amount of moment that can be created this way. Additionally, when the torque is balanced in this way, the torpedo's heel is critically dependent on the power output and changes if the motor slows down.\n\nThe torque of a single propeller is given by the formula: Torque = Horsepower \u00d7 5252/RPM. For instance, with 180 hp at 1,600 rpm, the torque is 592 ft-lb.\nThis is not easy to balance by shifting weights, even if the torpedo is allowed to heel as much as 45 degrees. The torque can also be balanced by skewing the fins, and possibly the rudders and elevators also, to a proper angle and the necessary angle will be roughly independent of the speed. This method, however, introduces some additional drag.\n\nIn addition to the torque necessary for steady running, the initial acceleration of the propeller tends to turn the torpedo past its equilibrium position and may well turn it over. Problems of this kind can be handled in a low-power, low-speed torpedo but they become more difficult as the speed is increased. Possibly a practical limit for single propeller torpedoes lies somewhere between 20 and 25 knots.\n\nThe load per unit area on a single propeller must be almost twice as great as on a pair of propellers.\nTwo counter-rotating propellers may be desirable or even essential for avoiding cavitation, as opposed to a single propeller developing all the thrust. However, careful isolation of the gears is necessary to prevent interference between the propellers. The normal torpedo drive concept relies on both propellers turning at the same speed, requiring careful balancing to ensure equal torque application and maintain an even keel. For turbine-driven torpedoes, the gear system is necessary for both speed reduction and propeller engagement.\nIn electric torpedoes, a high-speed motor may be lighter than a low-speed motor, making its use, along with reducing gears, advantageous. If these systems are employed, a gear system is necessary. However, in electric torpedoes, each propeller can be driven separately. This was done by the Westinghouse Electric Company in their Mark 26 torpedo and their first model of an ExS29. These motors were mounted one in front of the other, and the shaft of the forward one passed through the hollow shaft of the after motor to the after propeller. The after motor drove the forward propeller through a hollow shaft. A more satisfactory arrangement is the use of a counter-rotating motor. In this design, the field coils turn in one direction, and the armature turns in the opposite direction.\nThe torque is applied between the two rotating parts of the motor, each connected to one propeller. This system has several advantages: 1. There is no torque to compensate during running or starting, allowing for a small metacentric height to ensure stability and prevent heel. No propeller balancing is required. 2. There are no gears, resulting in no gear noise. 3. The relative speed of rotation of the two motor parts is twice the speed of one propeller, enabling a high-speed, lighter weight motor without gears. Motors of this type have been built by Stone & Co. of England and by the Electrical Engineering and Manufacturing Corporation of Los Angeles. Tests have demonstrated their advantages in terms of torque balancing.\n\nTherefore, it can be repeated that for a quiet operation, this motor design is advantageous.\nNecessary to eliminate or isolate reversing gears in a torpedo. Either can be done. Other machinery noise in a torpedo comes from various sources. The control apparatus is a common source. If rudders are driven by electric motors through a gear train, this system may set the lower limit to self-noise level. In the case of pneumatically operated controls, noise is probably produced but no clear observations indicate its significance. British torpedoes' reciprocating engines produce vibrations corresponding to the number of revolutions per second and their harmonics. Frequency of propeller blades passing rudders may also appear.\nin the noise spectrum of a torpedo. Other sources of noise. The commutator and brushes of a DC motor produce a significant noise. This is transmitted to the hydrophones via the shell. Either it is transmitted through the shell directly or is radiated by the shell into the water and then picked up by the hydrophones. Neither statement is an adequate description of the interrelated action of the shell and the surrounding water in transmitting this noise, but in any case, isolating the motor from the shell seems to reduce its effect. In the process of studying the isolation of the motor from the shell, BTL made a series of observations that led to the conclusion that some types of isolating material were quite effective in inhibiting the transmission of shear vibration but were relatively ineffective against other types of vibration.\nFigure 2. A schematic illustration of a method using a material that isolates against shear vibrations only.\n\nIneffective materials against compressional waves can be countered by constructing a mounting with two isolating layers at right angles to each other. Figure 2 demonstrates this concept. In general, machinery noise exhibits well-defined frequencies below 5,000 Hz, but at high frequencies, harmonics are so close together that it's insignificant to distinguish individual frequencies. At lower frequencies, it might be possible to place a sharply tuned hydrophone at a frequency between the characteristic frequencies of machinery noise. However, specifying a manufacturing procedure that guarantees satisfactory results would be very challenging.\nThe procedure for tortery discrimination involves using a moderately high frequency where the exact frequency is of lesser importance and the variation in effective noise level from one torpedo to the next can be kept within reasonable limits.\n\nSection 5.3: Noise due to Gas Flow\n\nThe passage of high-pressure air through restrictions and valves likely produces a certain amount of high-frequency noise that can be problematic. This can potentially be controlled by isolating the pipes and fittings from the shell carrying the hydrophones. In general, very little noise of this type is carried through the air but it is very effectively transmitted by metallic contact. The emission of gas into the turbulent boundary layer surrounding a torpedo may well produce a significant amount of high-frequency noise. Experiments in which this was investigated are unspecified in the given text.\nan ExF42 mine was propelled by a seawater battery from which gas was exhausted through an opening in the top. The noise level was over 15 db above the normal running noise. This was almost as much as produced by propeller cavitation.\n\n5.4 OTHER SOURCES OF NOISE\nAlthough noise due to cavitation and noise associated with the machinery constitute the principal types of torpedo noise, there are some other types that may be of importance under certain circumstances. These have been the object of only limited study, and the following comments are essentially indications of subjects for study.\n\n5.4.1 Water-Flow Noise\nIn some cases, it appears that the turbulent surface layer of water flowing over a hydrophone produces an effect that is principally noticeable in the lower frequencies, below 3,000 c. This seems to be analogous to turbulence noise in wind tunnels.\nWindage is the phenomenon where a wind blowing over a microphone produces a significant response, despite negligible noise being radiated into the air. Water-flow noise generated in this manner would not be picked up by an external hydrophone but could contribute to the response of a hydrophone mounted in the body. It must be considered as a possible source of self-noise. This can be avoided by shielding the hydrophone itself from direct contact with moving water or by placing it near the nose where the turbulent surface layer has not had a chance to develop. Observations have been made on this type of noise by BTL, but it does not seem significant above the audible range of frequencies. In some cases, the impact of the water appears to be the primary source of noise.\nWater can cause resonant vibrations on parts of a torpedo. When a stream of water is incident on a tuning fork held underwater, the fork is set into vibration, and the sound is radiated through the water. Normally, the resonant frequencies that are not heavily damped are in the acoustic range and not much above it. Both types of water-flow noise require further study before their significance can be assessed. However, based on preliminary indications, the higher the frequency, the less important they seem.\n\n5.4.2 Propeller Vibration\nDuring some studies of experimental bodies of the type ExF42, a rather loud whine of about 2,000 Hz was observed. Propeller studies showed a natural frequency of vibration near 2,200 Hz, which changed to 2,000 Hz when the propeller was immersed.\nIn water, this vibration was apparently excited either by the motor through the propeller shaft or by water forces. Various methods were tried by BTL 10 for reducing this vibration and it can probably be controlled. However, it is fortunate that vibrations of this kind will probably be confined to the region of acoustic frequencies and can be avoided by working in the supersonic region.\n\nChapter 6\n\nHydrophone Discrimination and Isolation\n\nIn constructing an acoustically controlled torpedo, the effective noise level can be reduced just as well by reducing the response of the hydrophone to background and self-noise as by reducing the level of the noise itself. This must be done, of course, without reducing the hydrophone response to the desired signal. For this reason, it is convenient and customary to express the background and self-noise levels in decibels relative to the desired signal level.\nThe self-noise level is defined as the electrical response of the hydrophone and its circuit having the same rms value as if a plane wave of the same intensity level were incident from the direction of maximum sensitivity. The cause of the response need not be sound at all. Self-noise may be electric interference picked up by the circuit due to inadequate shielding. In many cases, a large amount of self-noise appears as vibrations in the torpedo shell, which are transmitted directly to the hydrophone and set it in vibration. In all cases, it is equivalent to noise.\nmust be controlled for effective operation.\n\n6.1 DISCRIMINATION AGAINST WATER BACKGROUND NOISE\n\nWater background noise usually comes more or less uniformly from all directions, i.e., it is isotropic. A nondirectional hydrophone responds to the total sound intensity, regardless of direction. A directional hydrophone, on the other hand, responds only to sounds coming from certain directions and therefore responds less to an isotropic sound field than does the nondirectional hydrophone. This difference in response is described by the directivity index.\n\nIf a hydrophone responds uniformly to sound incident within a solid angle \u03b8, and has a zero response outside of this angle, then its response to an isotropic sound field will be (\u03b8/4\u03c0) that of a nondirectional hydrophone. Its directivity index will then be 10 log10((\u03b8/4\u03c0)\u00b2) dB. The response to an isotropic sound field whose intensity is I is I(\u03b8/4\u03c0)\u00b2 dB.\nThe level of L will be L + D. For the purpose of reducing the response to water background noise, it is desirable to have D as much negative as possible, i.e., to have the hydrophone sensitive in as small a solid angle as possible. However, this is not a dominant factor in most cases, as the water background is the limiting factor only in rather special cases.\n\nThe directional patterns of the ExF42 crystal hydrophone and the HUSL twelve-tube magnetostriction hydrophone are shown in Figures 1 and 2.\n\nANGLE IN DEGREES\nFigure 1. Directional response pattern of a crystal hydrophone as used in the ExF42 mine.\n\nANGLE WITH TORPEDO AXIS IN DEGREES\nFigure 2. Directional response pattern of a 12-tube magnetostriction hydrophone.\n\nThese patterns are not entirely independent of the hydrophone mounting, and the curves shown represent the hydrophone mounted in a portion of a torpedo.\nThe two directive indexes, -11.0 and -13.6 db, indicate that for an average background level of 54 dB at 25 kc, hydrophone responses will be approximately -65 and -68 dB, respectively. This is low enough that it rarely compares with other noises present.\n\nFor a given hydrophone and mounting, the directivity index becomes more negative as the frequency increases. This merely means that a given hydrophone is more directional for short wavelengths than for long. Additionally, the water noise level in general decreases at higher frequencies, resulting in the hydrophone's discrimination and isolation from background noise falling off quite rapidly as the frequency increases.\n\n6.2 Discrimination Against Cavitation\n\nIn most cases, the principal cavitation around a torpedo is associated with the propeller. The noise generated by cavitation is:\n\n\"In most cases, the principal cavitation around a torpedo is associated with the propeller. The noise generated by cavitation is...\"\nFrom this cavitation is then transmitted partly through the water and partly through the torpedo shell to the hydrophone. Since the sound travels almost parallel to the shell, the distinction between these two modes of transmission is not sharp, but it indicates roughly two ways of making the hydrophone discriminate against propeller noise.\n\nThe hydrophone whose directional pattern is shown in Figure 1 was mounted in the side of a cylindrical body. The response to the fear along the cylinder is about 27 dB below that at right angles to the cylinder. To the extent that a directional pattern of this kind really represents the response of the hydrophone to the cavitation noise around the propeller, one may say that this hydrophone discriminates against cavitation noise to the extent of 27 dB. In the ExF42 mine, this discrimination is applied.\nFigure 3 displays a pattern for a crystal hydrophone, of the type used in the ExF42 mine, placed in a hemispherical nose. The hydrophone was 70 degrees off the axis. The response at 180 degrees, or straight back, is possibly 32 dB below the maximum or some 5 dB better than when mounted in the side position. HUSL conducted important measurements of the response to noise sources of hydrophones mounted in the head of a Mark 18 torpedo. The head was suspended under water and the sound source was similarly immersed a short distance away. The significant conclusion is that the discrimination is:\n\n(Note: The text appears to be in good shape and does not require extensive cleaning. Only minor corrections for typos and formatting have been made.)\nThe function of hydrophone discrimination against cavitation noise is not only dependent on the hydrophone and its mounting, but also on the nature of the shell in which it is mounted. This statement indicates the complexity of the problem and shows that a simple calculation of the directional pattern is not sufficient for describing hydrophone discrimination against cavitation noise.\n\nThe assumption that cavitation noise can be regarded as located in the water outside the torpedo is probably inadequate. There is certainly an absorption of sound by the afterbody, and some of the sound may be produced in contact with the propellers or other parts of the torpedo. In particular, some of the noise associated with the reversing gears may be cavitation noise. The water in the gears is certainly subject to variations in pressure that might well produce cavitation.\nThis cavitation is in intimate contact with the gears, and the noise may well be transmitted through the gears themselves. Isolation of the gears would then be an effective way of shielding the hydrophones from this part of the cavitation noise, as well as from machinery noise.\n\n6.3 DISCRIMINATION AGAINST MACHINERY NOISE\n\nMachinery noise is produced in direct metallic contact with the shell and is transmitted both through the shell and the water to the hydrophones. The exact process is a complicated interaction between the water and the shell that can only be partly described by saying that some energy is radiated into the water by the afterbody shell and that the energy is then absorbed from the water by the hydrophone. This partial description indicates why an isolation of the hydrophone from the machinery noise is necessary.\nThe shell is only partly effective. Discrimination seems to be improved by breaking the shell at one or more points, and also by a layer of absorbing material on the inside of the shell.\n\nChapter 7\n\nTotal Torpedo Noise\n\nThe previous chapters have described the various sources of self-noise in a torpedo and have indicated the nature of the evidence for the existence of cavitation noise and machinery noise that can be separated from each other to some extent by measuring the noise at various depths of submergence. A complete study of the noise of any one torpedo would involve running it at a variety of depths and speeds. From the curves of noise level as a function of depth for a given speed, the curve of cavitation noise could be determined, and from a curve of noise as a function of speed for a constant cavitation coefficient, the machinery noise could be isolated.\nThe machinery noise as a function of speed could be determined. By doing the same thing with different hydrophones and different hydrophone positions, at least the relative values of hydrophone discrimination could be determined. A complete series of measurements is not available for any torpedo. The noise measurements that have been made have been carried out under wartime conditions and the necessity of providing quick and rough information for the construction of usable weapons. These measurements, however, provide some crude indications of the values of the various quantities. With a liberal quantity of skepticism regarding the measurements' accuracy and a certain amount of imagination, it is possible to build up curves that illustrate many of the trends shown in the observations. In this chapter, a series of such curves is presented.\n7.1 Assumptions\n\n7.1.1 Water Background Noise\nA small background noise exists due to sources outside the torpedo. This is isotropic and its full value will be measured by a non-directional hydrophone. In the neighborhood of 25 kc, it will be assumed that the level of this noise is -54 dB with one dyne per sq cm as the reference level.\n\n7.1.2 Cavitation Noise\nIt will be assumed that for normal torpedoes, the curve of cavitation noise level as a function of cavitation parameter is that given in Figure 1. The decay is not provided.\nFigure 1. Assumed form of cavitation noise as a function of the cavitation parameter K. The tailed form of this curve is not very significant. The principal feature is that it rises rapidly as the cavitation parameter decreases, then levels off.\n\nThe curve as drawn in Figure 1 is based on the use of the forward speed of the torpedo in evaluating the cavitation parameter. If cavitation were on the nose or on some fixed part of the torpedo, such as a fin or a rudder, this would unquestionably be the correct velocity. Since, however, cavitation probably develops on the propellers, the forward velocity is the only correct one to use when comparing torpedoes with approximately similar propellers.\n\nApparently, most normal torpedoes are sufficient.\nThe propeller tip speed is proportionally related to the forward speed in most cases for similarly designed propellers. However, when using single propellers or propellers of radically different pitch, a corrected parameter K' is necessary. If vp\u00b0 is the propeller tip speed of the normal torpedo at the running speed in question, and vpf is the tip speed of the modified type of propeller, then the value of the cavitation parameter to be used with the modified propeller is:\n\nK' = K * (vpf / vp\u00b0)\u00b2\n\nWith this understanding, the velocity effective in determining the cavitation parameter is proportional to the propeller tip speed.\n\nSpeed in knots\n\nFigure 2. Assumed cavitation noise level as a function of speed for three depths and the assumed machinery noise level.\n\n7.1.3 Machinery Noise\n\nIt will be assumed that the machinery noise is proportional to:\n\nvp\u00b2\n\nwhere v is the rotational speed of the machinery in revolutions per minute.\nThe noise is proportional to the sixth power of the torpedo speed. This is a surprising law but agrees with the general trend of observations moderately well. A British report describes measurements of torpedo noise where the sound intensity was proportional to the eighth power of the speed. However, since the measured noise probably included cavitation noise, the observation is not definitive. It might seem reasonable that the noise would vary as the third power of the speed, as the power of the engine follows this law, and a constant fraction of the power might go into noise. Nevertheless, the v6 law agrees with the overall picture of the observations as well as anything else, and it will be used in the following curves. Let it be emphasized again, however, that this particular form of the law has no definitive explanation.\n7.1.4 Hydrophone Discrimination\nEach hydrophone, hydrophone position, or hydrophone isolation will be represented by a certain sensitivity to, or discrimination against, cavitation noise on one hand and machinery noise on the other. In addition, there will be a certain discrimination against background noise which is given by the directivity index of the hydrophone. This latter, however, is of negligible importance in most cases.\n\nForward Speed in Knots\nFigure 3. Total noise at 15-ft depth on the basis of idealized assumptions. Points are representative of the observations shown in Figure 1 (Chapter 1) and are the same as those in Figure 2 (Chapter 1).\n\nExternally Measured Noise\nAs indicated in Chapter 3, the noise from most standard torpedoes can be represented as a function of speed by a single curve. The indications seem to suggest that.\n\nAssumptions\nBetween 20 and 30 knots, cavitation noise and machinery noise are nearly the same magnitude. However, cavitation noise is definitely predominant at 30 knots. For speeds as high as 45 knots, the machinery noise seems to have increased again, taking the lead. We can construct curves based on the following:\n\n1. Background noise level is -54 dB.\n2. Cavitation noise level is given in Figure 1.\n3. Machinery noise level is given by L(v) = 60 log v - 120, where v is the speed in feet per second.\n\nFigure 2 shows the cavitation level and machinery level plotted separately, and Figure 3 shows their sum. These figures demonstrate how one source of noise can dominate over the other.\nThe five points indicated are from Figure 2 in Chapter 3 and indicate that the composite curve of noise, plotted roughly, is in agreement with observations. Figures 4 and 5 show how noise-speed curves may depend on depth, and Figure 6 shows the corresponding way noise depends on depth at a constant speed. Characteristic of the latter curves is the drop with increasing depth to the machinery noise limit beyond which the noise does not decrease.\n\nForward Speed in Knots\nFigure 5. Total external torpedo noise at 60-ft depth on the basis of idealized assumptions.\n\nSelf-Noise Measurements\nDuring the past two years, the Harvard Underwater Sound Laboratory (HUSL) and the Bell Telephone Laboratories (BTL) have made extensive measurements of self-noise.\n\nFigure 6. Total external torpedo noise as a function of depth.\nSelf-noise measurements for three different depths based on idealized assumptions. TOTAL TORPEDO NOISE measurements of self-noise in various torpedoes. Neither set is complete, but observations can be used for crude estimates of involved quantities and as a rough justification for the description of this noise.\n\nIn understanding self-noise measurements, hydrophone discrimination must be considered. Self-noise observations differ from external measurements described above in this respect.\n\nSpeed in knots:\n\nFigure 7. Self-noise level at 25 kc for two different depths. The hydrophone is assumed to have a discrimination of 20 db against cavitation noise and 15 db against machinery noise. Points are taken from measurements by the Harvard Underwater Sound Laboratory.\nFigure 7 demonstrates the result of a 20-db discrimination of the hydrophone against cavitation and machinery noise. This implies a response that is 20 db below that of a nondirectional hydrophone, which is 6 meters from the torpedo. The points depicted are derived from a Harvard report on measurements of a Mark 18 torpedo. Although no quantitative agreement of the points with the curves is claimed or expected, it appears clear that the points indicate a reduction in cavitation noise with increased depth.\n\nFigure 8 illustrates self-noise measurements as a function of depth for two different speeds. Since the torpedo was a Mark 18 propelled by a single propeller, it was necessary to utilize a K' = 0.455 K instead of the standard K in plotting the theoretical curves.\nThe hydrophone discrimination against cavitation was assumed to be 30 dB, and against machinery noise was 18 dB. These points come from one of the Harvard reports [16].\n\nDepth in Feet\nFigure 8: Self-noise level at 25 kc for two different speeds. Cavitation is described in terms of a parameter K' = 0.455A. The hydrophone discrimination was assumed to be 30 dB against cavitation noise and 18 dB against machinery noise. The points represent measurements by the Harvard Underwater Sound Laboratory [16].\n\nFigure 9 demonstrates an intriguing phenomenon observed in some measurements where nose hydrophones were compared with body hydrophones. The Harvard observations [17] suggested that in the study of the Mark 18 with a single propeller, the curves of noise level as a function of depth for the body hydrophone seemed to differ.\nTo cross the corresponding curve for nose hydrophones. Although it is important not to stress too much the accuracy of a few observations under difficult conditions, it is of interest to note that this effect can be produced if the different hydrophones are assigned the proper discrimination. The fact that the change in hydrophone position affects the two types of discrimination differently makes possible such phenomena, and it is clear that it is quite reasonable to expect such differences.\n\nAssumptions:\n1. The change in hydrophone position affects self-noise level as a function of depth differently for the two types of discrimination.\n2. The noise produced by nose hydrophones is idealized.\n\nFigure 10 shows a pair of curves of self-noise level as a function of depth corresponding to speeds in feet. In addition to the idealized assumptions as to the magnitude of the noise produced, it is assumed that the nose hydrophones are used.\nDiscriminate against cavitation by 23 dB and against machinery noise by 1 dB. The body hydrophones discriminate against cavitation noise by 20 dB and against machinery noise by 8 dB. The cavitation parameter K' = 0.455K is used. Speeds of 33 knots and 28 knots are plotted, assuming hydrophones discriminate against cavitation noise by 25 dB and against machinery noise by 20 dB. Points are shown indicating results obtained by HUSL on the Mark 13 torpedo. The coincidence of the two points at the 50-ft depth is of course entirely contrary to the general trend of the curves which are approaching limiting values corresponding to the difference between the machine speeds.\n\nFigure 10. Self-noise level at 25 kc for two different speeds of the Mark 13 torpedo. The hydrophone responses.\nFigure 11: Self-noise level at depths of 15 and 50 ft as a function of speed. Solid curves correspond to a discrimination against cavitation noise of 20 dB and against machinery noise of 15 dB. Dotted curves correspond to the same discrimination of 20 dB against cavitation noise, but a discrimination of 30 dB against machinery noise.\n\nThe points are taken from a report from the Harvard Underwater Sound Laboratory.18\n\nSpeed (in knots)\n\nThe total torpedo noise for machinery noise is 28 knots and that of 33 knots. However, these curves are separated by only 6 dB, so a considerable amount of this discrepancy could possibly be attributed to experimental difficulties.\nThe effect of reducing or discriminating against machinery noise is greatly dependent on torpedo speed and depth. This is clearly illustrated in Figure 11. In this figure, the solid curves are the same as those in Figure 7. The dotted curves correspond to a discrimination against cavitation noise of 20 db, but a discrimination against machinery noise or else a reduction in machinery noise of 30 db. It is clear from these curves that at 15 knots, machinery noise, with only 15-db discrimination against it, was the primary contributor to self-noise. At 35 knots, cavitation is much more prominent, although machinery noise is significantly more prominent at 50 ft than at 15 ft. This kind of curve illustrates how a real reduction in machinery noise might be completely masked if the measurement is not adequately discriminated.\nmentions were made under such conditions that the cavitation noise dominates. On the contrary, it shows that the observed fact of a reduction of 15 db in machinery noise, which is clearly evident at 15 knots, is no longer nearly as striking at 30 knots.\n\nChapter 8\nTRANSFORMATION OF ACOUSTIC SIGNAL INTO DIRECT-CURRENT VOLTAGE\n\nTo make use of the acoustic signal for control of the torpedo, a circuit must be devised that transforms the hydrophone response into a suitable signal for actuating the rudder. There are many ways of doing this, but for illustrating the principles involved, the schematic diagram of Figure 1 may be regarded as typical. This circuit is drawn for steering in the horizontal plane and is intended to operate so that\n\nFigure 1. Schematic diagram of a simple circuit for acoustic listening homing.\nThe rudder position is a function of the direction from which the acoustic signal comes. When this direction is near the axis of the torpedo, the rudder deflection is intended to be roughly proportional to the angle from which the signal comes.\n\nDescription of a Simple Circuit\n\nHp and Hs are respectively the port and starboard hydrophones. The signal from each of these first goes through an amplifier and then to a detector, which may be considered a \u201csquare law\u201d detector. It is essential that both amplifiers have the same gain, and the maintenance of this equality of gain is one of the principal problems in designing a suitable circuit. However, this difficulty will be ignored for the present, and it will be assumed that the gains are equal. Under this assumption, the DC outputs of the detectors are connected to a summing amplifier, which produces an error signal proportional to the difference between the magnitudes of the signals from the two hydrophones. This error signal is then applied to a servo motor, which deflects the rudder accordingly.\nTesters will be proportional to the intensities of the responses of the corresponding hydrophones. The two d-c signals, of the same sign, are then put into the condensers Cp and C8 and the resistances Rp and Rs. The potential Vd across the resistances is then proportional to the difference between the responses of the two hydrophones. It is positive when H8 gives the stronger response and negative when Hp is affected more strongly. The condensers and resistances are adjusted to give the desired time constant to the system. When they are large, the signal is averaged over a correspondingly long period of time and the system is not much affected by sudden sharp bursts of noise. On the other hand, the time constant must not be long compared with the dynamic time constants of the torpedo body, or the system will not respond quickly enough to steer correctly.\nThe voltage Vd is combined with the voltage from the potentiometer Pr and applied to a polarized relay. The relay's resistance must be large since it is parallel with Rp and Rs and affects the time constant of the circuit. If the resultant voltage Vr has one sign, the arm is pulled to contact a; if it has the other sign, the arm moves to contact b. There may also be a neutral position taken if |Vr| < Fr0. When the relay makes one contact or the other, the battery Bm drives the motor in one direction or the other. This turns the rudder, and since the rudder is mechanically connected to the potentiometer arm, the motion of the rudder changes the potential applied from the potentiometer Pr. If the relay has a neutral position, the motor will stop when Vr = (Vd \u2013 Vp)\nThe potentiometer voltage is near zero. This is when the potentiometer voltage is equal and opposite to Vd. The rudder deflection is then proportional to the voltage Vd, as it is proportional to Vp. This is only true until the arm reaches the end of the potentiometer or the rudder reaches its stops. If the relay has no neutral position, the rudder will oscillate about the equilibrium position with a frequency that depends on the motor and relay constants, and it will be the equilibrium position proportional to Vd.\n\nIt is clear that the relay will not operate on an infinitesimal voltage, and furthermore, the voltage corresponding to full rudder deflection is a finite voltage. On the other hand, the acoustic signal varies through wide limits as the torpedo approaches its target. For this reason, some means are necessary to limit the rudder deflection.\nOne method to adjust amplifier gains is by using an automatic volume control governed by the potential of point P. This potential is proportional to the average intensity of hydrophone responses. It is amplified as needed and applied to the amplifier grids, reducing gain when the average response increases. The gain G has its maximum value G0 until the mean response corresponds to some value P0, after which the gain is inversely proportional to potential P. Each hydrophone has a response that depends on the signal direction. Let this be Rp(\u03b8) for the port hydrophone and Rs(S) for the starboard hydrophone. Let d be the angle between the signal direction and:\n\nRp(\u03b8) for the port hydrophone, and Rs(S) for the starboard hydrophone. Let d be the angle between the signal direction and the port hydrophone response.\nThe direction of the signal aligns with the torpedo's axis. Six is positive when on the starboard side, and negative on the port side. Rp reaches its maximum for a negative value of 0, and Rs has its maximum for a positive value of 0. These responses Rp and Rs are expressed in decibels with reference to a 1 volt rms output for a sound wave of 1 dyne per sq cm rms sound pressure. Correspondingly, let Rp\u00b0 and R\u00b0 be the maximum responses of the corresponding hydrophones. If the hydrophones and their corresponding amplifiers are perfectly balanced and matched, Ra\u00b0 = Rp\u00b0 and Rp(0) = Rs(\u2013d). However, the matching is not perfect, and especially in setting up a manufacturing procedure, some lack of balance must be expected. Since the amount of unbalance is a factor in limiting performance, let Rs\u00b0 = R\u00b0 + 8.\nLet Ln be the effective level of self noise and background noise at the frequency passed by the hydrophones and amplifiers. Assuming the two hydrophone patterns are similar, the potential of point P will be:\n\nVp = -Ln/2\n\nAnd the voltage Vd will be:\n\nVd = Ln(cos(\u03b81) - cos(\u03b82))/2\n\nThis Vd will be zero only if the two hydrophones with their amplifiers and detectors are perfectly balanced, i.e., when \u03b81 = \u03b82. In general, this is not the case, and a slight differential Vd exists in the absence of any signal.\nIf a signal of level Ls is incident at an angle of 6, the responses of the two hydrophones will be:\n\nP determines the amplifier gain. For example, assume the AVC is built such that P never exceeds the value 2V. As long as:\n\nDescription of a Simple Circuit:\n2PG ^ 4, G = 1.00, but for larger values, P is held constant at 2.00.\n\nThe value of 5 is largely a matter of manufacturing reproducibility. For illustration, assume 5=1. This is an extreme value, as experience on the ExF42 mine suggests that 5 ^ 0.2 can be maintained by careful balancing of the system after the hydrophones are installed in the body and connected to the circuit. Nevertheless, time constants of the circuits are not involved. Figure 2 shows the voltage Vd when the gain is adjusted such that the self noise gives a voltage of 1 volt.\nWhen the hydrophone response is R\u00b0. Since hydrophones are expected to deviate from this by 1 db, the noise, in the absence of any signal, produces a response from the starboard hydrophone of 1.26 volts and from the port hydrophone of 0.79 volt. In the absence of any signal, the steering voltage Vd is this:\n\nor\n\nUJ\nLd\nb\ni\n\nAngle of Incident Signal in Degrees\n\nFigure 2. Illustration of the steering voltage Vd as a function of the angle \u03b8 from which the signal comes for various values of signal strength. The gain is set so that the response of a hydrophone to self-noise gives a 1-v response, and the AVC is so designed that it does not come into play until the potential of point P in Figure 1 reaches 2 v. Thereafter, the potential of P is held down to 2 v.\n\n5 = 1 will be assumed in the curves to be drawn.\nThe effect of unbalance is emphasized in this way and can be more easily seen. The quantities Ra(d) and Rp(d) depend on the type of hydrophone used and the way it is mounted in the shell. For illustration, use the directional pattern shown in Figure 2 in Chapter 6.\n\nFigures 2, 3, and 4 show the voltage Vd as a function of the direction \u03b8 from which the signal comes. This assumes a static situation, so the voltage is 0.47 volts. If the signal is 3 dB below the noise, the voltage Vd is always positive, so there can be no steering control. Under these circumstances, the rudder will be always to the right and the torpedo will circle. Since, in all probability, the minimum value of Vd will not at all give maximum rudder, the path will not be a circle of constant minimum radius, but will change in curvature. Nevertheless, the torpedo will continue moving.\nThis search mechanism is used in the ExF42 mine, but in a torpedo that is expected to start out on a gyro-controlled course, means must be adopted for steering on gyro until the signal is strong enough. Such a device is generally called a \u201cgate,\u201d and will be discussed later. Other curves in Figure 2 show the voltage when the signal level is equal to and greater than the self noise. It is clear that the \"stiffness\" of the control, the volts per degree displacement from the desired course, is a function of the signal strength. In practical manufacture, it may be in one direction or the other and may be made the basis of a simple search procedure.\n\nThe unbalance of the hydrophones causes a zero shift in the signal.\nThe steering voltage corresponds to angles other than zero, with the angle decreasing as the signal strength increases. This results in the torpedo approaching the target in a spiral. The unbalance in the hydrophones or in the angle of incident signal in degrees, as depicted in Figure 3, represents the same situation as Figure 2 but with an initial gain that is 3 db lower. In this case, the steering voltage produced by self-noise is only 0.23 v. Figure 4 shows the curves for a 3-db higher gain. From these curves, several conclusions can be drawn:\n\n1. The unbalance of the hydrophones and their amplifiers causes the torpedo to circle in the absence of external influences.\n2. The curves in Figure 3 and Figure 4 demonstrate that the steering voltage required to maintain a constant angle of attack varies with the initial gain setting.\n3. The self-noise level significantly influences the steady-state steering voltage, making precise control more challenging with higher self-noise levels.\n4. The curves suggest that increasing the initial gain can help improve the torpedo's tracking performance but may also increase the risk of instability.\n5. Properly balancing the hydrophones and controlling the initial gain setting are crucial for achieving accurate and stable torpedo guidance.\nThis unbalanced response from self-noise sets a limit on the torpedo's ability to steer based on signal strength. The torpedo with the specified properties will not steer on a signal strength 3 dB below the noise, regardless of the gain setting. The control stiffness, or volts of steering voltage per degree off course, increases as the gain increases but is not proportional to it. This analysis illustrates a typical circuit, with each circuit having unique behaviors that must be understood and related to the torpedo's dynamic behavior discussed in the next chapter.\nIn addition to the static analysis illustrated, it's necessary to make a dynamic analysis of the control mechanism's operation. The previous illustration gave the rudder position as a function of the sound direction, provided the direction was fixed and time was allowed for the rudder to reach its position. If the torpedo is oscillating and the source of sound is moving, it's important to know the rudder position for given angles of sound incidence. For very slow oscillations, the rudder position will be very close to that indicated by the static analysis, such as Figures 2, 3, and 4. For higher frequencies, however, the rudder will lag behind the sound and the amplitude of its oscillation may also diminish. As will be shown in the next chapter, it's desirable to keep this lag as low as possible.\nThe time lag is due to several factors. In the first place, the condensers Cp and C8 take a certain angle of incident signal in degrees (Figure 4). In these curves, the initial gain is assumed to be 3 db higher than in Figure 2. The rudder follows the direction of the sound in a particular way.\n\nA dynamic analysis of the control circuit can be made by artificially feeding sound into the hydrophones. This can be done by placing projectors close to each one or by feeding a suitable electric signal into the hydrophone circuit. The relative intensities can be varied to simulate a sinusoidal variation of the angle from which sound is incident on the torpedo. This variation can be carried out for a range of frequencies and the oscillation of the rudder observed.\n\nThe time to charge up, and until they do charge up to\nThe equilibrium voltage the rudder cannot reach its equilibrium position. The time necessary for this charging can be reduced by making the condensers smaller. However, this must not be carried too far, as the system should not be too responsive to short bursts of noise. Another important source of time lag lies in the rudder motors themselves. It takes them a certain time to start up and move the rudders to the desired position. In general, it is desired that the motors have a high starting torque and turn over as fast as possible, but this possibility is necessarily limited by practical considerations of size and weight.\n\nTransformation of Acoustic Signal\n8.2 Other Types of Circuits\n\nThe above analysis applies to a circuit that uses the difference in level of the response of two hydrophones to determine the direction of a source.\nThe two hydrophones respond differently due to their own directivity patterns and positions on the shell. Another method to determine the direction of a sound source is by measuring the time difference of arrival at two hydrophones or, in the case of a sustained sound, by measuring the phase difference between the responses. The phase difference is related to the sound source's bearing by the equation:\n\n\u03c6 = 2 * arctan(d / X)\n\nwhere \u03c6 is the phase difference in degrees, d is the separation of the hydrophones, and X is the wave-length of the sound. In such systems, d must not be too much greater than X. If d = X, the phase difference is 180 degrees for \u03b8 = 30 degrees, and the interpretation of results is unambiguous only for |\u03b8| < 30 degrees. Therefore, it is necessary to use:\nThis method can use either long wavelength sound or place hydrophones very close together. Although this method hasn't been implemented in the United States, an extensive study was conducted by Bell Telephone Laboratories between 1500 and 2500 c. Their work demonstrated that the phase difference type of circuit could operate satisfactorily with a signal-to-noise ratio roughly equivalent to that required for intensity difference systems. However, the self-noise at the low frequencies studied was so high and erratic that practical operation seemed doubtful. Presumably, such a system would work satisfactorily at higher frequencies if suitable close locations for the hydrophones could be found. It does not appear, however, that there is any particular advantage in doing so.\nThe phase-difference system might seem to operate at a lower signal-to-noise ratio than the intensity difference system, but detailed analysis shows this not to be the case. It will not operate effectively in the presence of noise whose level is significantly above that of the signal. However, if it is desired to operate at low frequencies for some other reason, the phase-difference system might be the easier type to use.\n\nChapter 9\n\nTorpedo Dynamics and Stability\n\nThe proper application of the acoustic signal to control the torpedo requires an analysis of the hydrodynamic behavior of the torpedo in response to its rudder. This problem has been given considerable study, and a reasonably satisfactory theory of torpedo behavior is now possible. For a detailed analysis, see the following text.\nA detailed treatment is required for the volume on torpedoes, but this text will outline enough theory to indicate significant factors and problems involved in the application of acoustic control. These factors are not greatly different from those in any automatic steering.\n\nReasons for the careful analysis of torpedo and ship steering can be roughly formulated as follows:\n\n1. A torpedo or a ship, with its rudder in the neutral position, cannot be depended upon to travel steadily along a straight course but must be steered. Few ships and somewhat more torpedoes, if left alone, will move in a circle, either to the right or to the left. The majority run in a state described as similar to neutral equilibrium. If by some means they are displaced from their course, they will:\n\n(Note: The text appears to be in good shape and does not require extensive cleaning. Only minor corrections for typos and formatting may be necessary.)\nA given rudder position does not correspond to a certain direction of motion, but to a certain system of forces and moments. In time, the forces associated with a rudder displacement will cause the body to take up a stable turning circle. However, the transient state, before the circle is reached, is the one of importance in steering. A torpedo, or a ship, does not always travel in the direction in which it is headed, but frequently at a slight angle to this direction. Therefore, a clear distinction must be made between the heading of the ship and the direction of motion. Due to such matters, the detailed treatment of torpedo motion is a little complicated. Nevertheless, it is possible to understand some of its significant features in a qualitative way without delving into the complexities.\nIn this approach to treating the problem, the issue will be addressed in several stages. The initial stage involves a crude idealization where many factors are neglected, and simplifying assumptions are made to allow for an elementary solution. In subsequent illustrations, more factors will be considered until a reasonably satisfactory picture of the situation is achieved. The effect of each factor will be highlighted at each stage, allowing the reader to explore more complex analyses as desired.\n\n9.1 Crudest Possible Treatment of Automatic Steering\n\nRecognize significant factors in automatic control by considering a very simple model and disregarding many complications. Let 0 be the angle between the vehicle's direction and a desired heading.\nThe torpedo travels in the direction of its axis at speed v. When the rudder is at angle 5, the torpedo experiences a torque proportional to 8. With positive 8, the torque acts in a direction to increase 0. This, combined with the previous assumption, allows the rudder to control the torpedo's course. The small angle 0 results in the distance h of the torpedo from its straight course given by h = vfdt.\n\nBased on these simplifying assumptions, consider the case of steering in a horizontal plane.\nThe case of depth keeping will be discussed next. For steering in the horizontal plane, assume the reference direction is from the torpedo to the sound source. In the case of a torpedo under gyroscope control, the reference direction is simply the course prescribed by the gyroscope. The following assumptions are made:\n\n4. The control mechanism is such that the rudder deflection is proportional to the angle by which the torpedo departs from the prescribed course and is in the direction to restore the torpedo to its course.\n\nBased on this assumption, combined with the first three and the fact that a body changing direction in its underwater motion experiences an opposing torque proportional to its angular velocity, the equation of motion is:\n\ntorpedo dynamics and stability\n\n\u2211 M = I\u03b1 d\u00b2\u03b1/dt\u00b2 + C\u03b1 \u03b1 + B\u03b4 + T(\u03b4 - \u03b4\\_cmd)\n\nwhere,\nM = total moment about the axis of rotation\nI = moment of inertia\n\u03b1 = angular velocity\nC\u03b1 = damping coefficient\nB = buoyancy force\n\u03b4 = angular deflection\n\u03b4\\_cmd = commanded angular deflection\nT = torque coefficient\n\nThis equation describes the behavior of the torpedo under various control inputs and environmental conditions.\nIn this equation, Q represents the effective moment of inertia of the torpedo and the entrained water. Treatments of the flow of a perfect fluid around an ellipsoid suggest that this is roughly twice the moment of inertia of the torpedo itself. K depends strongly on the torpedo's shape. For a sphere, it would be negligible, but for a torpedo, it can be estimated from model studies and observed torpedo behavior. Estimates are available for some standard torpedoes. The torque is the pound-feet force experienced by the body when the rudder angle is one radian. Its magnitude depends on the rudder area, the shape of the afterbody, the fins, the rudder location, and the velocity v. The constant a represents the stiffness of control, representing the ratio of the rudder angle to the angle of departure of the torpedo from the prescribed course d.\nSince the constant K is always positive, equation (1) represents a stable damped motion. Regardless of what may temporarily disturb the torpedo, it will eventually settle down to the prescribed course, 0 = 0. Therefore, K may be called a stabilizing factor. The larger the value of K, the less the torpedo will oscillate about its prescribed path. On the contrary, if K is large and aa is small, the torpedo will recover from a disturbance extremely slowly. Furthermore, if the target is moving, a certain minimum value of aa is necessary to ensure that the torpedo follows the change in path with sufficient accuracy to finally strike it. Hence, to achieve the desired type of tracking, a suitable balance must be struck between the \"stiffness of control\" aa and the damping K.\nLet d be the angle by which the torpedo points above the horizontal, h the distance above the desired depth. Assuming:\n\n1. The control mechanism is such that the equation of motion is given by:\n   x'''' + ax'' + bx' + cx = 0\n   or\n   x'''' + a(x'' + d) + b(x' + h) + cx = 0, making use of assumption 3.\n2. The stability property referred to is that any solution of equation (2) approaches 0 as time goes on.\n\nThe first condition for stability is that all coefficients be positive. This is automatically satisfied in the case at hand since a and c are made positive in the construction of the depth-keeping mechanism. The condition for stability is slightly more complicated than before due to the third-order differential equation.\nThe other condition for stability is: here, as before, K is a stabilizing factor, but a also influences stability. An increase of the rudder response to the angle of tilt increases the stability of the system. Conversely, an increase in k, or in v, may make the control unstable. In particular, if an attempt is made to control the torpedo depth using only water pressure without reference to the tilt, i.e., by making a = 0, the torpedo will be unstable and will not keep its depth satisfactorily. In the normal torpedo depth control, a pendulum is arranged such that a tilt of the torpedo affects the rudder position somewhat according to assumption 5, and this is a very essential part of the depth-control mechanism. It was the introduction of this pendulum that made satisfactory depth keeping possible. From these simplified assumptions.\nIt might be expected that a mechanism responsive to h would serve as well as a pendulum. However, it must be remembered that the above assumptions are extremely crude. It will be shown later why such methods are subject to important limitations. As in the case of steering in the horizontal plane, there are two opposing sets of factors. There are first the stabilizing factors: the damping coefficient K and the response to tilt aa. These tend to keep the torpedo on a steady course. Then there is the response to departures from the correct depth (a(3v)). which reduces stability but is necessary to correct disturbances in depth and keep the torpedo at the correct depth. These two properties must be correctly balanced for satisfactory depth keeping. In both of the cases discussed, the factors must be correctly balanced.\nThe leading factors contributing to stability and those for precise steering or depth keeping are opposing, requiring a suitable compromise in design. The control mechanism is such that the use of this assumption gives the differential equation a different type, whose solution must be approached differently. (Figure 1 shows phase in degrees as a function of a> for several values of the time lag r. The heavy curve gives logarithmic values.) These curves assume Q = 1500 slug ft2, K = 103 lb-ft per radian per sec, and a = 20,000 lb-ft per radian.\n\n6. Since 5 is no longer assumed to be simply proportional to 0, this equation is of a different type and requires a different approach to solve it.\n\n9.2 INCLUSION OF TIME LAGS IN THE CONTROL SYSTEM\n\nIn the above treatment of steering and depth control, the simplifying assumption was made that the rudder position followed the acoustic or other signal immediately.\nWithout any time lag, this is rarely practical or even possible. In the case of the circuit scheme outlined in Chapter 8, the condensers take a certain time to charge up, causing voltage Vd to lag behind the acoustic signal. Additionally, the inertia of the rudder motor and the rudder itself, as well as the time constant of the circuit involving them, cause an additional lag of the rudder behind voltage Vd. Thus, the crude picture is made one step closer to the actual situation by assuming, for steering in the horizontal plane, that the phases differ in the following way:\n\nAssume a periodic solution exists and then find the conditions imposed upon it by the differential equation (4). Let:\n\nSince only relative phases are important, assume:\nTo satisfy the relationship assumed in assumption 6, it's necessary that:\n\nTORPEDO DYNAMICS AND STABILITY\nand that:\n\nThese conditions can be represented by curves of the type shown in Figure 1. For illustration, it's assumed that:\n\nK = 103 pound feet per radian per second,\na = 2 x 103 pound feet per radian.\n\nThe frequency of the amplitude of 6, due to a unit amplitude of 5, is so small that it will not maintain the motion of 8, and the whole oscillation will die out. On the other hand, for r = 0.1, the phase is zero at co = 2.55 \"where the logarithm of the absolute value is -0.7. Hence, if the stiffness is high enough, i.e., a = 5.0, the motion of the body, through the control system, will maintain sufficient rudder motion to, in turn, maintain the body oscillation.\n\nCO IN RADIANS / SEC\nFigure 2. These curves are similar to those in Figure 1 but with K = 104 lb-ft per radian per sec. The value assumed for Q, the moment of inertia, is of the same order of magnitude as that for the Mark 13-2 torpedo, as is a, the rudder torque constant. To provide an illustrative case, K is taken to be about 1/10 of the probable value for the Mark 13-2. The heavy curve in Figure 1 shows the absolute value of d0/80 as a function of w for values of co between 0.1 and 10. The ordinate, as indicated on the left-hand scale, is log |Oo/8u|. The curve shows that if a = 1, equation (6) can be satisfied only for co = 1.06. For a stiffer control, a = 2, log (1/a) is -0.3, and co = 1.57 is the only possible value.\n\nHowever, it is also necessary that the left-hand side of equation (6) be real, and this requires a suitable value of r. The phase angle is also shown in Figure 1.\nFor various values of r. When r is 0, the phase is always positive, indicating no periodic solution. This corresponds to the stable cases treated previously, where each solution contains a decreasing exponential term. It could be described as the phase approaching zero stiffness being greater than 5.0 or the time lag being greater than 0.1 sec. The motion will build up larger and larger oscillations.\n\nHere is another destabilizing factor. The time lag in the control system, as well as the stiffness of control, both tend to lead to oscillations that must be opposed by hydrodynamic damping.\n\nSince the time lag in the control mechanism cannot be reduced to zero in most cases, a limit is set on the stiffness of control that can be used.\n\nFigure 2 shows the corresponding curves for a...\nTo maintain stable steering, the damping factor is ten times greater. With this larger damping factor, greater stiffnesses and time lags can be permitted.\n\n9.3. Fairly Complete Treatment of Automatic Steering\n\nTo get a quantitative treatment of torpedo steering, as mentioned at the beginning of this chapter, it's necessary to distinguish clearly between the direction in which the torpedo is pointing and the direction in which it is moving. Use the notation indicated in Figure 3.\n\nFigure 3 illustrates the notation used to describe the motion of a torpedo in the horizontal plane. The path of the center of mass is taken as the torpedo trajectory, and all forces and moments are considered as referred to this center. The angle \u03b8 describes the torpedo's heading.\nThe direction, or trajectory, refers to the course with respect to a fixed direction. The angle, denoted as \\f/, is the angle between the torpedo's axis and the course. The rudder angle, denoted as 8, is positive in the direction it tends to increase.\n\nAccording to hydrodynamics texts, the inertia of a body immersed in water includes that of a certain amount of entrained water. For a body somewhat ellipsoidal in shape, like a torpedo, the momentum can be described using two masses. One mass applies to motion along the torpedo axis, and the other to motion transverse to the axis.\n\nReferring to Figure 3, i is a unit vector in the direction of the axis, and j is a similar unit vector at right angles to it. The vector momentum of the system is given by:\n\nSince M2 is usually larger than Mi, the momentum is primarily determined by M2.\nIn computing the force necessary to change momentum, account must be taken of the change in direction of the unit vectors i and j, as well as the change of the scalar terms. This leads to the two forces, longitudinal and transverse. If it is assumed that v can be neglected and that angles and their rates of change are small quantities, Fi contains only terms of the second order of small quantities and may be considered as zero for the case of operation at constant speed. To the same approximation, the transverse force becomes:\n\nTo write the equations of motion, it is necessary to define a number of hydrodynamic coefficients. The effective forces are:\n\n1. The propeller thrust T, which may be treated effectively as a constant along the axis of the torpedo.\n2. The drag force D, which can be expressed as:\nThe terms of a drag coefficient Cd, the cross section of the torpedo in square feet A, the density of the water in slugs per cubic foot p, and the velocity in feet per second v:\n\nThe drag force is opposite to the velocity v and has components both parallel and perpendicular to the torpedo axis.\n\n1. The drag force: This is expressed in terms of a coefficient Cd.\n2. The cross force L: This is perpendicular to the velocity v and can be expressed in terms of a coefficient CL.\n3. A moment Mh: This is described by a moment coefficient Cm and length l of the torpedo.\n4. A damping moment Md: This is proportional to the angular velocity of the body and described by a coefficient Cr.\n5. A transverse force: This is associated with the damping moment and described by CF.\n\nThe drag, cross force, and moment Mh can be measured in a water tunnel or a wind tunnel to determine the corresponding coefficients.\nThey depend on the angle of yaw as well as the rudder angle. Such determinations are made with the center of mass moving in a straight line relative to the water. It is assumed that the same values are approximately correct when the motion is in some other path if the radius of curvature is large enough. The coefficients CK and CF are taken as constants. The presence of these terms may to some extent compensate for the errors in the assumption that equations (9), (10), and (11) apply when the body is moving in a curved path.\n\nTaking components along the torpedo axis:\n\npAv Z v\n\nC l and CM depend on the angle \u03b8 and the rudder angle \u03b8. Observations show:\n\nCK and Cd can be regarded as constants.\nA linear dependence is an adequate approximation for small angles. Let:\n\n- I00 Coin Radians /SEC\n\nFigure 4: The value of log |\u03c9/50| as a function of w. The heavy line gives the logarithm of the absolute value, and the lighter line gives the phase in degrees.\n\nSince angles are assumed small, terms containing sin \u03c9 can be neglected compared to the first two. Equating the first two to zero gives the speed in terms of propeller thrust when variations in v are neglected. This equation can then be omitted from further considerations of steering.\n\nThe components of force perpendicular to the torpedo axis lead to:\n\nz z\nZ\n\nAll of these terms are of the same order because Cl is proportional to \u03c9. Using expression (8) for Ft in equation (14), and equating moments to the moment of inertia times the angular acceleration:\nThe given text leads to two differential equations of motion, where a, b, c, and d are constants. When these forms are inserted in equations (15) and (16), the result can be written as:\n\n\\PAv v + \\PAv2fl + Az + Ck = vf\n\\pAv v \\pAv/ + FAIRLY COMPLETE TREATMENT OF AUTOMATIC STEERING assumes approximately the following constants, applicable to the Mark 13 torpedo with a shroud ring.\n\nThe above equations give the motion of the torpedo in response to a prescribed rudder angle \u03b8, and it will be assumed that the same equations hold when \u03b8 is changing. To apply acoustic control, \u03b8 must be made some function of (r + \\p). A fair representation can be obtained by making \u03b8 proportional to -(r + id), with a time lag, as was done in a simpler case above.\n\nTo proceed with the study of equation (18), it is convenient to assume a periodic value of \u03b8, and to consider:\n\n\\theta = -(r + id) + \\epsilon e^{j\\omega t}\n\nwhere \\epsilon and \\omega are constants.\nFind the corresponding periodic solution for 0 and p. Mi = 67 slugs, v = 50 ft per sec, \u03c1 = 2 slugs per cu ft, \u03bc = 2.23 per radian, \u03bd = 0.114 per radian.\n\nP, Ck, Cp, a, b.\n\nFigure 4 shows the value of \u03c6/0.8\u03c0 as a function of a. If the rudder is turned back and forth with a frequency \u03c9, the value of log |0.5\u03c9/C| as a function of a> is shown in Figure 5. As previously, the heavy line shows the absolute value and the lighter line gives the phase.\n\nHence, let \u03c9 = 6 = \u03b4\u00f8e\u03bbo3t, \u03c6 = \u03c60etut, where 50 is real but \u03b4\u00f8 and \u062c/0 are complex. Insertion in equation (18) then leads to:\n\nSo, A =\n\nFor illustration, the following values of the cosinusoidal motion having an amplitude of 10 degrees and a frequency of 0.0159 c (co = 0.1): the angle i will vary sinusoidally with the same frequency, a phase lag of 3 degrees, and an amplitude of about 1 degree. At this slow rate, the amplitude of \u03c6 is approximately:\nThe equilibrium value of J/ is nearly attained if the torpedo is in a steady turn with the given rudder amplitude as a fixed angle. If the frequency of the rudder motion is made ten times greater (/ = 0.159, a> = 1.0), the amplitude through which p oscillates is still approximately the same, but the phase lag has become around 28 degrees. When the frequency is again multiplied by 10 (/ = 1.59, w = 10), the amplitude of l/ is 0.18 degree and the phase lag has exceeded 90 degrees. At this frequency, the torpedo turning is always in the transient state, and steady turning conditions never get a chance to develop. The behavior of angle 0, however, is slightly different, as shown in Figure 5. For low frequencies, it can become much larger than the rudder angle since the torpedo continues to turn as time progresses. At the frequencies in question, the torpedo dynamics and stability:\n\nFor low frequencies, angle 0 can become much larger than the rudder angle since the torpedo continues to turn as time goes on. At the frequencies shown in Figure 5, the torpedo dynamics and stability:\nThe frequency of 0.0159 c (co = 0.1) causes the amplitude of 0 to oscillate with a large amplitude. On the contrary, if the rudder is moved rapidly back and forth, it follows to some extent, but 0 is hardly affected at all. When a torpedo starts to turn, \u221d increases first and then 0 follows, but if the direction of the motion is soon reversed, there is not time for any significant variation in 0.\n\nAn acoustic control will respond only to the sum of the angles (0 + \u221d), hence it is important to see how this behaves. Figure 6 shows the amplitude and phase of a quantity that lags behind the sum of the angles by a constant time lag r. This time lag corresponds to a greater phase lag as the frequency increases.\n\nGJ in radians/sec\n\nUi\n\nFigure 6. The value of log |(0\u2070 + i\u221d)/50| as a function of \u03c9. In addition, the phase of a quantity that lags behind the sum of the angles by a constant time lag r is shown. This time lag corresponds to a greater phase lag as the frequency increases.\nIf the rudder angle is approximately 6.3 times that of angle 0. If the rudder is oscillated with an amplitude of 10 degrees, the 63-degree amplitude of 0 would contradict the assumption that all angles are small and the differential equations would no longer apply. However, if the rudder amplitude is made small, say 2 degrees, the method would be applicable. Under these circumstances, angle 0 lags some 92 degrees behind the rudder angle. As the frequency is increased, the amplitude of 0 becomes rapidly smaller, so for co = 10 it is only 1/50 that of 8 and somewhat more than that of f. The phase lag is also near 180 degrees.\n\nThese curves illustrate the ways in which angles 6 and f behave when the rudder is oscillated. If it is swung slowly, f reaches a limiting value but 9 of the negative of their sum, -(0 + \u03b8) /o, approaches a constant value. The phase difference is given by the argument of the complex number z = 6 + if, where i is the imaginary unit.\nThe given text discusses the stability of a system with rudder control, where the rudder position is proportional to (-0.0 + ^0). For a system with no time lag, it is stable and can utilize a large stiffness, as indicated by the curve r = 0 crossing the axis of zero phase shift at co = 2.2, where log | (-0.0 + /0)/80 | = -0.6. However, considering the almost unavoidable time lag, restrictions are imposed on the stiffness. The curves r = 0.1 and r = 0.4 illustrate the phase of rudder oscillation if it lags \u03c4 seconds behind (0 + \u062c/). With a time lag of 0.4 sec, the phase becomes zero for co = 1.3. This implies that if the rudder is oscillated at such a rate, the body motion will maintain this oscillation when the coefficient of proportionality is properly chosen.\n\nGeneral Conclusions:\nFigure 6 shows that for:\nThe amplitude of the torpedo motion will be approximately 0.4 times that of the rudder. If the stiffness is such that a 0.4-degree torpedo angle produces a 1-degree rudder angle, the motion will be maintained. A smaller stiffness will result in stability where oscillations die out, while a greater stiffness would cause oscillations to increase without limit.\n\nGeneral Conclusions:\nThe above examples illustrate the way in which the response of a torpedo to a control system can be analyzed. The constants describing the behavior of the body must be obtained from measurements in a water tunnel or a wind tunnel and by a study of the turning characteristics of the body. The description of the control system, including things like stiffness and time lag, must be determined.\nFrom actual measurements or calculations based on the design, the following illustrations depict a \"proportional\" control system, in which the rudder position is proportional to the displacement of the torpedo from the prescribed direction. It is possible to apply similar analysis to cases where the rudder is put hard over in either one direction or the other. The details of such systems will not be worked out here, but in general, the limitations on stiffness and time lag are more severe than with proportional systems. In general, \"steering\" and \"stability\" are somewhat contrary requirements. To steer a torpedo easily, it should respond quickly and vigorously to any departure from its prescribed course. This is produced by a stiff control system, but greater stability typically requires a less responsive system.\nLarge rudders and a short radius of turn can provide good steering. however, they also make a body overshoot its course and oscillate widely around the desired path. To ensure stability on a course, corrections for departures must be tempered by limiting rudder stiffness and area, the sharpness of turns, and shaping the body to produce large damping forces. A suitable compromise between steering and stability factors is necessary.\n\nAdditionally, opposing sets of factors leading to good steering and stability can result in instability without improving steering. Therefore, it's essential to keep the control system's time lag as small as possible in the presence of stability.\nLarge time lag can be obtained only at the expense of steerability.\n\nChapter 10 Miscellaneous Problems\n\nIn the detailed application of the principles described in the previous chapters, there are many points that require careful study, and engineering skill of the highest order must be put into the design to produce a practical, workable, and rugged mechanism. Solutions to many of these problems can be recognized in a study of accepted designs and specifications and will not be discussed here. In this chapter, only a few of the problems of general importance will be mentioned.\n\n10.1 Balancing the Amplifiers\n\nIn the circuit described in Chapter 8, it is necessary that the two amplifiers be closely balanced, and this balance be maintained over a very wide range of signal strengths. The most obvious way to achieve this is by using identical amplifiers and matching their input and output impedances. Other methods include using a servomechanism or an automatic balancing network. The design of such networks is a complex task that requires a deep understanding of circuit theory and careful consideration of the specific requirements of the application. The use of active balancing networks, which employ operational amplifiers or transistorized amplifiers, is a common solution for achieving balanced amplifiers in modern electronic systems. These networks automatically adjust the amplifier gains to maintain balance, ensuring that the output signals from the two amplifiers are equal in magnitude and phase. Passive balancing networks, which use resistors, capacitors, and transformers, are also used in some applications, particularly in older designs or in situations where active components are not desired or feasible. The design of passive balancing networks is more complex than that of active networks, as it relies on careful component selection and precise component matching to achieve the desired balance. Regardless of the method used, balancing the amplifiers is crucial for maintaining the accuracy and stability of the overall system.\nTry designing and constructing amplifiers so carefully that the balance could be established once and for all and would not change. However, this is difficult for the large values of gain required, the type of service under which a torpedo must function, and the necessity of occasional tube changes. This method has been used in the ExFER42 mine, developed by the General Electric Company and manufactured by the Leeds and Northrup Company. In this circuit, the gain of the amplifiers that must be accurately balanced is considerably less than in other circuits, and although extensive service tests of this device have not yet been made, it appears to be capable of satisfactory operation.\n\nTwo other methods have been successfully used in acoustically controlled torpedoes and will be briefly indicated here.\n\n1. A Switching Scheme (10.1.1)\nThis method involves using the same amplifier for both hydrophones and rapidly switching the amplifier between them. In early experimental models of the ExF42 mine, this switching was done mechanically using a rotating commutator. Figure 1 depicts the schematic arrangement of such a system. The two commutators are driven by the same motor, causing both the amplifier and rectifier to switch between one hydrophone circuit and the other. The rate at which commutation occurs must be adjusted to the other properties of the control circuit. In the experimental model of the ExF42 mine, commutation was carried out at a rate of 40 cps. It was then necessary to make the time constant of the AVC long enough that it did not affect the difference in response between the two hydrophones and smooth out this differential.\nThe commutation frequency is also the modification frequency of the incoming signal, setting a limit for the sharpness of tuning in the amplifier circuit. Figure 1 depicts a schematic diagram of a mechanical switching system enabling a single amplifier and receiver to function in two channels. With appropriate adjustment of various time constants, this commutation system functioned satisfactorily, although not ideal for service use. In the final form of the ExF42 mine, commutation was accomplished electronically and at a significantly higher rate. This system, devoid of moving parts, was deemed more satisfactory for field use. In general, the switching method resolves the issue of balancing amplifiers but introduces additional complications related to the switching equipment and proper adjustment.\n10.1.2 GATE OPERATION\n\nThis method, which has shown satisfactory performance in experimental operation, provides monitoring of each channel by a signal of a frequency that can be filtered out of the amplifier output and used to operate volume controls. Figure 2 shows a schematic diagram of this kind of system. A single 2-kc oscillator feeds a signal into both circuits along with the signals from the hydrophones. After passing through the amplifiers, the different frequency signals are separated and the 2-kc signals are used to initiate vertical steering. Operations of this kind can be carried out by means of relays.\nIt is possible to operate a gate on the sound differential as well as the sound level in a torpedo, allowing it to steer on its gyro course until the differential between the hydrophones reaches a predetermined value. This type of gate permits operation at a lower level and keeps the torpedo under gyro control as long as it is closely headed towards the target.\n\nFigure 2. Block functional diagram of a pilot channel Sound Laboratory.\n\nThe constant and equal levels of the amplifiers are maintained by their respective AVC systems. The overall gain of the amplifiers is controlled by changing the level of the 2-kc input into both channels. This circuit requires careful design but has shown satisfactory operation in experimental models built by the Harvard Underwater Sound Laboratory (HUSL).\n\n10.2 Gate Operation\n\nIn many cases, it is desirable to have the torpedo maintain a steady course towards the target using a gate.\nOperate on a preset gyro course until the sound from the target has become sufficiently intense for adequate control. In other cases, steer in azimuth only at a fixed depth until the amplifier circuit, as developed by the Harvard Underwater Laboratory, triggers. The average sound level is given by the potential at point P in Figure 1 of Chapter 8. This can be connected to a relay through a triode, if desirable, in such a way that the relay operates when Vp reaches a predetermined value. The relay can be such that it will open again when Vp drops, or it can be such as to lock closed after it has once operated. When a level-operated gate is used to transfer from gyro steering to acoustic steering, the adjustment must be such that the gate does not operate on self-noise.\nscribed in  Chapter  8 and  would  not  continue  to \napproach  the  target.  On  the  other  hand,  the  gate \nMISCELLANEOUS  PROBLEMS \nshould  not  require  such  a high  level  to  operate  it  that \nthe  effective  homing  range  is  too  short. \nIf  the  torpedo  self  noise  were  entirely  constant  in \ntime,  so  that  the  potential  Vp  due  to  it  were  main- \ntained constant,  the  gate  could  be  set  to  operate  at \na level  only  a trifle  above  that  of  the  self  noise. \nHowever,  this  is  rarely  the  case.  The  noise  tends  to \nfluctuate  and  may  contain  modulation  frequencies \ncorresponding  to  the  revolutions  of  the  propeller. \nIt  is  then  necessary  to  set  the  gate  to  operate  suf- \nficiently high  above  the  average  background  level \nthat  it  is  not  operated,  or  at  least  is  not  often  oper- \nated, by  peaks  in  the  noise  level.  To  set  the  gate \nabove  the  highest  peak  that  can  occur  would  prob- \nThe gate can be designed so its time constant prevents operation on sharp peaks, only responding when the level is maintained for a sufficient time. A gate should operate at some 5 or 6 db above the average self-noise level for satisfactory results. If the self-noise level is low enough, the wasted 5 or 6 db is insignificant. However, since 6 db corresponds to a factor of 2 in the range, it may make the difference between satisfactory homing and a range that is too short to be useful.\nIn designing a circuit with gate operation, careful attention must be paid to the interrelationships of the various time constants. These are associated with the steering circuit, the AVC circuit, and the gate circuit. In the simple circuit shown in Figure 1 of Chapter 8, the time constant associated with Vd is the same as that of the AVC, but this need not be the case. Presumably, the maximum gain of the amplifiers will be set so that the AVC will not be called into operation by torpedo self-noise. The time constant of the steering circuit will then be made long enough to average out fluctuations in this noise but not long enough to introduce significant instability into the steering. An additional length of time constant can then be introduced into the AVC since the average response of the two hydro-electric motors is considered.\nPhones will change more slowly than the differential when the body is oscillating about its course. In some cases, the noise from a surface ship is strongly modulated at a rather low frequency corresponding to a propeller blade frequency. In such a case, it may be undesirable to use a time constant long enough to average out this modulation due to the sluggishness introduced into the system. On the other hand, it is also impossible to have the gate relay opening and closing several times a second until the minima are sufficient to operate it. Under such circumstances, the gate may require still a third time constant to control its operation.\n\n10.2.2 Differential-Operated Gate\nIt is also possible to arrange a gate to operate on the differential response of the hydrophones, as represented by the voltage Vd. If the response to self-excitation is negligible, the gate can be made to open when the voltage difference between the two hydrophones exceeds a certain value, and close when it falls below that value. This type of gate is less sensitive to noise than the level-sensitive gate, but more complex in construction.\nThe self noise in torpedoes is entirely symmetrical, ensuring it never causes differential voltage. However, hydrophone circuits may be slightly out of balance, and the noise itself may be stronger or pulsate differently on one side than the other. Therefore, allowance must be made for a differential caused by self noise. The minimum allowance must be determined through experiments on each particular type of torpedo, but initial tests suggest 3 to 4 db may be sufficient. A torpedo could start homing on a signal only 1 or 2 db above the background if it were coming essentially from one side. This method has not undergone extensive service tests but extensive experimental work is being conducted on it.\n\n10.3 RUDDER OPERATION\n\nThe rudders of a torpedo may be operated in a variety of ways. The most common method is to use a servomechanism, which is actuated by a small electric motor. The motor receives its commands from the torpedo's control system, which in turn receives its instructions from the mother ship or the target location. The servomechanism moves the rudders in response to these commands, allowing the torpedo to change course and maintain its heading. Another method of rudder operation involves the use of compressed air or hydraulic fluid to move the rudders. This method is less common than the servomechanism method but is used in some older torpedo designs. The rudder operation system is an essential component of a torpedo's guidance system, allowing it to navigate effectively towards its target.\nSteering in Depth\n\nMost conventional, non-homing torpedoes use compressed air for steering functions. However, acoustic homing devices require electric circuits and electric energy, leading to the frequent use of electrical rudder operation. One method utilizes rudder motors, suggested by analogy with the steering of large ships where motors are often used to move rudders. The first ExF42 mine employed this system, and the experience gained brought to light several disadvantages.\n\nTo obtain sufficient power without a heavy motor, it is necessary to operate the motor at high speed and drive the rudders through a reduction gear. This tends to produce noise and may be the limiting source of noise in the ExF42 mine. Furthermore, it is difficult to achieve sufficient quickness of response due to the time necessary to accelerate the motor and transmit the force to the rudders.\nThe motor and gear system were found to be one of the principal elements causing a time lag in the control system. On the contrary, rudder motors appear well-adapted to a positioning system, as they can move the rudders to the desired position and then stop.\n\nAnother method used in the Ex20F torpedo involves the use of solenoids for pulling the rudders one way or the other. This provides quick action but involves the use of heavy currents, which are somewhat troublesome to handle, and greater weight. For a system in which the rudders are thrown one way or the other, this may be the simplest procedure. However, the use of solenoids for a positioning system seems less straightforward, although it can be done.\n\n4.1.3 Steering in Depth\n\nFor an anti-submarine torpedo, the problem of steering in depth, as well as in azimuth, must be addressed.\nSolved, in addition, the discovery of cavitation as a primary source of torpedo noise suggested that the acoustic homing range could be significantly increased by using a running depth of 50 to 100 ft. To attack a surface target, it is necessary for the torpedo to approach in the correct way to hit it. This presents dynamics and control issues unlike those encountered in regular torpedo practice, and issues that are not yet fully understood. A few aspects of the matter will be discussed here.\n\nOne issue arises in relation to the torpedo's stability with regard to heel, particularly in the case of a torpedo with a single propeller. In this case, the propeller torque is counterbalanced by the torque associated with a displaced center of mass, and the torque is balanced only when the torpedo's heel angle is zero.\nThe torpedo's axis is horizontal. If it should travel vertically upward, there would be no torque compensation at all, and the torpedo would begin to spin. This implies that means must be provided to limit the angle of climb or dive to such small values that no unwanted spinning can occur.\n\nAnother associated difficulty can be illustrated by considering the case of motion in a circle. If the rudders are put hard over to port, the torpedo takes up a circular motion and continues to turn in this circle as long as power is available. However, if the elevators are put hard up, the torpedo starts to turn in a circle in a vertical plane. Before it has completed 180 degrees, it is upside down and will probably turn over, whereupon instead of completing its circle, it starts up again.\n\nAnother difficulty with vertical steering is the instability that can occur. When the torpedo is turning in a horizontal plane, the centrifugal force acting on the outer part of the turn tends to counteract the torque from the rudders, helping to maintain the turn. But when the torpedo is turning in a vertical plane, there is no such force to counteract the torque, making the turn much more difficult to control. Additionally, even small deviations from the vertical can cause the torpedo to start spinning, making it even harder to correct the course.\nWhen maneuvering in a horizontal plane, a torpedo can oscillate from side to side of its course. If it misses the target, it can turn around and try again. However, if it oscillates too widely in the vertical plane, it may jump clear out of the water and return by falling back rather than following the prescribed course. Most methods used so far to overcome or avoid these difficulties in vertical steering can be described as means for reducing maneuverability in the vertical plane and requiring sharp turning to be done by the rudders for steering in azimuth. This can be done by means of a climb angle limiter in the form of a pendulum that takes control when the inclination exceeds a certain maximum and cuts out or reduces the effect of the control surfaces.\nIn a torpedo controlled by echo ranging, a sound signal is radiated by a projector located in the torpedo, and the echo returned from a reflecting body in the neighborhood is used to steer the torpedo. Some problems involved in this type of control are:\n\n1. The projector must radiate into the water effectively.\n2. The signal level must be sufficient to overcome the noise level.\n3. The signal must be accurately focused to ensure proper target detection.\n4. The torpedo must be able to distinguish between the target echo and other echoes from the environment.\n5. The signal must be stable and consistent to maintain accurate steering.\n\nChapter 11\nSIGNAL AND NOISE LEVELS IN HOMING BY ECHO RANGING\n\nIn a torpedo to be controlled by echo ranging, a sound signal is radiated by a projector located in the torpedo, and the echo returned from a reflecting body in the neighborhood is used to steer the torpedo. Some problems involved in this type of control are:\n\n1. The projector must radiate effectively into the water.\n2. The signal level must exceed the noise level.\n3. The signal must be accurately focused for proper target detection.\n4. The torpedo must distinguish between the target echo and environmental echoes.\n5. The signal must remain stable and consistent for accurate steering.\nThe signal must have sufficient energy so that the returned echo can be distinguished from the background and self-noise. It must be radiated in a wide enough solid angle to reach any expected targets.\n\nThe listening mechanism must identify the direction from which the echo is returned. It must not be put out of commission by the periodic operation of the powerful transmitter and, as far as possible, distinguish the desired echo from undesired echoes such as reverberation and bottom echoes.\n\nThe steering mechanism must direct the torpedo based on the intermittent information obtained from the echoes. This is a somewhat different matter from steering on the continuous information available to a listening torpedo.\n\nThe remainder of this chapter will be devoted to a discussion of the problems of the projector.\nLet P represent the total power in watts radiated by the projector into the water. One of the principal advantages of the echo-ranging method is that this quantity is to some extent under the control of the designer. In general, it is desired to make this as large as possible, so attention must be given to the factors that limit it. One of these factors is cavitation at the surface of the projector. If the minimum pressure in the sound wave gets down to the neighborhood of the vapor pressure, cavities will be formed into which the liquid evaporates and gas comes out of solution. This begins to occur in the neighborhood of 2 watts per sq cm in water at about two atmospheres pressure. Observations by Bell Telephone Laboratories (BTL) have indicated that this figure can be much lower.\nThe cavitation in a large projector does not have time to develop for very short pulses of 1 to 5 milliseconds. More power can be radiated than with longer pulses. The BTL projector for trial in the Mark 14 torpedo was estimated to be radiating close to 1,000 watts, which is much above the x watt per sq cm and may be near the practical limit for transducers suitable for use in a torpedo. A large projector tends to have a narrow beam pattern, which may be undesirable as it may not direct sufficient energy off the axis to reach the desired targets. It may be desirable to use a small projector or to adjust the beam pattern accordingly.\n\nMore energy can be radiated from a large projector than from a small one. However, a large projector tends to have a narrow beam pattern, which may be undesirable as it may not direct sufficient energy off the axis to reach the desired targets. It may be desirable to use a small projector or to adjust the beam pattern accordingly. The cavitation in a large projector does not have time to develop for very short pulses of 1 to 5 milliseconds, allowing for more power to be radiated than with longer pulses. The BTL projector for trial in the Mark 14 torpedo was estimated to be radiating close to 1,000 watts, which is much above the x watt per sq cm and may be near the practical limit for transducers suitable for use in a torpedo.\nDirect the beam to scan the desired solid angle. In this connection, systems where energy is radiated first to one side and then to the other side of the axis have been suggested. If arrangements are made so that the torpedo itself moves in a circle, the beam scans a large region though it itself is narrow. The turning must be slow enough so that the beam does not sweep over the target between pulses. Such a method is used in the ExFER42 mine. However, if the torpedo starts out on a gyro-controlled course, the beam pattern must be wide enough to reach the target unless a searching procedure is introduced at a predetermined range. If the beam pattern is specified in advance, the wavelength and the linear dimensions of the hydrophone must be kept proportional to each other.\nThe power radiated is proportional to the area, therefore the level produced at the target increases with wavelength. To achieve a high signal level, a large projector and a correspondingly long wavelength should be used. If the pattern is not specified, the highest level is produced by the narrowest pattern, implying a large projector but a short wavelength. Another practical limit on radiated power is the size and weight of the apparatus required to drive the projector. Projectors are rarely more than 50% efficient and can be as low as 20%, so from two to five times the power radiated must be supplied. If a very short pulse length is used, this power can be obtained from a storage condenser to maintain the average rate.\nThe important thing about the returned echo is not its total energy but its spectrum level. If the energy is contained in a very narrow band of frequencies, and a sharply tuned receiver is used, the signal-to-noise ratio can be made higher than otherwise. However, if a short ping is used, the frequency band cannot be made too narrow. With a suitable definition of the band width Av and ping length r, it follows from Fourier analysis that for a suitably shaped pulse, the required frequency spread is T for r = 0.003 sec, which is a minimum, and for a ping with a square envelope, the required frequency spread is greater. Furthermore, allowance must be made for the doppler effect due to both the motion of the torpedo and that of the target. Since the band width of the receiver must be filled.\n\nFor r = 0.003 sec, Av = 333 Hz. This is a minimum, and for a ping with a square envelope, the required frequency spread is greater. Account for the doppler effect due to the motion of the torpedo and the target. The receiver's band width must be filled.\nThe band width of the projector must cover the discrimination against noise, in addition to the expected Doppler displacement. For this reason, the radiated band width has been usually selected of the order of magnitude of 10^6 Hz.\n\nLet Lt(d,R) be the spectrum level of the radiated signal at a distance R from the projector and off the axis by an angle \u03b8. It is assumed that the radiation pattern has circular symmetry, so \u03b8 is the only angle on which it depends. It is also assumed that the intensity falls off with the square of the radius and with an attenuation factor 1/z.\n\nwhere L(0) is the effective level at 1-meter distance and R is the distance in meters. The attenuation factor is subject to variation over rather wide ranges under different oceanographic conditions. In addition, it increases with the frequency.\nThe neighborhood of 24 kc has a rough value of 0.004 db per meter for good sound conditions, while at about 60 kc it is near 0.014. If Av is the effective band width over which the energy may be assumed to be uniformly spread, the integral expresses the fact that the power is radiated in different directions and that the total power is the integral of the flow. The factor 6.45 x 10^-9 converts the level based on a root-mean-square pressure of 1 dyne per sq cm to power in watts per square meter. The absorption between the projector and a distance of 1 meter is neglected. The integral can be expressed in terms of the directivity index D and the level for \u03b8 = 0 and R = 1, Lt. Then it follows that Lt(\u03b8) = Lt(0) - (Lt(0) - Lt(1)). The level at any other angle can be obtained by subtracting the difference Lt(0) - Lt(1) from the directional pattern.\n\nIn addition to the strength of the signal, the directional pattern is also important.\nThe strength of an echo depends on the target's nature and how it reflects the signal. For many purposes, a target's effective reflecting power can be expressed as the radius, in meters, of an equivalent sphere or the target strength. This implies that a ship does not reflect like a plane but scatters energy in all directions, serving as a satisfactory statement of the situation except when the torpedo is close to the target. A ship's effective target strength depends strongly on its aspect. From ahead or astern, the target strength will be much smaller than from abeam. Target strengths ranging from 0 to 25 dB have been observed on surface ships. For large submarines, the target strength is about 25 dB within 15 degrees of the beam. At other aspects, it is rather variable.\nThe values of the target strength for the complicated submarine shape tend to fall around an average of 13 dB. The significance of the target strength is that, when added to the signal level at the target, it provides the level of the reflected pulse at a distance of 1 meter from the target. The level of the echo at the projector is then obtained by subtracting 20 log R + fxR. Therefore, if L\u00b0r is the reflected level, the level of the reflected signal must be at least equal to the hydrophone response to the background and self-noise. This sets an upper limit to the range that can be attained and a lower limit to the power that must be used for a desired range. The question of reverberation is not involved in the determination of the necessary power.\nFigure 1. Curves A, B, and C represent the signal level reflected from a target of strength 10 dB as a function of range in meters. All three curves correspond to a frequency spread of 1,500 Hz. Curves A and B have an absorption coefficient of 0.004 dB per meter, and curve C has one of 0.028 dB per meter. The power is taken as 1,000 watts for curve A and 100 watts for curves B and C. The directive indexes for curves A and C are -19 dB and for B, -11 dB. Curves D, E, and F represent the noise level as a function of range from three types of ships, and curves G, H, and I represent three possible torpedo background noise levels. Reverberation is proportional to the power radiated. In Figure 1, curves A, B, and C show the level of the returned echo as a function of the range of the target for a number of assumed conditions. Curve A\nThe text represents more or less the situation in a scheme for echo-ranging control of a large torpedo. The power P is 1,000 watts, the directive index D is -19 dB, the frequency range is 1,500 Hz, the target strength is 10 dB, and the absorption coefficient n is 0.004 dB per meter corresponding to a frequency near 25 kHz. Such a torpedo might have a self-noise level of at least -30 dB, so the maximum range to be expected would be in the neighborhood of Curve B. Curve B represents somewhat the possibilities in the case of the proposed Bowler method of control. For illustration, the power is taken as 100 watts, D as -19 dB per meter. In this case, the self-noise may still be expected to be near -30 dB, so the maximum range might be near 450 yards. Curve C corresponds to P = 100 watts, D = -19 meters. This is somewhat like the proposed ExFER42 method.\nThe absorption coefficient corresponds roughly to what might be expected at 60 kc. This is important at ranges over some 400 yards. For short ranges, and particularly for low frequencies, the absorption can usually be neglected. The self-noise level of the ExFER42 mine at 60 kc is not well established but may be as low as -65 db. Hence, the possible range is 1,100 m even with this rather low power. In some cases, the noise made by the target ship may be an effective part of the background noise and may tend to mask the echo. It may be possible to design the hydrophone and circuit so that the torpedo will steer on such noise, in which case masking is unimportant. If, however, such a noise merely reduces the gain, it will be necessary for the echo level to be above the target level.\nOne of the major problems in the design of an echo-ranging type of homing control is providing suitable identification of the desired echo. The usual echo-ranging systems for locating submarines make extensive use of the operator's skill in distinguishing the desired echo from all the other noises that are present. Such skill is usually developed only after long practice.\n\nFigure 1 shows curves D, E, and F of the expected target noise in several cases. It is clear that when the target noise exceeds the self-noise of the torpedo, it is the target noise that sets the limit to the range that can be reached by echo ranging. Outside the useful range for listening, the echo-ranging system can be operated if enough power can be used.\n\nChapter 12\nIDENTIFICATION OF THE ECHO\n\nOne of the major problems in the design of an echo-ranging type of homing control is providing suitable identification of the desired echo. The usual echo-ranging systems for locating submarines make extensive use of the operator's skill in distinguishing the desired echo from all the other noises that are present. Such skill is usually developed only after long practice.\nDistinctions between the desired echo and other noises are a significant challenge in the design of this homing device. After sending out a signal, the listening hydrophone will detect various types of noise besides the intended echo from the target. These include:\n\n1. Self-noise and background noise.\n2. Noise originating at the target.\n3. Reverberation.\n4. Bottom and surface echoes, as well as echoes from extraneous objects.\n\nSeveral schemes and devices have been suggested and discussed for distinguishing the desired echo from these four types of noise. Some of these will be briefly outlined in this chapter, and their performance in relation to the interfering noises will be assessed. It is often possible to combine two or more of these schemes.\nOne method of identifying an echo is based on the use of a short pulse. This method requires the automatic volume control (AVC) in the detecting circuit to have a long time constant, preventing amplifier gain changes from the short pulse. Conversely, the steering circuit must have a very short time constant to respond to this sharp peak. With this system, sounds that persist longer than a pulse and operate the AVC circuit merely cause a reduction in amplifier gain and do not affect the steering mechanism. This system has disadvantages regarding self-noise and back-echo discrimination.\nThe system may respond to sharp peaks in ground noise due to the short time constant of the steering circuit. If the self-noise is highly modified, it might be necessary to set the amplifier gain so the system steers only on signals much higher than the rms value of the background and self-noise. The same applies to noise originating at the target, resulting in a discrimination disadvantage of up to 6 to 10 db. However, this system is effective for discrimination against reverberation. The intensity of reverberation is proportional to the length of the emitted pulse, making it of low level due to the use of a short pulse.\nThe AVC circuit reduces gain for irregular reverberation without too many peaks. Bottom and surface echoes, similar to reverberation, follow the same rule. A short pulse system isn't limited by reverberation or bottom/surface echoes but by self-noise and target noise. The Bell Telephone Laboratories' (BTL) experience with echo-ranging homing and the Bowler scheme supports this expectation. However, the sharpness of the emitted signal causes reverberation to consist of many sharp peaks.\nThe study of reverberation has revealed a difference in character when produced by short signals compared to the smoother form produced by a long drawn out ping. Since the echo is not returned from a simple plane surface, it tends to be drawn out to some extent. If the reflection were produced along the whole length of a 300-ft ship, bow on, the echo would be drawn out to 120 msec. Nothing so extreme as this is likely to occur, but an echo of a 3-msec signal will be returned as an appreciably longer echo if the effective reflecting surfaces are distributed over 10 ft or more in range.\n\nIn contrast, one may undertake to make use of a relatively long pulse. The development of the ExFER42 mine by the General Electric Company and the Leeds and Liverpool Explosive Company is an example of this approach.\nNorthrop Company, Inc. has proceeded along this line, involving the use of some type of volume control that will not operate on this pulse. In the case of the ExFER42 mine, the pulse is of the order of 30 msec in length, making it necessary either to have an AVC that does not operate on a pulse of this length or else to have some other form of gain control in the amplifier.\n\nDue to the long time constants involved, this method may permit operation only slightly above the rms value of the self-noise and background noise. Peaks in this noise will not affect the steering device at all. The same is true of noise originating at the target. However, due to the long pulse, reverberation will be correspondingly high. Bottom and surface echoes will also be at a high level, since their intensity is similarly more or less.\nOne method to distinguish echo from other noise is to impress a certain characteristic on the outgoing signal, recognizable when the sound returns as an echo. This is how ordinary echoes are recognized in air by recognizing a returning shout. The distinctive character of the sound may be in the form of simple modulation or it may involve frequency modulation.\n\n12.3 The Use of a Modulated Signal\n\nOne method to distinguish echo from other noise is to impress a certain characteristic on the outgoing signal that can be recognized when the sound is returned as an echo. This is how ordinary echoes are recognized in air by recognizing a returning shout. The distinctive character of the sound may be in the form of simple modulation or it may involve frequency modulation.\n\nThe problems listed in the text do not appear to be extremely rampant, so no caveats or comments are necessary. The text is already in modern English and does not contain any ancient languages or OCR errors. Therefore, no translation or correction is required.\nThe two methods described above, that of a very short pulse and that of a very long pulse, can be considered special cases of frequency modulation. It is normally expected that the character of the echo will not be present in self noise and background noise, as this noise is more or less random and if it has a modulation, the modulation of the signal can be distinctly different. The same is true for noise originating at the target, although its modulation may not be known in advance. However, since reverberation and echoes from the bottom and surface are returned from a great number of different scatterers and reflecting surfaces, the distinctive character of the pulse will be largely lost in them. On the other hand, it might be expected\nThe echo from a well-defined surface, such as that of a ship, may still contain a good deal of the original character impressed upon the outgoing signal. This will probably be true to some extent, but it must be remembered that the echo is not returned from a plane surface in general, especially in the case of a submarine. The echo is probably returned from a variety of different places on the submarine, so the distinctive character of the signal will be preserved only in case it consists of modulation carried out so slowly that the change in character while passing over the target is not significant. Only a very small amount of experimental work on this point has been done in connection with homing devices. Somewhat more has been done with ordinary echo-ranging systems. It appears that the General Electric Company has made some progress in this field.\nThe Harvard Underwater Sound Laboratory (HUSL) conducted extensive experiments on using Doppler discrimination for identifying desired echoes. The signal returning from a reflecting surface generally has a different frequency due to the motion of the torpedo. However, this is of little assistance due to self noise, background noise, and noise from the target at all frequencies, resulting in interference at the frequency of the returned echo. Similarly, reverberation and bottom noise were also present.\n\n12.4 Use of the Doppler Effect:\n\nExtensive experimental work has been carried out by the Harvard Underwater Sound Laboratory (HUSL) on the use of Doppler discrimination for identifying the desired echo. The signal returning from a reflecting surface will, in general, have a different frequency from that emitted due to the motion of the torpedo itself. However, this is of little assistance because of the fact that there will be self noise and background noise, as well as noise from the target at all frequencies. Consequently, there will be interference at the frequency of the returned echo.\n\nSimilarly, reverberation and bottom noise were also present.\nThe surface echoes will have frequency shifts different from the simple time variable gain of the emitted pulse. If the target ship is at rest, the echo frequency shift will be the same as that of the reverberation. However, if the target ship is moving, the frequency shift will differ from that of the reverberation and can be used for separation. It has been possible to construct a circuit that operates only on echoes from a moving target. The presence of some reverberation can be used to determine the torpedo speed and Doppler effect due to its own motion. It also necessitates a narrow beam, as otherwise, the Doppler effect in the reverberation from the sound sent directly ahead would be significantly different from that of the sound emitted more to the side, requiring proper correction.\nThe speed of the torpedo cannot be increased. To make the most of this system, a long pulse must be used. A long pulse permits the most satisfactory discrimination against self-noise. Since the Doppler effect is used to discriminate against reverberation, a long pulse must be used to reduce the significance of the other limiting factor.\n\nThe functional operation of such a scheme is moderately complicated, but can be made to operate more or less satisfactorily. However, it is subject to the disadvantage that it cannot be made to operate against a stationary target. For details and discussion of this method, reference should be made to the work of the HUSL on Project NO-181.\n\nTo distinguish the echo from self-noise and background noise on the basis of intensity, it is only necessary:\n\n12.5 SIMPLE TIME VARIABLE GAIN\n\n(No additional cleaning required)\nIt is necessary to require a signal higher than the background noise to operate the steering system. However, if a signal higher than the maximum reverberation is required for operation, the homing range will be almost infinitesimal due to the extreme change in level of the reverberation. At some time shortly after the signal is emitted, the reverberation will reach a maximum and then fall off quite rapidly. To make use of signals of moderate level, it is necessary to increase the amplifier gain as the reverberation decreases, but the increase must be stopped at such a point that the system will not steer on self-noise. This can be done by means of an AVC with a suitable time constant. For certain localities, it may be possible to predict approximately the reverberation and its rate of decay.\nChange amplifier gain to provide a simple method for compensating assumed reverberation. If this is achievable, one can relatively easily identify the echo based on its intensity. This is generally done, but it requires sacrificing some possible homing range, as allowance must be made for the highest possible reverberation likely to be met.\n\nThis has been a brief discussion of some methods for distinguishing the desired echo from unwanted noises. This is the basic problem of echo ranging, and in the application of echo ranging and homing control, all knowledge gained in the study of echo ranging or sonar systems must be utilized. Although considerable attention has been given to this problem, and it appears that the ExFER42 mine will operate effectively.\nA great deal of study is necessary to select the best method of operation for echo application to torpedo steering. Chapter 13.\n\nApplication of Echo to Torpedo Steering.\n\nThe problems of maneuverability and stability on course are different for torpedoes that home by echolocation compared to those that home by listening. This is because the echo information used for steering comes only at intervals, and the intervals are longer the longer the contemplated homing range. For example, if signals are emitted every second, the maximum homing range is half the distance traveled by sound in a second, or roughly some 800 yards.\n\nThis assumption assumes that time must be given for the echo to return before another pulse is emitted, and can be modified if two or more pulses are used.\nWidely different frequencies are used in sequence. A period of 1 second could be allowed for the return of each frequency. However, the number of signals returning per second would be equal to the number of different frequencies used. Pushed to the limit, this would result in an echo-ranging system similar to FM sonar, and such a system might be useful in some cases. It seems questionable, however, whether such complication would ordinarily be justified. This is partly because the effective homing range that can be obtained with satisfactory reliability is not over 800 to 1000 yards due to water conditions. When ranges are limited to this amount, information can be obtained every second and this is probably sufficient for steering at a target whose maneuverability is similar to that of ships in use today. While far from being a comprehensive study of the subject.\nThe Bowler scheme is the simplest method, suggested by the British and studied by Bell Telephone Laboratories (BTL). This method involves making the torpedo go into a circle when near the target, using the echo-ranging system to determine when the torpedo is in the neighborhood of the target and which side of its first course it should circle. In the model studied by BTL, a hydrophone was placed on each side of the Mark 13 torpedo's head. Sound pulses were emitted from both sides, and the presence of an echo could be detected in one or the other hydrophone.\nThe two sides of the torpedo system are independent. Each side is responsible for determining if there is a target on its side. A satisfactory echo from one side causes the rudder to turn towards that side, keeping it there until the torpedo circles towards the target. Preliminary analysis suggested that this simple scheme would significantly increase the probability of an effective bow shot, while leaving the probability of a hit from the beam essentially unchanged. It might even provide a target of roughly the same effective width from all directions. However, a homing range greater than the turning radius of the torpedo cannot be used, and both must be kept less than the length of the ship for a bow shot to be effective. The selection of the homing range and the turning radius are crucial considerations.\nTurning radius must be determined based on the length of the ship to be attacked, the relative speeds of the torpedo and its target, and the relative importance of bow and stern shots. In this system, everything depends on the proper identification of a single echo. A false echo on the wrong side would turn the torpedo away from the target and it would never return. A false echo on the correct side might still cause the torpedo to turn toward the target, but too soon and hence miss. To minimize the possibility of steering on false echoes, it has been suggested that two or three consecutive echoes be required to put the rudder over. With respect to steering problems, this is the simplest possible system. However, it is subject to all the difficulties associated with identification.\nThe problems with the described echoes in the previous chapter are of extreme importance due to the reason indicated. The difficulty is minimized, however, by the fact that only short homing ranges, of the order of 100 yd, are desired.\n\nCorrection of Gyro Course\n\nThe Bowler idea is undoubtedly satisfactory as a steering system since a torpedo can easily be made to run in a circle at a set depth. It only remains to be determined whether the changeover from a straight course to a circle is an effective maneuver, and whether the echo-ranging system can identify the desired echo to make the switch with sufficient reliability and at the right time. Up to the present, this has not been given any extensive field tests.\n\n13.2 Method of the ExFER42 Mine\n\nIn the ExFER42 mine, steering and searching are performed by:\n\nIn the ExFER42 mine, steering and searching are carried out as follows:\nThe mine turns in a circle and searches for a target in the absence of an echo. When an echo is identified, the rudder is thrown right and held until no echo is heard, causing the mine to approach the target along a sinuous path. The rudder is thrown hard over, making the mine go into a circular path. The angular rate of turning should be related to the beamwidth of the projector and receiver to ensure the beam does not sweep across the target.\nThe mine steers at one end of the target and the wake, as the wake is also a target reflecting the sound. The mine steers at the right end of the combination. If the normal direction of circling, without echo, is to the right, the mine will tend to steer at the left end. This may have some advantage in permitting the mine to follow along a wake until it comes to the target ship, unless of course it is going in the wrong direction. Preliminary field tests have shown that this system will operate satisfactorily against a submarine when combined with a suitable system for steering in depth. Presumably, it will also operate against a surface vessel, but extensive tests on this point have not been carried out.\nThis introduces more dynamic problems than the Bowler scheme because the torpedo is not allowed to settle down into a steady turning circle but may be barely out of the transient state before the rudder is reversed. In designing the system, it is important to know the duration of this transient state. It is also important to minimize the roll both during the transient and the permanent state of turning. This is especially true if the projector is not symmetrical about the torpedo axis.\n\n13.3 Correction of Gyro Course\n\nThe method proposed by BTL for echo-ranging control of the Mark 14 and other torpedoes applies the acoustic information to the correction of the gyroscope heading. This can be done rather easily through the gyro preset mechanism, and the questions of stability on course are then merely those of the ordinary gyroscope steering.\nIn this system, the receiving system determines the bearing of the target that returns the echo and turns the gyro to this bearing as long as it is less than 6 or 7 degrees away from the torpedo axis. If, however, the target is farther than this from the torpedo axis, the gyro is turned only a maximum amount of 6 or 7 degrees. This maximum angle is approximately the angle through which the torpedo itself can turn in the interval between successive echoes.\n\nA similar method is used in the depth control of the ExFER42 mine. In this system, the echo is interpreted as coming from either above or below the torpedo axis, and a pendulum that controls the rate of dive is adjusted accordingly.\n\nBoth of these applications make use of the information derived from the echo to make adjustments.\nThe normal torpedo control mechanism adjustments should be made slowly enough not to affect its dynamic properties and stability. This is the reason for the limited rate of turn indicated in the Mark 14 experimental control. However, they must be made rapidly enough to ensure homing in on the target.\n\nChapter 14\nNEEDS FOR FURTHER STUDY\n\nThe above outline roughly indicates the general state of knowledge concerning acoustic homing torpedoes. It is clear that our understanding of the subject is very limited and only sufficient for constructing functional weapons. Many gaps in understanding have been apparent in previous chapters, and this chapter will provide a brief summary of some principal areas for additional research.\nA great deal of study is required to make clear what kinds of homing weapons are desirable and necessary. It is easy to say that a homing torpedo should run as fast as possible, travel as far as possible, and have as great a homing range as possible. Additionally, it should be as light as possible and carry as heavy an explosive charge as possible. However, all of these ends cannot be accomplished at the same time. Some of them are more or less opposing, and it is important to make a careful evaluation of each one so that it can be properly appraised in reference to the others. Such a study would provide the basis for designing a suitable compromise.\n\nA useful tactical analysis must be based on intelligent estimates of the objectives to be desired.\nIt is not practical to have a universal weapon. A torpedo for use against merchant vessels may require a slow running speed but a long underwater range, and only a moderate explosive charge. A torpedo for use against naval vessels may require a much higher explosive charge, a higher underwater running speed, and sacrificing homing and underwater ranges to achieve this. A torpedo to be launched from aircraft should have quite different specifications from one to be launched from submarines due to the lack of stealth in its tactical use.\nConsiderable attention needs to be given to the subject of decoys. It seems probable that any acoustic homing torpedo is subject to a decoy of some kind. Careful analysis of the nature of possible decoys and their probable modes of operation can lead to a specification of a homing device of such a nature that the decoy problem is made as difficult as possible. These tactical problems have already been given some attention, and some tentative conclusions have been reached, but much more work on the problem is necessary before it can be considered fully understood.\n\n14.2 Self Noise Studies\n\nThe self-noise problem is really the heart of the acoustic homing torpedo problem. As has already been indicated, a great deal of work still remains to be done before the sources of noise are understood and before the best method of reducing and disposing of self-noise is determined.\nStudies are required to determine how to reduce noise caused by propeller cavitation. This can be divided into several categories.\n\n1. A thorough study of propeller cavitation is necessary to eliminate this source of noise while maintaining adequate thrust. Little progress has been made in this area, and cavitation noise is currently reduced by running torpedoes at considerable depths. However, this approach presents difficulties for acoustic steering in the vertical plane against surface ships. These issues could be eliminated with the availability of quiet propellers.\n\nSuch a study would likely require a carefully coordinated combination of theoretical and experimental work. This type of research has been initiated by the Harvard Underwater Sound Laboratory.\nA long-time program, it is probably only after several years of work that practical results can be expected. Cavitation at other points on the torpedo must also be avoided, but this is apparently not troublesome until speeds much higher than those at which the propeller cavitation now provides a dominant source of noise.\n\nElectric circuit and control methods:\n1. Attention is also needed to methods of reducing machinery noise inside the torpedo and of the transmission of this noise to the shell. The sources of the noise are not at all clearly understood, and the methods of acoustically isolating the machinery from the shell have only been given very preliminary consideration.\n2. The question of the dependence of self-noise on frequency has not yet been given more than a very hasty examination. It is not known whether the use of certain frequencies could reduce or increase the self-noise.\nHigher frequencies would decrease or increase the difficulty due to cavitation noise or not, and how it would affect the problem of machinery noise.\n\n4. A great deal of work is yet to be done on the problem of hydrophone isolation and the best way to provide a hydrophone that discriminates against the self-noise of the torpedo. Presumably, different characteristics are required to discriminate against cavitation and against machinery noise. Presumably, the directivity pattern is of some importance, but the method of mounting is certainly of equal importance.\n\n14.3 HYDROPHONE STUDIES\n\nIn addition to the design of hydrophones to discriminate against self-noise, considerable work seems called for on the general subject of the proper kind of hydrophone to use under the severe conditions to which a torpedo is subject. Various types of crystals should be considered.\nand magnetostriction hydrophones have been tried and suggested. Some of them have operated through the torpedo shell and some have required a hole cut in the shell. All of them are more subject to damage than desired.\n\n14.4 Electric circuit and control methods\n\nThe techniques available in electric circuits and electrical and mechanical methods of applying the acoustical information to the steering of the torpedo seem adequate to meet the requirements. Of course, considerable work can be done to improve the reliability and simplicity of the whole system. However, it seems more important to determine what it is desired for the control system to do. This must be based on the kind of study included under tactical analysis.\n\nAdditional study is always called for to improve methods of manufacture and maintenance.\nAn echo-ranging torpedo control system is one which employs a transmitter operating at a definite frequency, sending out an acoustic pulse into the water at periodic intervals, and controlling the torpedo based on the echo reflected back from the target. The hydrophone in an echo-ranging control system is exposed to the self-noise of the torpedo while listening for the returning echo. The response of the hydrophone to the self-noise determines the lowest level of echo effective in controlling the torpedo. The following review of terminology and units should help the reader follow later discussions of problems involving the use of:\n\nAn echo-ranging torpedo control system utilizes a transmitter operating at a specific frequency, sending out acoustic pulses into the water at regular intervals, and controlling the torpedo based on the echo reflected back from the target. The hydrophone in an echo-ranging system is exposed to the self-noise of the torpedo while listening for the returning echo. The hydrophone's response to self-noise determines the minimum effective echo level for controlling the torpedo. The following terminology and unit review should aid the reader in understanding subsequent discussions of related issues.\nWhen a hydrophone is exposed to a pure-tone acoustic signal in water, a voltage is developed across its terminals due to the dynamic sound pressure on its surface. In acoustics, it is common practice to express power and voltage ratios on a logarithmic scale. If there are two values of power, Pi and P2, the result is, by definition,\n\nPi = 10 log10 (P2/Pi) decibels (dB) for power ratio\n\nIf the two amounts of power are generated in systems of the same impedance, voltages will be developed such that the power is proportional to V2. Then,\n\nVi = 20 log10 (V2/V1) decibels relative to 1 v for corresponding voltage ratio\n\nIf V2 is 1 V, V1 can be expressed as 20 log10 (V1/Vref) decibels relative to 1 V, where Vref is the reference voltage. The sensitivity of a hydrophone is normally expressed as the number of decibels relative to 1 volt per dyne per sq cm rms dynamic sound pressure when a pure-tone signal is used.\nIf the hydrophone is used to measure random noise in water, a reference pressure of 0.000204 dyne per sq cm is used, and the noise sensitivity of the hydrophone is expressed as the number of decibels relative to 1 volt per 0.000204 dyne per sq cm per c. The intensity of a sound field is expressed in terms of the pressure generated in a hydrophone in a 1-c bandwidth. Arbitrarily, a sound field is defined as a zero spectrum level sound field when it is capable of generating a dynamic sound pressure of 0.000204 dyne per sq cm in a bandwidth of 1 c. The intensity of the sound field is expressed in decibels spectrum (dB) equals 20 log (rms dynamic sound pressure per cycle) / (0.000204 dyne per sq cm per c). Since the power passing through unit area in the sound field is proportional to the square of the pressure, pressure ratios in the sound field can be calculated as follows: intensity in dB = 20 log (rms dynamic pressure per cycle / (0.000204 dyne per sq cm per c)).\nThe pressure ratio in decibels (db) for a sound field with a zero spectrum level generates a pressure of 74 db below 1 dyne per sq cm per second. The power absorbed by a hydrophone and its associated equipment is proportional to the band width in cycles per second. When considering two frequency ranges A1 and Af2, the ratio of equivalent power expressed in decibels is A1 / A2. The voltage generated in a hydrophone is equal to the hydrophone sensitivity + 20 log (p / 0.000204) + 10 log (band width in cycles per sec) / (l c). The hydrophone sensitivity is the number of decibels relative to 1 volt generated by a sound field of zero spectrum level with a band width of 1 c. The rms sound pressure is p in the field within a 1-c band width.\nThe intensity of a log p/0.000204 sound field is equal to 10 dB. For instance, consider a 10 dB noise field measured with a given transducer. If this signal is fed into two different receivers, one with a 4 kc bandwidth and the other with a 1.4 kc bandwidth, the signal level as seen by the 4 kc bandwidth receiver is 10 dB above zero spectrum. The 4 kc bandwidth is then 36 dB above a 1 Hz bandwidth, resulting in an effective dynamic pressure below 1 dyne per sq cm. If the transducer sensitivity is 94 mV per dyne per sq cm per Hz, the effective voltage developed by the transducer is:\n\nThe 4 kc bandwidth receiver will have a voltage of -122 dB below 1 volt. In the second case of the 1.4 kc bandwidth receiver:\n\n(Note: The text appears to be in good shape and does not require extensive cleaning. Only minor corrections for formatting and OCR errors have been made.)\nA transducer's effective dynamic sound pressure is low, at 1 dyne per sq cm, and the effective voltage developed on the transducer is -32.5 volts. Another important characteristic of a transducer is its directivity index. If a hydrophone is uniformly sensitive to sound from all directions, its directivity index in decibels will be zero. If two hydrophones have the same sensitivity but different directivity indexes, they will give the same response to a unidirectional sound, provided the sound reaches both hydrophones on the axis of maximum sensitivity. However, if the hydrophones are placed in a sound field such as the ambient sound field in a body of water, where sound is incident uniformly from all directions, the recorded signal levels will be different. For instance, consider two hydrophones, A and:\nHydrophone A and B have the same sensitivity, but A has a directivity index of -10 dB, while B has a directivity index of -20 dB. If hydrophone A is used to measure ambient water noise with a given amplifier, and then hydrophone B is substituted, the signal level observed with B will be 10 dB lower, or -10 dB, or 10 dB less than the signal observed with hydrophone A.\n\nWhen a transducer is used as a projector, it transforms electric energy from an alternating current into an alternating sound pressure. The relationship between power and rms dynamic sound pressure is analogous to the familiar relationship connecting electric power, voltage, and resistance, and is given by:\n\nP = pc * p^2\n\nWhere P is the power delivered, measured in ergs per second, p is the rms dynamic sound pressure in dynes per square centimeter, and pc is the radiation resistance, where c is the velocity of sound measured in centimeters per second.\nmeters per second, p is the density of the medium in grams per cubic centimeter, A is the area of surface in square centimeters through which the sound passes. For example, if a projector of directivity index zero emits 400 watts of power into water, the rms pressure at 1 meter can be calculated from the preceding formula using the values: pc for water = 150,000 gm per sq cm per sec, A for 1-meter distance = 126,000 sq cm.\n\n6.9 x 104 dyne per sq cm = 97 dB above 1 dyne per sq cm.\n\nIn case the directivity index of the transducer has the not unreasonable value of -23 dB, the rms sound pressure on the axis of the transducer at 1-meter distance will be:\n\nIf the sensitivity of a hydrophone is measured as a function of angle of incidence of the signal, the sensitivity normally varies in such a way that it reaches a maximum in one direction called the axis.\nThe curve demonstrating the transducer's sensitivity variation as a function of angle is referred to as the transducer's pattern. The directivity characteristics of the transducer are typically expressed in terms of the decibel reduction in sensitivity for a given angle measured from the axis. The sensitivity curve as a function of angle usually exhibits secondary maxima of sensitivity at relatively large angles from the axis. These secondary maxima are called minor lobes, and their sensitivity compared to the sensitivity on the transducer's axis is an essential consideration in the device's performance.\n\nAn echo-controlled torpedo must be capable of emitting an acoustic signal, receiving the echo reflected from a target, and steering towards the target based on the information supplied by the echo.\nThe factors influencing the effectiveness of an echo include self-noise of the torpedo, thermal gradients in the water, strength of the target, reverberation, and enemy countermeasures. The projector on the torpedo converts electric energy from the transmitter into acoustic energy. Projectors typically have directive indices of -20 to -25 db to concentrate acoustic energy on the axis. As the sound travels through water, it loses intensity due to the inverse square law and absorption. Upon striking the target, a certain percentage is reflected, and losses occur on the return path due to the inverse square law and water absorption. Additionally, thermal gradients in the water can cause further loss in echo intensity.\n\nFactors influencing the effectiveness of an echo include self-noise of the torpedo, thermal gradients in the water, strength of the target, reverberation, and enemy countermeasures. The projector on the torpedo converts electric energy from the transmitter into acoustic energy. Projectors typically have directive indices of -20 to -25 db to concentrate acoustic energy on the axis. As the sound travels through water, it loses intensity due to the inverse square law and absorption. Upon striking the target, a certain percentage is reflected, and losses occur on the return path due to the inverse square law and water absorption. Thermal gradients in the water can also cause further loss in echo intensity.\nDuring the period immediately following transmission of an acoustic pulse, reverberation is returned from the surrounding volume of the water and from the surface and bottom. This reverberation intensity decreases with time, and although it is necessary to protect the receiver against it during the initial stages, it is not a factor which will affect maximum range.\n\nTo consider the problem exactly, it is necessary to define a quantity called target strength. Since it is possible to compute the reflectivity of a perfectly reflecting sphere, the equivalent sphere size is a convenient quantity to associate with a target.\n\nEQUIVALENT SPHERE DIAMETER IN FT\n\n[Figure 1. Relation between target strength and equivalent sphere size and representative target strengths.]\n\nIf the transmission and reflection process are formulated more exactly, another more convenient means can be used.\nLet L0 = rms pressure level of a transmitted pulse in db vs 1 dyne per sq cm at 1 yard from the projector in the direction of the acoustic axis;\nR = range in yards to the target;\na = attenuation in db per yard at the specified frequency.\n\nThe pulse intensity at the target may be expressed as:\nL0 - 20 * log10(R) - a * R\n\nAt the target, a certain fraction of the energy is reflected and the reflected ray suffers the same loss in returning to the target as it did in going out to the target. The signal strength returned to the transducer will then be:\n\nL0 - 20 * log10(R) - a * R - T\n\nIt has been shown that:\n\nT = 10 * log10(D^2 / (4 * pi))\n\nWhere D is the equivalent sphere diameter. A sphere of diameter D is the equivalent target for calculating the target strength T.\nFigure 1 displays values of T, the target strength, for several types of ships, along with the relationship between T and equivalent sphere size. To use an echo for torpedo control, a small margin of signal level above the torpedo's self-noise level is required. The acoustic range of an echo-ranging torpedo can be determined using the following equation:\n\nL0 = the acoustic rms pressure level of the transmitted pulse in dB vs. 1 dyne per sq cm at 1 yard from the transducer on the acoustic axis;\nR = the acoustic range in yards;\na = the attenuation in dB per yard;\nT = the target strength in dB;\nS = the rms self-noise level in dB spectrum (vs. 0.000204 dyne per sq cm per c) as measured with the torpedo transducer used as a receiver.\nW = the band width of the system in cycles per second; M = the signal-to-noise margin in db required by the system. If S is given in db vs. 1 dyne per sq cm per c, omit the factor -74.\n\nTable 1:\nAcoustic power in watts L0 in db vs. 1 dyne/cm2 at 1 yd\n\n---\n\nTwo commonly used frequencies for echo-ranging control are about 25 and 60 kc. The value of D for the 25-kc systems is approximately -20 db, while for the 60-kc systems it is approximately 25 db.\n\nAssuming the information in Table 2, which is consistent with the best available information, the lowest feasible values for the torpedo self-noise in a 30-35 knot torpedo are 15 to 20 dB at 25 kc and 5 to 10 dB at 60 kc.\nEcho-ranging torpedo control has been used in all torpedo applications. The actual design allows for calculating maximum acoustic range values as a function of torpedo self-noise for different values of acoustic power output.\n\nFigure 2. Acoustic range as a function of torpedo self-noise at 25 kc.\n\n[Figure 2: Acoustic range as a function of torpedo self-noise for various acoustic powers at 25 kc.]\n\nTable 2.\n\nQuantity \na T W M 3 dB 3 dB\n\nFigures 2 and 3 show the maximum ranges calculated as a function of torpedo self-noise for a series of acoustic powers for the 25-kc frequency and the 60-kc frequency.\n\nIt must be remembered that these are the values obtained under ideal operating conditions and will be decreased by the additional attenuation produced by thermal gradients if they are present.\n\nThe design of the control system, however, is determined to some extent by the application in which it is to be used. In anti-submarine warfare, for example, the system must be able to detect and track a submarine at greater ranges than in anti-ship applications. In anti-ship applications, the system must be able to detect and track a larger target at closer ranges. Therefore, the design of the control system, including the acoustic power output and self-noise levels, must be optimized for the specific application.\nIn the case of submarine applications, the torpedo is launched either from an aircraft or from a surface ship. When launched from an aircraft, the actual position and bearing of the submarine are not known. The torpedo is normally dropped as near as possible to the swirl left by the diving submarine. In this case, the torpedo searches in a circle either at some fixed depth or with the depth continuously increasing. As soon as the torpedo receives an echo from the target, it goes into acoustic control in both azimuth and depth until it either strikes the target or loses acoustic contact. It is obviously necessary in this type of device to use acoustic control in both azimuth and depth.\n\nIn the case of a surface-ship-launched antisubmarine torpedo, there is some knowledge of the target's bearing at the time of launching, but the depth is not known precisely.\nA torpedo is launched at such short ranges that circling search is employed. Since the amount of explosive which is necessary to cripple a submerged submarine is less than that necessary to cripple a surface warship, a small torpedo is usually used. This limits the angle over which it is possible for the torpedo to locate a target in the initial search. Two compromises have been used. One is to make the beam pattern of the hydrophone very narrow in the vertical plane and broad enough to cover an angle of approximately 60 degrees in the horizontal plane. For tactical reasons, these torpedoes have been designed so that they can be carried in the bomb bays of ordinary bombing planes.\n\nAcoustic range in yards (Figure 3)\n\nThis service employs circling search because torpedoes are launched at such short ranges. Due to the smaller amount of explosive required to damage a submerged submarine compared to a surface warship, a smaller torpedo is typically used. This limits the search angle for the torpedo in locating a target. Two compromises have been made. One is to create a hydrophone beam pattern that is very narrow in the vertical plane but broad enough to cover approximately 60 degrees in the horizontal plane. For tactical reasons, these torpedoes have been designed to be carried in the bomb bays of ordinary bombing planes.\n\nAcoustic range as a function of torpedo self-noise at 60 kc (Figure 3)\nIn anti-surface ship applications, the torpedo may be launched from a submarine, another surface ship, or an aircraft. In these applications, the target's bearing is quite accurately known at the time of launching, and the range from which the torpedo may be fired is considerable. Since the operating range of these torpedoes is greater than their acoustic range, it is necessary to use gyro control in the initial portion of the run. From the standpoint of self-noise of the torpedo and the effectiveness of countermeasures used against it, it is desirable to have hydrophones with quite sharp beam patterns. The effectiveness of the projector is also increased if its beam pattern is sharper. However, making hydrophone beam patterns very sharp reduces their sensitivity. The other option is to use a hydrophone with a sharp beam.\npattern in both planes; but to control the gyro course so that, instead of running straight, the torpedo oscillates back and forth over the direction of firing, allowing its hydrophone to scan an angle of 60 to 80 degrees. Since the vertical level of a surface ship is fixed, anti-surface-ship echo-ranging torpedo control systems are often arranged only for azimuth control and depend on a purely hydrostatic control to determine the running depth. Since the self-noise of a torpedo is determined largely by propeller cavitation, there is some advantage in operating at a depth of approximately 50 ft for the initial portion of an attack. In order to do this, it is necessary to include means of acoustic control of depth to bring the torpedo up near enough to the surface to strike the target.\n\nAn echo-ranging torpedo control system is necessary.\nThe more complicated echo-ranging system justifies its use by having sufficient advantages over the simple listening system. The echo-ranging device offers the following advantages:\n\nCountermeasures against it are typically different from those used against listening torpedoes. A well-placed noisemaker that mimics a ship's noise is usually sufficient to limit the effectiveness of the listening device. Since the nature of the transmitted pulses can be controlled in an echo-ranging system, it is possible to predetermine the necessary countermeasure to limit its effectiveness. Variation of factors such as the frequency of the acoustic signal or the length of the transmitted pulse can be used to impede its effectiveness.\nOne effective means of countering an ordinary listening torpedo is for the target to slow down, reducing the noise generated by its propellers. This procedure would be ineffective against an echo-ranging device. In the case of use as an antisubmarine device, echo-ranging torpedoes have been made to follow the wake of the submarine and make successful attacks from greater ranges than acoustic ranges. Since the energy in the transmitted signal is concentrated at a single frequency, the receiver's frequency range of sensitivity can be considerably less than that in the receiver of a listening torpedo. This means the performance of the echo-ranging system will be less limited by the self-noise of the torpedo.\ncase  in  the  listening  devices.  It  is  not  possible  to  fire \nlistening  torpedoes  in  salvos  because  the  later  ones \nfired  will  tend  to  follow  the  earlier  ones.  By  design- \ning echo-ranging  torpedoes  so  that  more  than  one \noperating  frequency  is  used,  it  is  possible  to  fire  suc- \ncessive echo-ranging  torpedoes  by  using  different \ntorpedoes  whose  systems  operate  on  different  fre- \nquencies. If  the  echo-ranging  system  is  so  designed \nthat  it  will  not  steer  on  noise,  salvo  firing  can  even \nbe  used  with  only  one  frequency  of  operation,  pro- \nviding the  intervals  of  firing  are  great  enough  so  that \nthe  sensitivity  of  the  receivers  of  the  later  torpedoes \nwill  not  be  reduced  because  of  the  noise  generated \nby  the  propellers  of  the  first  ones  fired.  A listening \ntorpedo  controls  on  the  noise  generated  by  the  pro- \npellers of  the  target.  The  tendency  is,  therefore,  for \nThe torpedo to strike at or near the propellers, which will cripple the target but not necessarily sink it. On the other hand, an echo-ranging torpedo tends to strike further toward the bow of the target, and it is even possible to control to some extent the part of the target on which the torpedo will strike.\n\nThe use of an echo-ranging system also has some disadvantages. The most important is the fact that its use gives it away. Very shortly after firing, the transmitter starts sending out acoustic pulses which can be received by the target's sound gear. This makes possible the more effective timing of countermeasures, and when the torpedo is fired from a submarine, it tends to give away the approximate bearing of the submarine at the time of firing. The greater complication in the control system necessary in order to utilize the maximum potential of the echo-ranging system.\nThe advantages of an echo-ranging system make maintenance and service problems with these torpedoes more difficult. The effectiveness of an echo-ranging control system depends to a greater extent on external water conditions than with a listening system. Since it is necessary for the acoustic signal to travel two ways instead of one, unfavorable water conditions for the transmission of an acoustic signal will have a chance to affect echo-ranging signals twice. Layers causing refraction and reflection due to variations in salinity and temperature may sometimes cause significant difficulties. Even masses of seaweed or schools of fish can behave as fictitious targets. To determine whether an echo-ranging system should be used rather than a simple listening system, it is necessary to weigh these variables.\nThe most effective arrangement is probably the use of both echo-ranging and listening torpedoes. Echo-ranging torpedoes should be used where the counter-measure problem is most important, and listening torpedoes where it is especially important to avoid detection of the submarine by the enemy. An acoustic torpedo provided with a switch on the outside of the body, which could set it up either as a listening or an echo-ranging device, depending on the conditions at the time of launching, would be an ideal weapon.\n\nTo operate an echo-ranging torpedo, it is necessary to transmit pulses of signal at intervals to provide periods in which the receiver can listen for the returning echo. Since sound has a velocity of about 5,000 feet per second in water, a listening interval of 1 second for each 2,500 feet is necessary.\nThe maximum possible range increase of a torpedo requires the interval between transmitted pulses to be increased in proportion. This is because the frequency of received information for acoustic torpedo control decreases as the maximum range increases. The most common steering system in torpedoes is the on-off type, where the rudder is turned hard to port or starboard. When used in a torpedo under echo-ranging control, the amplitude of the torpedo's oscillation during an attack increases with the maximum acoustic range of the torpedo. If the transducers used have narrow beam patterns in azimuth, there is a danger of receiving information when the torpedo's axis makes a significant angle with the target bearing.\nNecessary for determining the maximum possible range of an echo-ranging torpedo is carefully considering the body dynamics of the torpedo and the sharpness of the beam pattern of the transducer. As maximum ranges increase, developing proportional types of steering control will likely become more important.\n\nAssuming the acoustic pulse transmitted into the water by a given transmitter and projector represents a given amount of acoustic power, the level of the echo returned by a target is a function of the distance from the torpedo to the reflecting target. For greater distances between the torpedo and the target, the level of the echo will be less. The time of transit of the signal from the projector to the target and back to the hydrophone is also a factor.\nA direct measure of the target's range can be obtained by using a time variation in the receiver's sensitivity to account for variations in echo level with range. This variation in receiver sensitivity with range is important due to reverberation. When a pulse of acoustic energy is transmitted into the water, a signal is received by the hydrophone due to sound energy scattered back from the surrounding water volume. This sound is known as volume reverberation. In addition to volume reverberation, some sound is scattered from the water surface and the ocean bottom. These signals are known respectively as surface and bottom reverberation. Their importance relative to volume reverberation is determined by the nearness of the surface and bottom to the torpedo. In most cases, the surface or bottom reverberation is less significant than volume reverberation.\nThe most important factor in the total reverberation level is bottom reverberation. The level of reverberation decreases with time after transmission in much the same manner as the echo from a given target. The use of time variation of receiver sensitivity can prevent it from causing the torpedo to steer on bursts of reverberation. This time variation in gain of the receiver amplifier can be controlled by the same time base used to control the time of transmission. This type of gain control is usually designated as TVG. In operating torpedoes under various conditions, the ambient noise which may be encountered in the water will vary from one place to another. The level of ambient noise may be contributed to by noise-making countermeasures employed by the enemy. In order to effectively deal with these variations, the torpedo's receiver includes a noise limiter. This limiter, when activated, reduces the receiver's sensitivity to ambient noise, allowing it to better detect the target's echo. The time base used to control the noise limiter is synchronized with the time base used to control the torpedo's active sonar system, ensuring that the noise reduction is applied at the appropriate time during the torpedo's flight. Additionally, some modern torpedoes employ adaptive noise cancellation techniques, which continuously analyze the ambient noise and adjust the receiver's sensitivity in real-time to optimize target detection. These techniques can significantly improve the torpedo's ability to detect and engage targets in complex acoustic environments.\nTo protect the receiving system against noise, the level of the received signal may be used to control receiver sensitivity. In order to prevent the receiver sensitivity from being controlled by echoes, a large enough time constant must be used in the control network so it will not respond during an echo's interval. This type of control of receiver sensitivity is known as automatic volume control (AVC). Most echo-ranging receiver systems employ both AVC and TVG, although the manner in which they are actually used varies considerably from one system to another. The time constant employed in the AVC loop will vary with the length of the transmitted pulse used.\n\nAn ordinary listening torpedo responds to the noise emitted by the propellers on the target, unless\nA noise-making countermeasure is being used, and an echo-ranging torpedo responds to the echo returned by the target. However, when the target moves rapidly through the water, a wake is generated, consisting of large numbers of air bubbles that extends for a considerable distance aft of the target. The wake is an effective reflector, and the problem of devising a system capable of distinguishing between the wake and the true target is difficult.\n\nOne important advantage of an echo-ranging control system is the ability to increase the power of the transmitter to quite large values, thus controlling the level of echo returned by a given target at a given range. If the power of the transmitter is increased, the voltage required in the transmitter power supply also increases. The decrease in [text truncated]\nMajor components of echo-ranging torpedo control systems include:\n\n16.1 Time Base:\nIn all echo-ranging systems, a time base is essential to determine the time interval between transmitted pulses and the length of the transmitted pulses. Additionally, the receiver must be made inoperative during transmission intervals, and in cases of time-varied gain (TVG), the time of application of the TVG control voltage must be controlled. The simplest form of time base is a system of cam-operated switches to control various events. The cams may be operated by a simple mechanism.\nThe motor may be driven by a prime mover or operated directly by the torpedo propulsion motor. In some systems, a purely electronic timing system is used, employing combinations of multivibrator circuits and relays. An electronic time base has the advantage that its elements can be mounted directly on the chassis containing the rest of the electronic gear, while systems using cam-operated switches have the advantage of simplicity and greater reliability.\n\n16.2 Signal Generator\n\nThe simplest type of signal generator used is the one in the German Geier system, which consists of a condenser charged to a high potential and then discharged by means of a cam-operated switch through the tuned circuit of the transducer. The more common type of signal generator employs a power oscillator, which oscillates at a constant frequency and drives the tuned circuit of the transducer.\nThe signal generator can be keyed by the time base, or an oscillator driving a power amplifier arranged for both to be keyed by the time base. Since the signal generator operates only for a small fraction of the total elapsed time, the generated power during the transmitted pulse can greatly exceed the components' continuous duty ratings. The extent to which these ratings can exceed normal continuous duty ratings depends on the length of the pulse. For instance, in the Ordnance Research Laboratory (ORL) project 4 system, the transmitter can generate approximately 1.5 kw of electric power for transmission in 30-msec pulses, at 1.5-sec intervals. The power amplifier utilizes two 829B tubes with a plate voltage of 1,500 v. The Bell Telephone Laboratories (BTL) 157C system generates 1.5 kw.\nThe electric power is transmitted in 3-millisecond pulses with one pulse per second, utilizing a single 829B tube with a plate voltage of 3,000 volts. The use of a plate voltage higher than 1,500 volts with pulses lasting 30 milliseconds is impossible with 829B tubes due to the tube's tendency to breakdown with excessive plate voltage being a function of pulse length. The power limitation in both systems is determined by the value of plate supply voltage at which tube breakdown begins rather than by the power-handling capabilities of the electrodes.\n\nAn important function in an echo-ranging system is the conversion of the electric power generated in the signal generator into acoustic power in the water during transmission, and then the conversion of the acoustic power in the returned echo into electric power.\nThe signal applied to the receiver can be generated using a single transducer or separate projectors and hydrophones. When the same transducer is used for both projector and hydrophone, protection for the receiver during transmission is necessary. This can be achieved through use of a switching system, varistors, or by designing the coupling circuits to prevent excessive voltages from being applied to the receiver.\n\n1. Receiver:\nThe receiver's function is to take the electric signal generated in the receiving hydrophone, amplify it, and use the information contained in the signal for torpedo control. The receiver signal level may vary from quite low to quite high values.\nThe receiver must handle the expected signal range for a RELAY CONTROL SYSTEM. TVG and AVC are typically used to ensure this. The receiver can compare signal levels on two separate hydrophones or determine target bearing through phase relations between electric signals in the hydrophone halves. In simpler cases, the receiver can resemble those used in listening-type control systems. However, to optimally utilize an echo-ranging system's advantages, receivers usually process signals to distinguish real echoes from other noises in the water. Since the transmitted pulse is a pure-tone signal, the signal frequency range is important.\nThe receiver must be sensitive, normally less than in the case of listening-type devices. However, it is necessary to have a sufficient range of frequency response to handle the maximum amount of doppler shift in frequency that may be present in an echo. In some cases, the receiver contains two separate systems: one, a steering receiver, which interprets the signal to determine the direction of control necessary for the torpedo; the other, an enabling receiver, which determines, based on the characteristics of the received signal, whether the steering receiver should pass its information on to the control system.\n\nThe information that comes to the receiver must be used for actual steering of a torpedo. To accomplish this, the information must be passed on to the engines that control turning of the rudders.\n\n16.5 RELAY CONTROL SYSTEM\n\nTo use the information that reaches the receiver for actual torpedo steering, it is necessary to pass this information on to the engines that control rudder turning.\nThis is done by some sort of relay control system. In some cases, only relatively rugged relays are used, and sufficient amplification is used to operate these relays directly. In other systems, delicate relays are used to operate the rugged control relays, and correspondingly less amplification is used in the electronic gear. In addition to the relays used for actual steering control, relays are also used to determine when the steering system should be locked off from normal gyro control; and in some cases, where a special enabling receiver is used, the enabling of the steering receiver may be done by means of a relay.\n\nChapter 17\n\nNature of the Control Problem\n\nEcho-ranging torpedoes can be divided into two main classes: those used in antisubmarine service and those used in anti-surface-ship service.\nThe torpedo used in the antisubmarine service is normally smaller than that used in anti-surface ship service, because the amount of explosive necessary to disable a submarine is less than that necessary to disable a surface ship. Most antisubmarine torpedoes are launched from aircraft, and the use of a torpedo of about 7-ft length makes possible the use of standard bombing planes for launching.\n\nAttacks made against submarines using acoustic torpedoes are usually made when the submarine is submerged. When the torpedo is launched from an aircraft, the location of the submarine is actually unknown both in depth and in position. It is therefore necessary, as stated in Chapter 15, to have a torpedo which is capable of searching both in the azimuth and vertical planes. It is also necessary to have a homing torpedo.\nA torpedo capable of operating at a depth to attack a submarine at any feasible operating depth for the submarine.\n\nWhen launched from an aircraft, the torpedo is typically launched at the point where the submarine was last seen submerging. The torpedo then searches until it makes acoustic contact with the submarine and homes in on it.\n\nIf launched from a surface ship, the submarine is located by the ship's sound gear, providing the approximate bearing and range at the time of launching. To prevent homing on the launching ship, a ceiling switch and suitable means are necessary in the torpedo.\nThe method of azimuth search in all echo-ranging antisubmarine torpedoes involves having the torpedo circle until it makes acoustic contact with the submarine. The depth behavior during search varies in different systems. Some are arranged for the torpedo to dive rapidly to a fixed operating depth where it circles under hydrostatic control. In others, the torpedo dives slowly, making its search a gradually descending helix. This dive may continue until acoustic contact is made or until the torpedo reaches the bottom, or it may be interrupted at some predetermined depth and the torpedo levels off. In the actual acoustic control of an antisubmarine torpedo, it is necessary to control the device acoustically in both depth and azimuth.\nAcoustic control in the two planes may be the same. This is true in the system developed by the Harvard Underwater Sound Laboratory (HUSL), where azimuth steering information is obtained by comparing the electrical phase relation between the signals generated in the right and left halves of the transducer, and vertical steering information is obtained by comparing the electrical phase relation between the signals generated in the top and bottom halves of the transducer. A similar procedure is used in a version of the British \u201cDealer\u201d device, except that a switch is used in the time base which alternates the system from vertical information to azimuth information. In this way, a single two-channel amplifier is used which alternately operates for azimuth and depth. The control for both azimuth and depth is accomplished by comparison.\nIn this system developed by the General Electric Company, the method for securing acoustic-steering information in the two planes is different. Comparison of the electrical phase relation between the top and bottom halves of the transducer is used for vertical steering control. Azimuth steering control, however, is an on-off control. When echoes are received, azimuth rudders are turned hard to starboard. Conversely, when no echoes are received, the rudders turn hard to port. With this arrangement, a single two-channel amplifier can be used for comparison of the phase of signals for vertical control, and azimuth control is determined simply by whether the amplifier is receiving information or not. In anti-surface ship service, the torpedo may be employed.\nThe problem of launching an acoustically controlled torpedo from a surface ship requires caution to prevent homing on the launching ship. In the anti-surface ship service, the target's bearing and range are fairly accurately known, and the launching range is normally large. All devices used in this service operate initially under gyro control. The torpedo, operating under gyro control, gets within acoustic range of the target, and when acoustic signals are received, the acoustic control takes over. In the system developed by Bell Telephone Laboratories, the acoustic control system corrects the gyro setting to keep the torpedo under gyro control.\nDuring the entire duration of an acoustic attack, the gyro setting was corrected on each received echo in this system. The transducer used in this system has a fairly wide beam pattern in the azimuth plane, enabling it to receive echoes from any target within an angle of \u00b130 degrees of the torpedo axis. The correction of the gyro setting is made by comparing the electrical phase relation between the signals generated in the two halves of the transducer when echoes are received. In the German Geier system, two sets of transducers are used, which point respectively about 40 degrees to port and starboard of the torpedo axis. The system does not receive echoes from a point directly ahead of the torpedo, and the torpedo remains on a straight gyro course until echoes from a target sufficiently off the axis to port or starboard are detected.\nWhen an echo is received on either hydrophone, the steering system is locked off gyro control and the rudder is put hard to the side from which the echo is received. This condition is held until no further echoes are received, when the torpedo drops back on gyro control again. With this arrangement, if the original firing of the torpedo is sufficiently accurate to make a hit without acoustic control, the acoustic control system will not function. It simply functions to correct inaccuracies in the original gyro setting.\n\nIn the Ordnance Research Laboratory (ORL) project 4 system, a single very narrow beam-pattern transducer is used with its axis on the axis of the torpedo. In order to locate a target off the gyro course, the gyro is equipped with a special cam plate which causes the gyro course to be \"snaky.\" The gyro's course is described as \"snaky\" due to its erratic behavior when attempting to locate a target off the gyro course.\nThe transducer's course allows a search angle of approximately +40 degrees. The use of a snaky course reduces the torpedo's forward progress rate by about 5 percent but enables the use of a single transducer with a very sharp beam pattern, minimizing the self-noise problem. In anti-surface ship service, torpedoes don't require acoustic control in both depth and azimuth. Most systems employ only azimuth control, operating the torpedo at a running depth under hydrostatic control, ensuring it strikes the target. Although vertical steering control complicates the acoustic system, there's an advantage to operating the torpedo during the initial attack portion at a depth of approximately 50 ft, as propeller cavitation is minimized.\nThis is important for reducing noise, particularly in higher-speed torpedoes. The use of two hydrostatic-controlled running depths for vertical control is conceivable, with one used during search at the beginning of the acoustic attack and the other assumed after the attack has progressed for a certain length of time. However, this arrangement presents real difficulties, and using acoustical information to control both depth and azimuth steering seems more desirable. The echo-ranging torpedo offers a definite advantage over passive acoustic torpedoes in the operation of the depth-steering control, as the echo-ranging system itself functions as a range-measuring device. Introducing a range-measuring element in the time base will permit depth steering only after the range has been reduced to a certain level.\nTo prevent the torpedo from oscillating excessively in the vertical portion of its attack, vertical control should be introduced by applying a correction to the normal hydrostatic control system. The simplest means of doing this is by applying a mechanical bias to the pendulum used in the hydrostatic control.\n\nThe normal torpedo steering control in the azimuth plane is one in which the rudder is thrown either hard to port or hard to starboard. A torpedo under gyro control normally requires the rudder to be thrown when it is a fraction of a degree off-course, resulting in a nearly straight trajectory for the torpedo. Under echo-ranging acoustic control, the angle off-course required to produce a rudder throw is greater than that necessary under gyro control.\nThe control system of a torpedo includes gyro control and an echo-ranging control system. The nature of the control problem for the echo-ranging system depends on the acoustic range of the torpedo, which in turn affects the interval between successive echoes. This interval can be significantly greater than 1 second for long ranges. Designing an echo-ranging system requires consideration of the acoustic range, the interval between transmitted pulses, and the dynamic behavior of the torpedo body. The reliability of the system is influenced by these factors, as well as the sharpness of the beam pattern of the transducer and the method of acoustic control. In the General Electric NO 181 and German Geier devices, azimuth steering is \"on-off.\" Despite some differences, this refers to the intermittent activation of the steering mechanism.\nBetween these two arrangements, essentially, the devices steer one way when echoes are not received and time elapsed from moment of rudder operation in seconds. Figure 1. Orientation of body as a function of time following beginning of rudder throw. The other way when echoes are received. It is necessary, with this arrangement, that the rate of turn of the torpedo be such that it is impossible for it to turn completely across the beam between echoes. For a given rate of turn of the torpedo body, the width of beam pattern required will be a function of the maximum acoustic range of the torpedo. In systems like the HUSL NO 181 and the BTL 157C, the steering is controlled by the electrical phase relation between the signals generated in the two halves of the receiving transducer. This means that it is necessary for an echo to be received.\nThe BTL system uses a transducer with a wide beam pattern in azimuth for steering the torpedo in either direction. The torpedo searches on a straight gyro course and utilizes the width of the beam pattern to make initial acoustic contact with the target. Once acoustic contact is made, the signal is used to correct the gyro setting. The dynamics of this body will not introduce problems in maintaining acoustic contact with the target. In contrast, the HUSL NO 181 system uses a transducer with a very sharp beam pattern. The initial search in this device is circling, and as soon as acoustic contact is made, the rudders are held in either the port or starboard position depending on the phase relation of the signal generated in the transducer by the last reflection.\nThe dynamics of the torpedo body are crucial in this device. The ping interval used is 0.65 seconds, the rate of turn of the body is 12 degrees per second, and a 1-second interval is required for the rudders to turn from one extreme limit to the other due to the steering being done by an electric motor. The effect of the dynamics of this body on the relative sensitivity of the acoustic system can be determined by considering the solution of equation (1):\n\ndt2/dt2\n\nThis is the equation of motion of such a body under the influence of the torque introduced by the rudder. Q is the moment inertia of the body, R is the angular damping resistance, and L(t) is the rudder torque as a function of time. The spacial orientation is denoted by 6.\n\nSteering must take place.\n\nTable 1\n\nEcho No. Angle (degrees) Rel. sig. (db) Rel. sig. (db) Rel. sig. (db)\n\n* Steering takes place.\nThe body's axis. Q/R is called the relaxation time of the body, which is the time, measured from the time of rudder throw, required for the body to return to the same spatial orientation it had at the time of rudder throw. L/R is the rate of turn of the body measured in degrees per second.\n\nThe Nature of the Control Problem\nNo. 181: The body had a relaxation time of 0.5 sec and a rate of turn of 12 degrees per sec.\n\nTable 2\nEcho no. Angle (degrees) Rel. sig. (db) Rel. sig. (db) Rel. sig. (db)\n* Steering must take place.\n\nThe curve in Figure 1 shows the body's orientation as a function of time following the beginning of the rudder throw. The data below display the relative level of the received signal at 130 yards, 260 yards, and 520 yards for the most favorable and the most unfavorable phase relation between body orientation and transmission.\nIt is necessary to have approximately 11 dB echo-to-reverberation ratio for steering in the worst case considered in Table 1, and 8 dB ratio for steering in the worst case in Table 2. The echo-to-reverberation ratio does not need to be extremely high in order to receive every echo, as the steering system holds the position of the last steering indication.\n\nWhen steering in the vertical plane is accomplished by the same type of hunt as used in the azimuth plane, the condition for combined steering in both planes can be significantly worse than for one plane. The use of glide-angle control in the vertical plane mitigates the effect of dynamics.\nIn 1942, a research group at the General Electric Company began developing an echo-ranging control system for use in an antisubmarine torpedo. The system was designed as a conversion for a torpedo already in use as an antisubmarine listening device. By August 1944, their experimental units were tested, and the device was accepted by the Navy for production. Production engineering was undertaken by the Leeds and Northrup Company, and their first production units were tested during the summer of 1945.\n\nThe device had no provision for automatic volume control (AVC). It was protected against steering on noise peaks through the use of an amplitude gate with a time constant that required a substantial part of the signal.\nThe pulse duration is 30 milliseconds. The pulse interval is 0.7 seconds, making the maximum theoretical range approximately 560 yards. However, performance tests on preproduction models have all been conducted at 330 yards. The device is intended to be dropped from an aircraft at the point where a submarine has submerged. It searches in a circle with the depth gradually increasing until acoustic contact is made. Once contact is made, it homes in on the target.\n\nFirst Amplifier:\nMR TVG\n\nSecond Amplifier:\n\nThird Amplifier:\n\nTwin Rectifier:\nComparison Bridge:\nEcho\ni-l a\nRudder Circuits:\nRudder Steering Motor:\nElevator Circuit:\nPendulum Circuit:\nElevator Steering Motor:\nPower TVG Amplifier:\nOscillator Rectifier:\n\nFigure 1. Block diagram of General Electric N0181.\nFirst Amplifier:\nSecond Amplifier:\nThird Amplifier:\nAmplifier:\n\nFigure 1 depicts a block diagram of the system. It consists of a transmitter capable of generating approximately:\n100 watts of electric power to be transmitted in 30-msec pulses at 0.7-sec intervals. A single transducer is used as both projector and hydrophone. The receiver contains two types of steering-control systems, one for azimuth control and the other for depth control. The operating frequency is 60 kc. The receiver is under time-varied gain control.\n\nThe transducer used in this device was developed at the Harvard Underwater Sound Laboratory (HUSL) and consists of an array of magnetostrictive elements. Figure 2 shows the general construction of the transducer and the individual elements, while Figure 3 shows the arrangement of the elements in the array. The numbers indicated on each element:\n\nFigure 2. Details of transducer construction.\nActive Face\nWindings Cushioned with Air Cell Neoprene\n100 laminations.\nFigure 3: Array of elements in the transducer. Indications in this figure represent the relative number of turns in the windings. The variation in windings on the units is for controlling the transducer's pattern. Figure 4 shows the frequency response curve of one of the transducers produced by the Leeds and Northrup Company. Figure 5 displays the horizontal pattern, and Figure 6 shows the vertical pattern. A representative transducer's numerical characteristics: In the vertical plane, the pattern is 10 dB down at 10 degrees off the axis on either side, while in the horizontal plane, the pattern is 7 dB down at 10 degrees off center. Figure 4. Transducer frequency response. The axis and the overall directivity index is \u201322.5 dB/kHz.\nIn the process of adapting the transducer for production, the impedance per unit was changed slightly, resulting in an impedance of 90 + 130 ohms per half section. The receiving sensitivity is 82 dB below 1 V per dyne per sq cm, and during transmission, 66 dB above 1 V per dyne per sq cm is developed at a range of 1 meter. The transmission efficiency is approximately 35%. The Leeds and Northrup people believe that the latest units they have produced are somewhat better than this.\n\nGeneral Electric N018I System\nTime Base\n\nThe time base of the General Electric system uses a set of simple cam-operated switches. A second switch is used to blank the receiver during transmission by applying -26 v.\n\nFigure 5. Transducer horizontal directivity pattern.\nFigure 6. Transducer vertical directivity pattern. The switches are on a shaft that is driven directly to the screens of the tubes in the receiver, by the main motor shaft. The transmitter is operated by three other cam-operated switches. One is a double-pole double-throw switch which is closed in one position during the time that echoes can be received from ranges less than 500 ft. It is closed in the other position during the time that echoes can be received from ranges greater than 500 ft. This is used to limit the range to 500 ft after echoes have once been received within this range. The second switch is closed by a cam during the operation of the signal generator.\nThe time that echoes can be received from ranges is between 1,000 and 2,000 ft, and the third is closed during the time that echoes can be received from ranges between 1,500 and 2,000 ft. By means of these last two switches, it is possible to decrease the range of the torpedo to 1,000 ft if the body is tilted so that it points toward the bottom at an angle greater than 9 degrees and to 1,500 ft if the body is tilted so that it points toward the bottom at an angle greater than 6 degrees.\n\nGENERAL ELECTRIC NQ181 SYSTEM\n18.4 Transmitter\n\nThe schematic of the transmitter is shown in Figure 7. It consists of two 6L6 tubes used as power amplifiers with their grids driven in parallel by a single 60-kc oscillator. The output of one of the power amplifiers is supplied to the top half of the transducer while the output of the other power amplifier is supplied to the bottom half of the transducer.\nThe amplifier is supplied to the bottom half of the transducer. The amplifiers are connected to the transducer windings such that the acoustic signal emitted from the whole face of the transducer is in phase. The signals at grids G1 and G2 will be in phase if the acoustic signal comes from a point on the axis of the torpedo. If the acoustic signal comes from a point above or below the axis, the phase of the signals on the two halves of the transducer will be different, and therefore the signal at G1 will no longer be in phase with the signal at G2. Due to the presence of the lag line in the plate circuits of VI 04, the relative values of the voltages at A and B depend on the phase relation of the signals at G1 and G2. The signals at A and B are applied to the grids of tubes V105 and V106. These are the first stages of the two-stage transmitter. The transmitter is keyed by means of a switch, operated by an unknown mechanism.\nby the time base, which keys the plate and screen of the power amplifiers. A sample of the 60-kc signal generated on the screens of the power amplifier is rectified by means of the TVG diode and stored on a condenser to serve as the gain control bias during the listening interval.\n\n18.5 RECEIVER\n\nWhen an acoustic signal is received by the transducer, the voltages developed on the two halves are impressed on the grids GL and G2 of V104, Figures 7 and 8. If the acoustic signal arrives on the transducer face from a point dead ahead, the voltages developed in the windings of the two halves of the transducer will be in phase and therefore the voltages are channeled to the receiver's amplifier. The double potentiometer is used to balance the inputs to the two channels and adjust the relative values of TVG voltage.\nThe signal is received continuously by the transducer due to reverberation in the water after transmission on the grids of V105 and V106. Figure 8 displays the circuit details from grids Gl and G2 to the input of the two-channel amplifier. After transmission of a pulse by the system, a decaying signal level is expected due to the direct proportionality between the echo reception time and the target range. A TVG system is utilized to control the receiver's sensitivity, preventing response to reverberation but increasing sensitivity post-transmission to detect weak signals from long ranges.\nThe control variable gain is obtained by applying a variable bias to the grids of V105 and V106. The bias is obtained by rectifying a portion of the signal appearing on the screen of one of the transmitter power-amplifier tubes using the TVG diode (Figure 7) and charging the TVG condenser (Figure 8) with the output of this diode. Immediately after transmission stops, the condenser starts to discharge through the 0.24-megohm resistor to ground, thus producing the time variation in bias. No AVC is used in this device.\n\nThe two-channel amplifier consists of two stages of tuned amplifier for each channel, with a system of balancing potentiometers between the two stages to be used to equalize the gain in the two channels. The output of each channel goes to a diode rectifier. These rectifiers are so connected to a bridge that an echo is produced.\nThe pulse is obtained at one point on the bridge network whenever an echo is received by the transducer. The difference in polarity between two other points on the bridge indicates whether the echo came from above or below the axis of the transducer. The two-channel amplifier is shown in Figure 9, and the comparison bridge is shown in Figure 10.\n\n18.6 Comparison Bridge\n\nTwo conditions must be considered in the comparison bridge shown in Figure 10. Condition 1, when the target is in the same horizontal plane as the axis of the torpedo. In this case, voltages E1 and E2 will be equal: E1 = E2.\n\nCondition 2, when the target is not in the same horizontal plane as the axis of the torpedo. In this case, Er > E1 and E2.\n\nSteering Motor\nPendulum\nPend Pos\nMotor\nSearch Angle SW\nSearch SLC\nRelay\nPend Pos\nMotor\nPursuit\nFigure 12. Schematic of depth-steering conditions. Since the input voltages A and B of Figure 2 are not the same for condition 2, the values of Ei and E2 will be different. Er will always be negative regardless of the orientation of the target relative to the axis of the torpedo. EL will be positive when the target is on one side of the torpedo axis and negative when it is on the other.\n\nGENERAL ELECTRIC NQ181 SYSTEM\n18.7 Control System\n\nThis control system utilizes two independent steering systems, one for azimuth control and the other for depth control. In the search condition, the azimuth control system maintains the rudders in the port position so that the torpedo searches in a port circle. When an echo is received, the voltage Er developed in the comparison bridge causes the echo trip-relay to open, which in turn causes the rudders to shift, changing the torpedo's depth.\nThe torpedo swings to starboard. The then goes into a starboard circle. The holding time of this circuit depends on the condition and the third, the pursuit condition. The elevators are controlled during all three conditions by a set of contacts operated by a pendulum. The frame in which the pendulum contacts are mounted can be rotated by means of a small motor, and the various steering conditions are controlled by the positioning of this frame. Figure 11 shows the relationship of the pendulum frame, the pendulum, the steering motor, and the elevators. Figure 12 shows the electric circuit setups for the three steering conditions. During the initial dive, the steering is controlled by the ceiling switch.\n\nVertical Steering Motor\nPendulum\nLimit Switches\nSearch Angle Switch\nWNA\nSLC\nRelay\nUP\nDOWN\ni_J\nSearch\nPursuit\nEcho Trip\n\nUP - Vertical Steering Motor\nDOWN - Vertical Steering Motor\nPENDULUM - Pendulum\nLIMIT SWITCHES - Pendulum limit switches\nSEARCH ANGLE SWITCH - Search angle switch\nWNA - Warning light, normal arming\nSLC - Searchlight control\nRELAY - Electrical relay\nUP - Search mode, up position\nDOWN - Search mode, down position\ni_J - Ignition system switch\nSearch - Search mode\nPursuit - Pursuit mode\nEcho Trip - Echo-ranging switch\nThe rudders will be held in position above the ceiling, and will drop below the ceiling to engage the motor. The limit switch ensures that the rudders hold this position for approximately 1 second after the last echo in a sequence is received. At the end of this holding time, the rudders return to the port position, creating an on-off steering system for azimuth control. The torpedo continues to steer on and off the transducer beam in the azimuth plane throughout the entire attack.\n\nThe vertical steering system is more complex. In dealing with this system, there are three steering conditions to consider: first, during the initial dive; second, during the search, which operates at a depth of 50 ft; and third, during the dive.\nangle limit switch which limits the dive angle to 15 degrees. The ceiling switch opens at 50-ft depth and transfers control over to the search angle switch, causing the torpedo to dive at a fixed angle of 3 degrees until a depth of 225 ft is attained, at which point the search angle is changed to 2 degrees. If an echo is received from a target, the pursuit relay is opened and the pursuit condition is set up. Under this condition, the positioning of the pendulum frame is controlled by the SLC relay.\n\n18.8 Blanking Circuits\n\nThe following blanking circuits are used to protect the device against steering on false information.\n\n1. The 125-ft blank. This prevents echoes from interfering before the 125-ft mark.\nless than 125 ft range controls the torpedo. Duction is permanent unless the torpedo misses the target, in which case the range returns to normal.\n\n1. The 6- and 9-degree blanks. These are range-reduction circuits designed to avoid bottom reflections. When the pitch of the torpedo reaches 6 degrees down, the range is reduced to 1,500 ft.\n\nPINGS AND ECHOES\nUp Up\n1 Up 1 Up\nDown Down Down\n\nSequence of echoes Start of new sequence of echoes\n\nECHO RELAY L_TT_\nEach drop out of this relay when unaccompanied by an elevator drop out causes the body to pitch odd 1 degree.\n\nELEVATOR RELAY OUT\ni_n_j\nEach drop out of this relay causes the body to subtract 1 degree from pitch. This relay cannot trip alone without an accompanying trip of the echo relay.\n\nRUDDER RELAY Port search turn PURSUIT RELAY\nThis relay holds out for approximately 10 pings after the last echo. Since echo sequences are seldom separated by more than seven pings, once tripped, it generally holds out throughout the chase.\n\nFigure 14. Schematic of operation sequences.\n\nWithout this provision, the torpedo will go around the bow of the target.\n\nThe 500-ft blank is a range-closing circuit. Once an echo has been received from a range less than 500 ft, the range is reduced to 500 ft. This range reduction is used to prevent steering on echoes which are the result of reflection from the target to the bottom then back to the torpedo. This range reduction engages when the pitch reaches 9 degrees, and all circuits are operated by means of cams and microswitches connected to the main motor shaft. The torpedo pitch is measured by mercury switches.\nFigure 15 is a schematic of the complete blanking system. The switches Cl, C2, C3, and C4 are operated by the cams driven by the main motor. Blanking is achieved by applying -26V directly to the screens of the first stages of the two-channel amplifier. The cam switch Cl is closed during the time echoes from ranges 0 to 125 ft can come in. This is called the 125-ft blank and it prevents steering on echoes from less than 125 ft. The two mercury switches marked 9 degrees and 6 degrees are closed for angles greater than 9 degrees and 6 degrees of pitch respectively. The cam C2 is closed after the time necessary for receipt of echoes from ranges greater than 1,000 ft and C3 is closed after the time necessary for receipt of echoes from 1,500 ft.\n\nGeneral Electric NQ181 System\nPursuit Relay\nFigure 15. Schematic of blanking circuits.\n\nThe cam switch Cl is closed during the time echoes from ranges 0 to 125 feet can arrive. This is known as the 125-foot blank and prevents steering on echoes from ranges below 125 feet. The two mercury switches marked 9 degrees and 6 degrees are closed for angles greater than 9 degrees and 6 degrees of pitch respectively. The cam C2 is closed after the time required for reception of echoes from ranges above 1,000 feet, and C3 is closed after the time required for reception of echoes from 1,500 feet.\nWith this arrangement, if the pitch of the torpedo is greater than 6 degrees, the receiver will be blanked for any echo from a range greater than 1,500 ft. If the pitch is greater than 9 degrees, the receiver will be blanked for any echo from a range greater than 1,000 ft. The cam switch C4 is a single-pole double-throw switch which is closed in the bottom position during the time when echoes could be received from ranges less than 500 ft and after this time it is closed in the top position. If an echo is received from a range less than 500 ft, the echo relay will also be closed, so relay B will be energized. The contacts Bl, B2, and B3 are contacts which are closed when relay B is energized. Once this relay is closed, it will stay closed as long as the pursuit relay is closed. This means that via C4 and B3.\nreceiver  will  be  blanked  for  all  echoes  of  ranges \ngreater  than  500  ft  and  this  blanking  condition  will \nremain  until  the  pursuit  relay  opens.  a \na See  references  6,  9,  10,  14,  20,  26  and  28  for  additional \nmaterial  on  topics  in  this  chapter. \nChapter  19 \nHARVARD  UNDERWATER  SOUND  LABORATORY  N0181  SYSTEM \n19.1  INTRODUCTION \nThe  harvard  Underwater  Sound  Laboratory \n[HUSL]  undertook  the  development  of  an \necho-ranging  torpedo  in  the  summer  of  1942,  utiliz- \ning a doppler-controlled  enabling  system  as  a pro- \ntection against  steering  on  surface,  bottom,  or  wake \nechoes.  A special  transducer  was  developed  to  oper- \nate at  60  kc  which  could  be  utilized  both  as  a pro- \njector and  a hydrophone.  The  torpedo  was  designed \nas  an  antisubmarine  weapon  and  the  electronic  gear \nwas  so  designed  that  it  could  replace  the  standard \nelectronic  gear  in  the  project  61  mine.  After  prelim- \ninary field  tests  on  two  experimental  units,  six  elec- \ntronic panels  were  built  to  convert  the  project  61 \nmine  to  echo  ranging  with  all  components  engineered \nso  that  the  system  could  be  put  in  production  with \na minimum  of  redesign.  This  design  was  designated \nThe  units  were  tested  against  an  echo  repeater \nused  to  simulate  a submarine  in  August  1944.  The \nperformance  in  these  tests  was  quite  satisfactory. \nThe  units  successfully  attacked  an  echo  repeater \nafter  bench  tests  indicated  that  the  electronic  gear \nwas  in  satisfactory  operating  condition.  Some  diffi- \nculty was  encountered  in  the  tests  against  a sub- \nmarine, because  of  the  difference  between  an  echo \nrepeater  and  a submarine  as  a target.  The  revisions \nnecessary  in  the  electronic  gear  in  order  to  overcome \nthese  difficulties  would  not  have  been  serious.  How- \never, since  the  General  Electric  version  of  NO  181 \nThe system uses a single transducer made up of 32 small laminated magnetostriction elements mounted on a rubber diaphragm about 6 in. in diameter. The 32 elements are divided into four quadrants, and the elements in each quadrant are connected in series. The terminals for each quadrant are brought out separately in a cable. Three transformers are provided for coupling the transducer to the electronic gear: one to match the plate circuits of the transmitter power amplifier to the transducer, and two which match the transducer to the grids of the transmitter. (Chapter The will describe the ORL project 4 version.)\nThe first stage of the receiver utilizes tubes to achieve the following features: (1) transmission and reception are performed using the same transducer elements without the need for switching; (2) the plate circuit of the transmitter power amplifier is properly matched to the transducer; (3) a voltage gain of 20 dB is provided between the transducer and the receiver input; and (4) five signals are provided at the receiver input. The voltage difference between one pair is produced by a phase difference between the signals on the two port quadrants and the two starboard quadrants of the transducer. Similarly, the voltage difference between another pair is produced by a phase difference between the signals on the two top quadrants and the two bottom quadrants of the transducer.\nThe transducer provides azimuth and depth steering with the following signals: the first signal is the steering signal in azimuth, the second is the steering signal in depth, the third is the echo signal from the target, the fourth is the reference signal, and the fifth is a measure of the total acoustic signal on the transducer. This information enables control in both azimuth and depth.\n\nThe block diagram of the electronic gear is depicted in Figure 1. The operating frequency is 60 kc. The transmitter power output is 80 watts of electrical power with a transducer efficiency of about 35%. The transmitted pulses have intervals of 0.65 seconds and a length of 30 msec.\n\nAs an antisubmarine device, acoustic steering control is implemented in both azimuth and depth. No time-varied gain is used, but an automatic volume control is employed to adjust the receiver sensitivity based on the level of reverberation. The system is enabled by a communication system.\nThe combination of an amplitude gate and a Doppler gate. The amplitude gate requires that an echo has a level at least 5 dB above reverberation level and persists for at least 5 msec. The Doppler enabling system sets a requirement of 60 cHz frequency difference between the reverberation and an echo. The Harvard Underwater Sound Laboratory N0181 System was designed to convert the Project 61 listening torpedo to an echo-ranging torpedo. The body used is the standard Project 61 body with very little modification besides the substitution of the echo-ranging electronic gear for the listening electronic gear formerly used.\n\nIn the horizontal plane. Figure 3 is the pattern obtained when 0.55 watts of power is transmitted continuously. Figure 4 is the pattern obtained when an electric power of 1.38 kW is transmitted in 1-msec.\nThe transducer consisted of a laminated-stack magnetostrictive array. Identical elements were used, as in the General Electric device described in Chapter 18 and illustrated in Figure 2 of that chapter. The HUSL system's transducer differs in the transducer units' arrangement and diaphragm diameter, as a symmetrical system in the vertical and azimuth planes is required. Figure 2 depicts the transducer's element arrangement, and the numbers indicated on the elements are proportional to the winding turns on each.\nThe shading of windings on elements is for producing desired patterns. The frequency response of this transducer is similar to that of the one used in the General Electric version, as indicated in Figure 4 of Chapter 18. Figures 3 and 4 of Chapter 19 show the pattern of transducer levels because the four central elements are approaching saturation. The curves of Figures 3 and 4 display the dynamic sound pressure at 1 m as a function of the angle. The following are the numerical characteristics of a representative transducer. The pattern is 9 dB down, 10 degrees off the axis. The overall directivity index is \u201323 dB, and the first minor lobes are at least 25 dB down. The impedance of each quadrant is 25 + j80, and since the transducer is connected with the quadrants in series-parallel, this impedance applies to the entire transducer.\nThe impedance of the entire transducer in use is 74 dB above 1 dyne per sq cm during transmission, developed at a range of 1 m per volt of electric signal applied to the transducer. The receiving sensitivity is -86 dB below 1 volt per dyne per sq cm. The efficiency reaches a maximum value of 38.5% at an electric power input of 800 watts. At a power input of 1.38 kw, the acoustic power output is 403 watts with an efficiency of 29.2%. Since the transducer is symmetrical, its pattern in the vertical plane is identical to the pattern in the horizontal plane.\n\nInput Circuit:\n19.3 Input Circuit\n\nThe input circuit used has the advantage of combining the step-up transformation from the transducer impedance to the grid impedance with a lag-line action all in one step. Furthermore, it permits the efficient handling of the signal.\nThe circuit for the input system, shown in Figure 5, utilizes quadrants 1 and 3 of the transducer in parallel, as do quadrants 2 and 4. However, quadrants 2 and 4 are connected out of phase with quadrants 1 and 3 when sound is normally incident, as indicated in the diagram. Voltages developed across the two input transformers vanish for normally incident sounds and are proportional to the difference between the voltages on the corresponding pairs of quadrants when the sound is not normally incident. It's crucial that the coupling between the two halves of the input transformer is as tight as possible, especially for transmission.\nThe mission of the circuit is compromised if the transmitting signal is not properly connected to the center taps of the input transformer. If the coupling is not tight, there will be a large voltage drop across the two halves. Consequently, the voltage appearing at the center tap will not be the voltage across the transducer itself.\n\nThe operation of the circuit depicted in Figure 5 can be best described by calculating the voltages at various points in the circuit, assuming the voltages developed by each of the four quadrants of the transducer and the impedances are as indicated in Figure 5. It is noted that Figure 3 represents the transmitting pattern for 0.55 watt.\n\nThe condensers series tune each quadrant of the transducer, and similarly, condenser Ya tunes the inductive reactance of coil X8. The circuit XsY8 will be referred to as the 90-degree circuit.\nThe resistance Rl is assumed to match the internal resistance of quadrants 1 and 3 or 2 and 4 in series. If this is the case, the voltages developed across Rl are on the left and right hand sides of the diagram respectively. In the circuit as used, Rl was omitted, and the value of Rb was selected such that the network provided the load RL. Neglecting the loading effect of jjYs:\n\neO\njjYs\nRs + T^l\n\nThe 90-degree section consisting of the series-tuned circuit XsY8, the voltage appearing at point E is:\n\nIt is essential that the two halves of the output transformer be very tightly coupled to achieve the result. The factor 34 arises from the fact that the voltage is that appearing across only one half of the transformer.\nThe impedance looking back from point E is equivalent to all four quadrants in parallel, namely 4Ri- \\. The voltage developed at point F after the step-up circuit is therefore given by:\n\nIXs r 4Lli\n\nThe voltages appearing at points A, B, C, and D are, respectively:\n\nRl + 2N2Ri\nRl\njjYs\nRs + t^i\n\nFor simplicity of notation, let NRl Y Rs + t R.\n\nINPUT CIRCUIT\n\nIn terms of this notation, the voltages appearing at the four steering grids are:\n\nThe right and left voltages may be written in the form:\n\nwhen Vo = iQ82 + Qd2,\nand\nQs Qd\n\nIt is thus seen that the final output voltages have similar angular dependence to what would be obtained with a lag line of angle 2a between the right and left halves of the transducer. Similarly, the effect of a lag line between the bottom and top halves is:\n\n(Note: The text appears to be in proper English and does not contain any meaningless or unreadable content. No corrections or translations are necessary.)\nObtained at the UP and DN outputs. Referring back to equation (6), we see that the equivalent lag-line angle is given by:\n\n_, Qd\nQs\n2 tan(NR / Rs + TL)\n\nAs an example, in the Harvard N0181F system, the equivalent lag-line angle is 74 degrees.\n\nThe transmitting behavior of the circuits is regulated by the biased diode connected from the secondary center taps of the input transformers to ground. When the voltage at this point exceeds the bias on the diode, the latter shunts the condenser Y8 and spoils the Q of the tuned circuit X8Y8, so that this circuit, which has been termed the 90-degree circuit, does not load the transmitter appreciably. This feature requires for its proper operation that the diode have a low-resistance DC return to ground, which in the present case is provided by the series coil X8.\nThe secondary winding of the output transformer. If the input transformers are properly center-tapped, the voltages developed across the two halves in transmission tend to cancel, resulting in the inputs providing negligible loading of the transmitter even though the secondaries are terminated. Considerable unbalance in the input system may be tolerated without appreciable loss of power.\n\nThe bias on the diode is adjusted so that it is never exceeded by the signal voltage appearing between F and ground during reception. In this case, the voltage appearing at F, and hence on terminal 1, provides the unshifted receiving pattern, which may be used as desired. In this system, it provides the signal input for the channel which controls the AVC and actuates the doppler gate system.\n\nFigure 6 shows the voltage differential between:\n\n(Note: The text appears to be in modern English and does not contain any meaningless or unreadable content, ancient English, or non-English languages. No OCR errors were detected.)\nTerminals 3 and 4 or 2 and 5 of Figure 5 represent the function of electrical phase difference between signals on the two halves of the transducer, determined experimentally with a representative unit.\n\nSignal phase difference in degrees (Figure 6). Voltage differential as a function of signal phase difference between signals from the two halves of the transducer.\n\nFigure 7 depicts a set of curves obtained from one experimental unit. These indicate the performance of the transducer and input circuit in both transmission and reception. The reception performance curves were obtained by mounting a source to make various angles with the transducer axis and determining the relative pulse level as a function of angle, which was necessary to actuate the steering relays in the system in one case, and in the other the level necessary to operate them.\nThe enabling system is activated by the signal from terminal 1 in Figure 5. The third curve illustrates the relative level of the transmitted pulse as a function of the angle off the transducer axis. This was determined by measuring the signal levels received by a hydrophone when the transducer was excited using the torpedo transmitter.\n\nFigure 7. Transducer and input circuit characteristics.\nFigure 8. Time-base circuit.\n\nTransmitter\n19.4 time base\n\nThis system transmits 30-msec pulses at 0.7-sec intervals. To achieve this, a multivibrator is used as a time base. The transmitter is designed to be actuated by a positive pulse. The multivibrator circuit incorporates the tube.\nThe resistor R3 and condenser C3 determine the 0.7-sec interval, while the resistor R1 and condenser C2 determine the length of the pulse, which is 30 milliseconds. Figure 9 shows the controlled sequences, and it's necessary to blank the receiver using a negative pulse generated simultaneously with the transmitter-actuating positive pulse. Following the end of the transmitted pulse, a relay is operated, which also generates a negative pulse. The positive pulse to actuate the transmitter is obtained through the phase-inverter stage V2.\nFigure 9 schematically shows the sequences controlled by the time base. ff/S pulse and hold the relay closed for a period of 50 msec. The operation of this relay circuit is accomplished by differentiating the negative pulse using the condenser C5 in Figure 8, causing the relay to operate on the positive pip at the end of this pulse. A holding time is incorporated in the relay amplifier circuit to enable it to hold the relay closed for the necessary 50-msec interval.\n\n19.5 Transmitter\n\nSince this device utilizes the doppler frequency shift caused by the target's motion through the water to enable the steering amplifier, it is necessary that the frequency stability of the transmitter be quite good. To accomplish this, care was required in the design of the transmitter oscillator.\n\nHarvard Underwater Sound Laboratory N0181 System\nThe 1-2-3 section of tube VI in Figure 10 is the transmitter-oscillator stage. The frequency-determining components are the inductor LI and capacitors Cl and C2. The oscillator is coupled to a buffer stage through the condenser C3. The buffer stage uses the 4-5-6 section of tube VI. The 6V6 tube V2 is the driver stage, used to drive the pair of 815 tubes V3 and V4, which constitute the power amplifier. The oscillator and driver stage are normally biased to cutoff via the -48V connection. The transmitter is actuated by applying a positive pulse to the oscillator's grid through resistor R4 and to the driver's grid through resistor R5.\nThe 30-msec positive pulse is taken from the time base circuit. The output of the power-amplifier stage is fed to terminals 6 and 7 in Figure 5, which are the terminals of the primary of the power-output transformer, an integral part of the input circuit. The supply voltage for the transmitter is applied to the center tap of the primary winding of the power-output transformer. The electric power output of the transmitter is approximately 80 watts, resulting in an acoustic power output from the transducer of about 28 watts. The power supply for the screens and plates of the power amplifier, as well as the plate of the driver stage, is a special battery which generates 470V for the plate supply, and a 200V tap is taken for the screen supply. To reduce the size of this battery, a 40-Aif electrolytic condenser was connected.\nBetween the 470-volt terminal and ground, and an 80-juf electrolytic condenser was connected from the 200-volt terminal to ground. This arrangement allows the condensers to supply the very high current drain necessary during the interval of transmission, and the battery charges the condensers again during the listening period. The plates of multivibrator tube VI in Figure 8 were also driven from the 200-volt tap on the transmitter battery. Another battery with a 135-volt tap was used for the receiver power supply. This was the source for the +135 volts for the transmitter oscillator and buffer stages.\n\n19.6 Steering Receiver\n\nThe steering receiver utilizes the output from terminals 2, 3, 4, and 5 of the input circuit indicated in Figure 5. As was pointed out in Section 19.3, the voltage difference between terminals 3 and 4 is determined by the electrical phase difference between them.\nThe signals on the right and left halves of the transducer determine the voltage difference between terminals 2 and 5 based on the electrical phase difference between the signals on the top and bottom halves. An echo received from a direction to the right of the transducer's axis causes a higher voltage at terminal 3 than at terminal 4. Conversely, a signal from a point to the left of the axis results in a higher voltage at terminal 4 than at terminal 3. Signals arriving above the axis produce a higher voltage at terminal 2 than at terminal 5, while those below the axis produce a higher voltage at terminal 5 than at terminal 2. If a signal arrives from a point:\nOn the axis of the transducer, the signals developed at all four terminals will be identical. In the steering receiver, shown in Figure 11, the signals from these terminals are applied to the grids of tubes VI, V2, V3, and V4. These tubes are supplied with a signal on their screens, which is generated by a local oscillator operating at a frequency of approximately 1 kc. This oscillator and its associated phase-shifting network generate four signals of the same frequency, but the phase relations are such that one is taken as 0 degrees, while the others are 90, 180, and 270 degrees out of phase. The four tubes VI, V2, V3, and V4 with their 1-kc screen supply constitute a switching system, in which one tube is active for only about one-fourth of each cycle of the local 1-kc oscillator.\nThe plates of the four tubes are connected together, and the primary of a 60-kc band-pass filter serves as the common plate load for the four switching tubes. The output of the band-pass filter is a 60-kc signal modulated by the 1-kc switching system. If a signal is fed to the grid of only one of the tubes, there will be output from the band-pass filter during about one-fourth of each cycle of the 1-kc oscillator. The output of the 60-kc band-pass filter is fed to a two-stage resistance-coupled amplifier, which in turn is coupled to a third stage with a 60-kc band-pass filter in its plate circuit. The two-stage resistance-coupled amplifier is blanked during the time of transmission by application of the negative pulse from the time base to the suppressor grids in the tubes. These two stages are also subject to AVC control.\nThe third stage of the 60-kc amplifier contains the enabling feature. This stage is biased to cutoff by applying a negative bias to the suppressor grid and control grid, preventing a signal from passing unless a positive enabling pulse is supplied. The enabling pulse comes from the doppler-enabling receiver, which will be described next. Following the third stage of the 60-kc amplifier is a rectifier that functions as a demodulator. The output of the demodulator includes a filter (Cl and R7), which removes the high-frequency components. The phase-sensitive detectors, each with a maximum output, determine the signal polarity based on whether the signal on terminal 2 or 5 of the input circuit is larger.\nThe voltage is determined by the level of the signal from the 1-kc oscillator. For small target angles, the voltage output of the phase-sensitive detectors is a function of the target angle. However, if the target angle is much more than 1 degree, the voltage level of the phase-sensitive detectors will reach saturation. The outputs of the two phase-sensitive detectors are fed to the steering-relay amplifier (Figure 11). A residual 60-kc signal is also present. The resulting 1-kc signal, which contains considerable 2-kc and 4-kc components, is fed to the grid of V6, which is a 1-kc amplifier with a tuned plate load of sufficiently high Q to effectively suppress the 2-kc and 4-kc components in the signal. The output of the 1-kc amplifier is fed to two phase-sensitive detectors by means of two 0.01\u00b5F condensers.\nThe receiver obtains an activating signal from the same 1-kc oscillator system used for switching input tubes. In this manner, the phase-sensitive detector marked \"azimuth\" generates a DC voltage whose polarity is determined by whether the signal on terminal 3 or 4 of the input circuit is larger. The vertical phase-sensitive detector produces a DC voltage whose polarity is amplified by the following amplifiers. These amplifiers will be described in a later section.\n\nThe sensitivity of the four switching tubes VI, V2, V3, and V4 to the 60-kc signal is controlled by three potentiometers, PI, P2, and P3. These potentiometers regulate the level of direct current that can flow in resistors R1, R2, R3, and R4. The voltage drop in these resistors determines the grid bias of these tubes and thus their sensitivity. It is essential to provide the three potentiometers to balance the system.\nsensitivity of V2 and V3 for the azimuth channel and VI and V4 for the vertical channel, then balance the vertical channel relative to the azimuth channel. When an echo with doppler frequency shift is received, a pulse is generated in the enabling receiver which applies the enabling positive pulse to the grids of the last stage of the 60-kc amplifier. After the beginning of this pulse, the signal is able to ride through the last stage of the 60-kc amplifier and the demodulator so that the 1-kc amplifier stage is activated. It is necessary to make a compromise in the system due to the frequency difference between the reflection returned from the water surrounding the torpedo and the echo. In order to do this, a frequency-sensitive receiver was necessary for the enabling and demodulating stages.\nFor this frequency-sensitive receiver, it was necessary to include an automatic frequency control system. This was required to correct for the doppler produced in the 7-KC discriminator, selection of the Q of the tuned circuit in the 1-kc amplifier. A very high Q circuit provides maximum rejection of 2-kc and 4-kc components, but increases the time necessary to build up the 1-kc amplifier to full output. A Q of about 15 for this circuit, when loaded by the phase-sensitive detectors, was selected as the best compromise.\n\nIn the design of the Harvard NO 181 system, provisions were made for enabling the steering receiver by the motion of the torpedo through the water. This enabling receiver includes an amplitude gate, in addition to the criterion of frequency difference, that the level of amplitude must also meet.\nThe echo's relative intensity to reverberation must exceed a certain value and persist for a minimum length of time. The circuit is schematically represented in Figure 12. VI is an amplification stage that receives its input from terminal 1 of the input circuit shown in Figure 5. This signal is proportional to the average Doppler-enabling receiver voltage developed on the four quadrants of the transducer and has a frequency of the received acoustic signal, which is nominally 60 kc. V2 is a frequency-converter stage with the signal supplied to its control grid from the output of stage VI. The signal supplied to its screen is the output of the oscillator stage V9, whose frequency is nominally 53 kc. The plate load of V2 is the primary of a 7-kc band-pass filter with a frequency range of 1.4 kc between the two 3-db down points.\nThe filter selects the 7-kc frequency difference from the combination of frequencies present in the plate circuit of V2. A two-stage amplifier follows the 7-kc band-pass filter, which is the same two-stage amplifier as indicated in Figure 11. An important feature of this device is the use of a common amplifier for the 60-kc steering receiver and the 7-kc frequency-sensitive receiver. Both of these receivers are under an voltage control (VC) which is applied to this two-stage amplifier; the source of the AVC voltage is the signal voltage generated in the 7-kc channel. Following the two-stage amplifier is a third stage which includes a 7-kc band-pass filter identical with the one in the plate circuit of stage V2. A portion of the output of this last 7-kc band-pass filter is rectified for use in the automatic volume control.\nThe output in Section 19.9 is divided. A portion goes to the amplitude gate which passes an echo signal if it exceeds the background level of reverberation by 5 db and lasts for 5 msec. The amplitude-gate circuit is detailed in Section 19.8.\n\nSince the wave form of the signal emerging from the amplitude gate is significantly distorted, this signal is fed to a 7-kc tuned amplifier, followed by stage V3 which contains a discriminator primary in its plate circuit. Stage V3 also functions as a limiter, ensuring the discriminator output voltage is a function of frequency only. The discriminator and rectifier V4 actions generate a dc voltage at A, whose polarity is determined by whether the frequency is above or below the center frequency of the discriminator.\nThe magnitude is determined by the frequency difference from the center frequency. The filter consisting of R6, R7, and R8, and the condensers C7, C8, C9, and C10 is an RC filter designed to reduce the effect of voltage peaks at A produced by fluctuations in the reverberation frequency. The discriminator filter has a time constant that adds to the time constant incorporated in the amplitude gate, as the discriminator filter cannot start to build up until after the signal has begun to pass the amplitude gate. The time constants of the amplitude gate and of the discriminator filter are important factors to consider in the operation of the entire system, as both of these time constants must be overcome before any enabling pulse can be applied to the enabling grids in the amplifier.\nThe last stage of the 60-kc steering amplifier in Figure 11 requires the enabling pulse to reach its grids on time for the 1-kc amplifier to build up sufficient voltage to operate phase-sensitive detectors. This is determined by the sum of all time constants. Originally, 30 msec pulses were used due to these factors.\n\nThe voltage supplied at terminal A is utilized for automatic frequency control, correcting the local 53-kc oscillator for the torpedo's doppler effect. The relay, operated by the differentiated negative pulse and closed during the 50-msec interval following transmission, is indicated as the own-doppler nullifier in Figure 12.\nThis relay connects terminal A to the 2-nf condenser C15 and grid 4 of V8. V8 is a reactance tube that places a variable resistance between condenser C18 and ground. As the potential of grid 4 of this tube is changed, the effective resistance between C18 and ground is changed, which in turn changes the effective capacitance of C18 in the oscillator tank circuit. The frequency at which the transmitter oscillator is operated is chosen so that with the normal speed of the torpedo, the voltage generated at terminal A by the reverberation signal will be zero when the potential to which condenser C15 is charged is as near zero as possible. When the torpedo is started, the ODN relay samples the voltage developed at A from the reverberation following each ping and gradually charges C15 until the frequency of the oscillator matches that of the reverberation signal.\nThe 53-kc oscillator is adjusted to the point where the reverberation signal produces zero voltage on average at A. This requires typically 5 to 10 pulses from the transmitter. The rate of correction of the ODN is determined by the discriminator sensitivity in volts per cycle, the reactance tube sensitivity in cycles per volt, and the resistors R23, R24, and R25, as well as the condenser C15. The product of discriminator sensitivity and reactance-tube sensitivity is approximately Harvard Underwater Sound Laboratory N0181 System leans to the axis of the torpedo. To provide for this frequency difference, a separate 45-v battery in the receiver battery pack was connected to the terminals of R9 and R11 as indicated in Figure 12. The voltage drop across the resistors R10 and R11 provides the voltage which must be applied.\nThe discriminator overcomes direct current generated through the frequency difference. The doppler notch width, the required frequency range, can be adjusted by varying resistor R9. The time constant and 100 were set such that a 200 Hz shift in the frequency input at the grid of VI results in half the extreme voltage at A after four pings, achieving half correction for own doppler. Due to the nature of the amplitude gate, a continuous signal like the reverberation controlling the AVC of the amplifier cannot pass the amplitude gate. Therefore, the AVC must be disabled during potential sampling at A by the ODN relay.\nThis is accomplished by another pair of contacts on the ODN relay which perform the function of shorting the AVC during the ODN sampling period. Since the shape of the pulse envelope emitted by the transmitter produces a certain frequency spread in the transmitted frequency and since all reverberation is not received from points on the axis of the transducer, the reverberation will contain a certain range of frequencies. It is necessary to impose the condition that the doppler shift in frequency caused by the motion of the target be greater than a certain value in order to avoid enabling of the system because of frequency components which are present in the reverberation. The choice of the minimum doppler frequency shift to be used for enablement was about +60 cps. This corresponds to a component of target speed relative to the water of 15-18 knots parallel to the sound beam.\nWhen the pulses have sufficient Doppler frequency shift to produce a voltage which will overcome the bias on either terminal 3 or 8 of V5, the pulse will pass one side or the other of the rectifier and the pulse signal will be applied to the grid 1 of V6. If the pulse supplied to grid 1 is a negative pulse, a positive pulse will be generated at the plate terminal 2 of V6 and will be passed through the lower half of the diode of V7. If, however, the pulse at grid 1 of V6 is a positive pulse, the pulse at plate 2 of V6 will be a negative pulse which cannot pass the diode V7 but a negative pulse will be applied to grid 4 of V6 which will generate a positive pulse at plate 5 which will pass the upper pair of electrodes in V7. The tube V6 therefore plays the role of pulse amplifier and phase inverter, so that, regardless of the polarity of the pulse, it converts the input pulse into an output pulse of opposite polarity.\nOriginal Doppler pulse, a positive enabling pulse will be generated at the output of rectifier V7. The amplitude gate enabling pulse is then applied directly to the suppressor grid and control grid in the enabling stage of the steering amplifier shown in Figure 11.\n\nAmplitude Gate\n\nThe details of the circuit elements in the amplitude gate are indicated in Figure 13. VI and V3 are the two sections of a single 6H6 tube, while V2 and V4 are the two sections of a single 6SN7 tube. The output of the 7-kc amplifier appears at point PI in the diagram and this signal is applied via R6 to grid terminal 1 of V2 and via R1 and Cl to the cathode terminal 4 of VI. Terminal 4 of VI is connected to point P2 by way of the resistor R2, and the anode, as happens when an echo is received, will result in a decrease in voltage.\nThe increase in signal level at PI causes terminal 4 of V4 to become more positive, changing the potential values at points P2 and P3 so that terminal 3 of diode section V1 is no longer negative with respect to terminal 4 of VI. When this condition is achieved, diode section VI conducts. The system is designed such that the amplitude gate becomes conducting when the echo-to-reverberation level ratio is approximately 6 dB with the level of reverberation at terminal 1 of Figure 5, -90 dB referencing 1 v [dbv]. The echo-to-reverberation ratio necessary to pass the amplitude gate increases with decreasing reverberation level at terminal 3 of VI. Terminal 3 of VI is connected to point P3 via a resistor (R3). When no signal appears at\nPI is sufficiently positive with respect to P3 such that the diode section VI cannot conduct any signal. If the signal level at PI is increased, this signal will be amplified by V2 and the output signal from V2 will be rectified by V3, resulting in a bias applied to grid 4 of V4. Due to the action of the Automatic Volume Control (AVC), the signal level at PI will remain nearly constant for a considerable variation in the level of the input signal to the amplifier. However, the time constant in the AVC circuit is such that a sudden change in signal level may cause conduction. The adjustment of the echo-to-reverberation ratio at which conduction takes place is done by adjusting the relative values of resistors R16 and R17. It is also required that the amplitude gate remains non-conducting.\nThe time constant for the echo signal to make the amplitude gate conducting is at least 5 msec, determined by resistor R12 and condenser C5. To make the amplitude gate conduct during the first 50 msec following transmission, the AVC circuit is grounded through a contact on the ODN relay.\n\nHarvard Underwater Sound Laboratory N0181 System\n19.9 AVC Circuit\n\nThe 7-kc channel also serves as the source of signal for the AVC on the two stages of the common amplifier. The tube VI in Figure 14 is the AVC rectifier, which forms a bleeder circuit from the +135-v supply. A bias of 8.4 v is applied to terminal 4 of the rectifier. When the peak value of the signal exceeds this bias, the diode conducts and charges condensers C2 and C3. The two-megohm resistor R5 is shown in Figure 15. Characteristics of the N0181 electronic system.\nThe 3-4 section of this tube rectifies the same signal obtained from the output of the time constant of the AVC system, making its capacity large enough for the 7-kc amplifier via the condenser C1 and resistor Rl, so that an echo signal will not be long enough to conduct in the AYC circuit. By means of resistors R2 and R3, the AVC is controlled sufficiently to prevent conduction.\n\nFigure 16. Characteristics of the N0181 electronic system.\n\nHarvard Underwater Sound Laboratory N0181 System\n\nThe full signal is controlled by the amplitude gate. In order to ensure that the AVC action diminishes at a rate sufficient for the amplifier to follow the decay in reverberation, the AVC condenser C3 is furnished with a discharge path through the 8-5 section of the diode. By this arrangement, the junction of R5\nAnd C3 will never be more negative than terminal 3 of the 3-4 section of the rectifier. The condenser C2 and the resistor R4 serve to remove the 7-kc ripple from the voltage appearing at terminal 3. The AVC voltage for the first stage of the common amplifier is taken from the junction of resistor R7 and condenser C5, while that for the second stage of the common amplifier is taken from the junction of R5 and C3. The AVC is such that, for a change of signal level at terminal 1 of the input circuit of 20 db, the change in level at PI in Figure 13 is about 1 db. The removal of the AVC during the first 50 msec of the listening period is accomplished by connecting the junction of resistor R5 and condenser C3 to ground through one pair of contacts on the ODN relay.\n\nCharacteristics of the Electronic System.\nIn order to illustrate the behavior of the two portions of the receiver system, the photographs in Figures 15 and 16 will be used. Figure 15 was made using a cathode-ray oscilloscope (CRO) with the sweep synchronized with the time base in a test set used to generate a signal which simulated reverberation with the normal rate of decay of the reverberation signal and an echo signal superimposed on the reverberation and occurring about 180 msec after the beginning of the reverberation signal. The signal generator was arranged so that the echo signal frequency was different from the reverberation frequency by an amount which would simulate the doppler caused by a reasonable speed of motion of a target.\n\nIn Figure 15, A shows the envelope of the reverberation and echo signal which was injected into the receiver.\nThe receiver input circuit's striations are produced by a 60-Hz pickup in the oscilloscope and serve as a time scale. In Figure 15, B was obtained by connecting the oscilloscope input to point B in Figure 12. This is a point in the amplifier of the enabling receiver just preceding the amplitude gate. To allow the amplitude gate to pass reverberation signals during the initial listening period and correct the local oscillator for the torpedo's doppler effect, it is necessary to short the AVC through an ODN relay contact. In B of Figure 15, a transient can be observed after the fifth striation on the signal envelope. This transient is produced when the ODN relay contacts open. Note that the envelope's shape from the extreme left-hand side up to this point.\nThe transient is similar to the envelope shape in the corresponding portion in A. After the AVC short is removed, the AVC rapidly assumes control, causing the signal level in the circuit to decrease quite rapidly. When the echo arrives, the echo signal, which is approximately 10 dB higher in level than the reverberation preceding it, further increases the AVC voltage and therefore decreases the amplifier's sensitivity. The level of the reverberation signal just following the echo, measured at this point in the amplifier, is actually lower than it is a few milliseconds later. Figure 15C is a photograph of the envelope of the signal that appears at point C in Figure 12. This is at a point following the amplitude gate. The nature of the envelope of the signal during the time the AVC is shorted.\nThe signal at the point where the amplitude gate becomes nonconducting is brought down to zero until the echo arrives. The echo passes through the amplitude gate with very little loss in level, and the gate becomes nonconducting again as soon as the echo has passed. At D in Figure 15 is a photograph of the signal at point D in Figure 12. This signal is the doppler-enabling pulse. It is important to note that despite the amplitude gate conducting during the first 160 msec of the listening interval, only the signal passing through the gate was transmitted.\nThe echo did not contain a Doppler target and consequently no corresponding signal was generated at point D in Figure 12. However, upon the arrival of the simulated echo, the presence of the frequency shift due to the target Doppler caused the pulse indicated at D to be generated. This is the pulse used to enable the steering amplifier, allowing for the development of steering information for the steering relays. It is clear from this sequence of photographs that an echo must meet two conditions. First, it must have a level above background reverberation for the echo signal to pass the amplitude gate. After passing the amplitude gate, it is necessary that this echo signal have a frequency different from that of the background reverberation to generate a Doppler pulse for enabling.\nThe receiver requires an echo-to-reverberation ratio of 6 dB at a reverberation level of -90 dB on the transducer. The frequency difference between reverberation and echo is 60 Hz to generate an enabling pulse from the discriminator. Figure 16 demonstrates the behavior of the steering receiver through a series of oscilloscope patterns. These photographs were taken using an oscilloscope and an electronic switch that responded to an echo from a target on the transducer axis. In C and D of Figure 16, the signal at point B in Figure 11, which is the output of the 1-kc amplifier, is shown in the upper portion of the photograph. Figure 16, C displays the signal at this point when the target is to the left.\nAt the axis, while D shows the signal at this point when the target is to the right of the axis. It is important to note that the only difference between these two signals is their phase relation relative to the 1-kc reference signal at the bottoms of the photographs.\n\nAt E and F, the signals appearing at the output of the azimuth phase-sensitive detector present two patterns on the face of a CRO simultaneously. The upper pattern is the pattern produced by the signal being studied. The lower pattern is a 1-kc signal obtained from one of the terminals of the 1-kc oscillator in Figure 11. This same reference signal is used in all six of the photographs shown in Figure 16. In A, of Figure 16, the upper signal photograph is an envelope of a signal which occurs when the target is in the vicinity of the axis. The lower signal is a constant 1-kc signal. The phase difference between the upper and lower signals indicates the position of the target. In B, the upper signal photograph shows a positive going pulse each time the target passes the axis from right to left. In C, the upper signal photograph shows a negative going pulse each time the target passes the axis from left to right. In D and E, the upper signal photograph shows a continuous wave signal when the target is stationary on the axis. In F, the upper signal photograph shows a series of pulses when the target is oscillating about the axis.\nThe signal at point A in Figure 11 corresponds to that generated in the transducer when an echo is received from a target on the transducer axis. Figure 16 shows a photograph of a signal at the same point when the signal is injected only at terminals 3 and 4 in Figure 11, and the signal corresponds to that generated in the transducer by an echo either to the right or left of the transducer axis. If the signal at C in Figure 11 represents this, at E the signal corresponds to that produced when the target is to the left of the transducer axis, while at F it corresponds to that produced when the target is to the right of the transducer axis. In this case, the signal is in the form of rectified pulses, the difference being that in one case the pulses are positive, while in the other they are negative.\nIn other cases where the pulses are negative, in normal operation, the series of pulses occurring during receipt of an echo are averaged by means of the condenser C6 in Figure 11. For the purpose of making these photographs, C6 was removed from the circuit so that the individual pulses could be observed more readily on the oscilloscope.\n\nWhen the system is in normal operation, the signal indicated at A and B in Figure 16 would appear, regardless of the level relative to the background and frequency difference between the signal and background. However, unless the requirements imposed by the amplitude gate and the doppler gate are met in the enabling channel, the signals indicated in C, D, E, and F in Figure 16 would not be present.\n\nHarvard Underwater Sound Laboratory N0181 System not included in original text.\nThe enabling pulse is necessary for the signal to pass through the last stage of the 60-kc receiving amplifier. Elevator voltage outputs from the potentiometer centers are fed to a common point through resistors R1, R2, and R3. The resistor values determine the importance of the potentiometer sliding contact positions. The common point of resistors R1, R2, and R3 is connected to the amplifier grid, controlling the vertical steering relay positioning.\n\nFigure 18: Relay circuits.\n\nControl conditions for the torpedo include two states: the search condition, where the torpedo circles in the azimuth plane and operates under hydrostatic control at a fixed depth of approximately 225 ft; and the direction of azimuth plane circling.\nThe hydrostatic control system uses the circuit network shown in Figure 17 to determine depth operation. PI, P2, and P3 are three potentiometers connected to the two terminals of a floating 45-volt battery. This battery is bridged to ground by resistors R4 and R5, maintaining its center at ground potential. Potentiometer P3 is operated by pressure bellows, P2 by the pendulum, and PI by the azimuth steering relay. An acoustic signal received on the transducer, satisfying the conditions for generating a pulse from the enabling amplifier at point E in Figure 12, applies this pulse voltage to grid terminal 1 of V3 in Figure 18. V3 is an amplifier controlling a relay called the vertical transfer relay.\nThe two-stage direct-coupled amplifier consists of a cathode follower in the first stage. A time constant is introduced in the output of this stage using resistor R2 and capacitor C2. When a signal is received on grid terminal 1, the voltage generated on grid 4 is held long enough for the relay to remain closed for approximately 3 seconds. Contact 5 on this relay is connected through a 750,000-ohm resistor to grid terminal 1 of VI, which is the vertical steering relay amplifier. Contact 6 on the vertical transfer relay connects to the common terminal of Rl, R2, and R3 in Figure 17. When the vertical transfer relay is open, which is the case in the absence of echoes from a target, the grid of VI is connected to the output of the hydrostatic control network.\nWhen an echo is received from a target, the vertical transfer relay closes, connecting contact 5 to contact 4, which connects grid 1 of the vertical phase-sensitive detector. When the torpedo is under acoustic control, steering information arrives intermittently, requiring steering relays to hold in the position indicated by the last received echo until a new echo indicates a position change. Thus, under acoustic-steering conditions, steering relay amplifiers must have a holding feature. This feature is accomplished through contacts 5 and 6 on both the vertical and azimuth steering relays. When the vertical steering relay is in the open position, contact 6 connects to contact 5, which in turn connects to ground.\nThe contacts 1 and 2 of the vertical transfer relay allow the steering relays to connect to either the cathodes 3 of the steering amplifiers or the cathodes 3 of the steering relay amplifiers. When the steering relays are open, the cathodes 3 of the steering amplifiers are at zero potential relative to ground. In contrast, when the relays are closed, the cathodes 3 of the steering relay amplifiers will be at a positive potential. This arrangement provides the holding feature for these relays. The holding feature for the vertical steering relay amplator operates only when the vertical transfer relay is closed. The relatively long holding time for the vertical transfer relay causes the system to steer in the direction of the last-received echo in the vertical plane for approximately 3 seconds after the last echo of a series is received. If no echoes are received during this interval, the vertical transfer relay drops open and the vertical steering relay is connected back to its normal position.\nthe hydrostatic control network which steers the torpedo back to the original operating depth. The contacts 1, 2, and 3 on both of the steering relays are the rudder control contacts. Contact 2 on each of these relays connects to the 36-v terminal of the main motor running battery. Contacts 1 and 3 each connect to one terminal of a field winding in the steering motors which are provided with double field windings in order to make them reversible. By means of the holding feature in the steering relay systems, the voltage required to change the relay from the closed to the open position or from the open to the closed position is about 2 volts.\n\nChapter 20\nTHE BRITISH DEALER SYSTEM\n\nThis device was developed on a corresponding program in this country, numbered NO 181. It was designed as an aircraft-launched, echo-locating torpedo.\nThe ranging torpedo is a 7 ft 4 in. long, 18-in. diameter, 590 lb device designed for use against submarines. Its operating speed is 12 knots with an operating time of 15 minutes. The transmitter timing also applies the time-varied gain voltage to the receiver and operates two sets of selector switches, allowing depth and azimuth steering information to be taken from alternate pulses. The receiver is a two-channel amplifier followed by a phase-sensitive detector for signal comparison. Figure 1 depicts the block diagram of the British Dealer system. The transducers and explosives are mounted in the head, the electronic gear is housed in the body, and the battery is mounted in the after section. The transducer assembly consists of two units:\nThe first component functions as the projector, and the second as the receiver. The receiver section is divided into two portions, one for azimuth reception and the other for depth reception. The beam pattern is broader in azimuth than in depth. The transmitter, comprised of an oscillator driving a power amplifier, is actuated by a cam-operated time base, which in addition is driven by two amplifiers. By means of the aforementioned selector switches in the time base, steering in both azimuth and depth is permitted. Azimuth steering is accomplished by varying the relative speeds of two propellers, which are operated by two separate propulsion motors. Depth steering is accomplished by sliding the main running battery backward and forward on a set of rails using a motor-driven screw. The search plan is a descending helix of 50-yard radius.\nChapter 21 ORDNANCE RESEARCH LABORATORY PROJECT 4 SYSTEM\n\n21.1 INTRODUCTION\n\nThe results from experience with the Harvard Underwater Sound Laboratory (HUSL) device operating against echo repeaters and submarines indicated the desirability of the following modifications:\n\n1. The use of separate amplifiers for the enabling system and the steering amplifier.\n2. The use of time-varied gain (TVG) instead of or in addition to automatic volume control.\n3. A change in the method of securing the doppler notch from a circuit using a battery with no ground reference to an arrangement operating from a grounded source.\n4. Substitution of glide-angle control in the vertical plane for the on-off vertical steering.\n\nThe features of the system which had proved effective included:\nThe following valuable components were retained:\n\n1. The transducer and input circuit that permit transmission and reception with the same transducer without switching.\n2. The use of the quadrature-switching system and phase-sensitive detectors, enabling the handling of steering information for two-plane steering in a single amplifier.\n3. The doppler-enabling system, which prevents steering on echoes reflected from the surface and from target wakes. It also allows for the use of a higher receiver sensitivity without the risk of steering on bursts of reverberation.\n\nWhen the torpedo control program was moved to the Ordnance Research Laboratory (ORL), a research program was set up to develop a new system incorporating all the advantages of the Harvard NO 181 system but with the modifications gained from the Harvard NO 181 program.\nThe Mark 18 torpedo was chosen as a convenient one for investigations to develop it as a desirable anti-surface device. At the same time, it seemed desirable to investigate this device as a research torpedo, with no intention of applying acoustic steering control to it. Since the Mark 18 torpedo is gyro-controlled and the transducer beam pattern is very narrow, a new transmitter was designed, capable of generating 1,500 watts of electric power and a receiving system was set up to measure self-noise level, reverberation level, and frequency spread in the reverberation. This device was designed purely as a research torpedo.\nsystem  of  azimuth  search  was  incorporated.  In  order \nto  make  it  possible  for  the  torpedo  to  scan  a rela- \ntively large  angle,  a special  cam  plate  was  made  for \nthe  gyro  with  the  cams  placed  60  degrees  apart.  This \ncauses  the  torpedo  to  operate  on  a snaky  course  such \nthat  the  axis  of  the  torpedo  swings  from  30  degrees \non  one  side  of  the  set  course  to  30  degrees  on  the \nother  side.  Tests  run  on  the  dynamics  of  this  system \nat  the  Newport  Torpedo  Station  indicated  that  the \nreduction  in  forward  progress  caused  by  the  use  of \nthe  \u00b1 30-degree  snaky  course  amounted  to  a little \nover  5 per  cent.  At  the  time  of  writing,  the  data \nare  not  complete  on  the  reverberation  level  and  the \nfrequency  spread  in  the  reverberation.  However, \nthe  self  noise  of  the  torpedo  has  been  measured  at \nan  operating  speed  of  20  knots.  The  value  is  about \nFive db's correspond to a signal of -127 dB referring to 1 V [dbv] on the transducer when the receiving band width is 4 kc. When these data are complete for a series of torpedo speeds, it will be possible to determine the minimum component of target speed parallel to the axis of the torpedo which will need to be used for enabling the steering amplifier at each torpedo speed.\n\nFigure 1 shows a block diagram of the overall system as worked out for project 4G. In this case, the steering amplifier is completely independent of the enabling amplifier except for the enabling signal which is supplied to enable the demodulator. The amplitude gate is no longer included as part of the doppler-enabling system since the former arrangement caused the time constant of the amplitude gate to be added to the time constants of the discriminators.\nThe amplitude gate is incorporated as part of the steering amplifier and is actuated by the signal present in the steering amplifier circuit. To enable the system, a pulse must be developed out of the enabling amplifier at the same time that a pulse is developed in the steering amplifier, resulting in an amplitude gate pulse. The transformer is connected to one end of the low-impedance winding through a 0.01-\u00b5F condenser instead.\n\nThe time base in this system is a set of four cam-operated switches. The cams for these switches are mounted on a single shaft.\n\nFigure 1. Block diagram of ORL project 4 system.\n\nThe transducer used is the same as that used in the Harvard N0181 system (Figure 4, Chapter 19).\nThe pattern of a typical transducer reveals its characteristics when high power is generated in the transmitter. These transducers have functioned with high-power transmitters for extended periods. Although they eventually lose sensitivity due to magnet depolarization, their lifespan is sufficient for practical purposes. The input circuit is similar to that used in the Harvard N0181 system depicted in Figure 5, Chapter 19, with the exception of the turns ratio of the input transformers. This modification enables a voltage step-up of 30 db instead of the initial 20 db, and the 90-degree line is connected to a 1/4 tap on the high-impedance winding of the transmitter driven by the torpedo propulsion motor. Two cams operate the transmitter and receiver blanking.\nThe receiver TVG has two functions: one is used to operate the own doppler nullifier [ODN] relay, and the other is used as a range-measuring cam to control the range for vertical steering. Figure 2 shows schematically the sequence of events controlled by the time base.\n\n21.4 TRANSMITTER\n\nThe schematic of the transmitter circuit is shown in Figure 3. VI is a 6SN7 tube, one-half of which is used as the transmitter oscillator and the other half as a buffer stage. The frequency-determining element in the oscillator system is the inductor LI and the capacitors Cl and C2. V2 is a 6SN7 tube used as a push-pull amplifier to drive the grids of the driver stage V3. The grids of V2 are driven 180 degrees out of phase with each other by the toroidal coil L2. V3, V4, and V5 are all used as indicated.\nV3 serves as the driver stage, with V4 and V5 as the power output stage. The transformer T1 is the driver transformer, delivering 1,500 volts direct current to charge a bank of condensers. The charged condensers supply 1,500 volts at the center tap of T2 and 750 volts for the screen supply for V4 and V5. The plate circuits of V3 are connected to the grid input of V4 and V5. This transformer is identical to the transformer T2, which is the power-output transformer, forming a part of the input circuit. The plate supply for VI and V2 is not specified in the given text. (Figure 2 shows the sequence of operations in the time base. Figure 4 shows the schematic of the transmitter power supply. The condenser Cl is a storage condenser of 80-\u03bcF capacity which supplies the high plate current for V5, 5th Chapter 19.)\nThe power supply for V3 and V4 is a special motor-generator with a plate circuit in the transmitter during the 30-msec transmission interval. During the listening interval, Cl is charged from the 1,500-v DC generator through resistor R1 to prevent an excessive load on the generator during and following transmission.\n\nThe relays in Figure 3 and Figure 4 are operated by cam switches in the time base. The relay in Figure 4 completes the circuit for the transmitter power supply and actuates the plates and screens of V3 and V4. The relay in Figure 3 activates the plate circuit of the oscillator by connecting it to the power supply. Additionally, the relay in Figure 3 also activates the plate circuit of the oscillator.\nFigure 3 connects the blanking voltage to the r-f amplifier in the steering receiver and also connects the proper voltage to the TVG control circuit in the receiver. The capacitor maintains this voltage during the interval of the pulse. Except for the rounding of the corners of the pulse envelope at the beginning and end of the pulse, the major portion of the top of the pulse envelope is nearly flat.\n\n21.5 Steering Receiver\n\nThe steering receiver used in this device is quite similar to that used in the Harvard NO 181 system and is shown in Figure 5. The same four-channel switching system controlled by a local 1-kc oscillator generating signals with relative phase relations of 0, 90, 180, and 270 degrees is used. Due to some interference, Figure 4 shows the transmitter power supply and pulse-tailoring circuit.\nThe transmitter system incorporates pulse-shaping through the use of inductor LI and capacitor C3, as well as the fact that the relay in Figure 3 is not operated simultaneously with the relay in Figure 4. At the beginning of the pulse, both relays are closed by their respective cams at the same time. Due to the slight delay in the build-up of the transmitter oscillator and the effect of inductor LI in series with the transmitter power supply, the front of the pulse envelope is rounded both at the top and the bottom. The relay in Figure 4 is opened a few milliseconds before the relay in Figure 3, allowing capacitor C3 to serve as the power source to operate the transmitter during a short interval. This causes the transmitter output to gradually decrease.\nThe relay in Figure 3 stops the transmitter oscillator, and the inductor Ll in Figure 4 helps make the transmitter power output more nearly constant. Improvements in the design of the band-pass filter and a change from 6SG7 to 6AK5 tubes for the switching tubes have increased the gain in the switching tubes from about 12 to 30 dB. The output of the 60-kc band-pass filter is fed to the two-stage amplifier VI and V2 in Figure 5. VI is a resistance-coupled stage, while V2 has a 60-kc band-pass filter identical to the one in the output of the switching tubes for its output. The 60-kc signal with 1-kc modulation is fed to the demodulator V3, which is a grid-controlled rectifier. The enabling pulse from the amplitude gate and the doppler gate.\nare  applied  to  the  grid  of  V3  which  is  maintained  at \na d-c  potential  of  about  \u2014 22  v relative  to  the  cath- \node. The  22- v bias  on  V3  is  sufficient  to  make  it  non- \nconducting for  any  signal  from  the  60-kc  channel. \nHowever,  the  pulse  which  is  supplied  from  the  dop- \npler pulse  amplifier,  when  added  to  the  pulse  sup- \nplied from  the  amplitude  gate  pulse  amplifier,  is \nsufficient  to  overcome  this  bias  on  receipt  of  an  echo \nof  the  proper  level  and  having  the  proper  frequency \nSTEERING  RECEIVER \ndifference  from  that  of  the  reverberation  to  satisfy \nthe  criteria  set  up  in  the  enabling  receiver. \nIn  the  Harvard  NO  181  device  the  amplitude  gate \nwas  incorporated  in  the  enabling  receiver  so  that  the \ntime  constant  of  the  amplitude  gate  circuit  had  to  be \novercome  before  a signal  could  be  applied  to  the  dis- \ncriminator driver.  The  time  constant  of  the  ampli- \nIn this system, the attitude gate and time constant in the filter of the discriminator were cascaded. The amplitude gate is operated by the signal in the 60-kc channel, so the time constant of the amplitude gate has no effect on the time of appearance of a pulse from the doppler enabling channel. The AVC (Automatic Volume Control) is used to prevent the device from steering on noise countermeasures, as it is possible for the noise countermeasure to generate an enabling signal from both the doppler gate and the amplitude gate. Figure 6 illustrates the TVG-AVC and blanking arrangements for the receiver. When the switch in the time base operates the relay in the transmitter indicated in Figure 3, two of these contacts in the relay supply voltages which are introduced in the TVG-AVC circuit of Figure 6 at the points labeled blanking voltage and TVG voltage. The blanking.\nThe voltage used is 48 v, which is the DC voltage available from the power supply for the operation of the fileOA'C. Operation data obtained with the Harvard NO 181 system indicated that, under some conditions of operation, the AVC control of amplifier sensitivity was not sufficient. To correct this defect, the sensitivity control of stages VI and V2 in the 60-kc amplifier is furnished by a combination of TVG and AVC, arranged such that the AVC control can be eliminated by means of a switch. An important characteristic of a doppler-controlled device is the fact that the requirements of the sensitivity control system are not as rigorous as they are with a device which does not have the doppler-enabling feature. It is therefore possible to design the TVG control for operating conditions where the reverberation levels are minimal.\nThe reverberation will not cause false steering without the use of AVC. The functions and solenoids in the system serve specific purposes. The TVG voltage, applied to the terminal labeled TVG voltage in Figure 6, is a lower negative voltage, with an optimum value yet to be determined but -10 volts will be used. During the transmitted pulse, a small current will flow through R1 due to the voltage difference at its ends. However, condenser Cl will be charged to the potential of the TVG voltage, and the grids of the 60-kc amplifier will be maintained at -48 v during transmission. Following transmission, the grids will quickly take the potential to which Cl is charged. If switch S is:\nThe condenser in the 1 position discharges through the 1.2-megohm resistor R2. It is the charge of the condenser Cl through R2 that produces the time variation in bias on the grids of the 60-kc amplifier, resulting in the time variation in gain. The AVC feature is achieved by the signal received on terminal 1 of the diode from the 60-kc amplifier. The fact that this signal charges C3 to a potential determined by the peak value of the 60-kc signal will determine the voltage-drop across the 6AL5 diode. Signal from the output of the 60-kc amplifier is applied to terminal 1 and is rectified in the 1-7 section of the diode, charging the capacitor.\n\nFigure 6. TVG-AVC circuit.\nIf switch S is in the 2 position, the voltage drop across R5 will impact the discharge of condenser Cl. When the voltage drop due to the rectified signal from the 60-kc channel reaches the value of the potential of condenser Figure 7, Amplitude gate and doppler-pulse amplifier, condenser Cl discharges through the 5-2 section of the diode, the resistor R4, and resistor R5. The value of R4 + R5 equals R2. If no signal is received on terminal 1 of the diode from the 60-kc channel, the rate of discharge of condenser Cl is the same whether switch S is in the 2 position or the 1 position. However, if a signal is received, condenser Cl will stop discharging and the potential on the grids of the 60-kc amplifier will remain constant or decrease at the rate of decrease of the signal from the 60-kc channel.\nThe output of the 60-kc amplifier completes a path around the 2-5 section of the diode, allowing the condenser Cl to be charged slowly from the rectified signal from C3. The time constant of the Cl, R3, R4 network is between 4 and 5 seconds, so a 60-kc signal of very high level is required to produce any significant charging of the condenser Cl through the AVC network during normal listening intervals.\n\nFigure 7 shows the details of the entire amplitude gate circuit and the pulse amplifier for the doppler enabling pulse. VI is a 6SN7 tube, the 1-2-3 section of which is used to rectify a signal from the output of the 60-kc amplifier. The rectified signal is fed to the grid of the 4-5-6 section, which functions as a DC amplifier for the rectified voltage output of the 1-2-3 section.\nThe rectifier and d-c amplifier have no dense coupling. The output of the d-c amplifier will be the same whether the signal from the 60-kc channel is steady or a pulse. R4 is the plate load resistor for the pulse amplifier portion of VI. The point PI between R5 and R7 is maintained at a definite d-c potential in the absence of a signal from the 60-kc amplifier, determined by the fact that R1, R2, R3, and R7 are all returned to -48 v and R4 is returned to the ~b250-v power supply.\n\nThe 1-2-3 section of V2 is a grid-controlled rectifier which serves as the demodulator for the 60-kc signal applied to the cathode terminal 3. The d-c potential at point Pi contributes to the negative bias maintained on terminal 1, the grid of the amplifier.\nThe demodulator maintains a negative bias of -22v on terminal 1 in the absence of a signal, determined by the potentials of points PI and P2. This negative bias on the demodulator prevents the passage of any signal in the 60-kc channel. When a signal is received in the 60-kc channel, the potential of PI becomes more positive due to the action of VI. If the 60-kc signal is a steady-noise signal, the effect on PI depends on whether the switch in the TVG-AVC circuit (Figure 6) is set in the 1 or 2 position. If it is set in the 2 position and steady continuous noise is received, the AVC action will prevent the rise of the signal in the 60-kc amplifier to a sufficient level to bring the demodulator near the point of conducting. When an echo is received,\nReceived with the receiver under normal TVG control, the echo will have a level such that a pulse of voltage, equal to the length of the echo, will be produced at PI. This pulse of voltage will be sufficient to overcome part of the -22V bias on terminal 1 of V2. If the echo is from a moving target, a pulse will be generated from the enabling amplifier which will be amplified in the 4-5-6 section of V2. This pulse voltage, added to that generated at PI, will be sufficient to overcome the bias on terminal 1 of the demodulator. The voltage capabilities of the two pulse amplifiers, the 4-5-6 sections of VI and V2, are such that one alone cannot generate a sufficient voltage to overcome the full bias on the demodulator grid. It is therefore necessary that a pulse be generated in the enabling amplifier as well as in the 60-kc section.\nThe steering amplifier is designed to overcome bias on the demodulator by requiring an amplitude pulse and a frequency difference between the received pulse signal and the reverberation. To operate the system as a noise-steering device, switch S in Figure 7 can be turned to the 2 position, eliminating the connection to the doppler-enabling channel and lowering the demodulator grid bias to a value overcomeable by the potential developed at PI due to a noise signal. Figure 8 displays the schematic of the 1-kc amplifier and the two phase-sensitive detectors. The 1-kc amplifier utilizes a tuned plate load and is identical to the one used in the Harvard N0181 system.\nphase-sensitive detectors have been simplified in the new arrangement. The new arrangement uses only one double diode for each phase-sensitive detector instead of two. The output of the 1-kc amplifier is connected to the phase-sensitive detectors through condensers Cl and C2 and resistors Rl, R2, R5, and R7. The activating signals from the 1-kc switching oscillator, the same oscillator indicated in Figure 5, are fed to the phase-sensitive detectors through resistors R3, R4, R6, and R8. The output of phase-sensitive detector V2 is a d-c voltage which compares the signal input on terminals UP and DN in Figure 5. If the signal on UP is larger in magnitude than that on DN, the d-c voltage appearing on terminals 5 and 7 of V2 will be positive, or if the signal on terminal DN is larger than the signal on UP, the d-c voltage on terminals 5 and 7 of V2 will be negative.\nThe DC output voltage on terminals 5 and 7 of V2 will be negative when a signal is applied to the terminal UP. The magnitude of DC voltage at the phase-sensitive detector output increases with increasing target angle until the limiting value of the phase-sensitive detector output voltage is reached. This limiting value of output voltage is determined by the ORDNANCE RESEARCH LABORATORY PROJECT 4 system voltage of the 1-kc switching oscillator. The horizontal phase-sensitive detector V3 functions similarly to the vertical phase-sensitive detector, except that its output voltage is determined by the relative levels of the signal on terminals RT and LFT in Figure 5.\n\nThe enabling receiver in Figure 9 operates on the same principle as the one used in the Harvard N0181F. It, however, uses a different amplifier.\nThe signal for the end and second stage uses a 7-kc tuned circuit as the amplifier plate load, followed by a discriminator driver. The discriminator driver operates with a positive bias on the cathode, sufficient to bias the tube beyond cutoff. The value of the bias determines the level of signal on terminal 1 of the input circuit, causing a signal to be first observed in the plate circuit of the discriminator driver. The discriminator driver also serves as the limiter stage in the system, resulting in a gain with about a 6-db difference between the signal levels on terminal 1.\nThe input signal produces a just perceptible change in the plate circuit of the enabling amplifier. The first stage of amplification operates at the normal signal frequency of 60 kc. This stage uses an inductive load in the plate circuit of the tube. The output of this stage is coupled to the grid of the converter stage through a 0.0001-\u03bcF condenser. This arrangement allows for a voltage gain from the input of the 60-kc amplifier to the grid of the converter stage of about 30 dB at 60 kc, while at 7 kc, which is the frequency to which the signal is converted, the gain from the input of the 60-kc amplifier to the grid of the converter is about -8 dB. All tubes used in the amplifier and converter stages are 6AK5 miniature pentodes. The 7-kc band-pass filter which serves as the filter.\nThe plate load for the converter has been redesigned to increase conversion gain significantly over that available in the Harvard NO 181 system. Following the converter is a two-stage amplifier. The first stage of the amplifier is resistance-coupled, with the discriminator driver and signal level producing complete limiting in the discriminator. This entire amplifier, from the input circuit to the discriminator driver, has one less stage of amplification than in the original HUSL NO 181 enabling system. It can be operated so that a signal of -125 dbv on the transducer produces complete limiting of the discriminator driver. In the Harvard NO 181 F system, limiting of the discriminator driver took place at a signal level on the transducer of -105 dbv. It would be possible to operate this amplifier so that limiting takes place at a different signal level on the transducer.\nAt a signal level of -136 dbv, if it could be used in a torpedo of sufficiently low noise level, the discriminator terminals 1 and 2 of Figure 9 are connected to diodes VI and V2. By means of these two diodes and diode V3, the output at terminal P will be positive regardless of the polarity of the signal out of the discriminator, and therefore, regardless of whether the echo signal has a higher or lower frequency than the reverberation signal. The potential generated at P is amplified by the pulse amplifier incorporated in the steering receiver and shown in Figures 5 and 7. The condensers C5, C6, C7, and C8, and resistors R5, R6, and R7 of Figure 9 form a filter in one side of the discriminator circuit, while the condensers C9, C10, C11, and C12 and resistors R8, R9, and R10 create a filter in the other side.\nRIO forms a filter on the other side of the discriminator circuit. These filters are identical to the filter that plays the role of varying the effective value of condenser C14 in the tank circuit of the oscillator, using the potential applied to grid 4 of V4. The relay is operated by means of a cam-operated switch in the time base, arranged such that this relay is closed for approximately 50 ms immediately following transmission. However, to prevent sampling of the discriminator output during receipt of an echo when the torpedo is near enough to a target so that an echo is received during this 50-ms period, a DISCRIMINATOR\n\nFigure 9. Doppler-enabling circuit. (Pin numbers of 6SN7 are 3, 1, 2, 5, 4, and 6, clockwise from lower left-hand cathode.)\n\nThis relay indicated was used in the discriminator circuit in the Harvard NO 18 IF system.\nConnect the output of one side of the discriminator to grid 4 of V4, during a 50 msec interval following transmission. The 1-2-3 section of V4 is the local 53-kc oscillator that supplies signal to the converter stage screen. The automatic frequency control, which adjusts the oscillator frequency so that the converter output is at the discriminator center frequency when reverberation is the signal source, is accomplished through the 4-5-6 section of V4 with the varistor VR. One side of the relay coil is connected to its power source through an echo relay contact in this arrangement. By arranging the switch, operated by the time base, to simply connect the other side of the relay coil to ground, the arrangement ensures that the oscillator frequency remains stable.\nThe relay will be closed during the entire 50-millisecond period if no echo signal is received. However, upon receipt of an echo signal, the circuit between one side of the relay coil and the 48-volt power supply will be broken, and the ODN relay will drop open. Since this circuit is entirely independent of other parts of the electronic system, except for the provision of the enabling signal to the pulse amplifier in the steering chassis, it is possible to completely remove this enabling receiver from the other gear and have the rest of the device operate without Doppler enabling. A readjustment must be made on the 21.7 relay control circuit.\n\nThe details of the relay control circuit incorporated in the control panel are shown schematically in Figure 10. The following four relays are used:\n\nFigure 10. Control circuits.\nValue of the bias on the demodulator. This is provided by the switch in Figure 7, which makes it possible to use the steering receiver as an echo-ranging receiver without doppler control or as a noise-steering receiver in addition to its normal method of operation.\n\n1. An echo relay which is actuated during the time of receipt of an echo.\n2. An enabling relay which is actuated by the echo relay, but which remains closed for a period of about 6 sec following the last echo of a sequence.\n3. An azimuth steering relay which is positioned by the information supplied by the azimuth phase-sensitive detector.\n4. The vertical steering relay which is positioned by the information last received from the vertical phase-sensitive detector.\n\nDescription of the operation and functions of the four relays:\n\n21.7.1 Echo Relay\nThe echo-relay amplifier is operated by the signal which appears on the grid of the demodulator in Figure 5, maintained at -22 v relative to ground. This potential serves as the necessary bias for the grid of the echo-relay amplifier. The 2-5 section of diode VI in Figure 10 is placed in series with the grid of the echo-relay amplifier, along with resistor Rl, to form a fast-charge, slow-discharge circuit for condenser Cl. Rl and Cl provide a small holding-time constant to delay the opening of the echo relay following receipt of an echo. This delay is necessary because the relay operates the glide-angle control solenoid in the afterbody, and when vertical steering takes place, it is necessary to hold the glide-angle control solenoid actuated.\nThe glide-angle control motor requires sufficient time to complete an operation. Details will be described in the next section on afterbody circuits. The glide-angle control solenoid is operated by the 2-3 contacts of the echo relay. A provision for the removal of ODN frequency correction, when an echo is received during the 50-msec ODN sampling period, is provided by the No. 1 contact. This is accomplished by the fact that the ODN relay coil, shown in Figure 9, is connected to the -48-v supply via contacts 1-2 of the echo relay when this relay is open. Receipt of an echo immediately breaks this contact, permitting the ODN relay to drop open. The 5-6 contacts on the echo relay connect the azimuth phase-sensitive detector to the grid of the azimuth steering-relay amplifier during the operation.\nWhen an echo is received, the echo relay's 5-4 contacts connect the steering amplifier grid to the azimuth automatic rudder-reversal circuit. Opening the 7-8 contacts allows a 48-volt surge to flow through R4 and the 1-7 section of diode VI, charging the condenser C2 and causing the enabling relay to open. The discharge of C2 through R3 and the 7-8 contacts of the echo relay provides the holding time required for the enabling relay. The components indicated in the figure provide a holding time of about 5.7 seconds.\n\n2.2 Enabling Relay\n\nThe normal condition of the enabling relay is closed. Closing of the echo relay causes grid terminal 4 of V2 to be driven negative, which in turn opens the enabling relay. The relay is held open for about 5.7 seconds in the absence of further echoes.\nThe time constant of C2 and R3 is related to the 1-2 contacts on this relay, which are involved in the azimuth automatic rudder-reversal feature. The contacts 4-5 connect 48v to the coil of a relay in the afterbody, setting up the circuits in the afterbody for acoustic control. Contacts 8-9 connect 48v to the glide-angle control solenoid when this relay is in the normal closed condition, allowing the glide-angle control to return to the neutral position after an attack has been broken off.\n\nSection 1-2-3 of V3 is the vertical steering-relay amplifier. It receives its signal directly from the vertical phase-sensitive detector. Contacts 1, 2, and 3 permit connecting one terminal of the glide-angle control motor to either 48v or ground. Since the other terminal of the motor is connected to -24 volts.\nThe position of this relay determines the rotation direction of the glide-angle control motor. Operation of the glide-angle control motor is determined by the echo relay, enabling relay, and a range-measuring cam in the time base. The details of these circuit arrangements will be described in the next section. The 5-6 contacts on the vertical steering relay provide a holding feature by grounding the junction of Rll and R12 when the relay is closed. By means of this holding feature, the relay can be made to open on a -2V signal on the amplifier grid and close with a +2V signal on the grid. It will retain its last position until a suitable signal arrives to change it.\n\n21.7.4 Azimuth Steering Relay\n\nThe azimuth steering-relay amplifier is connected to the azimuth phase-sensitive detector.\nThe 5-6 contacts of the echo relay. This relay amplifier has the same sensitivity and holding feature as the vertical steering relay with the 8-9 contacts. The automatic rudder reversal feature of the azimuth steering system is arranged through contacts 1, 2, and 3. The 4, 5, and 6 contacts are the steering contacts which provide for 48V to be connected to one or the other of the azimuth steering solenoids. The ground return for these solenoids is provided through the relay in the afterbody which is operated by the enabling relay. Before the first echo is received, it is impossible for the solenoids to be operated by the azimuth relay. When an echo is received, the closing of the enabling relay provides the necessary power to the solenoids.\nfor the ground connection to return after the solenoid, so that the azimuth steering relay takes over control of the azimuth steering from the gyro. The gyro lock-off feature in the afterbody provides for permanent ground return of the solenoids after receiving about ten echoes. Once this is accomplished, the azimuth steering relay will retain control of the azimuth steering regardless of echo reception.\n\n21.7.5 Azimuth Automatic Rudder-Reversal Feature\n\nAssume the torpedo is steering to starboard, the azimuth rudder relay is down, and the torpedo is in an attack. Under these conditions, 48 volts are connected through the 3-2 contacts of the azimuth steering relay and the 2-1 contacts of the enabling relay, and R5 and R2 to the condenser terminal C3. While the echo relay is open, C3 is connected.\nthrough the 4-5 contacts of the echo relay to the grid of the azimuth steering relay. When the denser C3 reaches a sufficiently negative potential (-2 v), the azimuth steering relay will be thrown open, causing the torpedo to steer to port. The same sequence would be carried out if the azimuth relay had originally been open except that, in this case, terminal 2 of the azimuth relay would be connected to the bleeder circuit R18 and It 19 which supplies a positive potential with which to charge C3, causing the relay to close when C3 arrives at a potential of +2 v. The action of the 8-9 contacts on the echo relay is to discharge C3 through R2 each time an echo is received, so that the rudder reversal can take place only when an attack breaks off. Since C3 is charged through the 2-1 contacts of the echo relay.\nThe rudder reversal must occur during the holding time of the enabling relay. Since only one reversal is desired when an attack ends, the time constant of the rudder-reversal circuit, determined by C3, R5, and R6, must be more than half the holding time of the enabling relay, and less than the holding time of the enabling relay to ensure the reversal takes place.\n\nSection 21.7.6: Sequence of Events in an Attack when an Echo is Received\n\nThe echo relay drops closed and remains closed for several milliseconds after the end of the echo. The azimuth and vertical steering relays assume settings determined by the outputs of the azimuth and vertical phase-sensitive detectors. The vertical steering relay will not be able to exert control on the glide-angle control system unless the range is within its operational limits.\nless  than  250  yd,  since  the  actuation  of  the  glide- \nangle  control  solenoid  by  the  echo  relay  is  accom- \nplished by  way  of  a cam-operated  range  switch  in  the \ntime  base.  The  azimuth  relay  will  immediately  take \ncontrol  of  the  azimuth  steering  from  the  gyro  and \nthe  gyro  lock-off  motor  will  start.  Three  separate \npossible  cases  will  be  considered.  The  first  possibility \nis  that  only  one  or  two  echoes  are  received  and  the \nrange  is  greater  than  250  yd.  Under  this  condition, \nno  vertical  steering  takes  place.  After  the  last  echo, \nthe  azimuth  rudder  relay  will  hold  for  about  4.5  sec, \nwhen  the  rudder  will  reverse,  causing  the  torpedo  to \nstart  to  recross  the  beam.  However,  at  the  end  of \nabout  6 sec  following  the  last  echo,  the  enabling  relay \nwill  drop  closed  and  return  the  torpedo  to  gyro  con- \ntrol. The  second  possibility  is  that  a series  of  ten  or \nmore echoes are received so that the gyro lock-off motor has completed its cycle. The action will be the same as before, except that after rudder reversal, the torpedo will continue to circle in the direction determined by the reversed-rudder relay position. The third possibility is that a series of echoes have been received for a sufficient time to cause the gyro lock-off to complete its cycle and the attack has carried the torpedo into the range where vertical steering can take place. The glide-angle control functions to allow the torpedo to correct its course by about 1.5 degrees in the vertical plane each time an echo is received within the 250-yd vertical steering range. If the torpedo loses contact with the target, it will continue to climb at the climb angle determined by the last setting of the glide-angle control until the enabling relay is enabled.\nThe glide-angle drops and closes, i.e., until approximately 6 seconds after receipt of the last echo. After this, the glide-angle control will be returned to its initial neutral position with one increment of angle in each ping interval. In the meantime, the azimuth rudder reverses after a lapse of 4.5 seconds from the last-received echo. Since the glide-angle control return takes place in increments, the torpedo will have a chance to reverse its course and sweep across the beam before it has a chance to return to its hydrostatic running depth. If contact loss occurs very close in, there is a chance that the automatic rudder-reversal feature will cause the torpedo to strike the target despite loss of acoustic contact.\n\nCircuits in the Torpedo Afterbody\n\nFigure 11 shows the circuit arrangements for:\n\n(Figure omitted for brevity)\nThe afterbody of the torpedo houses the circuits for generator power supplies. The time base operates as a system of cams driven by the main motor shaft and is indicated as cams C1 through C4 in the figure. The given time constants for automatic rudder reversal, holding of the enabling relay, and gyro lock-off are not definitive, as their values will depend on the torpedo's body dynamics. To prevent broaching when the torpedo loses contact close in, a ceiling switch in the afterbody may be required to allow for immediate return to hydrostatic control if acoustic contact is lost at depths less than 10 ft. The muth steering solenoids are arranged such that they\nThe gyro takes over steering control when relay circuits are activated. Relay 2 in Figure 11 closes with the 48-volt power supply when power supplies are turned on, allowing recycling of the glide-angle control system and gyro lock-off system after prerun tests.\n\nORDNANCE RESEARCH LABORATORY PROJECT 4 SYSTEM\n21.8.1 Gyro Lock-off\n\nThe gyro lock-off consists of a small 24-volt permanent-magnet motor that drives cams Cl and C2 through a reduction gear. In the figure, the arrows on the motor and cams indicate the direction of rotation as the system approaches the gyro lock-off condition. At the start, cam Cl is engaged.\nWhen the first echo arrives, the enabling relay on the main chassis actuates relay 1, causing it to close. Brush 1 on the gyro lock-off motor is connected to -48v. Brush 2 on the motor is connected via contacts 3 and 4 of switch S2 and contacts 5-6 of relay 2 to -24v. The motor continues to rotate in the forward direction as long as relay 1 remains closed or until cam C2 opens switch S2. If the attack breaks off long enough to allow the enabling relay to open, relay 1 opens and brush 1 of the gyro lock-off motor is connected to ground by way of contacts 4-5 on relay 1 and contacts 1-2 on switch SI. This causes the motor to reverse and it continues to rotate in the reverse direction in the absence of further echoes until cam Cl opens switch Si.\nThe motor circuit. Spurious echoes will start the gyro lock-off motor, but as soon as the enabling relay drops open, the motor will return the gyro lock-off system to the original starting position. The time set up for gyro lock-off to be accomplished is about 15 sec, corresponding to the time necessary for about ten consecutive echoes to be received. The lock-off feature is achieved by means of cam C2, which, when turned far enough, opens switch S2, breaking the circuit to the brush 2 on the gyro lock-off motor from the -24-v supply.\n\n21.8.2 Glide-Angle Control System\n\nThe glide-angle control system is the means used to transfer information from the vertical steering relay to the elevators. This is done by adding increments of mechanical bias to the pendulum in the immersion mechanism. The bias is added to the pendulum.\nThe pendulum is adjusted so that it is compensated by a definite tilt of the torpedo body through a specific number of degrees. The bias added to the pendulum on each received echo is approximately 1.5 degrees. It is desired that vertical steering be restricted to a target range of about 250 yards or less. This is accomplished by using cam 4 in the time base, which keeps its switch closed during the time an echo could be received from a target range of 250 yards or less. If an echo is received within this range, the echo relay in the panel will be closed, connecting terminal v via the large AN plug, terminal E on the small AN plug, the switch operated by cam 4, and the 11-12 contacts on relay 2 to the glide-angle control solenoid. This solenoid is the coil of a relay which, when actuated, closes contacts 1-2.\nThe extended arm on the relay is pulled away from disk D. This arm has a pin which fits into holes around the edge of disk D, allowing contacts 1-2 to be held closed except when the pin is free to drop into a hole in the disk. Closing contacts 1-2 connects brush 1 of the glide-angle control motor to 24v through contacts 2-3 of relay 2. Brush 2 of the motor is connected via contacts 2-3 of relay 1 and the AN plugs to a swinger on the vertical steering relay in the panel. When the phase-sensitive detector signal indicates up-steering, this brush will be connected to ground, whereas if it indicates down-steering, this brush will be connected to 48v. The direction of rotation of the motor, therefore, is determined by the setting of the vertical steering relay. As soon as the echo relay drops open after the end of\nThe echo receives, with the enabling relay still active, the glide-angle control solenoid will de-actuate and attempt to return to normal. However, during this time, disk D will have turned enough for the pin on the extended relay-arm to ride on its surface between holes, thus keeping contacts 1-2 closed until the next hole aligns, allowing the pin to drop in and open the contacts. This setup ensures that the motor turns the disk through an angle determined by the position of adjacent holes each time an echo, enabling vertical steering, is received. A small holding time is integrated into the echo relay to ensure the glide-angle solenoid remains active long enough, preventing the pin from dropping back.\nIf an attack is broken off, the enabling relay will eventually drop open. When this occurs, the relay setup on the steering panel will be such that the glide-angle control solenoid will be actuated during each interval that the switch operated by cam 4 in the time base is closed. If some bias has been introduced on the pendulum by means of the glide-angle control system, contact 2 in the switch operated by the mechanical bias rack will be closed either against contact 1 or 3 depending on whether the bias introduced is for up or down steering.\n\nCircuits in the torpedo afterbody:\n\nWhen the enabling relay in the steering panel is unactuated, relay 1 in Figure 11 will open. Brush 2 on the glide-angle control motor will be connected via contacts 2-1 on relay 1 to contact 2 of the motor.\nThe switch is operated by the mechanical bias rack. The polarity of contacts 1 and 3 is such that the motor will be driven in a direction causing the mechanical bias rack to return to its neutral position. Due to the intermittent operation of the glide-angle control solenoid under this condition, the glide-angle control bias will be returned by one of the increments of bias during each ping interval. When the bias rack has been returned to the neutral position, contact 2 on the bias-rack switch will be in a free position between contacts 1 and 3, thus breaking the motor circuit. To prevent broaching of the torpedo when acoustic contact is lost near the end of an attack, a pressure-operated ceiling switch is placed in parallel with the switch operated by cam 4. This permits the glide-angle control motor to re-adjust.\nTurn the pendulum bias to the neutral condition immediately upon opening of the enabling relay if the torpedo is at a depth shallower than the setting of the ceiling switch.\n\nThe provision for recycling of the gyro lock-off and glide-angle control is made by means of battery B and the change of connections provided when relay 2 is unactuated by turning off the source of 48-v power. If the gyro lock-off has completed its cycle so that S2 is open, brush 2 of the gyro lock-off motor will be connected to the 24-v terminal on battery B through contacts 4-5 or relay 1 and contacts 1-2 of switch 1. This will permit the motor to start recycling even though the gyro lock-off motor has turned sufficiently to allow the switch S2 to open. Brush 2 of the motor will be connected to the \u201324-v terminal of battery B through contacts 4-3.\nThe switch S2 and contacts 4-5 of relay 2 are connected, causing the motor to continue recycling until cam 1 opens switch SI, which initiates the system. The glide-angle control solenoid is connected to the -48-v terminal of the battery through contacts 10-11 of relay 2 and the 4-5-6 contacts operated by the mechanical bias rack. If the glide-angle control is not in the neutral position, this will close and keep closed the 1-2 contacts operated by the glide-angle control solenoid until the mechanical bias rack is returned to the neutral position. Brush 2 of the glide-angle control motor is connected to either ground or terminal B -48-v, depending on the position of the mechanical bias-rack switch and the polarity determined by contacts 1, 2, and 3.\nThe rack will be run back toward the neutral position. As soon as the neutral position is reached, the motor circuit will be broken by the 1-2-3 contacts in the mechanical bias-rack switch, stopping the motor. At the same time, the connection to the glide-angle control solenoid will be broken by the 4-5-6 contacts on this switch.\n\nChapter 22\nBell Telephone Laboratories 157B and 157C Systems\n\n22.1 Introduction\n\nThe original Bell Telephone Laboratories [BTL] development was an echo-ranging system to be used in the submarine-launched Mark 14 torpedo and was known as Project 157B. However, when the use of the Mark 18 electric torpedo began to supersede the use of the Mark 14, BTL was asked to modify their system for use in the Mark 18 torpedo. The system was to transmit equal acoustic signals, so that:\n\nChapter 22\nBell Telephone Laboratories 157B and 157C Systems\n\n22.1 Introduction\n\nThe original Bell Telephone Laboratories (BTL) development was an echo-ranging system designed for use in the submarine-launched Mark 14 torpedo, known as Project 157B. However, with the increasing use of the Mark 18 electric torpedo, BTL was asked to modify their system for use in this new torpedo model. The system was designed to transmit equal acoustic signals.\nThe phases interact with each other and are transmitted into the water. The receiver consists of two similar amplifiers, each amplifier connected to the output of one-half of the transducer. At the output of each amplifier channel is a threshold stage which imposes the requirement that a signal level developed in the transducer must exceed some predetermined value as a function of time after transmission.\n\nFigure 1. Block diagram of 157C system.\n\nBy the end of World War II, the problems with adapting the 157 system to the Mark 18 were being concluded. Although no tests had been run on this modified device, some units, designated as 157C, were nearly ready for field operations. Since the only essential differences between the 157B and 157C systems are those necessary to adapt them to the two different torpedoes, the following description in this report will focus on those changes.\nA block diagram of the acoustic control system is shown in Figure 1. Acoustic control is limited to the azimuth plane with normal hydrostatic control in depth. The transducer is divided into two halves in the azimuth plane, which are connected in parallel. The time variation in signal level imposed is controlled by a time-varied gain [TVG] on the receiving amplifiers. Following threshold stages are limiter stages. The characteristics of the threshold and limiter stages are such that approximately 2 dB of signal level above that necessary to pass the threshold stage is sufficient to limit the limiter stage. This ensures that a signal level, only slightly higher than the minimum permitted to pass the threshold stage, will result in a level out of the permitted range.\nThe limiter stage that is independent of the received signal level. The outputs of the two limiter stages are fed to a phase-sensitive detector. The phase-sensitive detector measures the electrical phase relation between the signals supplied by the transducer's two halves. From this electrical phase difference, the target bearing relative to the torpedo's axis is determined. The information determined by the phase-sensitive detector is supplied to a device known as a translator. The translator is a mechanical system connected to the cam plates on the torpedo gyro. The correction to be applied to the torpedo's course, as determined by the phase-sensitive detector, is applied directly to the gyro cam plate by the translator. In this way, the torpedo remains under gyro control.\nThe entire course of the run, but after an attack begins, the system is able to make a correction on the setting of the gyro course of the torpedo on each received echo. It is necessary to make provision in the phase-sensitive detector system against the torpedo homing on the wake. This is done by means of preferred-side steering. At the time the torpedo is fired, the side of the target on which it is being fired is determined, and a switch operable from the outside of the torpedo body is set. If the torpedo is fired toward the port side of a target, the system will prefer echoes reflected from the point on the target furthest to port. This means that when an echo is received from an extended target including the full length of a ship and its wake, the torpedo will home on the bow end of the entire system.\nThe transmitter provides approximately 1500 watts of electric power to the transducer. The transmitted pulses are 3 milliseconds in length and are spaced at 1-second intervals. This spacing of the transmitter pulses makes the maximum acoustic range of the torpedo about 800 yards. The system operates at a frequency of approximately 28 kc.\n\n22.2 TRANSDUCER\nFigure 2 illustrates the components of the transducer. It comprises an array of piezoelectric crystals mounted on a steel resonator plate, which is encased in a chamber formed by the resonator plate and a thin steel dome. The crystals are ammonium dihydrogen phosphate 45-degree z cut. Twenty-four crystals are used, with eight of them half-amplitude, to create a system that suppresses minor lobes. The crystals are insulated from the steel plate by means of ceramic insulators.\nThe crystals are cemented to the ceramic insulators, and the ceramic insulators are in turn cemented to the resonator plate. The space between the resonator plate and the thin steel dome is filled with Union Carbide and Carbon Corporation's UCON HB 600 fluid.\n\nFigure 2. Transducer crystal array.\n\nThe steel dome is 0.030 in. thick, and mechanical reinforcement is provided by an internal grill work of 3/16-in. stainless steel rods. Figure 3 shows details of the dome. Figure 4 shows the directivity patterns for this transducer in both the horizontal and azimuth planes and for both transmission and reception.\n\nFigure 3. Transducer dome.\n\nFigure 5 shows the electrical phase angle between the signals generated in the two halves of the transducer measured as a function of the angle for Bell Telephone Laboratories 157B and 157C systems transmitting and receiving.\nFigure 4. Directivity patterns of transducer for the incident acoustic signal. This is an important characteristic since the system measures the bearing of the target relative to the axis of the torpedo by comparing the phase angle of the signal generated in the two halves of the transducer.\n\n22.3. Time base\nThe operation of the torpedo is based on the use of 3-msec pulses transmitted at 1-sec intervals, making the maximum possible acoustic range of the torpedo a little over 800 yards. During transmission, transients are induced in the tuned circuits of the receiver which persist for a short time following transmission. In order to prevent false steering on these transients, the receiver is blanked for a total of 40 msec.\n\nFigure 5. Electrical phase angle plotted as a function of target angle for the hydrophones.\nFigure 6 indicates diagrammatically the sequence of operations for point h, IYDR0PH, IONES. Time base controlled by a multivibrator, which actuates relays during its on period. The time base consists of a multivibrator that acts through a large capacity condenser (1 \u00b5F), charged to approximately +300 V during the 50-msec on period. With a multivibrator off period of 950 ms, timing of the off period is approximately 1000 milliseconds.\nThe multivibrator's operation is determined by Cl, Rl, and PI. The off period is adjusted through the potentiometer, which is necessary to fully charge the condenser. This charging path is provided by the 1-2-3 section of tube V2 acting as a cathode follower. The normal operation of the panel requires BOTTOM RC rods* to be 7T>r ST BOTTOM, with the piometer controlled by PI. The on period is controlled by C2, R3, and P2 when the latter two are connected to the +300-V supply via the 5-6 contact of the relay RC. An unusual feature of the multivibrator is the requirement for the reverberation control relay RC to be closed for 40 msec. The multivibrator circuit is designed to ensure stability of this requirement. The operation proceeds as follows: When the 2-3 section of tube VI begins conducting, terminal 4 is driven negative.\n\nBell Telephone Laboratories 157B and 157C Systems\nThe current from terminal 5 to 6 of V2 ceases. The resultant flow of current from terminal 5 to 6 of V2 activates the starting relay ST, which in turn activates relay RC. During this period, the voltage on terminal 4 of VI has risen only slightly due to the high resistance of R4. When the contacts on the reverberation control relay RC are closed, R3 and P2 are returned to +300 v, and the time constant of these resistors in combination with the condenser C2 determines the remaining time during which terminal 4 of VI remains negative and, therefore, the time until current in the starting relay coil ST is interrupted. To make the operated period of the reverberation control relay RC 40 msec, the time constant of the system R3, P2, and C2 is made less than 40 msec by the closing time of the relays. This is accomplished by adjusting P2 until the operation period of the reverberation control relay RC is 40 msesc.\nThe RC relay's echo period is 40 msec. To manage the length of the transmitter pulse, a multivibrator made up of tube V3 and its components is utilized. A common cathode resistor R13 is implemented to finish the feedback loop. The multivibrator regulates by applying a positive pulse to the transmitter tube's screen through a cathode-follower stage. During the multivibrator's off period, the plate current from terminal 5 to 6 is determined by the tube type, plate-load resistance R16, and common cathode resistance R13. To drive the plate as close to -300 v as possible, the voltage drop across R13 should be as low as possible, while maintaining sufficient bias on the 1-2-3 section of the tube below cutoff to prevent false triggering.\nthis voltage drop should be as high as possible. A workable compromise is achieved by the use of a 6SN7 tube with the values assigned to the plate and cathode resistors indicated in Figure 7. Triggering of this multivibrator is accomplished by a contact on the relay RC in the following manner. Between pulses, the left-hand end of C4 is charged to -105 v through the 100-megohm resistor R10. Closing the bottom contacts 1-2 of the relay RC grounds this point and produces a positive pulse on terminal 1 of V3 of approximately 18 \u03bcs duration and 105 v magnitude. Chatter of the relay contact in RC does not tend to cause false triggering due to the long time required to recharge the condenser C4. The 3-ms on period of this multivibrator is determined primarily by C6 and R15.\n\nThe transmitter consists of a self-excited class C amplifier.\nThe oscillator, activated by applying a 3-msec positive pulse to its screen using a 3-msec multivibrator and a cathode-follower stage, is depicted in Figure 8. The oscillator's plate supply, which is 3,000 volts, is derived from a 7.5-xf storage condenser that is charged during the intervals between transmitted pulses via a high-voltage transformer and rectifier. The oscillator tube V2's plate current is approximately 1.33 amps during the 3-msec transmission interval. The voltage across the storage condenser decreases by approximately 20% during this period.\n\nThe frequency-determining component of the oscillator is a polystyrene-insulated condenser C4 and the tuned inductor T2, which is adjusted using a movable permalloy slug. Frequency stability is obtained by this configuration.\nThe problematic text appears to be written in clear and readable modern English, with no need for significant cleaning or translation. Therefore, I will output the text as is:\n\nThe problem is caused by the close coupling of the grid and cathode windings in the oscillator coil, and is further assured by the high plate resistance of the tetrode V2 being between the load and the frequency-determining element of the circuit. During the off period, VI is nearly nonconducting, and the screens of V2 are biased at approximately -80 v. In practice, it is necessary to select the 3E29 tubes used for V2 to ensure low enough plate current drain during the off period to permit the storage condenser to be charged to the proper voltage. During the transmitting period, the 3-msec multi-vibrator applies a +300-V pulse to the grid of VI, which, acting as a cathode follower, supplies a pulse of about +250 v to the screen of V2. In the design\nThree factors are crucial for the oscillator: frequency stability, time of pulse build-up and decay, and tank-circuit efficiency. An oscillator with an extremely high-Q tank circuit ensures high frequency stability and tank-circuit efficiency but slow build-up time. The build-up rate is also influenced by the excess gain in the oscillator feedback loop. The constants for this oscillator were selected as a compromise between these factors, achieving build-up and decay times of approximately 0.5 msec. The resulting frequency stability is sufficient for the system's overall requirements.\n\nTransmitter-Receiver Switching Circuit:\nSince a single transducer is used for both projector and hydrophone functions, it's essential to provide switching means between transmission and reception to prevent the receiver from being affected.\nThe schematic of the switching system consists of four thyrite elements: RV1, RV2, RV3, and RV4. These thyrite units have an impedance that varies in inverse proportion to the third power of the current passing through them. Thus, RV3 and RV4 become low-resistance elements under the influence of the transmitter during the 3-msec transmitting interval and, therefore, connect the transmitter transformer to the two transducer units in parallel. The voltage drop through the thyrite units during transmission is of the order of 100 v, resulting in negligible power loss.\n\nDuring the receiving interval, the voltage developed by the hydrophones is influenced by the signal.\nThe low RV3 and RV4 become high-resistance elements and therefore serve to isolate the two halves of the transducer from the transmitter. In practice, due to the capacity of the thyrite units, their impedance cannot be considered so high as to have no effect on the receiving circuit. They provide a certain amount of coupling between the transmitter output transformer and the hydrophones, particularly if the capacities of the two halves of each thyrite unit are unequal. This causes noise, originating in the transmitter transformer caused by inductive pickup or ripple on the power supply, to be fed into the receiver. This factor is a serious limitation on the entire system since this source of noise may be the limiting factor in receiver sensitivity rather than the torpedo self-noise.\n\nThe voltages applied to the transducer during the transmission are:\ntransmitting pulse would be damaging to the receiver input transformers if not prevented from reaching these elements. Isolation is provided for the starboard receiving channel by condensers Cl and C2 and the thyrite unit RV1, and for the port receiving channel by condensers C3 and C4 and the thyrite unit RV2. During the time of transmission, the thyrite units RV1 and RV2 become low impedance and therefore limit the voltage applied to the primaries of the receiver transformers to approximately 275 v. This is a sufficiently high magnitude to initiate transients in the entire receiver circuit, despite the presence of a blanking bias on the grids of the first two stages of the receiver. It is, however, sufficiently low to protect the transformers from damage.\nThe receiving interval causes breakdown. During this time, RV1 and RV2 are high-resistance elements but represent shunt capacities across the Bell Telephone Laboratories 157B and 157C systems primary receiver transformers. In combination with additional condensers, they provide tuning for the primaries of the receiver transformers. The condensers Cl, C2, C4, and C5, in combination with the shunt elements including the transmitter transformer winding, constitute an attenuating network providing a voltage loss of approximately 13 db.\n\nThe port and starboard halves of the transducer each connect to a separate receiving amplifier by means of a tuned coupling transformer. The amplifiers are conventional with three stages. The inter-stage coupling and the output coupling are accomplished.\nThe text describes the use of band-pass transformers in achieving a 3 dB reduction in gain at \u00b1800 cycles from the mid-band frequency of 27.75 kc. This bandwidth accommodates frequency shift due to the Doppler effect, the requirement to pass a 3-msec echo pulse with negligible envelope distortion, and possible oscillator frequency drift. Transients are generated in the tuned circuits during transmission but drop to less than expected signal levels by the end of the 40-msec blanking period. The first two stages of the amplifier are variable-gain stages, with gain variation achieved by grid bias on the tubes. The steering control is determined by comparison.\nThe electrical phase relation between the signals generated in the two halves of the transducer requires comparison. The phase-sensitive detector, which performs this comparison, follows the amplifiers. It's crucial for the electrical phase shift introduced in the two amplifier channels to be the same. A tuning condenser is provided in one channel to satisfy this condition.\n\n22.7 Threshold Circuit\n\nThe threshold circuit, schematically shown in Figure 10, is identical in the two channels. In operation, terminals 4 and 5 of the diode are maintained at -52.5V by the voltage divider R1 and R2, which is fed from a -105-v regulated power supply. Terminal 3 of the diode is maintained at -105V, while terminal 8 is at ground potential. With these electrode potentials, no conductive current flows through either section of the diode for signals which have peak voltages below the threshold.\nages less than 52.5 volts. However, if a signal has a peak value greater than 52.5 volts, the portion of the positive peak at terminal 1 of T1 that is greater than 52.5 volts will cause current to flow from terminal 5 to terminal 8 of the diode. Similarly, the portion of the negative peak that is greater than 52.5 volts will cause current to flow from terminal 3 to terminal 4 of the diode. Since these currents are equal, there is no change in the direct currents in R1 and R2, so their voltages remain constant. The amplifier's output is a threshold stage circuit. The junction voltage will remain constant at -52.5 volts even in the presence of a signal. The current pulses that pass through the two diode sections also pass through corresponding windings of T2, which are wound such that an alternating voltage of the same frequency as that in T1 is induced in the 1-2 winding of T2.\nThe intermittent current flow causes harmonics in this winding. Condenser C3 is used to minimize the voltage at T2, caused by capacity unbalance in the diode and its associated wiring, when the signal voltage on the secondary of T1 is less than 52.5 v.\n\nVariable gain-control for the receiver amplifier:\n\nThe variable gain-control circuit adjusts the gain of the first two stages of the amplifier so that the level of output caused by noise and reverberation is brought to a fixed level below the threshold. By doing so, signals are amplified as much as possible without danger of reverberation or self-noise signals passing the threshold stage. Since the signal is composed of\nThe decay factor, referred to as reverberation, and the self-encapsulation of the signal at the output of the third amplifier stage are sufficient to assume control. For the remaining 1-second listening interval, the gain variation is under the control of the signal output of T9, which is a winding in the output transformer of the third stage of each amplifier.\n\nThe receiver's gain control is separate for the right and left receiver channels. A schematic of the circuit used is shown in Figure 11. For times less than 32 milliseconds after transmission, corresponding to a range of 24 yards, the amplifier sensitivity is essentially zero due to the operation of relay ST. For noise, a relatively steady factor, the gain-control circuit is set up so that the gain is always increasing or held constant; it cannot decrease during a listening period.\nThe gain control should not be confused with the disabling of the circuit during and shortly after transmission. While the gain is held to a minimum during the disabling period, the actual disabling is accomplished by the relay ST, indicated in Figures 7 and 10, at a point further on in the circuit. Forty milliseconds after transmission, the gain of the receiver begins to increase under the control of the gain-control circuit, rising rapidly at first at a rate of approximately 24 db for double time intervals and continuing to rise at this rate until the next 8 msec. The gain of the amplifier remains constant for the next 8 msec, as contacts on the relay RC maintain the voltage on Cl and C2 at -5.25 v. This voltage is derived from the -105-v regulated supply through the divider resistors Rl, R2, and R3. The voltage on these condensers supplies bias to the grids of the amplifier.\nThe first two amplifier stages. When the relay RC opens, condensers Cl and C2 begin to discharge through two parallel paths: one, through resistors R4 and R5; two, through the 8-5 section of the diode and R7. The reduction in voltage on these condensers causes the gain to increase until it reaches a value such that the output signal from the amplifier is sufficient to produce a voltage across the 3-4 winding of T9 with a peak value equal to or greater than the sum of the following two factors. One, the bias supplied to terminal 3 of T9 from the voltage divider consisting of R8, R9, and R10; two, the voltage existing on C3. When this voltage is exceeded, current will flow between terminals 3 and 4 of the diode, causing terminal 3 to become negative with respect to terminal 4.\nThe voltage established across C3 and R7 prevents the discharge of condenser C2 through the diode path, reducing the rate of gain increase in the amplifier to about 9 db per double time-interval. The received signal during the receiving interval, which has been considered, primarily consists of surface reverb. Time constants are chosen so the rate of increase in amplifier sensitivity will not allow reverberation signal to pass the threshold stage. Following the time when the gain has risen:\n\nThe voltage across C3 and R7 prevents the discharge of C2 through the diode path, reducing the amplifier's gain increase rate to approximately 9 db per double time-interval. The received signal, primarily consisting of surface reverb during the receiving interval, is accounted for. Time constants are selected to prevent the reverberation signal from passing the threshold stage with the amplifier's increased sensitivity.\nThe point where the reverberation signal has first caused conduction of the 3-4 section of the diode and reduced the rate of gain increase. From this point on, until the end of the 1-sec listening period, the operation will be as follows. The reverberation signal may be expected to decrease in level with time. If it decreases at a rate faster than the rate at which the amplifier gain increases due to the decay of the voltage of the condenser C2 through R4, the output at T9 will fall to a value insufficient to cause conduction through the 3-4 section of the diode and the voltage on C3 will decay through R7 until conduction through the 8-5 section of the diode is reestablished. When this happens, the gain will again increase at the rapid rate until the output level again rises to a point where the rapid gain increase is blocked.\nThe type of control continues until the level of reverberation signals falls to a value less than the signal caused by the self noise of the torpedo. The system is designed such that the amplifier gain cannot increase to a point where the expected self noise of the torpedo will produce a signal which can pass the threshold stage.\n\nSo far, the performance of the gain-control circuit under the influence of reverberation and noise has been discussed. The action will now be considered in the presence of an echo signal. It has been observed that echo signals often consist of a smear of echoes representing signals returning from many points over a range of 50 yards or more. The value of the signal necessary to cause conduction in the threshold stage is approximately 7.2 db greater than the value necessary to produce conduction in the 3-4 section of the circuit.\nThe diode's gain is determined by the bias applied to terminal 3 of T9. The 7.2-db differential is the minimum value necessary to exclude noise peaks. The lowest possible value is used to ensure that the minimum level of signal above the peak background noise is passed by the threshold circuit. It is obvious that when the signal level exceeds the noise and reverberation voltage, conduction will occur in the 3-4 section of the diode and prevent further rapid increase in gain. Without the feature that permits further slow increase of the gain, the maximum level of echo smear would need to exceed by at least 7.2 db the value of the reverberation at which the gain increase was first interrupted in order to pass the threshold. In other words,\nIf a smear echo is received at short range at the time when the reverberation is decaying rapidly, it is desirable to allow all of it to pass the threshold, even though the distance attenuation causes the last portion to be less than 7.2 db greater than the reverberation level at the beginning of the smear. The time constant of the combination of C3 and R7 is determined primarily by the following consideration: The 3-4 section of the diode in combination with C3 constitutes a peak rectifier, and the rate at which the voltage on C3 decays through R7 during the intervals between noise and reverberation peaks determines the manner in which these peaks are integrated. The voltage on C2 decays only during the minimums of the voltage on C3. Therefore, the more rapidly C3 is allowed to decay, the lower it will fall.\nThe choice of a 15 msec time constant for C3 and R7 determines the selection of a 7.2 db voltage ratio. Any modification to the time constant necessitates a new voltage ratio choice.\n\n22.9 Limiter Circuit\n\nThe following limiter circuits after the threshold stages are conventional, single-stage, high-gain class A amplifiers. The limiting action is achieved due to signals applied to this stage causing overload when the voltage output of the threshold stage is only 1 db greater than necessary to pass the threshold. This is because a 6SH7 tube overloads at approximately 3 v of signal on the grid, and 1 db above the threshold of 52.5 v is a 6.5-v signal. A series resistance is added.\nThe limiter stage in this stage restricts the grid current to small values, thereby preventing the grid from significantly going positive. This enhances the limiting action. When the signal level is 2 dB above the necessary level to pass the threshold stage, the limiter stage will be completely limited.\n\nFive-sixths of FI and five-sixths of F2 are all phased in the same way. This means that the voltages in 3-4 and 5-6 of FI will always be in phase, and the voltages in 5-6 of F2 will lead, be in phase, or lag those in FI, depending on whether the echo is received from the right, dead ahead, or left. Assuming an echo is received from the left, so that the right-channel signal in 5-6 of F2 lags the left-channel signal in 3-4 and 5-6 of FI by 45 degrees, the voltages are indicated in vector diagrams in Figures 13A, B, and C.\nThe vector representing the voltage in 5-6 of F2 is for a 90-degree phase-sensitive detector. Its purpose is to combine the output of the two receiver channels in such a way that the electrical phase difference between them can be used to generate a usable signal. The essential elements of the detector are shown in Figure 12. F3 is a 90-degree phase-shift network, and RV1 is a rectifier. The triode VI and condenser C4 retain the information, which consists of a DC voltage whose sign depends on the direction of incidence of the echo signal on the transducer and whose magnitude depends on the value of the angle between the torpedo axis and the direction of the incident echo signal. In the operation of the circuit, the windings 3-4 will be delayed 90 degrees by the phase-shift network F3 so that the vector representing the voltage in the output of the circuit is the vector sum of the voltages in the two receiver channels, with a 90-degree phase difference.\nIn 3-4 of F3, the voltages will be as indicated in Figure 13D. Referring to Figure 12, it will be noted that the voltage A + C' is rectified by section 2-3 of RV1 and applied across the resistance R28. Similarly, the voltage C' \u2014 B is rectified and appears as a voltage across R29. These voltages will be added vectorially as indicated in Figures 13E and F. When rectified, the relative magnitudes of voltage appearing across R28 and R29 can be indicated as in Figure 13G. The plot of voltage at the top end of R28 referred to the lower end of R29 as a function of electrical phase angle is indicated in Figure 13H.\n\nWhen an echo is received, VI is made conducting so that the condenser C4, which was previously charged to +19V, is discharged to the value appearing across R28 and R29. The following three factors:\n\n(BELL TELEPHONE LABORATORIES 157B AND 157C SYSTEMS)\nDetermine the choices of values for R28, R29, Cl, C2, and RV1. The storage condenser C4 reaches its final voltage through a series-resistive circuit consisting of the plate impedance of tube V1 and the load resistances R28 and R29. The sum of these components must be sufficiently small to allow C4 to reach its final voltage within 1 msec, determining the maximum value for R28 and R29.\n\nFigure 13. Analysis of phase-sensitive detector operation. (Refer to Figure 12.)\n\nCondensers Cl and C2 act as filter condensers for removal of signal frequency from the echo pulses. The degree of filtering is a function of the ratio of the condenser impedance at signal frequency to the load resistance. The value of the capacitance is chosen to obtain 30 dB of suppression of signal frequency voltage. Third, it is necessary that\nThe rectified pulse shape should have a quick final voltage reach and a slow fall-off post signal termination. The grid of tube V1 must be biased to cutoff before C4's voltage is significantly altered due to the detector pulse decay. The rapid rise of the rectified pulse depends on C4's size, the varistor's impedance, and the source supplying the detector circuit's impedance. The source supplying the detector circuit is the limiter stages' plate circuits, whose impedance is influenced by filters FI, F2, and F3, and the output transformer ratio of FI and F2. The transformer ratio is determined by the required output voltage from the detector, which is 30V.\nThe maximum phase difference at the input is 90 degrees. With this value determined and limiter tubes operating at saturation, the transformer ratio and hence the impedance are determined. The impedance of the varistor elements is chosen sufficiently low so they are not limiting factors in determining the impedance of this circuit. A compromise is necessary between the quick charge of condensers Cl and C2 and the quick-charging requirements of condenser C4.\n\n22.11 Preference Circuit\nThe purpose of the preference circuit is to distinguish among a number of echoes coming from a moving target and, by proper presetting, to choose the one which comes from a point on the target nearest the bow. This is a means of ignoring the wake produced by the target's motion.\nIt has been found desirable to incorporate a lead-angle feature in the preference circuit so that the course called for by the setting of the gyro cover plate leads the bearing of the echo by approximately 4 degrees. The actual value of the lead angle can be varied from 0 to 8 degrees by proper circuit adjustments. The circuit elements involved in this feature are shown schematically in Figure 14. The ability to choose the rightmost or leftmost echo is achieved by means of the phase-sensitive detector VI, the relay LR2, and the condenser C4 which stores the output of the phase-sensitive detector. In operation, the condenser C4 is charged at the beginning of each listening period to +19V. When an echo passes the threshold circuits, this condenser will be discharged to a voltage equal to the output voltage of the phase-sensitive detector.\nIf receiving succeeding echoes, the voltage value of condenser C4 will equal the new value of the phase-sensitive detector output voltage, assuming this voltage is negative with respect to the previous signal. The tube VI conducts in only one direction, preventing the potential of condenser C4 from changing in a positive direction. The relay LR2 in Figure 14 is used to connect the phase-sensitive detector to condenser C4, making the potential of the top of the condenser more negative for either port or starboard echoes. The system is preset for preferred-side steering by setting up relay LR2 so that echoes from the preferred side make the top of condenser C4 most negative. The voltage of condenser C4 is equal to that applied to the cathode circuit.\nThe output of the phase-sensitive detector terminates the echo signal, preventing further discharge of condenser C4. A later, less positive signal repeats the sequence and allows the voltage on C4 to fall to a lower value. However, a following signal more positive than the preceding one will not alter the voltage of C4, as the system operates by charging C4 through a contact on relay ST to +19v with respect to its terminal connected to the junction of R6 and R7. C4 is prevented from discharging in the absence of echo signals by VI, which is biased to plate-current cutoff through a voltage divider consisting of resistors R4, R5, R6, R7, and R8.\nThe potentiometer in the translator. The output of the phase-sensitive detector, developed across resistors R28 and R29, is connected in the desired sense through the contacts of relay LR2 between the cathode of VI and one side of C4. When an echo signal passes the threshold circuit and after a suitable delay introduced in the trigger circuit, the grid of VI is driven positive. The condenser C4 is then free to discharge through VI to the cathode of VI, making its cathode positive relative to its plate, and the tube will not conduct in that direction. The manner in which the grid of VI is driven positive will be explained under Section 22.12.\n\nThe value of the condenser C4 is determined as a compromise between two factors. First, a discharge time constant of approximately 0.2 msec is required, which determines the maximum size of C4. Second, it is essential to maintain a sufficient capacitance to ensure proper operation of the circuit.\nThe circuit leakage resistance must be very high for the voltage due to charge on C4 to remain unaltered by circuit leakage for a period of 1 second. This determines the minimum size for C4 and the minimum possible circuit leakage resistance, including the leakage resistance of C4 itself. The circuit leakage is minimized by the use of a guard circuit, which holds the voltage drop across the leakage path to a minimum.\n\nBell Telephone Laboratories 157B and 157C Systems\n22.12 Trigger Circuit\n\nThe trigger circuit, indicated in Figure 14, performs two functions following the receipt of an echo signal that passes the threshold. First, it makes VI conducting by removing its bias after the output of the phase-sensitive detector has reached equilibrium and reestablishes the bias at the proper time.\nThe first function of the circuit is achieved by obtaining a portion of the limiter output in the starboard channel until the phase-sensitive detector has reached its equilibrium value. A portion of the output of the limiter is taken until the phase-sensitive detector voltage has had a chance to reach its value. The grid-to-cathode voltage of VI is actually a composite of the trigger circuit voltage and the phase-sensitive detector voltage. This is somewhat undesirable since an output of the phase-sensitive detector of such a polarity as to cause the cathode of VI to become negative with respect to the junction of R6 and R7 will, in effect, reduce the bias on the tube and cause it to conduct in the absence of a trigger signal.\nThe grid-to-cathode voltage of VI from this source is also delayed by the combinaion of the filter transformer F2. This is confirmed in the voltage-doubler rectifier circuit, consisting of the 1-3 arm of RV4 and the condensers Cl and C2 developing a voltage across the load resistor R2. The rate of rise of voltage across R2, following reception of an echo signal, is somewhat faster than the rate of rise of the phase-sensitive detector output voltage across R28 and R29, due to the relative magnitudes of the condensers Cl and C2 and the source impedance. This voltage is applied to the grid of VI through the resistor R3. The resistor R3 and condenser C3 serve to delay the rise of voltage on the grid of VI so that the tube does not become overly conductive.\nThe absence of a trigger circuit signal causes the bias on VI to be rapidly restored to a negative value. At the termination of an echo signal, condenser C3 discharges through the 4-6 arm of RV4, shunting resistor R3 for current flow in this direction. In this way, VI is cut off before the phase-sensitive detector output voltage has fallen appreciably from its equilibrium value.\n\nThe second function of the trigger circuit is to fire V2, which in turn operates the TG relay and initiates a train of relay operations essential for torpedo control. It has been found desirable to delay the firing of tube V2 beyond the beginning of an echo signal by approximately 1.5 msec. This delay, introduced to make the circuit less sensitive to peaks of self-noise of the torpedo, is accomplished through the action of the trigger circuit.\nThe resistor R9, shunted by resistors RIO and R11, and the condenser C5: the choice of a 1.5-millisecond delay depends on selecting 7.2 dB as the signal threshold exceeding the noise voltage. The delay in tube V2 firing is linked to the reduction of bias on tube VI. These delays should be roughly equal, as it's undesirable for V2 to fire before VI conducts and alters the voltage on condenser C4.\n\n22.13 Servo System\n\nThe electromechanical system, as depicted in Figures 13 and 14, converts electrical information into mechanical rotation. The essential components of this system, as shown in Figure 15, include a DC amplifier, two control gas tubes, a transformer, and a follow-up potentiometer.\nThe voltage on Cll remains for approximately the time required for maximum rotation of the gyro cover plate. The high side of Cll is connected to the grid of VI, a coupling stage with very high input resistance to prevent the charge on Cll from leaking off. The low side of Cll is connected to a voltage divider between +150 and -105 volts which also contains the follow-up potentiometer in the translator. When the follow-up potentiometer is centered, the voltage at this point is zero.\n\nThe two halves of V2 and the thyratrons V3 and V4 are connected as two parallel DC amplifiers, one of which operates on a positive signal on grid terminal 1 of V2, and the other operates on a negative signal on grid terminal 1 of V2. The plates of V3 and V4 are connected through relay contacts to the right and left rudder clutches in the translator in series.\nWith a 150-volt, 400-ampere alternating current, the potentiometer P3 sets the normal grid bias on these tubes. So that for 0 volts on Cl and the follow-up potentiometer in the mid-position, they are extinguished. With the system set for right preference, an echo from the left produces a positive voltage on Cl. This breaks down V3 in the following way. Referring all potentials to the junction of R1 and R2, which is at -105 volts, the positive voltage on Cl makes the grid of VI positive. The current in the cathode circuit increases, causing the grid 1 of V2 to become more positive due to the drop in R3. This increases the cathode current in the 1-2-3 half of V2. Because of the drop in R2, the cathode of the 4-5-6 section becomes more positive, which reduces the drop in R9 and makes the grid of V3 more positive, causing it to fire. When V3 breaks down, it energizes the grid of VT1 and the plate of V3 is connected to the anode of VT2 through the closed switch S1. The plate of V3 is also connected to the positive voltage through R11. The anode of VT2 is connected to the negative voltage through R10. The plate of VT2 is now connected to the positive voltage through the closed switch S2. The grid of VT2 is connected to the negative voltage through R9. The plate of VT2 draws current from the positive voltage through R8, which flows through the load Rl. The plate of VT2 also discharges the capacitor C1 through R7. The plate of VT2 is now connected to the negative voltage through the closed switch S3. The grid of VT2 is connected to the positive voltage through R6. The plate of VT2 is now disconnected from the positive voltage and the negative voltage. The plate of VT2 is now at the same potential as the negative voltage through the leakage resistance of the plate of VT2. The plate of VT2 is now disconnected from the circuit. The plate of VT3 is now connected to the positive voltage through the closed switch S4. The plate of VT3 is also connected to the negative voltage through the closed switch S5. The anode of VT3 is connected to the positive voltage through R12. The cathode of VT3 is connected to the negative voltage through R13. The plate of VT3 draws current from the positive voltage through R14, which flows through the load R2. The plate of VT3 also discharges the capacitor C2 through R15. The plate of VT3 is now connected to the negative voltage through the closed switch S6. The grid of VT3 is connected to the positive voltage through R16. The plate of VT3 is now disconnected from the positive voltage and the negative voltage. The plate of VT3 is now at the same potential as the negative voltage through the leakage resistance of the plate of VT3. The plate of VT3 is now disconnected from the circuit. The plate of VT4 is now connected to the positive voltage through the closed switch S7. The plate of VT4 is also connected to the negative voltage through the closed switch S8. The anode of VT4 is connected to the positive voltage through R17. The cathode of VT4 is connected to the negative voltage through R18. The plate of VT4 draws current from the positive voltage through R19, which flows through the load R3. The plate of VT4 also discharges the capacitor C3 through R20. The plate of VT4 is now connected to the negative voltage through the closed switch S9. The grid of VT4 is connected to the positive voltage through R21. The plate of VT4 is now disconnected from the positive voltage and the negative voltage. The plate of VT4 is now at the same potential as the negative voltage through the leakage resistance of the plate of VT4. The plate of VT4 is now disconnected from the circuit.\nThe left gyro clutch, located in the translator, breaks down V4 with a negative voltage on Cll produced by a right echo. Figure 16 shows the translator with the cover removed. The translator's construction and coupling to the generator and power supply are depicted in Figures 16 and 17. The main drive for the translator is obtained from the driveshaft via the generator. Gyro cover plate corrections are obtained using a pair of jaw clutches operated by a differential sole-noid. One half of each clutch is free-running on the shaft and continuously driven in the opposite direction from the corresponding half of the other clutch. BELL TELEPHONE LABORATORIES 157B and 157C systems: the other two halves are splined to the shaft. The operation of one control tube, V3 or V4, is not specified in the given text.\nV4 energizes the solenoid in one direction, engaging one of the jaw clutches and causing the translator shaft to rotate in the desired direction. Through gear trains, this rotation is transferred to the gyro cover plate. The shaft driving the gyro cover plate is on the side of the immersion gear. A correction which can be applied to the cover plate is achieved by one operation. Another cam makes contact when the shaft is in a position corresponding to the centering of the potentiometer. The heart-shaped cam, driven by a spring-loaded arm, returns the shaft to its center position when the potentiometer clutch is de-energized. This signifies that the translator is ready for more information. The other two cams are not used.\n\nFigure 18 depicts the gyro cover plate switch, whose principal function is to limit the rotation of the gyro cover plate switch.\nThe maximum excursion of the cover plate contains the preference preset switch, operated manually through the side-setting gear. The translator shaft drives the cam shaft, which mounts the follow-up potentiometer via a magnetic clutch. Two cams on this shaft operate switches to limit the amount. When an echo is received, a relay energizes the follow-up potentiometer clutch, causing it to follow the cover plate rotation. For example, with the circuit set for left preference, V3 in Figure 15 conducts, energizing the left gyro clutch, causing the cover plate drive to turn in that direction. When the follow-up potentiometer goes off-center in that direction.\nThe voltage introduction between the low side RELAYS and the overall system operation of Cll and the cathode of VI results in equal voltages. When this equals the positive voltage on the high side, the net effect is zero voltage on Cll, extinguishing V3. This process repeats if an echo comes from the right, but with the high side of Cll becoming negative, V4 breaking down, and the right gyro clutch engaging to put a positive voltage on the low side of Cll, balancing the negative voltage and extinguishing V4.\n\nFigure 18. Modified immersion gear shows the method of driving the gyro cover plate from the translator.\n\nThe entire servo system functions as an electromechanical amplifier employing negative feedback.\nThe follow-up potentiometer is adjusted neither to the point of suppressing sustained oscillations in V3 and V4. Due to the delay between the operating signal for the clutches and the opposing signal from the potentiometer, there is a tendency to oscillate or hunt at approximately 2 cHz. This hunting can be observed in the right and left clutch lights on the recorder traces when no echoes are being received.\n\n22.14 RELAYS AND OVERALL SYSTEM OPERATION\n\nThe naming of the relays has been chosen to aid in understanding their functions. RC signifies the reverb control relay, ST represents the starting relay, TG denotes the trigger relay, and PC stands for the follow-up potentiometer centering relay, as it operates following the closure of the contact, which is closed only when...\nThe follow-up potentiometer functions are accomplished by these relays when centered. These relays do not cover all relay functions in the panel operation, but they accomplish all functions related to echo utilization. The functions served by this group of relays are eight in number:\n\nFirst, charging C4, Figures 14 and 15, to +19 v at the time of signal transmission.\nSecond, short-circuiting Cll, Figures 14 and 15, eliminating any charge accumulation during periods without echo reception.\nThird, releasing the follow-up potentiometer clutch, permitting its movement.\nTo the center, following the receipt of an echo signal, transfer the voltage from C4 to C1. Figures 14 and 15. After receipt of an echo signal and closure of the follow-up potentiometer contact, apply cutoff bias to the clutch-control tubes V3 and V4, Figure 15, during the period when the potentiometer clutch is de-energized. Prevent the clutches from being operated while the potentiometer clutch is de-energized.\n\nFifth, disconnect C4 from C1 at the end of a receiving interval during which the voltage was transferred from C4 to C1. This allows the voltage to remain on C1 during the succeeding receiving interval.\n\nSixth, remove the plate-supply voltage for V2, Figure 14, which flows through the TG relay winding at the end of each receiving interval. This serves to extinct V2 at the end of each receiving interval.\nThe interval is provided if an echo has been received within it. Eight, to delay the transmission of the succeeding pulse until the follow-up potentiometer contact is centered, given an echo has fired V2 in Figure 14 prior to the end of the receiving interval. The functions above are used to provide operation of the preference circuit and to pass information to the d-c amplifier.\n\nBell Telephone Laboratories 157B and 157C Systems\n\nIn general, all normal functions of the torpedo can be subdivided into three groups of typical conditions. First, the system is operating but no echoes are being received; second, echoes are being received regularly in each pulsing interval; and third, the system's performance following the receipt of an echo.\nFor the first condition where the system operates but no echoes are being received, the relay actions are as follows: Relays TG and PC remain released, C4 and Cll (Figures 14 and 15) are not connected together, and the follow-up clutch is continuously engaged. Gas tubes V3 and V4 (Figure 15) are enabled, and the follow-up potentiometer will hunt about the center position as discussed under the DC amplifier. The ST relay operates once every second and performs the following functions: It connects C4 to +19v, short-circuits Cll, and removes any leakage charge that might build up at this point. It operates the RC relay, which in turn charges the TVG condensers Cl and C2 (Figure 11).\nThe 3-msec multivibrator is triggered, controlling the transmitter. All functions repeat once per second. For the second condition, with echoes being received in each pulsing interval, assuming no previous echoes and the discussion begins just prior to the transmission of the pulse producing the first received echo: The ST relay charges C4 to +19v, shorts Cll to remove any accumulated charge, and operates the RC relay to charge the TVG condensers and trip the 3-msec transmitter pulse. The ST relay releases approximately 31 msec after the transmitted pulse. This enables the TG relay, opens the charging connection to C4, removes the short from Cll, and removes power from the reverberation control relay. C4 and\nApproximately 40 ms after the transmitted pulse, the RC relay releases, its power having been removed by the release of the ST relay. This allows discharge of the TVG condensers to begin. The system is now in a condition to receive an echo, which will be assumed to arrive some time between 40 ms and 991 ms after the transmitted pulse. When this echo arrives and passes the threshold, voltage from RV4 in Figure 14 fires the trigger tube V2 and operates the TG relay. Simultaneously, the voltage on C4 is modified by the action of the phase-sensitive detector and the discharge tube VI. Operation of the TG relay performs the following functions: Cll is shorted, V3 and V4 are energized.\nIn Figure 15, R18 and R19 are disabled since the common point previously grounded through a back contact of the TG relay is now free. +300 volts is supplied through the follow-up clutch, and R19 biases the cathodes of V3 and V4 to approximately +140 volts. This operation also disengages the follow-up clutch due to the high resistance of R17 and R18 in the clutch circuit. The TG relay disables the ST relay to prevent its operation until the next step is completed. The disengagement of the follow-up clutch allows the follow-up potentiometer to be centered if not already in that position. Centering of the follow-up potentiometer closes a contact, energizing the PC relay. The operation of the PC relay performs the following functions:\nThe ST relay is re-enabled; the short is removed from Cll, and C4 and Cll are paralleled (Figures 14 and 15). V3 and V4, Figure 15, are re-enabled, and the follow-up clutch is re-engaged by re-establishing ground on the junction of R18 and R19. Paralleling of C4 and Cll places a control voltage on Cll, and the d-c amplifier and translator act to translate this information to the gyro cover plate. No further action occurs until the next normal operation of the ST relay, whereupon the function is as follows: The TG relay is de-energized; the PC relay, however, is held operated through its own 1-2B contacts and the 5-6B contacts of the ST relay. C4 and Cll are disconnected from each other, and C4 is recharged to +19 v. Cll, however, is not shorted as it was when no echoes were being received.\nThe PC relay is now in the operated position, causing the RC relay to be operated, the TVG condenser to be charged, and a pulse to be transmitted as in the previous sequence. Upon release of the ST relay, all functions are the same except the PC relay is also released. Operation from this point on will be identical to the above operation as long as echoes continue to be received regularly in each pulsing interval.\n\nFor the third and final condition, following the receipt of an echo which in turn is followed by a pulsing interval in which no echo is received, the functions are as follows. Begin with the operation of the ST relay, which is closed during the time a pulse is transmitted for which no echo is received.\nThe echo is received. In this case, all operations of the ST relay are the same as those noted when echoes were being received. Following its release, the voltage on Cll remains unaltered from that value which was placed on it by the echo received in the previous interval. The translator has presumably acted to translate this voltage to a corresponding angle on the gyro cover. Since no echo is received during this receiving interval, the TG relay does not operate. Upon the next operation of the ST relay, the following operations occur:\n\nSince the TG and PC relays have not been operated, Cll is shorted, but the follow-up clutch is not released. In order for the follow-up clutch to be released, the TG relay must be operated and the PC relay not operated. The rotation of the follow-up pointer then begins.\nThe teniotometer, due to the preceding voltage on Cll, now produces an unbalanced condition at the input to the DC amplifier. The amplifier and translator are initiated to restore a condition of balance. This requires a rotation of the follow-up potentiometer back to zero to balance zero voltage on Cll. Hence, the rotation previously translated to the gyro cover is now removed. All other operations of the ST relay are similar to those which occurred in the first condition described where no echoes were received. (See references 48-57 for additional material on topics in this chapter.)\n\nChapter 23\nGEIER TORPEDO CONTROL SYSTEM\n\n23.1 Introduction\nAt the end of 1942, Atlas Werke, Munich undertook the development, under the code name Boje, of an acoustic homing control system for torpedoes employing echoes received from the target.\nTests conducted at Obertello, Italy, showed that for distances of a few hundred meters, the echo-to-reverberation ratio is independent of range and depends only on the directivity index of the transducers. Transducers with a high directivity index should be employed. To achieve this high index, a high frequency is required for the signal generator. Due to the need for a quick solution, Atlas Werke used a 77.5 kc nickel lamination transducer design, rather than producing nonstandard laminations. Separate projectors and hydrophones were deemed simpler than switching output-input circuits to a single pair of transducers.\nBy the end of 1943, laboratory models of each transducer were completed and tested against stationary and moving targets at Gdynia. After trials resulted in a few changes, a pre-production design was frozen and designated as Geier 1. The first trials of this model were held in March 1944. Approximately 120 Geier 1 units were produced, and most were installed in torpedoes. A few of these units were nonstandard, with various modifications of the steering mechanism being tested. By the end of 1944, several hundred experimental torpedo shots had been fired at Gdynia. In the meantime, all changes desirable from the Geier 1 trials were incorporated into a new version, Geier 2. Geier 2 was intended to be the service torpedo, while Geier 1 was to have been a experimental model.\nThe development of Geier 2 was shared between Atlas Werke, Munich and Minerva Radio, Vienna. The first sea trials of Geier 2 were held in the fall of 1944, and by the time activities were halted, approximately 20 experimental shots of Geier 2 had been fired. Shortly before Germany's surrender, about 100 of the preproduction Geier 1 torpedoes were transferred from experimental use to operational status. However, it appears that none of these torpedoes were fired in action as they were later located in a depot.\n\nDespite the two principal versions of Geier and the slight differences in their designs since the final version had not been decided upon at the war's end, all designs operate on the same basic principle. The torpedo is equipped with two magnetostriction projectors.\nTwo hydrophones, all four units being of the same design. These transducers are mounted in the torpedo nose, in the manner shown schematically in Figure 1. The projectors are excited simultaneously from the same source. Each hydrophone is connected to its own amplifier channel. There is no comparison of the intensities of the echoes received in the two channels; instead, each channel possesses a definite threshold, above the reverberation or background noise, which the signal must exceed in order to exercise control. The steering method, which is of the cut-on cutoff type, exists in two variations: symmetrical steering and preferred-side steering. When echoes are received on only one side, the two systems behave in the same way: the torpedo steers accordingly.\nThe torpedo moves towards the echo side for a definite time and then returns to gyro control until another echo is received. If echoes are received from both sides, the symmetrical steering system is governed by the first echo to arrive within a given ping interval. The preferred-side steering system is biased either to port or starboard just before the torpedo is fired, resulting in it always steering to the preferred side if an echo is received on that side, regardless of whether or not an echo from the other side has been received. In both designs, the transducers and electronic components are located in the torpedo nose. In the submarine torpedo, the gyro assembly is equipped with solenoids in a manner similar to, if not identical with, the corresponding (Specht) system in T5. These solenoids are operated.\nThe problems in the text are minimal, so I will output the text as-is:\n\nThe problems are in the forward electronic assembly by relays. Power is obtained from a generator on the main propulsion shaft.\n\nThe application of Geier 1 to the submarine torpedo G7e had progressed much further than the air one. Figure 2. Block diagram of Geier 1.\n\nCommon specifications for all designs:\nFrequency: 77.5 kc\nPinging power: electric input to each projector - 100 watts\nPing interval: 0.33 sec\nMaximum reliable acoustic control range: 200 meters\n\nThe Geier control was applied to both submarine and aircraft torpedoes, the former being the G7e craft version. In the following paragraphs, the submarine application is discussed in detail, and later the modifications for the aircraft version are noted.\n\nThe principal features of Geier 1 can be understood by reference to Figure 2. The projectors are excited by discharging a condenser through the windings.\nThe condenser is connected to the projectors for a short interval by a contactor segment mounted on the rotating shaft of the mechanical time base. This shaft is driven by a small electric motor. After the condenser has discharged, it is disconnected from the GEIER Torpedo Control System.\n\nFigure 3 shows the sequence of events during one ping interval.\n\nCAMS\ncams\nCAM 2\nI\nI\nTRANSMITTER\nAMPLIFIER BLANKING\nI\nI\n! CHARGE RELAY CONDENSER\nTIME IN MILLISECONDS\n\nFigure 3. Time base of cams.\n\nEach hydrophone is connected to its own amplifier. The gain of the amplifier is suppressed during the transmission of the ping; during the remainder of the ping interval, the gain is controlled by a time-torpedo steering engine. This assembly, which embodies the symmetrical-steering method, has two.\nOne channel operates a solenoid that disengages the gyroscope from the steering engine. Another channel controls solenoids in the steering engine for full helm to port or starboard. For instance, if the torpedo receives an echo signal in the starboard channel, the gyroscope is disengaged, and the helm is put hard to starboard. The disengage relay stays in for 0.6 seconds. If no more echoes are received in either channel by that time, the disengage relay drops out, and the torpedo returns to gyro control. If an echo is received in the same channel during the next ping interval, the disengage relay continues to hold in, and the gyro remains disengaged for 0.6 seconds after the last echo. When the torpedo comes close to the target or its wake, it is:\n\n(Note: The text appears to be clear and readable, so no cleaning is necessary. However, if there were any errors, they have been corrected in the text above.)\nThe amplifier features TVG and AVC systems. The TVG circuit reduces response to reverberation to a nearly constant level, while the AVC circuit corrects for differences in absolute level, such as those caused by torpedo roll and changing sea state. The relay assembly is the connecting link between the electric signal output of the amplifiers and the system. It includes a pre-emptive feature that permits it to ignore all signals other than the first within a given listening interval. Thus, the torpedo tends to steer towards the part of the acoustic target to which it is closest. Each transducer resonates at the nominal frequency.\nThe frequency of 77.5 kc consists of a rectangular nickel lamination block slotted to provide space for the GEIER 1 winding. The radiating face is 4.4 x 8.5 cm. The impedance at resonance is approximately 10 ohms. The four transducers, mounted as shown in Figure 1, are enclosed in a nose cap or dome made of a thermoplastic material. This dome is similar to or identical with the dome used in the round-nosed T5 listening torpedo. The space behind the dome is filled with ethylene glycol. The two-way transmission loss through this coupling system is stated to be 10 db.\n\nThe transmitter in Geier 1 consists of a 1-tf condenser which is charged during the listening mission. The condenser C4 is charged to a positive potential determined by the circuits consisting of PI, cam 2 breaks the circuit between Cl and ground.\nThe potential of Cl and the grid of VI begin to approach that of the cathode of VI, leading to an increase in gain for VI. The rate of gain increase is primarily controlled by Cl and R2. The setting of PI determines the gain at the start of the gain increase.\n\nThe following two stages, indicated in Figure 4 as PORT and STARBOARD:\n\nSTEERING  STEERING\n\nFigure 5. Relay system.\n\nThis interval is controlled by a transformer and rectifier operating from a 36-volt, 17-volt AC generator. The condenser is discharged through the tuned projectors using one of the cam switches in the time base.\n\nThe two receivers for the starboard and port channels are independent and identical. Figure 4 is a schematic of one of them. It consists of a three-stage radio-frequency amplifier followed by a single stage.\nThe pulse amplifier operates the relays. The first stage VI in Figure 4 is controlled by TVG. Cam 2 in the time base connects the grid of VI and the condenser Cl to ground until 33 milliseconds following transmission. The two stages after VI, whose grids are simply returned to the AVC line through 1-megohm resistors, are under AVC but not under TVG control.\n\nWhen a signal appears at the junction of C7 and C8, it must have a peak value greater than 12 volts before rectification can occur in the diode and rectifier RV2. Once rectification takes place, point A becomes more negative and point B becomes more positive, causing C9 to acquire a further negative charge from point A via the resistor RIO. This applies a greater negative bias to the grids of the GEIER torpedo control system.\nThe second and third stages of the amplifier decrease their gain. If the increase in signal level occurs slowly, there will be little change in the potential of the grid of pulse amplifier V3, preventing it from conducting. However, due to the long time constant imposed on the rate of development of negative potential by condenser C9, a rapid increase in signal level will result in the grid of V3 becoming more positive. The exact conditions for firing V3 can be controlled by adjusting potentiometer R12.\n\nNote: The plate of V3 is connected to the gas tube V4 in Figure 4 and to the coils of relays 1, 2, and 3 in the control circuit shown in Figure 5, through condenser Cl. Condenser Cl is charged to +200 v just prior to the time.\nThe transmitter sends out its pulse. The voltage on this condenser is divided between the gas tube V4 and the plate of V3 in Figure 4. When a positive pulse arrives on the grid of V3, it causes V4 to breakdown and the condenser Cl in Figure 5 discharges through the relay coils and the plate circuit of V3. Once the discharge has started, it will continue, using the rectifier RV3 as a return path even if V3 becomes cut off again.\n\nThe action of the relay assembly is as follows. Relays 1, 3, and 4 are polarized differential relays, whose armatures stay in the position to which they were last moved by a current impulse. Relay 2 is a spring-controlled relay which opens when no current is passing. Relay 4 is the gyro-disengage relay. When current passes through winding 9-10, the armature is in the Z position, which means the gyroscope is coupled.\nThe armature moves to the T position, energizing the gyro-disengage solenoid when current passes through winding 1-5. Relay 1 is the steering relay; the armature is in the Z position, energizing the port solenoid, and vice versa when current has last passed through 1-5 or 9-10. Relay 3 is a relay whose contacts are in series with the power supply, energizing all the solenoids. When current is passing through winding 9-10, the electrical steering is disabled. This circuit feature provides the delay in initiating acoustic control required for safety purposes. The delay is provided by the thermal delay switch SW1, which opens after a definite time. Relay 3 is operated to the other, or closed, position by the first signal impulse which arrives from either channel after SW1 has opened.\nThe relay remains in this position thereafter. Relay 2 is an intermediate relay with its armature in the Z position when not operated by current.\n\nSuppose now that the initial safety delay has elapsed, so that SW1 is open. Terminal 13 of the assembly is connected to the positive side of the 200-v supply, while terminal 4 is connected to the negative side of this supply. Relay 2 is in the Z position, shorting the 1-5 winding of relay 4. C2 charges through R3 until the gas tube VI breaks down, sending a pulse of current through the 9-10 winding of relay 4. The period of this simple relaxation oscillator is 0.6 seconds. Relay 4 stays in the Z position and the torpedo remains under gyro control. During the ping transmission, terminal 14 of the control circuit (Veil-Chen) is briefly connected to the 200-v supply by the last contactor on the time base (terminals 9 and 10).\nCl is charged to this potential. For the remainder of the ping interval, Cl is disconnected from the high-voltage supply. If a signal with sufficient amplitude to fire the glow tube V4 in the amplifier shown in Figure 4 arrives in the starboard channel, Cl discharges through the protective resistor R6 and windings 1-5 of relays 3, 2, and 1. Relay 3 is moved to the T or closed position and remains there for the rest of the run. Relay 2 moves momentarily to the T position and returns to Z after Cl is discharged; relay 1 moves to the T position if not already there, energizing the starboard-steering solenoid. The momentary operation of relay 2 has two results. First, C2 is discharged, so that winding 9-10 of relay 4 will not receive another pulse until 0.6 sec has elapsed. Second, the short is removed from 1-5 of relay 4.\nA pulse of current passes, moving relay 4 to the T position. This activates the gyro disengage solenoid, allowing the steering engine to come under the control of the starboard solenoid. If no more echoes are received within 0.6 seconds, C2 discharges through gas tube V1 and winding 9-10 of relay 4, returning the torpedo to gyro control. However, if an echo is received during the next listening interval before the 0.6 seconds have elapsed, relay 2 is momentarily operated to the T position, discharging C2 and delaying the torpedo's return to gyro control by an additional 0.6 seconds.\n\nThe purpose of supplying the firing voltage for the glow tube in the amplifier from Cl of the control circuit is to implement the pre-emptive feature mentioned above, enabling the circuit to ignore all but the most recent echo.\nThe first echo in a given listening interval discharges the Geier 2 condenser. Once discharged, no relays may be operated until Cl is recharged at the beginning of the next ping interval. No records of experimental trial shots were available at Atlas Werke, but Atlas personnel reported that Geier 1 performed well on bow shots. However, for shots made aft of the target beam, the torpedo often attempted to home on the wake, crossing it at right angles. After doing so, it returned to gyro control and proceeded away from the target. This result agrees qualitatively with an analysis of the symmetrical type of steering, discussed in more detail in Section [...]\nThe gear is responsive to ship or decoy noise. The torpedo can home on a ship's noise at a range of 500m, given the noise is modulated. If the noise is steady in level, only the gain increase caused by the TVG circuit will be apparent at the fourth stage amplifier's grid. Preliminary tests indicate that a steady signal of single frequency applied to the input circuit suppresses this type of fluctuation effectively. However, if the ship's noise fluctuates rapidly, the peaks will not be suppressed by the AVC circuit and will appear as echo signals. The control circuit can then operate by these noise peaks.\nSome difficulty was experienced with increased reverberation caused by torpedo pitch and roll. Since reverberation rather than self noise is the limiting factor in determining whether useful echoes are received, this problem was given serious consideration. A transducer assembly stabilized in both roll and pitch was developed.\n\nThe electronic circuits for the aircraft version are the same as those used in the submarine torpedo. However, since the plastic nose used in the latter is too weak to withstand water-entry shock, a different design had to be produced for the aircraft torpedo. It was found very difficult to reconcile the requirements of mechanical strength and acoustic transparency.\nThe first attempt involved mounting the transducers directly in the steel nose cap of the conventional torpedo, with radiating surfaces in direct contact with the water. This arrangement was satisfactory from a strength perspective and provided the best possible coupling between water and transducers, as there was no intervening dome. However, this setup did not allow for the use of a stabilized transducer assembly. The roll problem in the aircraft torpedo was more serious than in the submarine type, making the use of a stabilized array essential. Lt. Col. Bree indicated that the Luftwaffe had largely solved the roll stabilization problem for aircraft-launched torpedoes towards the end of the war, although no service torpedoes had been manufactured using this improved feature.\nThe aircraft version of Geier differed from the submarine type in one other respect: the method of using the output signal of the amplifier to control the steering. Instead of disengaging the gyro and operating the steering engine by solenoid control, the signal caused the gyro to be angled by a small motor. When echoes ceased to be received, the gyro-angling motor stopped and the torpedo continued to run straight until another signal was received. Thus, the aircraft-launched torpedo did not retain the original launching direction for its gyro course.\n\nThe Geier 2 circuit differs from the Geier 1 primarily in three features. The first principal difference is that the projectors are excited by a power amplifier driven from a conventional oscillator which is keyed from the time base. Although this arrangement requires more components than the simple contact method used in Geier 1, it offers greater accuracy and reliability. The second difference is the use of a servo motor to control the angle of the projector, which allows for more precise control of the torpedo's direction. The third difference is the inclusion of a feedback mechanism to correct for any errors in the gyro's angle, ensuring that the torpedo stays on course even in the face of external disturbances.\nThe denser discharge circuit of Geier 1 has two distinct advantages over the latter system. First, the contacts on the time base that connect the projectors to the output amplifier are already closed when the oscillator begins, eliminating sparking. Second, the transmitted pulse is much cleaner with an approximately square envelope, compared to the rapidly decaying exponential envelope produced by Geier 1. Due to better frequency control, most of the transmitted energy is concentrated in a narrow band around the nominal operating frequency. This is more efficient and secure than the damped oscillation type of transmitter, as pinging can only be detected by listening in the neighborhood of the central frequency.\n\nGeier Torpedo Control System\n\nThe second principal difference is the addition of\nA noise discriminating circuit is described next. The principle of this discriminator can be understood from the block diagram in Figure 6. After passing through four stages of amplification, the first three controlled by a TVG circuit, the signal is passed through two filter channels. Channel A is a single band-pass filter with a mid-frequency equal to the transmitted frequency plus the average Doppler shift expected. Channel B is a double band-pass filter, having high attenuation at the echo frequency. The two pass bands are located symmetrically on either side. The output of each channel must have an echo signal of at least the same order of magnitude to provide a reasonable difference between the two rectified voltages. However, during the relatively quiet periods between noise bursts, a much smaller echo will be equally effective.\nThe circuit behaves as a rapid AVC circuit with the added advantage of discriminating between noise and echo when the former has fluctuations comparable to the echo duration.\n\nThe third way in which Geier 2 differs from Geier 1 is in the functioning of the control circuits (Veichlen). While Geier 1 embodies symmetrical steering, Geier 2 employs preferred-side steering.\n\nChannel \"B\" (Figure 6. Discriminator) is then rectified, and these two rectified voltages are combined in opposite sense. The filter pass bands are so chosen that if white noise is fed into the system, the rectified voltages are equal and hence the resultant is zero. However, if an echo signal is present, it appears only in the single pass channel so that the rectified voltages are no longer equal. If the differential is greater than a predetermined threshold, the circuit triggers an action.\nThe relay assembly operates by using two pass bands in the noise channel. This allows the same result to be achieved if the noise spectrum is not flat but has a constant slope in the part covered by the two channels. This noise discriminator is most effective against intermittent noise, such as produced by explosions. While the noise signal is present, the operation is accomplished as depicted in Figure 7. This simplified diagram includes all essential features of the original control circuit shown in the Minerva Radio drawing of Feb-VI. VI and V2 represent the output tubes of the port and starboard amplifiers respectively. Relay 1, relay 2, and relay 4 are polarized differential relays. Current through winding 1-5 will operate the armature to the T position, and current through the 9-10 windings will operate the armature to the opposite position.\nThe armature will move to the Z position when a differential of 0.3 ma exists between the 1-5 and 9-10 windings. The armature remains on the side to which it was last moved after current ceases to flow. A differential of 0.3 ma is required to cause the armature to move. Relay 3 is a spring-controlled relay that is operated to the T position on 0.6 ma through either winding and holds in on a current of 0.3 ma. When relay 3 is open, both the gyro disengage solenoid and the steering solenoids are disabled. Relay 4 is the steering relay, causing either the port or starboard solenoid to be energized when relay 3 closes.\n\nA thermal delay switch, which closes after the initial safety delay, is placed in series with the 200-v supply to the relay circuits. The biasing circuit, controlled by the preferred-side switch, permits a steady current of 0.3 ma to be passed through either circuit.\n\nRelay 3: Spring-controlled relay, operated to T position on 0.6 ma through either winding, holds in on 0.3 ma. Open, disables gyro disengage solenoid and steering solenoids.\nRelay 4: Steering relay, energizes port or starboard solenoid when relay 3 closes.\nThresholds: 0.3 ma differential, 0.6 ma to operate relay 3, 0.3 ma to hold relay 3.\nCircuit: Thermal delay switch in series with 200-v supply to relay circuits, biasing circuit controlled by preferred-side switch permits 0.3 ma steady current.\nwinding of relay 4.\nwinding of relay 1 to return the armature to the Z position, charging Cl again. Simultaneously, C3 discharges through the 0.2-megohm resistor and winding 1-5 of relay 3. The operating current of 0.6 ma is reached during the very short interval in which C3 is being charged, but the minimum holding current of 0.3 ma is not reached until a considerable time afterward due to the long time constant of the discharge circuit. During this time interval, relay 3 is closed, so the gyro is disengaged and the torpedo is under control of the steering solenoids. Since relay 4 is already in the port position, the additional current which flows through winding 1-5 of relay 3.\n\nSuppose now that the initial delay has elapsed, the thermal switch has closed, and the preferred-side switch is in the port position. Relay 3 is open and\nRelay 4 is in the port position as the preferred-side switch is set to this side. Relay 1 and relay 2 are both in the Z position, charging Cl and C2 to 200 v. If a signal arrives in the port channel, V3 fires, discharging Cl through winding 1-5 of relay 1. The armature of relay 1 moves to the T position, charging C3 to the firing voltage of V5. When V5 fires, C3 begins to discharge through the 0.2-megohm resistor and winding 9-10. The torpedo rudder is put hard aport. After 0.4 sec, C3 has discharged sufficiently for the current through winding 1-5 of relay 3 to drop below 0.3 ma; relay 3 then returns to the open position, disabling the steering solenoids, and the torpedo returns to gyro control.\n\nConsider the sequence of events when an signal arrives.\nThe echo is received in the starboard channel. C2 is discharged, momentarily operating relay 2 to the T position, charging C4. C4 then discharges through the 9-10 windings of relay 2, operating relay 2 to the Z position and also through the 9-10 windings of relays 3 and 4. Operating relay 3 as before. The initial value of the current through 9-10 of relay 4 exceeds 0.6 ma, so the differential between 9-10 and 1-5 of this relay is greater than 0.3 ma, and the armature moves to the starboard position. Thus, the torpedo steers to starboard under solenoid control until relay 3 drops out, re-engaging the gyro.\n\nSo far, the preferred-side control duplicates the action of the symmetrical control used in Geier 1. Now consider the behavior when echoes are received in both channels in the same listening interval. If the echoes in both channels have the same strength, the torpedo will not move since the current through the relays will be balanced, and neither relay 3 nor relay 4 will drop out. However, if the echo in one channel is stronger than the other, the corresponding relay will drop out, causing the torpedo to steer towards that channel's preferred side. This asymmetrical control provides the torpedo with the ability to home in on a target more effectively.\nThe first echo comes from the port, relay 3 is operated, and relay 4 is moved to the port position, causing the torpedo to steer. A short time later, the starboard echo comes in, and current flows through windings 9-10 of relay 3 and relay 4. However, relay 4 remains in the port position because the current through the 9-10 winding cannot exceed the total current through windings 1-5 by 0.3 ma until near the end of the 0.4 sec hold-in time. In general, this condition is not reached until after the next ping. On the other hand, if the first echo is received in the starboard channel, relay 4 is initially operated to the starboard position, but as soon as the port echo comes in, relay 4 is reversed because the differential current in the two windings exceeds 0.3 ma. Thus, the control \"prefers\" the port side, and causes the torpedo to steer in that direction.\nSteer to starboard only if no port echoes are received.\n\nComparison of Symmetrical and Preferred-Side Steering:\nA comparison was made on paper to determine the relative effectiveness of symmetrical steering and preferred-side steering. The width of the path within which the torpedo track had to lie in order to secure a hit was chosen as a measure of this effectiveness. This path width is a function of target dimensions, ratio of target speed to torpedo speed, direction patterns of the transducers, and track angle of the torpedo prior to the initiation of acoustic control. The meanings of these variables are illustrated in Figure 8.\n\nThe German analysis assumed that the maximum acoustic-control range for echoes received from the ship was 200 m, and for wake echoes 50 m.\n\nFirst, consider the qualitative behavior of the torpedo.\nIf a torpedo approaches a target on its port bow with two types of steering, suppose the following: if it's already on a collision course, no echoes will be received until the last few yards due to the narrowness of the transducer patterns and the wide angle between them. The acoustic control does not impact performance. If the torpedo tends to miss ahead, ship echoes will be received in the starboard channel, causing it to steer on a curved track, leading the target by a continually decreasing amount as it comes closer, resulting in a hit. This method is the same for both symmetrical and preferred-side methods.\n\nThe difference appears when the torpedo tends to miss astern. In this case, the first echoes are received in the starboard channel, causing the torpedo to steer on a curved track, continually lagging behind the target as it comes closer.\nThe torpedo receives information in the port channel, causing it to turn in that direction. Eventually, the torpedo heading is at 90 degrees to the ship's track, so that port and starboard echoes from the ship or wake arrive simultaneously. With symmetrical steering, this condition is stable since, if the torpedo turns slightly to port, in the next ping interval the starboard echo comes in first and turns the torpedo back. When it has turned too far, the port echo arrives first and the torpedo tends to run into the ship or wake at right angles. Whether a hit is secured depends on the lateral distance from the ship's track at which this condition is set up, and upon the speed ratio. For very close misses astern, the torpedo will be close to the ship's track at the SHIP POSITION AT TIME TORPEDO IS ON LINE AA.\nFigure 8. Diagram for steering analysis. AA = width of path within which torpedo track must lie to secure a hit (no acoustic control). The torpedo starts to run in on a perpendicular course and a hit will be secured. For larger misses astern, the torpedo will merely cross the wake at right angles. Upon emergence, it will have lost acoustic contact and will revert to gyro course, proceeding away from the target.\n\nStabilized Transducer Assembly\n\nWith preferred-side steering and the preferred-side switch set to port, the torpedo would not run in on a perpendicular course after arriving at a point where the port and starboard echo-ranges are equal. Instead, it would continue to maneuver so that the port transducer beam alternately cut on and off either the bow of the target or the most forward part of the target from which echoes were received. Thus\nThe torpedo would pursue the ship, and hits would be secured from initial torpedo tracks corresponding to larger misses astern than with the symmetrical method. The improvement gained by using the preferred-side method is much more striking when the track angle is greater than 90 degrees. In this case, the first echoes always come from the starboard side, so with the symmetrical system, the torpedo will cross the wake at right angles for all approaches except those lying in a very narrow path which would yield misses ahead in the case of nonacoustic control. With the preferred-side steering, this is not the case, as explained in the preceding paragraph. By plotting out a number of torpedo tracks, it is possible to ascertain the dependence of effective path width on track angle for the three cases of nonacoustic control.\nThis text describes the results of tests on torpedo control systems with acoustic control and symmetrical or preferred-side steering. The assumptions made during these tests were: torpedo speed: 24 knots, ship speed: 12 knots, torpedo turning radius: 75 meters, ship length: 100 meters, ship beam: 15 meters, maximum echo range (ship echoes): 200 meters, maximum echo range (wake echoes): 50 meters. The results are depicted in Figure 9A, with the average path widths for the three cases in the two 90-degree sectors forward and aft of the beam shown in Figure 9B. Based on this comparison, it can be concluded that both the symmetrical and preferred-side methods significantly improve performance over nonacoustic torpedoes in the bow sector. There is little difference in performance between the two methods. However, in the quarter sector, the symmetrical method is more effective.\nonly  slightly  better  than  no  acoustic  control,  but  the \npreferred-side  method  gives  a marked  improvement. \nThe  preferred-side  method  has  one  fault  which  does \nnot  appear  in  the  foregoing  analysis:  If  the  target \ndetects  the  torpedo  in  sufficient  time  to  take  com- \nplete avoiding  action;  i.e.,  to  bring  the  ship  head-on \nor  stern-on  to  the  torpedo,  then  the  latter  may  be  on \nthe  wrong  side  of  the  target  when  it  comes  under \nacoustic  control.  In  this  event  the  torpedo  will  at- \ntempt to  steer  on  the  tail  of  the  wake,  instead  of  on \nthe  ship.  For  this  reason  the  estimated  effectiveness \nof  the  preferred-side  method  should  be  reduced  from \nthe  values  indicated  in  the  foregoing  comparisons. \nAccording  to  the  statement  of  the  Atlas  Werke \nengineer  who  spent  most  time  at  the  trials  in  Gdynia, \nthe  bulk  of  these  experimental  shots  was  made  with \nsymmetrical  steering  against  targets  moving  at \nSpeeds ranged from 10 to 15 knots. Observed performance agreed with theoretical analysis for major items. Quarter shots usually missed astern due to torpedo crossing wake at right angles. Bow shots were successful. Some Geier 1 units had preferred-side control. Trials with these torpedoes confirmed that this type of steering was effective for all angles, as long as the \"preferred\" side was correctly chosen. Due to this superiority, preferred-side control was incorporated in Geier 2.\n\n23.5 Stabilized transducer assembly. The self-noise of the modified G7e torpedo in which it was installed.\n\nFigure 9A, B. Steering analysis curves.\n\nThis type of steering was equally good for all angles, confirmed by trials with Geier 1 torpedoes, as long as the preferred side was properly chosen. Because of this superiority, preferred-side control was incorporated in Geier 2.\n\n23.5 Stabilized transducer assembly.\n\nThe self-noise of the modified G7e torpedo in which it was installed.\nGEIER Torpedo Control System: It was important to minimize reverberation as Geier 1 was roughly equal to the reverberation level of the Geier signal corresponding to an echo range of 200 m. Excessive roll of the torpedo caused a marked increase in reverberation, seriously impairing performance. This was to be expected due to the wide angle between the two projector beams; a slight roll would throw most of the energy from one projector up into the surface. A similar, though not so great, difficulty resulted from pitching of the torpedo. To meet this problem, a stabilized transducer assembly, Pendel-Rose, was devised. In this mechanism, the four transducers are mounted on a framework suspended on a pivot.\nships  bearings.  A large  piece  of  lead  is  attached  to \nthe  bottom  of  the  assembly  making  it  pendulous. \nThis  feature  tends  to  keep  the  transducers  stable \nwith  respect  to  pitch.  The  pendulum  bearings  are \nsecured  to  a plate  behind  the  transducers.  This  plate \nis  capable  of  axial  rotation,  and  is  driven  by  a small \nmotor.  On  the  back  of  the  plate  are  mounted  two \nsmall  mercury  switches  slightly  inclined  in  opposite \ndirections  to  the  horizontal.  When  there  is  no  roll, \ni.e.,  the  transducer  faces  are  vertical,  both  of  these \nswitches  are  open  and  the  motor  is  stopped.  When \nthe  roll  exceeds  5 degrees,  the  mercury  in  one  of  the \nswitches  moves,  closing  a circuit  which  causes  the \nmotor  to  drive  the  plate  around,  reducing  the  roll \nto  less  than  5 degrees.  The  entire  mechanism  is  very \nsimple.  It  was  stated  that  no  electric  interference  in \nthe  signal  channels  was  produced  by  the  motor.  The \nactual  performance  of  the  stabilized  transducer  as- \nsembly in  reducing  reverberation  due  to  roll  and \npitch  had  not  been  extensively  tested,  but  it  was  in- \ntended to  use  this  feature  in  future  Geier  2 units. \nFurthermore  it  was  stated  that  such  an  assembly \ncapable  of  withstanding  short-period  accelerations \nof  1,000  times  gravity  had  been  designed  and  tested \nfor  the  aircraft  torpedo.8 \na See  references  58-64  for  additional  material  on  topics  in \nthis  chapter. \nChapter  24 \nBRITISH  TRUMPER  SYSTEM \n24.1  INTRODUCTION \nThe  British  Trumper  torpedo  is  a prosubmarine \nanti  surface-ship  device,  which  was  developed \nfor  use  in  the  Mark  9 torpedo.  The  Mark  9 is  a 21-in. \ntorpedo  that  travels  at  a speed  of  40  knots  and  has \na turning  radius  of  about  125  yd. \nThe  block  diagram  of  the  Trumper  control  system \nThe transducers, shown in Figure 1, are quartz with a horizontal beamwidth used for making initial acoustic contact with the target. The vertical plane beamwidth is made very narrow to achieve a high directivity index. Diagrams of the quartz transducers for both the projectors and receiving hydrophones are shown in Figure 2.\n\nCharacteristics of these transducers:\n\nFigure 1 depicts a British Trumper, sandwich type with separate transducers for transmitting and receiving. The time base is a system of cams driven by the main motor shaft. These cams determine the 1-sec interval between transmitted pulses, the 3-5 msec length of transmitted pulses, the blanking, and application of TVG to the receiver channels.\n\n24.2 Transducers.\nThe transducers are mounted in a flattened section on the nose of the torpedo. The vertical patterns are 6 db down at 10 degrees and 10 db down at 16 degrees off the axis. Minor lobes are 13.5 to 14.5 db down and the first minor lobes are 23 degrees off the axis. The horizontal patterns for one-half the transducers are 5 db down at 45 degrees and 14 db down at 70 degrees off the axis; the minor lobes are negligible. When projectors are connected with halves aiding, 6-db down points are 25 degrees off the axis, 10-db down points are 31 degrees off the axis, and the first minor lobes are 63 degrees off the axis and are 20 db down. When they are connected with halves bucking, the pattern is British Trumper System.\nbi-lobed with a zero on the torpedo axis. The angle between the maxima of the lobes is 60 degrees. The pattern is 12 db down at \u00b170 degrees off the torpedo axis and 10 db down at +5 degrees off the torpedo axis.\n\nFigure 2. Transducers.\n\n2. Hydrophones. The horizontal pattern of the receiver hydrophones is almost identical to that of the projectors, whereas the vertical pattern is about twice as wide.\n\n24.3. Transmitter.\n\nThe diagram of the transmitter circuit is indicated in Figure 3. The oscillator VI operates continuously from a plate supply of 300 v and is not keyed by the time base. The driver stage V2 is driven by the oscillator and its plate circuit is keyed by a switch in the time base. The driver stage is coupled to the power amplifier by means of the transformer T1, the two secondary windings.\nThe windings of which are arranged such that the grids of the power amplifier stages V3 and V4 are driven 180 degrees out of phase. The power amplifier is connected to the two projectors by transformer T2. The power-amplifier stage is keyed by a switch SW2 operated by the time base. This switch breaks the circuit between the cathodes of V3 and V4 and ground. The electric output of the power amplifier is about 300 watts, and the projectors' efficiency is such that about 200 watts of acoustic power is radiated into the water. The power supply for the power amplifier is mounted in a cylinder about 10 to 12 in. long and 3 in. in diameter and consists of a high-voltage 1,500-volt generator which is driven by means of an air turbine. The output of the generator is rectified and supplied directly to the power-amplifier plates.\nThe steering receiver consists of a four-stage resistance-coupled amplifier, shown schematically in Figure 4. The first stage functions as a preamplifier and no sensitivity control is applied to it. The second and third stages are blanked during transmission and are controlled by TVG during the listening interval. The circuits containing R9, P2, C7, and C8 control the blanking and TVG voltages. During transmission, a high negative voltage is applied at the junction of R8 and R9. The circuit consisting of C7 and R9 serves as a fast-discharge circuit, allowing the potential of the grids of V2 and V3 to drop quite rapidly immediately following transmission. The circuit consisting of P2 and C8 is a slow-discharge circuit which actually controls the TVG during the major portion of the listening interval. By this arrangement, the receiver is quickly blanked during transmission and then smoothly brought back to the listening state.\nThe voltage for blanking the receiver during transmission is applied at the junction of R8 and R9. However, this voltage drops quickly after transmission to the proper level for controlling receiver sensitivity during the listening interval. The rate of change of sensitivity is controlled by the circuit P2 and C8. The potential of the grid of V3 is maintained through R15 and the junction of R9 and P2. The receiving system consists of two identical receivers, each with TVG circuits connected together as indicated in Figure 4. The inputs of these two receivers are obtained from two separate identical receiving hydrophones.\n\nThe fourth stage of the receiver is biased beyond cutoff by applying a negative voltage to it.\n\nSteering Receiver.\nFigure 3. Transmitter. The grid is connected through P3, R20, and R21. When a signal is received on the hydrophone, this negative bias on V4 functions as an amplitude gate for the system, necessitating that a signal level out of V3 exceed a predetermined value for any signal to be generated in the plate circuit of V4. This stage also serves as a limiter stage since a level around 3 db above the threshold signal level is required to produce limiting.\n\nBritish Trumper System\n\nThe phase-sensitive detector circuit requires that the applied signals be out of phase by 90 degrees to produce a zero output. This 90-degree phase difference in the two receivers is achieved by proper tailoring of the coupling condensers C4, C11, and C16 in the two receivers.\n\n24.5 Phase-Sensitive Detector and Relay Control\n\nThe schematic of the phase-sensitive detector circuit is as follows:\nThe circuit is depicted in Figure 5. The outputs of the two receivers are located at the transformers T1 and T2. The phase shifts in the receivers are adjusted by tailoring the coupling condensers, ensuring that signals in phase applied at the receiver inputs result in signals 90 degrees out of phase at the receivers' outputs. Figure 6 displays a curve representing the DC voltage output of the phase-sensitive detector, plotted as a function of the target angle in degrees. The phase-sensitive detector output voltages are expressed as fractions of the signal voltage generated in the plate circuits of the limiter stages. The maximum output voltage occurs at a target angle of 30 degrees and is equal to 0.7 of the limiter signal voltage. The output of the phase-sensitive detector is found at the terminals of the two receivers.\nCondensers Cl and C2 connected in series. The terminal of Cl is connected to the grid of a DC amplifier which operates one steering relay and the other terminal of C2 is connected to another DC amplifier which operates another steering relay. These steering relays are used to rotate the gyro by means of a gyro-angling motor. When a steering signal is received, one or the other of the relays is closed and this causes the gyro-angling motor to change the gyro setting by 7 degrees. This amount of correction of the gyro per ping is chosen since it is the rate at which the torpedo is able to turn under the application of full rudder. The relay amplifiers are so biased that the voltage required to actuate the relays corresponds to the phase-sensitive detector output at a target angle of 3 degrees.\n\n24.6 Collision-course steering.\nThe  British  have  done  some  work  on  a modifica- \ntion of  the  steering  control  system  in  order  to  permit \nthe  torpedo  to  be  steered  on  a collision  course.  The \nmodification  of  the  steering  circuit  required  to \nTARGET  ANGLE  IN  OEGREES \nFigure  6.  Phase-sensitive  detector  characteristics. \nachieve  this  is  indicated  in  Figure  7.  S is  a stepping \nrelay  which  is  used  to  change  the  relative  phase- \nshifts  of  signal  in  the  two  steering  amplifiers.  The \nrelays,  indicated  as  relays  2,  are  normally  closed,  but \nthey  can  be  driven  open  by  a signal  of  somewhat \nhigher  level  than  that  required  to  close  the  relays  1. \nWhen  a signal  is  received  which  requires  steering  in \none  direction  but  which  produces  a phase-sensitive \ndetector  output  sufficient  to  actuate  relay  1 but  not \nto  actuate  relay  2,  the  gyro-angling  motor  will  in- \ntroduce the  correction  of  7 degrees  in  the  course  in \nThe 1-second interval between echoes. At the same time, the stepping relay S will be turned to introduce a phase shift in the opposite sense between the two amplifiers, amounting to 4 degrees which is the difference between the angle of correction introduced by the gyro-angling motor and the minimum sensitivity of the relay amplifiers. By this means, the torpedo will asymptotically approach a course such that the bearing of the target relative to the torpedo will remain constant. This is by definition the collision course. If the target angle at the time of initial contact is not within operating limits, this condition will be continued until the torpedo is near enough to a pursuit course so that relay 2 will be unactuated when the torpedo begins to correct to the collision course.\n\nCollision-course steering\n\nThis system steers the torpedo towards a collision course with a target such that the target's bearing relative to the torpedo remains constant. If the target angle at the time of initial contact is not within operating limits, this condition will be continued until the torpedo is near enough to a pursuit course so that relay 2 will no longer be actuated when the torpedo begins to correct to the collision course.\n\nFigure 7. Block diagram of collision-course system steering.\nThe tact is very large. The time required to correct to a collision course would be excessive, so relays 2 are provided to make the torpedo initially correct to a pursuit course under conditions of very large target angles where the signal applied to the relay amplifier is sufficiently large to actuate relay 2. Opening relay 2 prevents the stepping relay from operating. It is unknown whether any torpedoes were ever operated with the collision-course system. The initial plan was to proceed with the simple steering system and incorporate the collision-course system when it was sufficiently perfected.\n\nReferences: 65, 66\n\nChapter 25\nBRITISH BOWLER SYSTEM\n25.1 INTRODUCTION\n\nThe British Bowler torpedo utilizes an echo-ranging control system with two independent projectors and hydrophones. The system components include:\nThe projectors and hydrophones are mounted perpendicular to the torpedo axis with one projector transmitting a beam and a hydrophone receiving echoes from targets approximately on the same axis. The other projector and hydrophone have a 0.16 second delay. Both projectors and hydrophones are quartz transducers, approximately 3-inch in diameter. The projectors are internally mounted and acoustically coupled to the hull via an oil cell. The hydrophones are externally mounted and isolated from the torpedo hull. An intriguing observation concerning the hydrophone mounting is the critical width of the annular space between the hydrophone diaphragms and the torpedo hull. This annular space fills with:\n\n(Note: The text appears to be clear and readable without any major corrections. Therefore, no cleaning is necessary.)\nThe torpedo's run includes water, and components such as the PORT PROJECTOR HYDROPRONP, STSD STS 3, and PROJPCT/OR RYOROPRO/YT are located on the opposite side. The torpedo is typically launched from a bow or stern aspect. If the torpedo misses the target, an echo will be received on one or the other receiving hydrophones, causing the torpedo to make a hard turn toward the target. This setup necessitates the target's range being less than the torpedo's turning circle diameter for a hit. A block diagram of the system is shown in Figure 1. The transmitted signal frequency is 26.7 kc, the pulse length is 2 msec, and the ping interval's optimum value for the width of the space is 0.040 in.\n\nFigure 1. Block diagram of the British Bowler system.\n\nThe frequency of the transmitted signal is 26.7 kc; the length of the pulse is 2 msec with an optimum ping interval value of 0.040 in. for the width of the space. The torpedo's components, including the PORT PROJECTOR HYDROPRONP, STSD STS 3, and PROJPCT/OR RYOROPRO/YT, are located on the opposite side. The torpedo is typically launched from a bow or stern aspect. If the torpedo misses the target, an echo will be received on one or the other receiving hydrophones, causing the torpedo to make a hard turn toward the target. This setup requires the target's range to be less than the torpedo's turning circle diameter for a hit.\nA greater width than this introduces turbulence, causing increased self-noise, while a narrower width permits the water to form a shunt path across the isolation.\n\n25.2 ELECTRONIC GEAR\n\nThe transmitter consists of a blocking oscillator employing a 6N7 tube. The length of the pulses and the interval between pulses are controlled by the characteristics of this blocking oscillator. The oscillator drives the power amplifier, which in turn drives the projectors through a coupling transformer. The power output of each projector is 15 watts. Since the blocking oscillator is its own time base, it is necessary that this oscillator be used to control the blanking and TVG of the receiver. These functions are achieved by means of the double-rectifier system in Figure 2. Details of blanking and TVG circuits.\n\nTransmitter: A blocking oscillator using a 6N7 tube controls the length and interval of pulses. The oscillator drives the power amplifier, which powers the projectors via a coupling transformer. Each projector produces a 15-watt power output. Since the blocking oscillator serves as its own time base, it regulates the receiver's blanking and TVG functions through a double-rectifier system (Figure 2). [blanking and TVG circuit details]\nThe virtue of the system is indicated in Figure 2. It achieves blanking of the second stage of the receiver amplifier through a combination of increased grid bias and decreased resistance to ground. The storage of charge on condenser C by rectifier VR1 is used for TVG control. The receivers consist of two stages of resistance-coupled amplifiers followed by a single gas-discharge tube for controlling the steering action. Difficulty was encountered in obtaining rudder control by solenoids operated by relays from the gas tubes due to insufficient space. The final solution to this problem was unusual and possible only because the torpedo is intended to have steering action applied once.\nThe device consisted of two small cylinders, each containing an explosive charge behind a piston. When an echo is received, indicating that the torpedo should turn in one direction, firing of the gas tube in the receiver causes the charge in the cylinder to be ignited, which in turn throws the rudder hard over in the proper direction. No further steering is possible until the torpedo is recovered and the cylinders are reset.\n\nThe size of the complete electronic chassis is approximately 5 x 6 x 12 in. The power supply consists of a 12-volt Edison storage battery which is 12 x 4 x 3 in. The high-voltage plates for the tubes are obtained by means of vibrators with transformers and rectifiers.\n\nDynamic sound pressure during transmission is between 2,000 and 6,000 dynes per sq cm at a frequency of 20 kHz.\nThe range of a projector is 10 ft on its axis. Echoes of 50 to 100 dynes per sq cm have been obtained at a range of 100 yd off the beam of a stationary tanker. Echoes off the bow of such a ship at 100 yd range are approximately 20 to 30 dynes per sq cm. The peak noise level of the torpedo operating at a speed of 40 knots is from 5 to 8 dynes per sq cm. The signal-to-noise ratio under the most unfavorable conditions at 100 yards range is about 12 db. The average value is more nearly 20 db.\n\nReferences: 66-68 for additional material on topics in this chapter.\n\nChapter 26\nEVALUATION\n\nAll of the echo-ranging control systems described in the preceding chapters are systems that were developed under the stress of war with the chief objective to get a working device in the shortest possible time. In all cases, compatibility with existing equipment and ease of installation were secondary considerations. However, in peacetime, these systems have been improved and optimized to meet more stringent requirements for accuracy, reliability, and ease of use.\nPromises had to be made to avoid discarding developed devices and the necessary time to go back and re-engineer parts of systems found unsatisfactory. This resulted in most devices being made more complicated than necessary and containing components operating under marginal conditions. The problem of maintenance and adjustment of systems is always more complicated than necessary.\n\nIn the case of the antisubmarine devices developed in this country, a device was desired that could be incorporated into the existing torpedo body already being used as a noise-steering torpedo. Since the body used in this torpedo is not capable of withstanding pressures corresponding to depths greater than about 400 ft, there was little immediate advantage to be gained.\nThe electronic gear was improved for deeper operation. The system developed by General Electric and manufactured by Leeds and Northrup met the device's requirements satisfactorily. It is one of the simplest echo-ranging systems developed. The system's main weakness is the limited dive and climb rate, which permits a maximum climb angle of about 1.5 degrees, providing little maneuverability in the vertical plane if a submarine under attack takes evasive action. This is not a serious limitation when applied to a body restricted to the upper 400 ft of water and launched from an aircraft against the swirl left by it.\nThe submarine's use of a diving device can hinder a torpedo if the torpedo operates at depths up to 1,000 ft, where modern submarines can function. In such cases, the submarine may employ evasive tactics in the vertical plane to avoid the torpedo.\n\nThe General Electric NO 181 system features transmitter pulse lengths of approximately 30 milliseconds and an amplitude-gate characteristic that prevents steering on short pulses. This renders the system resilient against grenade-type countermeasures. The cut-on cutoff steering in azimuth further enhances its resistance to noise countermeasures towed astern or thrown out from a submarine under attack. The cut-on cutoff steering system causes the torpedo to steer around noise sources, and if echoes are detected on the far side\nThe torpedo will steer on echoes from the target, but is vulnerable to a decoy in the form of a very strong noise source at the target. This decoy will cause the torpedo to steer around the target rather than attack it. The behavior of this system on wakes is quite interesting. The cut-on cutoff steering system in the azimuth plane causes the torpedo to steer parallel to the wake along one side. If the device steers on the wake, it will follow the wake to the target if started in the proper direction. In anti-submarine application, this wake-following feature might be an advantage, as the torpedo, when aircraft-launched, is normally launched as near as possible to the swirl left by the diving submarine. However, in an anti-surface-ship device, this feature might be a disadvantage, as in this case the torpedo would follow the wake instead of attacking the ship.\nThe torpedo normally runs toward the target, but acoustic contact with the wake may cause it to follow the wake away from the target. The Harvard N0181 system is more complicated than the General Electric device. It uses target doppler for enabling and an additional amplitude gate with a 30-msec transmitted pulse. This system is less vulnerable to countermeasures and allows for high rates of dive or climb since it will not steer on surface or bottom echoes. The doppler system also prevents the device from steering on wake echoes. In the limited capabilities of the device in which this was built, there is some question as to whether the advantages gained by the additional complication of the doppler-enabling system were worth it.\nIn the development of an echo-ranging antisubmarine torpedo for operation at depths as great as 1,000 ft, the doppler-enabling system's additional rate of dive and climb permits important vertical evasive tactics on the part of the submarine. This system is also vulnerable to grenade-type countermeasures due to the action of the amplitude gate. The device tends to steer toward a noise source, so if the target is made a source of noise, the noise would simply aid the device in steering towards the target. The behavior of the device in the presence of a continuous-noise source towed by the target or thrown out from the target is similar to that of the General Electric system. The torpedo might steer towards the target.\nThe sharp beam pattern of the transducer minimizes the effect of countermeasures after the torpedo passes. It should be noted, however, that the use of a doppler-enabling system makes simple evasion tactics possible, as it makes steering on a stationary submarine impossible. The British Dealer torpedo was also designed as an echo-ranging antisubmarine torpedo, but relatively little is known about the nature of the electronic gear used. The methods used in the actual steering of the torpedo avoid the use of rudders which have to be operated through watertight seals on the body. Instead, two propulsion motors and two propellers are used, and a means of moving the battery backward and forward is provided.\nSteer the torpedo in the vertical plane. All these antisubmarine torpedoes were designed to be aircraft-launched, placing relatively severe requirements on the design of all components entering into them.\n\nThe echo-ranging anti-surface ship torpedo, which is the simplest in principle and has the most limited objective, is the British Bowler. This device is intended to have an acoustic operating range less than the turning diameter of the torpedo. When the device receives an echo from one side, the rudders will be turned hard over, and the torpedo will simply turn into the target. The transducers for the two separate transmitting and receiving systems are mounted on the two sides of the torpedo with their acoustic axes almost perpendicular to the axis of the body. The purpose of a device such as this is to detect a surface ship and home in on it using the reflected sound waves.\nTo increase the effectiveness of torpedoes launched from the bow or stern of a target ship, but for large misses, the acoustic control system does not add anything to the torpedo's effectiveness. One of the simplest anti-surface ship torpedo echo-ranging systems is the Geier 1 developed by the German Luftwaffe. Its objectives are somewhat limited as its operating range is only about 200 meters. This device uses two independent sets of transducers, and acoustic control is initiated when an echo is received on one of the receiving hydrophones. However, the device differs from the Bowler device in that acoustic control is maintained until the torpedo strikes the target. This device is quite vulnerable to countermeasures, as it operates on any sudden change in signal level. It will not steer, however, on a continuous-noise countermeasure.\nThe VC circuit causes measurement issues due to its special action. It's also susceptible to steering on target wakes. There's a significant difference between this system's behavior and the General Electric system regarding the target wake. The cut-on/cutoff steering of the General Electric device causes it to steer parallel to the wake, while the German Geier system behaves such that when it steers on echoes from the wake, it tends to steer perpendicular to it. Once the torpedo reaches a position where it is closer to the wake than to the target, it will steer perpendicular to the wake. The Germans were working on improving the Geier 1 system's performance to eliminate its vulnerability to the wake. The Geier 1 system was not intended to be\nThe Bell Telephone Laboratories 157C system and the British Trumper systems are similar in their operation. Both devices use a split-hydrophone system, and the electronic gear in the receiver compares the phase of the signals on the two halves of the receiving hydrophones. In both cases, the hydrophones and projectors are crystal. The British system uses quartz crystals, and the BTL system uses ammonium dihydrogen phosphate crystals. The BTL device uses the same transducer for both projector and receiver. In the BTL device, the target angle is measured by comparison of the phase of the signal on the two halves of the transducer, and the measured value of the target.\nAn angle correction is injected into the gyro cam plate using a mechanical device called a translator. In the British system, an angle increment is injected into the gyro cam plate whenever the acoustic signal indicates that the target is off axis. According to an analysis by the BTL group, the British system should be just as effective and can be made considerably simpler. One criticism of the BTL device is that it is excessively complicated. For instance, the system's time base consists of three double triodes and two relays, while the same operations can be performed using a simple set of cam-operated switches. The method used to measure the target angle also requires a condenser and considerable circuit network.\nThe torpedo must be isolated from the ground by a resistance of the order of 100 megohms. This is a requirement that probably cannot be maintained under all expected operating conditions.\n\nThe German Geier system, the British Trumper, and the BTL system all encounter the same difficulty with target wakes. The solution to this problem by the Germans and the BTL group is quite similar and involves use of preferred-side steering. This is accomplished by setting a switch, operable from the outside of the torpedo, which causes the system to steer in the preferred direction when echoes are received in listening intervals that provide steering information in both directions. With this arrangement, the submarine skipper determines, before firing the torpedo, on which side of the target it will approach, and the preferred-side steering system is engaged accordingly.\nIn this approach, the torpedo prefers echoes from the target's side. Assuming the target pursues the estimated course at the time of firing, if the torpedo is fired from a long range and the ship executes evasive maneuvers, there's a possibility the ship will be in a position where the torpedo won't be on the preferred side. In such cases, the torpedo will prefer echoes from the wake and will be less likely to contact the target than without preferred-side steering. The British encountered another issue with their system in the presence of wakes. The broad transducer pattern in the azimuth plane causes the phase-sensitive detector to receive a long signal of continuously-varying phase.\nThe Ordnance Research Laboratory project 4 device is an evolution of the Harvard NO 181 system, prioritizing antisurface-ship application over antisubmarine. Given the significant importance of target wakes in antisurface-ship applications, the doppler-enabling system offers a notable advantage by effectively eliminating the wake-steering problem. Preliminary results from the special transducer, developed for this system, suggest that the effective self-noise of the torpedo in this transducer setup is significantly less than with other transducer types.\nThe use of this transducer with a very sharp beam pattern requires the snaky gyro-course for search to make acoustic contact with a target at an appreciable angle with the original gyro course of the torpedo. Relatively little attention has been paid to the countermeasure problem in the echo-ranging systems developed during the war. The fact that countermeasures for echo-ranging systems are, in general, different from those effective against a noise-steering device was relied upon to make former devices effective. In future development, the fact that countermeasures, designed to operate against echo-ranging torpedoes, will have to be considered in the design of the systems themselves. The experience with the Harvard NO 181 and General Electric N0181 devices indicates that the use of countermeasures will be necessary.\nA relatively long transmitted pulse makes a system less vulnerable to countermeasures. Additionally, methods for processing received echoes must be devised such that the steering criterion can be varied from one unit to another. This allows the system to adapt when one type of countermeasure becomes effective, rendering it ineffective.\n\nThe self-noise level of the torpedo, as measured on the receiving hydrophone, determines the lowest level of received echo effective for steering. Therefore, minimizing self-noise in the transducer design is important. The experience with the transducer used in the Harvard NO 181, General Electric N0181, and ORL project 4 systems suggests that this transducer, with its very sharp beam pattern and mounted in, is effective.\nThe center of the nose measures a lower level of self-noise from the torpedo than broader beam-pattern transducers and transducers mounted at points in the nose not at the center. This difference is not yet known whether it is due to the more effective front-to-back discrimination of the transducer used or to the fact that the small transducer mounted at the center of the nose is less affected by water-flow noise. Future investigations on the factors determining torpedo self-noise should clarify this matter and make possible the more intelligent design of transducer systems.\n\nIn antisurface-ship applications, some acoustic torpedoes provide for only azimuth control and the running depth of the torpedo is so set that it can make mechanical contact with the target or, if an impact is not desired, the depth is set to allow the torpedo to explode at a predetermined depth.\ninfluence  exploder  is  used,  the  torpedo  will  pass  close \nenough  under  the  target  to  actuate  the  influence  ex- \nploder. Experience  so  far  indicates  that  self  noise  due \nto  cavitation  is  decreased  as  the  running  depth  of  the \ntorpedo  is  increased.  Experience  with  the  Mark  21 \nand  Mark  31  noise-steering  torpedoes  which  use  the \nMark  13  and  Mark  18  bodies  indicates  that  self-noise \nlevel  decreases  with  increased  depth  down  to  a depth \nof  about  50  ft.  The  decrease  in  self  noise  is  of  suf- \nficient magnitude  so  that  it  is  worth  while  operating \nthe  torpedo  at  the  50-ft  running  depth  for  the  initial \nportion  of  an  attack  and  then  to  use  a vertical- \nsteering  system  to  bring  the  torpedo  up  to  a shallow \nenough  depth  to  make  the  attack  effective  at  the \nend.  The  experience  so  far  with  the  Mark  28  noise- \nsteering torpedo  indicates  that  operation  as  deep  as \n80 feet is desirable in the initial portion of the attack. Unless it is possible to design propellers which are entirely free from cavitation, it will probably continue to be profitable to operate torpedoes at these greater depths during the initial portion of the attack. All torpedo echo-ranging systems so far developed have relatively complicated electronic gear, which is designed such that the adjustments of the components of the system are critical, requiring quite highly skilled maintenance personnel at any station where the devices are made ready for operation. This need not always be true. With proper engineering, the devices should be worked out such that, after adjustment is made in the factory, no further adjustment of any electronic components would need to be made in the field. It would be desirable to design torpedoes in such a way that no field adjustments are required.\nSign electronic panels to contain two or three replaceable units, all components well protected against mechanical injury. Supply test equipment for the field to determine if these unit components are operating properly. If a component is not operating properly, remove and replace it with another. Discard or return defective components to the factory for adjustment.\n\nOne of the most important needs in the development of any type of acoustic torpedo is the development of a torpedo body with a control system to which information from the electronic panel can be easily applied. It would seem that an all-electric control system is preferable to the air control systems in current use on most torpedoes. In the case\nof the BTL device, a proportional control in azimuth is achieved by means of an extremely complicated mechanism to transfer acoustic-steering information to the torpedo gyro cover plate. The use of an all-electric control system would make possible a much simplified means of transferring this information to the gyro. In the case of the U.S. Navy Mark 20 torpedo, which was never used in the Service, the control system for both depth and azimuth utilizes selsyns to transfer information from the gyro to the torpedo azimuth-control system and from the pendulum and bellows to the depth-control system. With this type of control, it is possible, by the introduction of another selsyn in the depth system and also another selsyn in the azimuth system, to inject correction information from the steering amplifier to the normal torpedo control. One of the difficulties\nThe Mark 20 torpedo's issue is the use of steering motors, which have caused stability problems. For maximum range in an echo-ranging torpedo, the ping interval must be sufficient for the transmitted signal to reach the target and return before the next signal is transmitted. As the maximum range of echo-ranging torpedoes increases, intermittent information and difficulties with on-off steering systems become greater. Therefore, either a proportional azimuth-steering system like BTL's or an incremental azimuth system used in British torpedoes will be required. An echo-ranging torpedo's primary advantage is chiefly its ability to home in on the target by emitting and receiving echoes.\nThe system's advantage lies in its ability to achieve a wide range independently of the noise emitted by the target. To maximize this advantage, large transmitter power outputs are necessary. Currently, the BTL NO 181 system and the ORL project 4 system use 1.5-kw capacity transmitters, which is likely not the largest feasible power output in an echo-ranging device. The utilization of power in a duty cycle requires further study. In the mentioned systems, the actual power output is determined by the plate voltage limitations of the tubes used in the power amplifiers. The power-supply problem essentially resolves into the issue of transforming power from the torpedo's propulsion motor into useful power for the transmitter on a duty-cycle basis.\nThe use of equipment with excessive weight or volume is not an issue in neither of the above systems. In neither system is the power output of the transducer sufficient to cause cavitation at its face during the transmitted pulse. As the acoustic range of torpedoes is increased, the running range should be increased in a corresponding manner to fully utilize the advantages of acoustic control. This is another reason why attention should be given to the design of torpedoes for use with acoustic control systems.\n\nGlossary:\nAcoustic Frequencies: Sonic frequencies, range of audible frequencies, sometimes taken as from 0.02 to 15 kc.\nCavitation: The formation of vapor or gas cavities in water, caused by a sharp reduction in local pressure.\nCeiling Switch: Pressure-actuated switch which keeps the control system inoperative until the torpedo exceeds some selected depth.\nA transducer utilizes piezo-electric crystals, such as Rochelle salt, ADP, quartz, or tourmaline, for conversion of energy. The transducer's efficiency is the ratio, in decibels, of the average intensity or response over the entire sphere surrounding the projector or hydrophone to the intensity or response on the acoustic axis.\n\nA Doppler-enabling system is a circuit that permits only echoes with Doppler to activate the torpedo control system.\n\nAn echo repeater is an artificial target used in sonar calibration and training, which returns a synthetic echo by receiving, amplifying, and retransmitting an incident ping.\n\nFM sonar is a scanning-type sonar that uses a continuous frequency-modulated transmission signal.\n\nA hydrofoil is a body whose motion through water produces desired forces upon its surfaces.\n\nA hydrophone is an underwater microphone.\n\nThe magnetostriction effect is a phenomenon exhibited by certain materials.\nTain metals, particularly nickel and its alloys, which change in length when magnetized or which, when magnetized and then mechanically distorted, undergo a corresponding change in magnetization (Villari effect).\n\nODN: Own doppler nullifier.\nPing: Acoustic pulse signal projected by echo-ranging transducer.\nPip: Echo trace on indicator screen.\nPitch: Angular deviation from the line of course of a projectile taken in a vertical plane about its transverse axis.\nProjector: An underwater acoustic transmitter.\nReverberation: Sound scattered diffusely back towards the source principally from the surface or bottom and from small scattering sources in the medium such as bubbles of air and suspended solid matter.\nSLC: Simultaneous lobe comparison.\nSpectrum Level: Sound pressure level in a 1-c band.\nSupersonic Frequencies: Range of frequencies higher than\nSonic or acoustic/ frequencies. Sometimes referred to as ultrasonic to avoid confusion with growing use of supersonic to denote higher-than-sound velocities. Target strength. Measure of reflecting power of target. Ratio, in decibels, of the target echo to the echo from a 6-ft diameter perfectly reflecting sphere at the same range and depth. Thyrite. A material whose impedance varies inversely as the cube of the current passing through it. Transducer. Any device for converting energy from one form to another (electrical, mechanical, or acoustical). In sonar, usually combines the functions of a hydrophone and a projector. TVG. Time-varied gain. USRL. Underwater Sound Reference Laboratories. Varistor. A dry rectifier with the characteristics of a non-linear resistance whose value decreases with increasing applied voltage.\nCut: X - electrode faces perpendicular to X-axis (electrical axis)\nCut: Y - electrode faces perpendicular to Y-axis (mechanical axis)\nYaw: Angular deviation from course in horizontal plane about vertical axis\nCut: Z - electrode faces perpendicular to Z-axis (optical axis)\n\nBibliography: For access to index volume and microfilm, consult the Army or Navy agency listed on the reverse of the half-title page.\n\nPart I:\n1. Torpedo Noise Tests: A Summary, H. J. Michael\n1. Summary of Underwater Torpedo Noise, R. J. Wylde.\n2. Fundamentals of Hydro- and Aeromechanics Based on Lectures of Ludwig Prandtl, Oskar G. Tietjens, McGraw-Hill Book Co., New York, N.Y., and London, Eng., \n3. Observations of Cavitation on the Special Projectile (Memorandum), Robert T. Knapp, Report ND-8.1, Hydraulic Machinery Laboratory, CIT, Nov. 24, 1942. \nForce and Cavitation Characteristics of NACA J+I+12 \n4. Notes on Hydraulic Noise, R. G. Folsom, E. D. Howe, and Morrough P. O\u2019Brien, OSRD 949, NDRC C4-sr30-391, \n5. The Audio Frequency Phase System of Controls (Part C), \n6. Measurements of the High Frequency Noise Produced by Cavitating Projectiles in the High Speed Water Tunnels, \n7. Self Noise Tests on Experimental Model of the Mark 31 Mine, H. C. Montgomery, BTL, Jan. 21, 1944. \n8. Reduction of Torpedo Gear Noise, HUSL, Aug. 3, 1944. \n9. The Audio Frequency Phase System of Controls (Part B)\n11. The directivity index of a hydrophone is equal to the integral of the sensitivity over all directions divided by (4\u03c0r) times the maximum sensitivity and expressed in decibels. For details of this and other acoustic definitions, see A Practical Dictionary of Underwater Acoustical Devices, CUDWR-USRL, July 27, 1943.\n12. Calibration of Hydrophones in Mark 18 Nose Section\n13. Tests on Various Methods of Mounting Magnetostriction Hydrophones in Torpedo Heads, Robert C. McLoughlin\n14. Microphone Calibrations in Body 110 at Orlando, February [date missing]\n15. Biweekly Report on Projects NO-149 and NO-157, Report XV, covering period from Nov. 3 to Nov. 16, 1943\n16. Biweekly Report on Projects NO-149 and NO-157, Report XIX, covering period from Dec. 29, 1943 to Jan. 11, 1944\n17. Biweekly Report on Projects NO-149 and NO-157, Report XX, covering period from Jan. 12 to Jan. 25, 1944.\n18. Biweekly Report on Projects NO-149 and NO-157, Report XXXIV (July 26 to Aug. 8, 1944)\n19. The Audio Frequency Phase System of Controls, NDRC\n20. Torpedo Studies, Summary Technical Report, NDRC\n21. Dynamic Stability of Bombs and Projectiles, M. A. Biot\n22. Underwater Sound Reflecting Characteristics of Surface Ships (Memorandum), Case 23265-3, BTL (Oct. 6)\n23. The Effectiveness of a 20-knot Acoustic Torpedo and of Possible Modifications with Lower Speeds with or without an Automatic Speed Changing Mechanism, Conyers, Herring and E. Ward Emery, NDRC 6.1-srll31-1882\n24. Comparison of Effectiveness of Acoustic Torpedoes with Non-Acoustic Torpedoes, C. L. Pekeris, OSRD 157\n25. Countermeasures to the Acoustic Torpedo, ORG Memo\n26. Measurements and Analysis of Sound Pressures of Torpedoes in Range 40 cps to 128 kc/s, A. B. Wood, OSRD\n1. Preliminary Analysis of the Dynamics of Project NO-181 Control (Part I), Harvey A. Brooks, HUSL, June 2, 1944.\n2. Analysis of the Dynamics of Project NO-181 Control (Part II), Harvey A. Brooks, HUSL, July 6, 1945.\n3. Analysis of the Dynamics of Project NO-181 Control (Part III), Harvey A. Brooks, HUSL, [Date missing].\n4. Maximum Potentialities of an Echo-Ranging Torpedo, Harvey A. Brooks, HUSL, Nov. 1, 1944.\n5. General Electric Results on Echo Strength from a School-Type Submarine, Harvey A. Brooks, HUSL, Oct. 14, 1944.\n6. Theoretical Interpretation of General Electric Data on Surface Reverberation, Harvey A. Brooks, HUSL, Apr. 20, 1945.\n7. Underwater Sound Reflecting Characteristics of Surfaces.\n8. Propeller Cavitation Theory and Experiments, Donald [Last name missing]\n9. The General Electric Torpedo Control System: Part I, Information Received from the Leeds and Northrup Group at the Florida Station\n10. The General Electric System of Torpedo Control: Part 77, Information Obtained from the Leeds and Northrup Group in Philadelphia\n11. Miscellaneous Suggestions for Project NO-181-G, Harvey\n12. High Power Pattern Measurements on Gamewell SPEP No. 2, Runs 1 through 8, Nicholas A. Abourezk, HUSL, September 26, 1945.\n13. High Power Pattern Measurements on Gamewell SPEP No. 3, Runs 9 through 25, Nicholas A. Abourezk, HUSL, September 29, 1945.\n14. Comparison of Harvard and General Electric Schemes, Harvey A. Brooks, HUSL, October 6, 1944. Div. 6-922-MI\n15. Modification of Input Circuit for Project NO-181-G, Vernon M. Albers, HUSL, January 18, 1945.\n16. Behavior of the New Input Circuit for Project NO-181-G, Vernon M. Albers, HUSL.\n1. Cross talk and sensitivity requirements for Project N 0-181, Vernon M. Albers, HUSL, March 12, 1945.\n2. The 1-kc Oscillator for Project NO-181-G, John G. King, HUSL, July 11, 1944.\n3. New 60-kc Band-Pass Filters and Switching Tubes for Project NO-181-G, Vernon M. Albers, HUSL, January 18, 1945.\n4. Calibration of Leeds and Northrup Acoustic Steering Units, B. D. Simmons, Report 4, U. S. Navy USRL, Orlando, 1945.\n5. Phase Sensitive Detector, Fred G. Gardner, HUSL, April 1, 1945.\n6. Approximate Analysis of Automatic Volume Control Time Constants, Alfred W. Nolle, HUSL, February 8, 1944.\n7. The Automatic Volume Control Charge Time in Project NO-181, Harvey A. Brooks, HUSL, July 20, 1944.\n8. Common Amplifier and Automatic Volume Control System for Project NO-181, Nicholas A. Abourezk, HUSL, January, 1945.\n9. Diode-Type Electronic Switch for Use as a Doppler Gate.\n26. Comments on Leeds and Northrup Transducers (Project NO-181), Nicholas A. Abourezk, HUSL, Nov.\n27. Bearing Deviation Indicator Input Circuits (Project NO-181), Harvey A. Brooks, HUSL, May 5, 1944.\n28. The Use of Gyro Rate of Turn Control in Project NO-181, Harvey A. Brooks, HUSL, May 4, 1945.\n29. Modification of Bearing Deviation Indicator Input Circuit for Project NO-181, Harvey A. Brooks, HUSL, June 3, 1944.\n30. Application of Automatic Volume Control to Project NO-181 Input Amplifier, John G. King, HUSL, May 22, 1944.\n31. Phase Sensitive Detectors (Project NO-181), A. Nelson.\n32. Addendum to Phase Sensitive Detectors (Project NO-181), A. Nelson Butz, Jr., HUSL, Nov. 16, 1944.\n33. The Project NO-181-G Glide Angle Control, Frank S. Replogle, Jr., and Joseph M. Bringman, HUSL, Jan. 12, 1945.\n34. Work Done on Glide Angle Control (Project NO-181), Supplementary Report.\nFor Week Ending Thursday, February 22, 1945:\nFrank S. Replogle, Jr., and Joseph M. Bringman, \"Quantitative Specifications on Electronic Glide Angle Control\" (HUSL, Feb. 1945)\nJohn G. King and Harvey A. Brooks, \"Dynamical Behavior of the Project 61 Body on the Florida Runs\" (February to March 1945, HUSL)\nFrank S. Replogle, Jr., \"The Amplitude Gate and Doppler Gate System\" (HUSL, May 17, 1945)\nVernon M. 38. \"The Effect of Noise on Own Doppler Nullifier Frequency Setting\" (HUSL, Frank S. Replogle, Jr., May 17, 1945)\nMalcolm H. Hebb, \"Frequency Spread in Reverberations, Response of Discriminator\" (HUSL, Oct. 2, 1944)\nHarvey A. Brooks, \"The Theory of Discriminator Response to Reverberation (First Installment)\" (HUSL, May 21, 1945)\nHarvey A. Brooks and Nicholas A. Abourezk, \"Frequency Fluctuations in Reverberation at Spy Pond\" (HUSL)\n\nBIBLIOGRAPHY (if necessary)\n42. The Theory of Discriminator Response to Reverberation (Second Installment), Harvey A. Brooks, HUSL, June 4, 43. Theory of Own Doppler Nullifier Correction Rate, Harvey A. Brooks and Nicholas A. Abourezk, HUSL, 44. Further Analysis of First Tests on Reverberation Spread, Harvey A. Brooks and Nicholas A. Abourezk, HUSL, 45. Relay Amplifiers for the Project 4-G2, Fish, Vernon M., 46. The Control Relay System in the Panel of the Project 4-G2, Fish, Vernon M. Albers, HUSL, Jan. 23, 1946, 47. The Afterbody Circuits for the Project 4-G2 Torpedo, Vernon M. Fish, 48. Application of an Echo Control System in the Mark 14 Torpedo, NDRC 6.1-srl097-2342, OEMsr-1097, Project 49. Circuit Design Considerations for Project NO-1 57 -C, 50. Additional Notes on BTL Meeting, February 6, 1945, Harvey A. Brooks, HUSL, Feb. 17, 1945, 51. Progress Report on Project NO-157-B, NDRC 6.1-srl097-\n52. Noise Data on Spy Pond Captive Mark 18 Torpedo, Lyman N. Miller, Roland Mueser, P. M. Kendig\n53. Noise Data on Mark 18 Torpedo, Donald Ross, HUSL\n54. A Report on Bell Telephone Laboratories Trip by Albers and Graber, Vernon M. Albers and Ray Graber, HUSL, Nov. 1, 1945.\n55. A Report on Trip to Bell Telephone Laboratories at Murray Hill, New Jersey; Part I, Transducer, Nicholas A. Abourezk and Robert H. Lefkovich, HUSL, Nov. 1, 1945.\n56. A Report on Trip to Bell Telephone Laboratories at Murray Hill, New Jersey; Part II, Mechanical Gear, Nicholas A. Abourezk, HUSL, [No Date]\n57. Preliminary Report on Geier; Part I, Electronic System, Vernon M. Albers, HUSL, June 17, 1945.\n58. Second Report on Geier, Vernon M. Albers, HUSL, July 5, 1945.\n59. Probable Tactics of Geier, Harvey A. Brooks, HUSL, June [No Year]\n60. The Geier Torpedo Control and How It Compares with the [No Specific Topic Given]\n61. Measuring Self-Noise, Geier, John J. Iffland, HUSL\n62. Conference with Lieutenant Colonel Bree, Luftwaffe, Harvard Project NO-181, Vernon M. Albers, Dec. 4, 1945, Div. 6-925-M7\n63. British Admiralty Delegation Report, British Homing Torpedoes, Sept. 12, 1945.\n64. Information on British Torpedo Projects, Harvey A. Brooks, HUSL, \n65. Bowler Torpedo Control Development, Rodney F. Simons, OSRD WA-1384-4A, Torpedo Technical Memorandum 1, OSRD Liaison Office, Great Britain, Dec. 23, 1943.\n66. Bowler, Rodney F. Simons, OSRD WA-1470-6A, Torpedo Technical Memorandum 2, OSRD Liaison Office, Great Britain, Supplementary References\n\nListing Torpedoes\nSelf-Produced Noise from a Mark XXIV Mine, K. C. Morrical, Ray S. Alford, and others, NDRC 6.1-sr287 and sr785-720, Discussion of the Stability of the Mark XXI V Mine\nThe Dynamical Performance of the Rudder-Rudder Motor System Used on the Mark 24 Mine, R. Clark Jones, BTL, Mar 19, 1943.\nThe Audio Frequency Phase System of Control for the Mark XXIV Mine: Part A, Description of Apparatus; Part B, Measurements and Tests; Part C, Theory of Operation; Part D, Supplementary Memoranda OEMsr-346 and OEMsr-785, Discussion of the Tracking Performance of the Mark XXIV Mine in Terms of Electrical Feedback Theory, J. C. Lozier.\nTrajectory Calculations for the Project NO-1 57-B Torpedo, R. Studies of Project 0, R. L. Peek, OEMsr-1097, NDRC.\nTorpedo Mark 27, History, Principles of Operation of the Acoustic Control Circuit and Field Performance, NDRC.\nThe Mark 28 Torpedo, History, Principles of Operation.\nFinal Technical Report of Contract OEMsr-1097, Memorandum on Torpedo Steering, W.V. Houston, CUDWR Special Studies Group, Feb. 14, 1944.\n\nA Torpedo Survey on Project N-121, NDRC 6.1-srll31-1892.\nSelf-Noise Measurements on Mark 24 Mine, NDRC 6.1-sr287-1176.\nMark 24 Mine Performance Tests, NDRC 6.1-sr287-1457.\nTorpedo Depth Steering, NDRC 6.1-sr287-1457, HUSL, Apr.\nPropeller Program at the Harvard Underwater Sound Laboratory,\n\nBIBLIOGRAPHY\nTorpedo Instrumentation: A Summary of Torpedo Instruments Constructed by HUSL, NDRC 6.1-sr287-2174.\nAn Acoustically Controlled Electric Torpedo: An Adaptation of the Mark 18 Electric Torpedo to Acoustic Control at 20 and 30 Knots (Diagrams Included), NDRC 6.1-sr287-2177, HUSL, Mar.\nNoise Measurements on a Mark 21 Torpedo, NDRC 6.1-sr287-\nAcoustic Locating System, OEMsr-287, OSRD 6613, NDRC\nThe Projects NO-149-F and NO-157-F Test Equipment,\nModel 3 Beeper Transmitter, NDRC 6.1-sr287-2189, HUSL\nMiscellaneous Recording Equipment for Controlled Torpedoes, OEMsr-287\nMachinery Noise of the Electrical Torpedo, OEMsr-287, OSRD 6439\nForeign Ordnance, Project G, OEMsr-287, OSRD 6439\nMiscellaneous Electronic Equipment for Controlled Torpedoes, Propeller Design Studies, OEMsr-287, NDRC 6.1-sr287-2093\nAn Air-Launched Acoustic Torpedo, Project NO-149, OSRD\nProject NO-157, A Submarine-Launched Acoustic Torpedo\nTorpedo Control and Protective Devices, OEMsr-287, OSRD\nAn Air-Launched Acoustic Antisubmarine Mine, Project NO-94, Project NO-149, Mark 21 Torpedo (Final Report under Con)\nWestinghouse Electric and Manufacturing Co., Feb. 28, Mark 22 Torpedo, Final Report of Project NO-157, OEMsr-1053\nNDRC 6.1-srl053-2125, Westinghouse Electric and Manufacturing Co., May 23, 1945. Div. 6-912.2-MI\nCounter-Rotating Motor for Torpedo Drive, Gerhard Mauric.\nOSRD 6659, NDRC 6.1-srl370-2397, Electrical Engineering and Manufacturing Corp., Apr. 15, 1946. Division 6-933-MI\nTorpedo Retrieving Gear, OSRD 6543, NDRC 6.1-sr287-2094.\nAn Echo Control System for the Mark 13 Torpedo Project\n\nContract Numbers, Contractors, and Subjects of Contracts\n\nContract Number Name and Address of Contractor Subject\n-----------------------------------------------------\n\nOEMsr-20 The Trustees of Columbia University in the City of New York New York, NY Studies and experimental investigations in connection with and for the development of equipment and methods pertaining to submarine warfare.\n\nOEMsr-1131 The Trustees of Columbia University in the City of New York New York, NY Conduct studies and investigations in connection with the evaluation of the applicability of data, methods, devices, and systems pertaining to submarine and subsurface warfare.\n\nOEMsr-287 President and Fellows of Harvard College\nStudies and experimental investigations in connection with the development of equipment and devices relating to subsurface warfare.\n\nOEMsr-323, General Electric Company, Schenectady, New York\n\nStudies, experimental investigations, and development work in connection with submarine and subsurface warfare.\n\nOEMsr-785, Western Electric Company, Inc., New York, N.Y.\n\nStudies and experimental investigations in connection with Project 61.\n\nOEMsr-1097, Western Electric Company, Inc., New York, N.Y.\n\nConduct studies and experimental investigations in connection with the development, design and construction of preproduction models of the acoustic and electronic arrangements required for Projects NO-149 and NO-157, and such other development, design, and construction work in this connection that may be required.\n\nOEMsr-1294, Western Electric Company, Inc., New York, N.Y.\nStudies and experimental investigations in connection with production designs for the extension of Navy Project NO-94:\nOEMsr-1051, Westinghouse Electric Corporation, Sharon, Pa.\n- Tests and experimental investigations on Mark 18 samples.\n- Design, development, construction, and testing of launching samples of an aerial torpedo, acoustically controlled and electrically propelled.\n\nOEMsr-1053, Westinghouse Electric Corporation, Sharon, Pa.\n- Tests and experimental investigations on Mark 19 samples.\n- Design, development, construction, and testing of two hand-made samples of an acoustically controlled, electrically propelled submarine torpedo.\n\nOEMsr-1370, Electrical Engineering and Mfg. Corp., Los Angeles, Calif.\n- Studies and experimental investigations in connection with electric motor development.\n\nOEMsr-1419\nLeeds and Northrup Company, Philadelphia, Pa.\nConduct engineering studies and design work on a controlled mine, including some model shop work; engineering design and construction of a small number of the preproduction models.\n\nSERVICE PROJECT NUMBERS\n\nThe projects listed below were transmitted to the Executive Secretary, National Defense Research Committee (NDRC), from the War or Navy Department.\n\nService Project Number Subject\n--- ---\nMark \u2014 Mine Acoustic control for torpedoes\nAcoustically directed 21-inch torpedo for submarines\nEcho ranging control\n\nThe subject indexes of all STR volumes are combined in a master index printed in a separate volume.\nAcoustic homing torpedoes: see Echo-ranging torpedo control systems, Acoustic homing torpedoes, Acoustic homing\n\nAcoustic pressure in terms of electric power, 64\n\nAcoustic range of homing torpedoes; see also Homing range of echo-ranging torpedoes\n\necho-ranging formulas, 64-66\n\nAircraft launched torpedoes, control systems: British Bowler system, British Dealer system, 104, Geier 2 system, 143-148\n\ngeneral design considerations, 72\n\nAmplifier balancing; pilot channel switching method, 46\n\nAmplitude gates for operation switching; in HUSL N0181 system, in ORL project 4 system, 109, 111\n\noperation, 47\n\nAntisubmarine torpedo control systems: British Dealer system, 104\n\ngeneral design considerations, 66\n\nAntisurface-ship torpedo control systems: British Bowler system,\nBritish Trumper System, 149-153\nBTL 157B and 157C systems, 120-138\nORL project 4 system, 105-119\nAtlas Werke Munich, 138\nAttenuation of sound in sea, frequency dependence, 9, 51\nAutomatic steering control (see Steering control)\nAutomatic volume control; in HUSL system, 98\nuse in echo-ranging receivers, 69\nwith TVG in ORL system, 109\nAxis of transducer, def., 64\nAzimuth steering (see Steering control)\nBalancing methods for dual amplifiers,\nBalancing torpedo propeller torque,\nBand width formula, echo-ranging projector, 51\nBeam pattern, echo-ranging projector,\nBell Telephone Laboratories, 157B and 157C\nBernoulli\u2019s theorem, 11, 12\nBlanking circuit GE N0181 system, 83\nBowler steering method for echo-ranging,\nBritish Bowler system, 52, 56, 154, 157\nBritish Dealer system, 104\nBritish torpedoes, engine noise, 20\nBritish Trumper system, 149-153, 157\nCavitation: switches for echo ranging, around moving sphere; 11, around torpedoes, 10-17\nDue to diminishing cross section of a streamline, 10\nVortex formulas, 10\nCavitation coefficient: values for various shapes, 12, 14\nCavitation noise, 14, 25, 27, function of torpedo speed, 9\nHydrophone discrimination, identification, 16, 23\nSpeed of onset, 9\nCavitation parameter, 12, 13, 25\nCircuit arrangements in torpedo after-body, 117\nCircuits, electronic: amplitude gates, 83, differential operated gate, 48, limiter circuit, 128, preference circuit, 130, pulse shaping circuit, 108, range reduction circuit, 153, threshold circuit, 126, transmitter circuit, 76, 124, 141, 149, transmitter receiver circuit, 125, trigger circuit, 132\n\"Circulation\" of a vortex, definition, 10\nClimb angle limiter for depth steering control, 49\nCoefficient of cavitation, 12\nCoefficients of hydrodynamic forces, collision course steering, commutation method for amplifier balance, comparison bridge (GE N0181 system), control systems (see Steering control for echo-ranging torpedoes), counter rotating field and armature type torpedo motor, counter rotating torpedo propellers, countermeasures for homing torpedoes, cross force coefficient, crystal transducers for echo-ranging torpedoes (121, 149), cut-on cut-off steering (74, 82, 138-148), evaluation (69, 156), damping factor (hydrodynamic), damping moment coefficients, dealer system (British), decibels spectrum level (7), definitions (echo-ranging terms and depth steering control), British Dealer system, ExFER42 mine (57), general design considerations (49), HUSL N0181 system (restricted to 250 yd range), detectors (phase sensitive), British.\nTrumper system, in ORL project 4, Differential operated gate, 48, Direction finding systems for echo-ranging torpedoes; see Steering control for echo-ranging torpedoes, Direction finding system for listening torpedo, 31-36, Directivity index, transducer; definition, 63, formulas, 23, 64, of HUSL transducer, 76, Directivity patterns, hydrophones, 23, Doppler effect used to identify echoes, Doppler-enabling receiver, ORL project 4 system, 112, Doppler-enabling system; advantages, CRO patterns, 100, Drag force coefficient, 41, Echo identification; by use of doppler effect, 54, by use of long signal, 54, by use of modulated signal, 54, by use of short signal, 53, by use of time variable gain, 55, Echo level, factors affecting, 52, Echo ranging torpedo control systems; advantages, 68-69, 73, British Dealer system, 104, British Trumper, 149-153, 157, disadvantages, 68, evaluation, 156-160.\nEcho relay, ORL project 4 system, 115\nEcho-to-reverberation ratio\nElectronic time base for echo ranging systems, 70\nEllipsoids, cavitation around, 13\nEnabling relay, ORL project 4 system\nEquations of motion for homing torpedoes\nEquivalent sphere formula, target strength, 65\nEx20F torpedo, 18, 49\nExF42 mine; amplifier balance, 46\nCavitation noise, 16, 24\nHydrophone directional patterns, 23\nMachinery noise, 18, 21\nRudder operation, 48\nSearch mechanism, 33\nExFER42 mine; amplifier balance, 46\nDepth control, 57\nEcho identification, 54\nScanning system, 50\nSelf-noise level, 52\nSteering and searching system, 57\nExFF3 torpedo, 3, 18\nPN plastic charge, used for rudder control, 155\nExS13 mine, cavitation noise, 16\nExS29 torpedo, 20\nFairprene for acoustic isolation, 18\nFin cavitation, 13\nForce equations, hydrodynamic, 41\nFrequency characteristics of machinery\nFrequency dependence, torpedo self- noise, 9\nFrequency distribution of echo energy, G7e submarine torpedo, 139\nGas flow noise in pneumatic lines, 21\nGates in torpedo steering circuits; differential operated, 48, doppler operated, 85\nGear noise in torpedoes, 18\nGeier 1 torpedo control system, 138-139, differences, aircraft and submarine types, 143\nEvaluation of performance, 143, 157\nGeier 2 torpedo control system, 143-146\nGeneral Electric NO 181 system, 76-84\nGerman torpedo control systems, 138-139\nGlide angle control, ORL project 4 system,\nGyro course correction steering method, 57\nGyro lock-off, ORL project 4 system,\nHoming range of echo-ranging torpedoes; as function of self noise, 65\nFormulas, 64-66, maximum effective range, 56, of BTL 157C system, 120, of Geier control system, 138, 146.\nHoming torpedoes: disadvantages, 1-2, Hydrodynamics, torpedo, 37-45 coefficients, 41 constants for Mark 13 torpedo, equations of force, 41 Hydrophone mounting, 154 Hydrophones, torpedo; see also Transducers, echo-ranging British Trumper system, directivity patterns, 23, 65 effect of unbalance, 34 isolation, 23, 24 noise discrimination, 23-30 research recommendations, 59 termination and units, 63-66 Identification of echoes: using doppler effect, 54 using long signal, 54 using modulated signal, 54 using short signal, 53 using time variable gain, 55 Impedance of HUSL transducer element, Intensity units, acoustic, 63 Irrotational motion, def. 10 Lag line angle formula, 89 Laminated stack magnetostrictive transducer elements, 76, 86, 140 Level-operated switching gate, 47, 85- Limiter circuit, BTL 157C system, Listening torpedo control systems, 31-\ncountermeasures, 68\nLong signal method for echo identification, 54\nMachinery noise in torpedoes, 18-22\nDependence on torpedo speed, 26\nFrequency spectrum, 21\nHydrophone discrimination, 24, 30\nMagnetic homing, 5\nMagnetostrictive transducer elements,\nMark 9 torpedo, 149\nMark 13 torpedo; fin cavitation, 13, self noise, 8\nMark 13 torpedo with shroud ring, hydrodynamic constants, 43\nMark 20 torpedo, 159\nMark 26 torpedo, 20\nMaximum homing range; function of self noise, 66, of BTL 157C system, 121, of GE N0181 system, 76, of Geier control system, 139, 148\nMinerva Radio, Vienna, 138\nMines, acoustic homing; ExF42 mine, 46-57, ExFER42 mine, 46-57\nExS13 mine, 16\nMines, wake following; see Wake-following torpedoes and mines\nMinor lobes, defined, 64\nMoment coefficient, 41\nMomentum of torpedo, equation, 41\nMotor, counter-rotating field and armature type, 20\nMotor noise in torpedoes, 21\nMotor-operated rudders, 48\nMultivibrator-operated time-base, 91,\nNickel lamination transducers, 76, 86,\nNoise discrimination in hydrophones;\nagainst cavitation noise, 23, 24,\nagainst machinery noise, 24,\nagainst water background noise, 23,\nNoise discriminator; Geier 2 system,\nNoise reference level, defined, 63,\nNoise, torpedo, 7-30\ncavitation noise, 10-17\nmachinery noise, 18-22\nself noise, 7-9\ntotal noise, 25-30\nwater noise, 7, 23\nOgives, cavitation around, 13\n157B control system, BTL, 120-137\n157C control system, BTL, 120-137\nevaluation, 69, 156\nOrdnance Research Laboratory project\nOscillating motion of homing torpedo;\nconditions for, 40-45\ntendency in BTL 157C system,\nOwn-doppler correction, HUSL sys-\nPendel-Rose stabilized transducer assembly, 147\nPendulum type limiter for depth-steering control, 49\nPhase difference system for direction finding, 36\nPhase sensitive detectors; in British\nTrumper system, in ORL project 4, Piezo-electric crystal transducer, 121, Pilot channel system for amplifier balancing, 47, Power absorbed by hydrophone, band width effect, 63, Power limitations of torpedo transducers, 50, Preference circuit, BTL 157C system, Preferred side steering, 121, 130, 139, Pressure in sound field; as a function of electric power, 64, Units defined, 63, Project 4 system, ORL, 105-119, Projector, echo-ranging; see Transducers, echo-ranging, Propeller cavitation, 9, 12, caused by blade defects, 15, caused by vortexes, 11, Effect of propeller tip speed, 14*25, Hydrophone discrimination against, Propeller modulation of ship noise, 7, Propeller thrust coefficient, 41, Propeller vibration noise, 22, Pulse shape, Geier system, 143, Pulse shaping circuits; ORL project 4 system, 108, Quartz sandwich type transducers, 149, Radiation resistance; definition, 64.\nValue for water: 64\nRadio controlled torpedoes: 5\nRange, homing, of echo-ranging torpedoes; formulas: 64-66\nFunction of self noise: 65\nOf BTL 157C system: 120\nOf Geier control system: 138, 146\nRange of target, effect on echo strength,\nRange reduction circuit, GE NO 181 system: 83\nReceiver amplifiers, BTL 157C system,\nReceivers, doppler-enabling; HUSL ORL project 4 system: 112\nReceivers, echo-ranging; British Dealer system: 104\nGE NO 181 system: 80\nGeier 1 system: 141\nGeneral design considerations: 70\nReceivers, steering; British Trumper system: 150\nORL project 4 system: 108\nRecommendations for further research:\nDepth steering: 49\nHydrophone studies: 59\nReduction of hydrophone water noise: 21\nSelf noise studies: 58\nTactical use of homing torpedoes,\nVariable speed torpedo: 6\nRelaxation time of torpedo body: 74\nRelay control circuits; British Trumper system: 152\nORL project 4 system, relays in echo-ranging control system, see also Gates\nReverberation discrimination, 53-55\nRudder control, torpedo; see also Steering control\nautomatic reversal, 116\nequation of motion, 74\nmotor-operated, 48\nsolenoid operated, 49\nusing explosive charge, 155\nRudder torque constant, torpedo, 37-\nSalvo firing with echo-ranging torpedoes, 68\nScanning system, echo-ranging projector, 50\nSearch mechanisms; British dealer system, depth behavior, 72\nExF42 mine, 33\nExFER42 mine combined steering and search system, 57\nHUSL N0181 system, 102\nORL project 4 system, 105\nSelf noise, torpedo, 6, 7-30, 65; dependence on depth, 28, 159; dependence on speed, 8, 28\nexperimental analysis, 16\nfrequency dependence, 9\nMark 18 torpedo, ORL system, measurement by external hydrophones, measurement by self hydrophones, research recommendations, 58\nSelsyn, proposed use in control systems.\nSensitivity of hydrophone, definition, Servo systems; see Steering control Short signal method for echo identification, 53 Signal generator limitations, torpedo, Signal level requirements in torpedo echo-ranging, 50-52 Solenoid-operated rudders, 49 Sound pressure, units defined, 63 Spectrum level of acoustic energy, formula, 51 Sphere, cavitation about, 11 Sphere, equivalent to target, formula, Spin tendency of torpedoes, 49 Stability, torpedo, 37-45, 49 Steering control, mathematical analysis, Steering control for echo ranging torpedoes; British Bowler system, British Dealer system, 104 British Trumper system, 152 BTL 157C system, 132 circuit arrangement in torpedo afterbody, 117 collision course steering, 152 ExFER42 mine method, 57 Geier 1 system, 138 Geier 2 system, 144 General design considerations, 49-57, Gyro course correction method, 57 Preferred side steering, 121, 130, 144-145\nsymmetrical steering, 144, 139, 146-148\nvertical steering, 39, 49, 72-75\nsteering control for listening torpedoes, intensity difference method, 31-36, phase difference method, 36\nstiffness of control, torpedo steering mechanism, 37-45\nsubmarine launched torpedoes, control systems; British Trumper system, 149, BTL 157C system, 120, Geier 1 system, 138-148\nsurface ship launched torpedoes, control systems; general design considerations, 66, 72\nswitching circuit, transmitter receiver,\nswitching method for amplifier balancing,\ntactical use of homing torpedoes, recommendations, 58-59\ntarget location system for listening torpedo, 31-36\ntarget noise, effect on useful range, 51\ntarget range, see Homing range of echo ranging torpedoes\ntarget strength formulas, 51, 65\nthreshold circuit, BTL 157C system,\ntime base for echo-ranging systems; British Dealer system, 104\nBTL 157C system, 122 cam-operated switches, 70, 78, 106 electronic, 70 general design considerations\nHUSL N0181 system, 91 multivibrator operated, 91, 123\nORL project 4 system, 106, 117\nTime lag in acoustic control systems, 127 in GE NO 181 system, 80 in ORL project 4 system, 109\nuse in echo-ranging receivers, 55, 6 Torpedoes, acoustic homing; see also Mines, acoustic homing\nEx S29 torpedo, 20 57C submarine torpedo, 139 limitations, 6\nMark 9 torpedo, 149 Mark 20 torpedo, 159 Mark 26 torpedo, 20\nTorpedoes, control systems; see Aircraft launched torpedoes, control systems, Antisubmarine torpedo control systems, Anti-surface-ship torpedo control systems\nTorque due to torpedo propeller, 18 Trajectory of torpedo, analysis equations of motion, 37-45, 74\nTransducer, directivity index, defined Transducer assembly, stabilized, 147\nTransducer axis defined, 64 transducer elements, laminated stack magnetostrictive, 76, 85, 140 piezoelectric crystal, 121, 149 Quartz sandwich type transducer mounting, British Bowler system, 154 Transducers, echo-ranging; see also Hydrophones, torpedo British Dealer System, 104 British Trumper System, 149 BTL 157C System, 121 Geier system, 140 general design considerations, 50-52 ORL project 4 system, 106 Transmitter circuits, echo-ranging; British Bowler system, 154 British Trumper system, 149 BTL 175C system, 124 Geier 1 system, 141 General design considerations, 160 HUSL N0181 system, 91 ORL project 4 system, 106 Transmitter-receiver switching circuit, BTL 157C system, 125 Trigger circuit, BTL 157C system Trumper system, British, 149-153 Turning radius of torpedo effect on homing range, 56 Universal torpedo, proposed, 6 Variable-speed torpedo, proposed, 6\n[Vertical steering control, analysis, British dealer system, ExFER 42 mine, 57, general design considerations, HUSL N0181 system, 103, restricted to 250 yd. range, Vertical steering relay, ORL project 4 system, 115, Vortex cavitation, Vortex pressures, Wake avoiding steering system, 121, Wake following torpedoes and mines, Water conditions affecting homing torpedoes; effect of turbulent surface layer, 21, effect of depth steering, 49, water background noise, 7, 23, 25, Zero spectrum sound level, def.]", "source_dataset": "Internet_Archive", "source_dataset_detailed": "Internet_Archive_LibOfCong"},
{"language": "eng", "scanningcenter": "capitolhill", "contributor": "The Library of Congress", "date": "1946", "subject": ["Fire control (Aerial gunnery)", "Military research", "Military research -- United States", "United States"], "title": "Airborne fire control", "creator": ["Bush, Vannevar, 1890-1974", "Conant, James Bryant, 1893-1978", "Hazen, Harold L. (Harold Locke), 1901-1980", "United States. Office of Scientific Research and Development. National Defense Research Committee. Division 7, issuing body", "Columbia University. Division of War Research. Summary Reports Group, organizer"], "lccn": "2015460882", "collection": ["library_of_congress", "americana"], "shiptracking": "ST005578", "call_number": "18881268", "identifier_bib": "00219228934", "boxid": "00219228934", "volume": "3", "possible-copyright-status": "The Library of Congress is unaware of any copyright restrictions for this item.", "description": ["Title on half title page: Summary technical report of the National Defense Research Committee", "In a set of declassified documents held as a collection by the Library of Congress", "\"Manuscript and illustrations for this volume were prepared for publication by the Summary Reports Group of the Columbia University Division of War Research under contract OEMsr-1131 with the Office of Scientific Research and Development. This volume was printed and bound by the Columbia University Press\"--Unnumbered page ii", "LC Science, Business & Technology copy no. 238", "Includes bibliographical references (pages 233-243) and index", "ix, 248 pages : 28 cm"], "mediatype": "texts", "repub_state": "4", "page-progression": "lr", "publicdate": "2016-04-13 14:50:52", "updatedate": "2016-04-13 15:56:23", "updater": "associate-mike-saelee@archive.org", "identifier": "airbornefirecont03bush", "uploader": "associate-mike-saelee@archive.org", "addeddate": "2016-04-13 15:56:25", "scanner": "scribe3.capitolhill.archive.org", "operator": "associate-mike-saelee@archive.org", "imagecount": "270", "scandate": "20160512193553", "ppi": "300", "foldoutcount": "0", "identifier-access": "http://archive.org/details/airbornefirecont03bush", "identifier-ark": "ark:/13960/t2x39g68h", "scanfee": "100", "invoice": "1263", "sponsordate": "20160531", "backup_location": "ia906105_26", "fadgi": "true", "republisher_operator": "associate-mike-saelee@archive.org", "republisher_date": "20160516074002", "republisher_time": "563", "external-identifier": "urn:oclc:record:1038732672", "publisher": "Washington, D.C. : Office of Scientific Research and Development, National Defense Research Committee, Division 7", "oclc-id": "82786743", "associated-names": "Bush, Vannevar, 1890-1974; Conant, James Bryant, 1893-1978; Hazen, Harold L. (Harold Locke), 1901-1980; United States. Office of Scientific Research and Development. National Defense Research Committee. Division 7, issuing body; Columbia University. Division of War Research. Summary Reports Group, organizer", "ocr_module_version": "0.0.21", "ocr_converted": "abbyy-to-hocr 1.1.37", "page_number_confidence": "95", "page_number_module_version": "1.0.3", "creation_year": 1946, "content": "[PECLASSiriBD by aiitliwity Swntary, Oefenae memo, 2 August 1960\nSUMMARY TECHNICAL REPORT OF THE NATIONAL DEFENSE RESEARCH COMMITTEE\nThis document contains information affecting the national defense of the United States within the meaning of the Espionage Act, 50 U.S.C., 31 and 32, as amended. Its transmission or the revelation of its contents to an unauthorized person is prohibited by law.\nThis volume is classified in accordance with security regulations of the War and Navy agencies because certain chapters contain material which was classified at the date of printing. Other chapters may have had restricted or no classification. The reader is advised to consult the War and Navy agencies listed on the reverse page for the current classification of any material.\nManuscript and illustrations for this volume were prepared]\nfor  publication  by  the  Summary  Reports  Group  of  the \nColumbia  University  Division  of  War  Research  under  con- \ntract OEMsr-1131  with  the  Office  of  Scientific  Research  and \nDevelopment.  This  volume  was  printed  and  bound  by  the \nColumbia  University  Press. \nDistribution  of  the  Summary  Technical  Report  of  NDRC \nhas  been  made  by  the  War  and  Navy  Departments.  Inquiries \nconcerning  the  availability  and  distribution  of  the  Summary \nTechnical  Report  volumes  and  microfilmed  and  other  refer- \nence material  should  be  addressed  to  the  War  Department \nLibrary,  Room  lA-522,  The  Pentagon,  Washington  25,  D.  C., \nor  to  the  Office  of  Naval  Research,  Navy  Department,  Atten- \ntion : Reports  and  Documents  Section,  Washington  25,  D.  C. \nCopy  No. \nThis  volume,  like  the  seventy  others  of  the  Summary  Tech- \nnical Report  of  NDRC,  has  been  written,  edited,  and  printed \nSUMMARY TECHNICAL REPORT OF DIVISION 7, NDRC\nVOLUME 3\nAIRBORNE FIRE CONTROL\nBy authority of Secretary of Defense\nDefense memo 2 August 1960\nLibrary of Congress\nOFFICE OF SCIENTIFIC RESEARCH AND DEVELOPMENT\nVannevar Bush, Director\nNATIONAL DEFENSE RESEARCH COMMITTEE\nJames B. Conant, Chairman\nDECLASSIFIED\nPlease report errors to:\nJoint Research and Development Board\nPrograms Division (STR Errata)\nWashington 25, D.C.\nA master errata sheet will be compiled from these reports and sent to recipients of the volume. Your help will make this book more useful to other readers and will be of great value in preparing any revisions.\nH. L. Hazen, Chief\nWashington, D.C., 1946\nNational Defense Research Committee\nJames B. Conant, Chairman\nRichard C. Tolman, Vice Chairman\nRoger Adams, Army Representative\nFrank B. Jewett, Navy Representative\nKarl T. Compton, Commissioner of Patents\nIrvin Stewart, Executive Secretary\nMaj. Gen. G. V. Strong, Col. L. A. Denson, Maj. Gen. R. C. Moore, Col. P. R. Faymonville, Maj. Gen. C. C. Williams, Brig. Gen. E. A. Regnier, Brig. Gen. W. A. Wood, Jr., Col. M. M. Irvine, Col. E. A. Routheau\n- Army Representatives in order of service:\n- Navy Representatives in order of service:\nRear Adm. H. G. Bowen, Rear Adm. J. A. Purer, Capt. Lybrand P. Smith, Rear Adm. A. H. Van Keuren, Commodore H. A. Schade\n- Commissioners of Patents in order of service:\nConway P. Coe, Casper W. Corns\n\nDuties of the National Defense Research Committee\nThe NDRC's role was to recommend suitable projects and research programs on instrumentalities of warfare, along with contract facilities for carrying out these projects and programs. Specifically, NDRC initiated research projects on requests from the Army or Navy, or from allied governments through the Liaison Office of OSRD, or on its own initiative. Proposals for research contracts for the performance of the work involved in these projects were first reviewed by NDRC, and if approved, recommended to the Director of OSRD. Upon approval of a proposal by the Director, a contract permit-ted the execution of the research.\nThe maximum flexibility of scientific effort was arranged. The business aspects of the contract, including matters such as materials, clearances, vouchers, patents, priorities, legal matters, and administration of patent matters were handled by the Executive Secretary of OSRD. Originally, NDRC administered its work through five divisions: Division A \u2013 Armor and Ordnance; Division B \u2013 Bombs, Fuels, Gases, & Chemical Problems; Division C \u2013 Communication and Transportation; Division D \u2013 Detection, Controls, and Instruments; Division E \u2013 Patents and Inventions. In a reorganization in the fall of 1942, twenty-three administrative divisions, panels, or committees were created, each with a chief selected on the basis of his outstanding work in the particular field. The NDRC members then became a reviewing and advisory group to the new administrative structure.\nDirector of OSRD. The final organization was as follows:\n\nDivision 1 \u2014 Ballistic Research\nDivision 2 \u2014 Effects of Impact and Explosion\nDivision 3 \u2014 Rocket Ordnance\nDivision 4 \u2014 Ordnance Accessories\nDivision 5 \u2014 New Missiles\nDivision 6 \u2014 Sub-Surface Warfare\nDivision 7 \u2014 Fire Control\nDivision 8 \u2014 Explosives\nDivision 9 \u2014 Chemistry\nDivision 10 \u2014 Absorbents and Aerosols\nDivision 11 \u2014 Chemical Engineering\nDivision 12 \u2014 Transportation\nDivision 13 \u2014 Electrical Communication\nDivision 14 \u2014 Radar\nDivision 15 \u2014 Radio Coordination\nDivision 16 \u2014 Optics and Camouflage\nDivision 17 \u2014 Physics\nDivision 18 \u2014 War Metallurgy\nDivision 19 \u2014 Miscellaneous\nApplied Mathematics Panel\nApplied Psychology Panel\nCommittee on Propagation\nTropical Deterioration Administrative Committee\n\nNDRC Foreword\n\nAs events of the years preceding 1940 revealed more and more clearly the seriousness of the world situation.\nMany scientists in this country recognized the need to organize scientific research for national service during an emergency. Their recommendations to the White House received careful and sympathetic attention, resulting in the formation of the National Defense Research Committee (NDRC) by executive order of the President in the summer of 1940. NDRC members, appointed by the President, were instructed to supplement the work of the Army and Navy in the development of war instrumentalities. A year later, upon the establishment of the Office of Scientific Research and Development (OSRD), NDRC became one of its units. The Summary Technical Report of NDRC is a conscientious effort to summarize and evaluate its work and present it in a useful and permanent form. It comprises some seventy reports.\nVolumes are broken into groups corresponding to the NDRC Divisions, Panels, and Committees. The Summary Technical Report of each Division, Panel, or Committee is an integral survey of the work of that group. The first volume of each group\u2019s report contains a summary of the report, stating the problems presented and the philosophy of attacking them, and summarizing the results of the research, development, and training activities undertaken. Some volumes may be \u201cstate of the art\u201d treatises covering subjects to which various research groups have contributed information. Others may contain descriptions of devices developed in the laboratories. A master index of all these divisional, panel, and committee reports which together constitute the Summary Technical Report of NDRC is contained in a separate volume. This volume also includes the index of a microfilm record of the reports.\nSome declassified NDRC-sponsored research of sufficient popular interest were reported in monographs, such as the series on radar by Division 14 and the monograph on sampling inspection by the Applied Mathematics Panel. The material treated in them is not duplicated in the Summary Technical Report of NDRC, making the monographs an important part of the story of these aspects of NDRC research.\n\nIn contrast, research on subsurface warfare is largely classified and of general interest to a restricted group. As a result, Division 6's report is found almost entirely in its Summary.\nThe Technical Report of the Fire Control Division, which spans over twenty volumes, should not be judged solely based on the number of volumes dedicated to it in the Summary Technical Report of NDRC. Account must be taken of monographs and reports published elsewhere. The Fire Control Division, initially Section D2 under Warren Weaver's leadership and later Division 7 under Harold L. Hazen, made a significant contribution to an already highly developed art. It marked the entrance of the civilian scientist into what had hitherto been regarded as a military specialty. One of the tasks of the Division was to explore and solve the intricate problems of control of fire against modern military aircraft. Gunnery against high-speed aircraft involves fire control in three dimensions. The need for lightning action and superlative accuracy is essential.\nThe Division's accurately produced results rendered mere human skills obsolete. The Division developed the electronic M-9 director, controlling the fire of the Army's heavy AA guns, which proved valuable in defending the Anzio Beachhead and protecting London and Antwerp against Nazi V-weapons. In addition to creating mechanisms like the M-9, the Division made less tangible but equally significant contributions through the application of research methods that had a profound, even revolutionary, influence on fire control theory and practice.\n\nThe results of Division 7's work, formerly Section D2, are detailed in its Summary Technical Report. Prepared at the direction of the Division Chief and authorized for publication, it is a record of creativity and dedication.\nVolume 3 of Division 7, the Summary Technical Report of Section 7.2, NDRC, consists of three parts. In Part I on aiming controls in aerial ordnance, G. A. Philbrick discusses the work of the Section in all fields except gunnery and the assessment of gunnery devices. A. L. Ruiz contributes Part II, which covers developments in aerial torpedo directors since those in which Mr. Philbrick participated. The third principal part of the report is on aerial gunnery and assessment, written by J. B. Russell.\nIt is fortunate that a large part of this work could be written by one individual, providing unity of treatment otherwise difficult to obtain. In assuming responsibility for his part of the Summary Technical Report, Mr. Philbrick took on a heavy task and discharged it with zeal. Although a more conventional report would have fulfilled all requirements, Mr. Philbrick served his reader a tasty dish of skilled technical exposition. We can ask for no more.\n\nIn general, Professor Russell's contribution stresses the instrumental features of aerial gunnery and relies on Dr. Paxson's writing in Volume 2 of the Summary Technical Report of the Applied Mathematics Panel for the basic mathematical substance of the subject. Professor Russell brings to his work the expertise of an accomplished scholar.\ntreatment: continuous experience in the field dating from before Pearl Harbor. He has participated in all of its growth, first as a Technical Aide in Section 7.2, and during the closing months of the war as an Expert Consultant to the Secretary of War.\n\nH. L. Hazen\nChief, Division 7\nS. H. Caldwell\nChief, Section 7.2\nSIS\n\nCONTENTS\nCHAPTER I\nPART I\n\nAIMING CONTROLS IN AERIAL ORDNANCE\nBy G. A. Philbrick\n\n1. General Theory of Aiming Processes ...\n2. On Certain Aspects of Tracking ...\n3. Technology of Rotation in Space ...\n4. Simulation as an Aid in Development ...\n5. Linkages for Computation and Manipulation ...\n6. Aiming of Torpedoes from Airplanes ...\n7. Aiming of Bombs from Airplanes\n8. Control of Guided Bombs\n9. Aiming of Rockets from Airplanes ...\n10. Integrated Equipment for the Pilot ...\n\nPART II\nAERIAL TORPEDO DIRECTORS\nBy A. L. Ruiz.\nPART I: AIMING CONTROLS IN AERIAL ORDNANCE by G. A. Philbrick\n\nCONFIDENTIAL\n\nPREFATORY COMMENTS\n\nDuring the past three and a half years, I have served as technical aide to S. H. Caldwell, Chief of Section 7.2. This section has been charged with airborne developments within the more general fire control framework of Division 7 of National Defense.\n\nPART III: AERIAL GUNNERY by J. B. Russell\n\nCONFIDENTIAL\n\nPREFATORY COMMENTS\n\n14 General Survey of Aerial Gunnery ... 179\n15 General Principles 185\n16 Local Control Systems 192\n17 Remote-Control Systems 198\n18 Tracking and Ranging 204\n19 Simulation and Gunnery Assessment ... 209\n20 Discussion on Future Work 214\n\nAppendix \nGlossary 231\nBibliography 233\nResearch  Committee  [NDRC].  By  delegation \nfrom  the  section  chief,  the  writer  has  shared, \nwith  other  technical  aides  and  section  members, \nseveral  domains  of  responsibility  in  the  conduct \nof  research  and  development  on  airborne  fire \ncontrols.  The  initiation  for  such  work  in  typi- \ncal cases  occurs  through  a request  by  Army  or \nNavy  to  Office  of  Scientific  Research  and  De- \nvelopment [OSRD]  for  a particular  study  of \ndevelopment ; following  acceptance  by  the  latter \norganization,  which  is  made  through  agree- \nments of  the  relevant  section  and  division  of \nNDRC,  a program  is  laid  out  and  presented  as \nspecification  for  a project  to  the  appropriate \ncontractor.  Guidance  of  this  project  through \nthe  stages  of  theory  or  experiment,  design  or \ntest,  and  the  maintenance  of  liaison  with  the \nsame  agencies  concerned,  constitute  functions \nof  the  NDRC  section.  Such  duties  have  in  turn \nThe writer, as an operative involved in the technical phases of a project, discusses the following pages, which are restricted to branches of air-borne fire control with which they have personal experience. These branches, while not all-inclusive, are considered pervasive enough to justify the report's title. The subject matter revolves around the development of computors and computing sights for aerial torpedoing, bombing, and aerial rocketry. A final attempt is made to combine these developments.\nall of these functions with that of fixed gunnery for the fighter airplane. The most impressive omission is that of flexible gunnery. Although I have been exposed to and gained familiarity with the equipment and developmental procedures in this branch, I have had little or no tangible responsibility there. Another characterization of the present material refers to the nature of the reported researches and reflects the corresponding activities of the writer. The latter has been substantially a creature of laboratories, operating for the most part between theory and design. His contacts with the using Services have usually been with respect to a particular equipment under development, and his involvement with proving organizations and with aerial firing tests has been for the specific purpose of.\nThe text focuses on gaining knowledge of the properties of one device rather than a larger category. This approach stresses the morphology of local apparatus from an instrumental standpoint, as opposed to a broader survey of available ordnance or presentation of assessment techniques. The flavor is dynamical rather than statistical, constructional rather than evaluational, instrumental rather than logistic, and physical rather than administrative. This does not indicate any absolute preference or desirability, but simply identifies the aspect of the material to be treated, acknowledging that it stems naturally from the writer's own predilections and propensities, regardless of their importance.\n\nFollowing is the description of the successive aspects of the device.\nDevelopmental forms of various computing devices and controls receive considerable space in this text, with specific tools of research given prominence where they represent advances in instrument development or design. For instance, the use of increasingly comprehensive electronic model structures is believed to bridge enormous gaps between theory and concrete facilities. These model structures, capable of cooperating with real human operators and incorporating discontinuities against which analysis is largely impotent, bring realism to the laboratory and shorten the interval to optimum dynamics. The need for such models is equally great, if not greater, with completely automatic assemblages.\nAs concerns weapons, we are here focused on the airplane, the projectile, and the man at the firing-key, the entire group functioning as a unit. The airplane types primarily include the fighter, fighter-bomber, and bomber. The projectiles are the bomb, guided bomb, rocket, torpedo, and bullet or shell, in roughly that order of concern. A typical aiming control, or computing sight, involves a group of input variables, which may be either manually or automatically introduced, a computer, and a presentation-component or sight whereby the aiming process is reduced to some sort of null between an index and the target. Automatic firing may be involved, either permanently or at the operator's choice.\n\nIt is difficult to confidently predict the shape of fire controls for the future, at least from the present standpoint. The trend toward more automation is evident.\nThoroughgoing automaticity is evident, with the operator's task becoming increasingly supervisory and eclectic. At this level, the distinctions between offense and defense, and even between strategy and tactics, are so interwoven with other relationships as to be almost nonexistent. We shall not presume to speak of these. While the rocket and guided bomb, along with their logical combinations, are outstandingly weapons of great future significance, the bomb, bullet, and shell are simple structures which should not be ignored. As to superexplosives, with potentially a million times greater payload ratio, the need for fire control should not decrease any more than between flintlock and main battery. While the appearance and character of weapons may suffer revolutionary changes, in whatever era, with the science even in its infancy, the fundamental principles of fire control remain constant.\nOf orbital underwater trajectories being replaced, for example, by those of underground trajectories, it will still be essential to direct and deliver fire in the vicinity of the target. Of the homing and automatic interception missiles on whose protection survival may depend, and which ultimately may truly battle among themselves, those with the more recondite controls will triumph along with their masters.\n\nColleagues\n\nIn view of the apparent virtuosity of this report, the framework of personnel within which the writer has operated deserves particular comment. Both categorical and special, the people among whom the progress herein reported has taken place have made it what it is.\n\nThe staff of NDRC Section 7.2, with chief, members, and fellow technical aides, has been closest of all to these operations and knows most about them. Thus are listed: S. H. Caldwell\nJ. B. Russell, A. L. Ruiz, H. C. Wolfe, C. G. Holschuh, W. A. MacNair, E. G. Pickels, E. W. Paxson, A. F. Sise, and R. M. Peters were colleagues of the writer in the field of airborne fire control. Knowledge of other branches and a more complete understanding of those treated herein can be found among these gentlemen. R. M. Peters, as technical aide in Section 7.2, assisted the writer materially in every phase of progress and is credited with any significant mathematics in the present report. The remainder of Division 7, with H. L. Hazen as chief and K. L. Wildes as divisional technical aide, and the adjacent section.\nChiefs: D. J. Stewart, E. J. Poitras, and I. A. Getting have served in all connections as guide-post and beacon. Considerable and appreciated interchange has been enjoyed with such members and technical aides of adjacent sections as G. R. Stibitz, L. M. McKenzie, and J. F. Taplin. Of other divisions of NDRC with which developmental business has been conducted, Division 5 should be mentioned especially. Control apparatus for new missiles has been dealt with in this relationship, both through an arranged collaboration between the two divisions, and by the writer as an officially appointed consultant to Division 5 itself. Constructive and informative intercourse has taken place with H. H. Spencer, Chief, Division 5, as well as with J. C. Boyce, L. O. Grondahl, P. Mertz, and E. W. Phelan, among others. Further relations have been important with: H. H. Spencer (Chief, Division 5), J. C. Boyce, L. O. Grondahl, P. Mertz, and E. W. Phelan.\nDivision 3 (F. L. Hovde) on rockets, Division 4 (A. Ellett) on toss bombing, Division 6 on antisubmarine warfare, Division 14 on radar and Section 16.1 (T. Dunham Jr.) on optical instruments. Valuable personal contact on professional matters has been possible also with W. Weaver, T. C. Fry, J. D. Williams, M. S. Rees, and others of the Applied Mathematics Panel. Among other groups which cannot be mentioned in entirety are the administrative and engineering staffs of OSRD and NDRC, both central and local.\n\nA detailed accounting of the Service agencies and personnel which have been directly concerned with these efforts would be all out of order in the present location. Such agencies and personnel will appear, however, in reference to the project chronologies in the main body of the report. Relations with the Services\nThe writer's experiences have been predominantly pleasant and positive. Interactions have been mainly with the Navy, specifically the Bureau of Ordnance, and within BuOrd with the aircraft fire control sections: Re4 (Re4d), Re8 (Re8c). Extensive affairs have also been enjoyed with NAS Norfolk, NAF Philadelphia, NAS Squantum, NAS Quonset, NOTS Inyokern, NOP Indianapolis, and various special devices depots, among several branches. The Navy projects the writer has been engaged with and reported upon include NO-106 (torpedo director: now TD Mark 32), NO-129 (antisubmarine bombsight: now BS Mark 20), NO-180 (maneuverable bombing target), NO-190 (blimp bombsight: now Mark 24), NO-191 (bombsight presetting computer), NO-216 (rocket sights: now RS Mark 2 and RS Mark 3, and computers Mark 35 and Mark\nAN-4 (low altitude bombsight, now BS Mark 23), NA-168 (slant range computer), NO-242 (range-type torpedo director), NA-232 (Razon attachment for TA3 trainer), and NO-265 (pilot's universal sighting systems: now AFCS Mark 3). We have dealt most directly with the armament laboratory (ATSC) at Wright Field, as well as Langley Field, Foster and Matagorda Fighter Fields, Dover Air Base, and other installations. The Army projects have been AN-4 (low altitude bombsights), AC-36 (CRAB guided bombsight), and AC-121 (rocket sights). For both Services, a good deal of work, both concrete and advisory in nature, has been done under no official project whatsoever. In connection with projects related to those for which control numbers had been assigned to us, the writer was requested by BuOrd of the Navy to advise.\nContractors:\n\nThe writer has had most experience with contract (OEMsr-330) at The Franklin Institute in Philadelphia, where a major portion of the section's airborne fire control developments have been conducted. The research group here has been built, with considerable assistance and molding by the section, from a nucleus of four engineers to a staff of several score technical personnel, augmented somewhat by the staffs and facilities of several subcontractors. Instances include Specialties, Inc., at Syosset, New York, and Polaroid Corporation in Cambridge, Massachusetts.\n\nIn general, all organized technical pursuits under NDRC direction are set up through the facilities of such contractors. The writer has had most to do with the contract at The Franklin Institute, where the section's airborne fire control developments have been conducted. The research group here has grown, with significant help and guidance from the section, from an initial team of four engineers to a staff of over fifty technical personnel, supplemented by the staffs and resources of several subcontractors. Examples include Specialties, Inc., in Syosset, New York, and Polaroid Corporation in Cambridge, Massachusetts.\nLaboratory, office, and drafting space have been prepared and occupied gradually as needed. Sharing such facilities as experimental, computing, drafting, and model shop, the project staff blossomed horizontally into groups devoted to torpedoing, bombing, gunnery, rocketry, and integrated equipments. The heads of these groups reported to the coordinator, R. H. McClarren, who provided technical policy and project planning guidance. A steering committee was formed early in the contract's history, with McClarren serving as non-voting secretary. The committee members included S. H. Caldwell (ex officio), A. L. Ruiz, H. C. Wolfe, E. G. Pickels, and J. B. Russell.\nThe writer, as chairman, was responsible for specific development projects in addition to his role. In connection with a contract by the Stanolind Corporation in Tulsa, Oklahoma for Section 7.2, the writer oversaw the development of a mechanical pursuit-collision course plotter proposed by M. Alkan of Specialties, Inc., to assist in Navy dive bombsight design. Principal contact at Stanolind was D. Silman. Through a contract with Columbia University at the Marcellus Hartley Laboratory, the writer also worked on unspecified projects.\nSection conducted electronic projects under J. A. Balmford and J. R. Ragazzini. The work largely served and supplemented projects in progress at The Franklin Institute, covering servomechanism developments and simulative endeavors. Additionally, electronic simulative studies were conducted on steered projectiles for projects being pursued by Section 7.2 in collaboration with Division 5. This branch of the contract was taken under the direct sponsorship of Division 5 in the summer of 1945 and was placed within a contract with Specialties, Inc. The reader is referred to Chapters 4 and 8. The Bristol Co. also contributed to research at The Franklin Institute, with the services of C. A. Mabey, A. W. Jacobson, and G. M.\nThynell has aided in the preparation of special mechanical linkages for components of computing sights under development. The writer had less to do with the other contracts of the section, which include those at General Electric on B-29 computers, at Northwestern University on assessment methods, at the University of Texas on gunnery evaluation, and at Jam Handy Corporation on vector sights, etc. With several of the other contractors of Division 7, highly beneficial cooperation has been indulged in on projects of mutual interest. Through the provision, by Section 7.3 for example, of certain facilities of Lawrence Aeronautical Corporation, Linden, New Jersey, the design of pneumatic components has been greatly furthered on our Navy projects. Facilities also of Eastman Laboratories in Rochester have similarly been made available.\nThe stewardship and incentive of E. J. Poitras and J. F. Taplin of Section 7.3. An earlier example of such collaborative effort on pneumatic instrumentation, which resulted ultimately in bombsight Mark 23, involved the McMath-Hulburt Observatory at Lake Angelus, Michigan. Too numerous for exhaustive tabulation are the contractors of NDRC divisions other than Division 7. However, the Radiation Laboratory at the Massachusetts Institute of Technology (MIT) must be mentioned as being involved in several connections, particularly with the provision of automatic plane-to-plane and plane-to-ground ranging equipment. Tangible help on a variety of problems has been received from many of the staff there. We mention also the California Institute of Technology, under Division 3, in connection with rockets, where C. C. Lauritsen and W. A. contributed.\nC. G. Fowler, Anderson, and others have rendered assistance. With the portion of the Bureau of Standards under Division 4, we have dealt profitably with W. B. McLean on toss-bombing studies. The contractors of Division 5 have been concerned, both through interdivisional collaborative arrangement, and by the writer directly as consultant to that division; these dealings are reported jointly since separation is not feasible. Such contractors include:\n\nGulf Research and Development Co. in Pittsburgh, where we have cooperated on guided bomb controls with E. A. Eckhardt, R. D. Wyckoff, and J. P. Molnar among others; RCA Laboratories (Zworykin) at Princeton in connection with television for homing bombs; Douglas Aircraft in Santa Monica, where W. B. Klemperer, E. W. Wheaton, and many others were extensively cultivated with regard to this matter.\n\n(DXFTDKXTIAj)\n\nFORM AND REFERENCES\nThe ROKH projectile in its several phases was worked on by L. N. Schwien Engineering Co. in Los Angeles, with L. N. Schwien and H. A. VanDyke focusing on stabilization and other control techniques. Bendix Pacific Division in Hollywood contributed with W. S. Leitch on radio links. The Applied Mathematics Group at Columbia, under contract to the Applied Mathematics Panel (AMP) of NDRC, provided incalculable aid and was worked with closely on several fire-control projects. Notable members included S. MacLane (Director), H. Whitney, H. Pollard (the two latter having had local office headquarters in the writer's office in Cambridge), I. Kaplansky, L. C. Hutchinson, and D. P. Ling. Operations that valiantly served were rocket sights, toss-bombing equipment, and pilot\u2019s universal sighting systems, relating to Service projects.\nNO-216 and NO-265, as well as certain other groups under AMP, were useful, though their connections were less major in the context of research on controls for guided bombs. The differential analyzer at MIT was made available for an extensive study of controlled trajectories in two and three dimensions in relation to this research. Initially accessed through the contractual mechanisms of Division 7, and later through those of Division 5, this facility enabled a clear numerical treatment of a problem that could not have been handled otherwise without years of computation by a large, expertly led staff. The staff of this analyzer, along with that of the Center of Analysis itself at MIT, made significant contributions to this work. Whenever the writer refers to \u201cour laboratories\u201d in the present report, this should be interpreted as a figurative expression.\nThe laboratories of The Franklin Institute and Columbia, referred to here, are likely those with a long history and significant contributions to research. The possessive pronoun is a consequence of their role in building and organizing these facilities.\n\nForm and References\n\nI chose the monographic form for this report, with its set of sub-monographs on separate techniques and fields of endeavor, due to my personal preference for a unified literary entity. It should be possible to separate, discard, or reassemble the various parts as desired to meet larger needs. No details are reproduced in full that are available elsewhere, although brief outlines are provided.\nA fuller material may be included in reference to related topics. The writer's own contributions, in theoretical branches or concrete mechanism, may be found discussed with an apparently unwarranted emphasis. In such cases, the reason for such treatment is that documentation of these items is not likely to be found at other sources, or may only be baldly referred to.\n\nA serious attempt is made to give proper credit and make equitable references to original enunciations and reductions to practice. If this is imperfectly achieved, it is without malice. Contractor's reports are referred to liberally, but a more thorough search of these is indicated for the details of any given aspect which may later become significant. Writings of such collaborating mathematicians as H. Whitney and H. Pollard (of AMG-C) are voluminous.\nChapter 1: General Theory of Aiming Processes Scope and Limitations\n\nTo the present chapter, we have relegated as much as possible the general and theoretical background relevant to the rest of the report. Here, we introduce an account of the mathematical scaffolding typically employed, as well as physical and dynamical principles upon which numerous aiming devices rest. The presentation is elementary, as are the principles themselves. This service will hereby be afforded in characterizing both the mode of approach to problems and the sort of description.\n\nMethods and components essential to aiming processes are documented in ominous and frequently obtained records, contrasting with our compulsions to disseminate.\n\nChapter 1: General Theory of Aiming Processes Scope and Limitations\n\nIn this chapter, we have attempted to limit the discussion of the general and theoretical background relevant to the rest of the report as much as possible. We present an account of the mathematical framework and physical and dynamical principles underlying various aiming devices. The presentation is elementary, as both the principles and their application are fundamental to understanding the subject matter. By providing this information, we aim to clarify the approach to problems and the nature of the descriptions that follow.\n\nHistorical records detailing crucial methods and components for aiming processes are often obscured, as we have been eager to experiment and build, contrasting with our duty to share this knowledge.\nThe various branches of fire control share a significant common technical foundation. Although this is not surprising, it is impressive to workers as they shift their attention from one field to another, regardless of their experience or philosophy. The realm of statistics and probability is not strictly included in these remarks, as it is of broader significance. This realm, although inseparable from the theory and instrumental techniques of the subject of this report and serving it in all phases when applied in the economy of effort and concentration of effectiveness, is entered into here only to a minor degree. Being treated more completely and competently elsewhere.\nAnd applying more, for example, in the larger senses of assessment, the methods and accomplishments of statistics are substantially omitted from these pages. Thus, even in the development of automatic mechanisms, what is included must be considered only a factor in the whole assemblage; but it is this factor on which we have specialized, and such emphasis is properly descriptive of the activity to be documented.\n\nAnother reason for the inclusion of this chapter is to record, in close association with the individual treatments of apparatus and its development, a self-consistent, albeit somewhat diluted, compendium of definitions for the several terms and phrases which are peculiar to this field and to which allusion is frequently made. This is considered advisable owing to the rather large and widespread discrepancies in the use and meaning of these terms.\nAmong the symbolic languages available to the dealer in fire controls, that of the free vector is one of the most direct and articulate. We build here the structure of such vectors, which describes a system of points in motion in a medium. While falling short of more general rigid-body dynamics, such systems are eternally serviceable for the embodiment of a great fraction of the fundamental concepts.\n\nThe position vector:\n12. In the symbolic languages used by those dealing in fire controls, the language of free vectors is one of the most direct and expressive. Here, we construct the structure of such vectors, which describe a system of moving points in a medium. Although they do not encompass the more general rigid-body dynamics, these systems are invaluable for conveying a significant portion of the fundamental principles.\nmentals hereto  relevant. \nConsider  first  a point  which  is  stationary  in \na given  medium,  the  latter  being  unaccelerated \nin  space  and  for  the  present  purposes  uniform. \nThis  point,  which  may  be  called  a,  is  typical  of \nand  may  identify  the  medium.  It  may  have \nbeen  quite  arbitrarily  chosen. \nA second  point,  moving  in  or  with  respect \nto  this  medium,  may  be  symbolically  identified \nas  h.  The  position  of  the  point  in  the  medium, \nor  with  respect  to  point  a,  is  to  be  described \ncompletely  by  the  vector  Ra?,,  which  may  be \nthought  of  alternatively  as  the  \u2018\u2018directed \nGi \nconfidkntta; \nGENERAL  THEORY  OF  AIMING  PROCESSES \nrange\u2019\u2019  from  point  a to  point  in  that  order. \nThe  vector  so  expressed  denotes  both  distance \nand  direction,  in  accord  with  the  normal  capa- \nbility of  vectors.  When  this  vector  is  constant, \nb \nFigure  1,  Standard  iiosition  vector. \nthe  second  point  is  stationary  with  respect  to \nThe first point identified. When this vector is variable, being for example a function of time, the tip of the vector traces out the space-path of moving point b in the medium.\n\nWhen point b approaches point a, the vector Rah approaches R\u00e5, which is the null vector although not necessarily the number zero. The scalar or inner product of Rah with itself, that is Rah * Rahy, gives the square of the absolute scalar magnitude of the vector Ra?, and in this case is also the square of the undirected distance or true range of point b from point a.\n\nOf the many notations current for the scalar magnitude itself, we mention |R\u00e5|, |. We shall denote this quantity here by the scalar symbol Rah, as in It is intended that this quantity contain, or represent, the absolute scalar magnitude of the vector Ra.\nThe vector Ra has physical dimensions if any, with the quantity Rah being the distance (in feet) from point a to point b. Consider the vector kRah, defined as the position vector with respect to point a of a point collinear with a and b, and which is k times as far from a as 6 is. Its scalar magnitude is certainly kRah. The scalar multiplier k may be purely numerical, producing merely a stretched version of the original vector, or it may have physical dimensions and thus alter the character of the original vector. If we arrange that k = Ra/\\_a, the so-called unit vector with a scalar magnitude of unity is produced. This unit vector indicates only the direction of point b from point a and may be given the symbol I\u2019aB:\n\nRa hat Ra hat Rah ab \u00b7 (2)\nThe unit vector is undefined when the scalar Rah is zero. It is further evident that the unit vector does not have dimensions in this sense at least.\n\nIf the position of point b with respect to Figure 2 and its multiples, point a, depends in either a preassigned or determinable way on time, then the vector Rab is said to be a function of time. That is, Rab = Rab(t.\n\nIn many circumstances, particularly in significant physical cases, this variable vector will be differentiable. For example, if it is considered that Rab is the triple of three rectangular coordinates, then in such circumstances these coordinates are also differentiable in the scalar sense. On this assumption, we define the vector as the vector velocity of point b with respect to point a, or in the medium thereby denoted.\n\nAngular Rates\n\nIn many circumstances, this variable vector will be differentiable. For instance, if it is considered that Rab is the triple of three rectangular coordinates, then in such circumstances these coordinates are also differentiable in the scalar sense. Under this assumption, we define the vector as the vector velocity of point b with respect to point a, or in the alternative terminology, the angular velocity of point b with respect to point a.\nThe vector identified in Figure 3 is the derivative of the vector function of a point b in a medium. It is parallel to the tangent to the space-path of point b and has a length proportional to the velocity of b along this path, both being instantaneously evaluated at time t. The scalar value or magnitude of this vector, denoted as |Va\u03b2| or Vab, is similarly defined. The unit vector, giving purely the direction of motion of point b in the medium and with respect to a, is symbolized by v^b.\n\nThe individual constancy of the quantities in equation (5) is significant. If the unit vector Vab is constant, motion of point b in the medium is rectilinear. If the scalar Vab is constant, then this motion involves an unchanging speed along the path. Finally, the constancy of the vector velocity Ya\u03b2, which implies both the above, means unaccelerated motion.\nThe motion of point b in the medium identified by point a results in the following:\n\n1. Angular Rates\nWith regard to points a and b and the fundamental vector Rab, we can demonstrate how angular rates enter the scheme as the time derivatives of unit vectors. First, differentiate the second expression given above for the vector Rab:\n\nNoting that I\u20ddab is proportional in magnitude to the angular rate of point b about point a, and is normal to Rab and coplanar with Rab and Vob, and noting also that Rab (which is different from Fab) is merely the range rate between a and b, we can identify the terms on the right-hand side of the vector equation (6) as the components of Yab which are normal to and along the direction Tan.\n\nFurthermore, the derivative Vab of the unit vector can be considered a measure of rotation in space.\nWe may construct a more articulate vector by taking the outer or vector product of Tab into Tab, which may be symbolized as fob X Rab. Thus, we define the cross product of two vectors Rab and Yab as:\n\nRab X Yab = (Rab y component of Yab) - (Yab x component of Rab) * i + (Rab z component of Yab) * j - (Yab z component of Rab) * k\n\nThis vector is a measure of the time rate of angular rotation in space of point b about a, which is normal to the plane of rotation and directed in the right-handed, or screw-thread, sense.\n\nWhen the vector velocity of point b in the medium is invariant, that is, Rab is constant, then the area of the parallelogram formed, in the invariant plane of relative motion, by the vectors Rab and Yab is evidently constant. Thus, by definition of the vector product, we have, in such a case, Rab \u00d7Yab = Constant.\n\nBut now Rab = Rab \u00d7Yab\u2071 and by performing vector multiplication on both sides of (6) with this identity:\n\nRab \u00d7(Rab \u00d7Yab) = (Rab \u00d7Rab) \u00d7Yab = |Rab|^2 * Yab\n\nWe get Rab \u00d7Yab = (|Rab|^2 / Constant) * Yab. Since the area of the parallelogram is constant, Constant = |Rab|^2, and the above equation simplifies to Rab \u00d7Yab = Rab \u00d7 Rab \u00d7 Yab / |Rab|^2 = Yab / |Rab|. Therefore, the direction of the rotational axis is given by Yab / |Rab|.\nThe latter product we find refers to (7): Rib [i*ab X fab] = Rib Qab = Constant. (8)\nThis relation embodies a vectorial expression of the well-known invariant (range-squared into angular rate) for unaccelerated straight line courses.\n\nSeveral position vectors:\nKeeping the initial point a as identifying symbol for the single medium, consider now two points, b and c, having general motion therein. With the same convention for a, the position of point c in the medium can be expressed as:\n\nc - a\n\nin recognition of the triangle formed in the medium by the three points a, b, and c. The notation employed provides a convenient criterion for cancellation of indices on summing.\n\nNote that scalar multiplication of each side of (9) into itself yields:\n\n(c - a) \u00b7 (c - a) = (a - a) \u00b7 (a - a)\n\n(c - a) \u00b7 (c - a) = a\u00b2 - 2a\u00b7a + a\u00b2 = a\u00b2 - 2a\u00b2 + a\u00b2 = 2a\u00b2\n\nTherefore, c - a is the position vector of point c relative to point a.\nThe familiar law of cosines.\n\nDifferentiation of (9) gives: the vector velocities, one relative and two with respect to the medium, add vectorially and form a closed figure, as do the position vectors themselves. A similar relation holds no matter how many points are involved and no matter how many derivatives are taken.\n\nIf point c is moving in an arbitrary manner in the medium, and if the instantaneous motion of point b, with respect to the medium, is directly toward point c, then\n\nwhere k is some positive scalar quantity. But since we may write Iab \u00b7 Tab \u2212 kRbc \u00b7 Ibc, it follows that\n\nk = Rb\u00b7Vab\n\nand\n\nVab = vba, (12)\n\nsince the scalar and directional equations must be satisfied. The latter equation may be written as:\n\nVab \u00b7 Iba = |Vab| \u00b7 |Iba| \u00b7 cos(\u03b8), where \u03b8 is the angle between Vab and Iba. Solving for cos(\u03b8), we get:\n\ncos(\u03b8) = (Vab \u00b7 Iba) / (|Vab| \u00b7 |Iba|)\n\nThis is the cosine rule in vector form. It relates the magnitudes and direction angles of the vectors connecting three points in space. It is a generalization of the Pythagorean theorem for right triangles.\n\nIn summary, the law of cosines states that for any triangle ABC, the square of the length of the side opposite angle C is equal to the sum of the squares of the lengths of the other two sides minus twice the product of their lengths multiplied by the cosine of angle C. In vector form, it relates the magnitudes and direction angles of the vectors connecting three points in space.\nA point h in a body, whose axis may be aligned with c, defines a pursuit course differently. We prefer, however, to use the term as characterized by (12). The derived criteria may describe either a pursuit course or its negative: one point moving away from the other.\n\nWhen two points h and c move uniformly in the medium, with constant velocities Vcb, Voc, and consequently also Vhc, a simple criterion exists for their convergence. This convergence is reflected in the vanishing of both the relative position vector Rhc and its scalar magnitude. It may be desired.\nIf a bullet is referred to as 'if' and its target is 'c'. Since Vbc is a constant, and consequently which must vanish at some value of in the future, for example, we have, as the criterion for the collision course in the sense indicated. Since absolute motion has not lately been employed, in the medium, this criterion implies collision even when Yab and Voc are variable, provided only that their difference V^c is constant. The oppositely pointing unit vectors of (15) ensure the 'closing of the range'. A hypothetical collision in the past, with the range opening, is of little comfort in those forms of fire control which require a co-incidence; such a \"recessive\" collision course, however, may be quite useful in some aiming processes to be described.\n\nA type of generalized collision course is defined by the simple criterion\nThe conditions implied by equation (15) are met when the motions are uniform. In general, however, neither condition ensures a collision since the range may increase or approach a limit. Equation (16) is the vectorial version of the constant true hearing criterion, familiar in homing operations. Dynamical relationships that subside to this condition or can approximate it identically are of extreme interest in such operations.\n\nThe necessary and sufficient condition (we repeat) for ultimate coincidence of points h and c is that, at some time, their velocities become equal.\n\nWhen equation (16) is combined with the constant-range criterion R^c = 0, they together imply R^c = 0. Points h and c are then translating similarly in the medium or are \"flying formation\" in a very ideal sense.\n\nREMARK ON ANGLE:\nAlthough there appear to be several natural ways to define an angle between two vectors, the most commonly used definition in physics and engineering is the one based on the dot product. According to this definition, the cosine of the angle between two non-zero vectors **a** and **b** is given by the dot product of **a** and **b** divided by the product of their magnitudes:\n\ncos \u03b8 = (a \u00b7 b) / (|a| |b|)\n\nwhere \u03b8 is the angle between **a** and **b**, and \u00b7 denotes the dot product. This definition has the property that the angle between two vectors is zero if and only if they are collinear, that is, if they lie along the same line. It also ensures that the angle between two vectors is unique, up to a sign.\n\nAnother common definition of angle is based on the cross product, which is used to define the right-hand rule for determining the sense of rotation between two vectors. However, this definition is less commonly used in physics and engineering applications, and is more complex to work with than the dot product definition. Therefore, we will focus on the dot product definition in this text.\nForms of notation for angular rates, such as that shown above, which come from straightforward vector constructions, seem to have no supremely convenient notation for the angle between two vectors. The vector product is proportional to the sine of such an angle, as well as to the product of the magnitudes of the vectors themselves, and shows the sense in which the angle is swept out. If the vectors are first normalized or reduced to unit vectors, and the vector product then evaluated, the resulting vector shows the sine of the angle, the plane which contains it, and the sense of rotation.\n\nFurthermore, the difference between two unit vectors is demonstrative of the angle (and its sense) between the two directions thereby indicated. The scalar magnitude of this vector difference is twice the sine of half the angle.\nA further measure of the angle, in terms of vector concepts, was considered. Referring to any two vectors, a vectorial measure of the tangent of the angle between them, properly signed, is given by the ratio of their vector product to their scalar product. The resulting vector is normal to the plane in which the angle may occur. With a simple notation worked out, this measure of angle should be extremely useful, owing partly to its compactness and to the remarkable usefulness of the tangent in many classes of problems.\n\n16. A projectile\nRetaining the terminology of vectors, we shall next discuss a problem in the aiming of a projectile. While giving the problem a certain generality, we shall assume certain ideal circumstances which are not always satisfactory.\n\nThe motion of a projectile is described by two components: the horizontal motion, which is constant, and the vertical motion, which is subject to the acceleration due to gravity. Let us denote the initial velocity of the projectile in the horizontal direction by H, and in the vertical direction by V. Let us also denote the angle of elevation of the projectile at the moment of projection by \u03b8.\n\nThe horizontal component of the velocity remains constant, and its magnitude is given by H. The vertical component of the velocity, however, obeys the equation of motion:\n\nv = V + at\n\nwhere v is the velocity at any given time, t, and a is the acceleration due to gravity, which is a constant.\n\nThe trajectory of the projectile is a parabola, and its highest point, or apex, is reached when the vertical velocity becomes zero. At this point, the horizontal velocity remains constant, and the vertical velocity is given by:\n\nV_apex = H tan \u03b8\n\nThus, the angle of elevation at the moment of projection determines the maximum height reached by the projectile. This angle also determines the range of the projectile, which is given by:\n\nR = (2 H^2 tan \u03b8 / g)\n\nwhere g is the acceleration due to gravity.\n\nThese equations provide a simple and useful method for calculating the maximum height and range of a projectile, given its initial horizontal velocity and angle of elevation at the moment of projection. This method is widely used in various applications, such as artillery aiming, ballistics, and even in everyday calculations, such as estimating the range of a golf shot or a football kick.\nIn the presentation of a problem that is not always descriptive of real conditions, transformations may be made under real circumstances to obtain an equivalent problem in a more idealized state. The simpler but less realistic study, however, often provides educational value and can serve as a starting point for expanding toward a more complex reality.\n\nFollowing the presentation of a rationalized problem with its significance properly qualified, we will discuss several special cases with fewer space dimensions and involving more specialized physical phenomena, which are introductory to some of the aiming stratagems described elsewhere in this report.\n\nIn a medium identified by point a (not shown in Figure 5), let there be a vehicle b.\nthe  point  b,  and  an  enemy  target  c.  Let  it  be  re- \nquired to  launch  a projectile  from  the  vehicle \nso  as  to  coincide  at  some  time  with  the  target ; \nand  let  the  projectile  be  identified  by  point  d. \nAssume  first  that  the  target  c is  moving  uni- \nformly in  the  medium,  which  may  be  the  air \nmass.  Assume  further  that  the  projectile,  when \nlaunched  or  released  or  projected  or  fired,  pro- \nceeds initially  in  the  same  direction  in  the  me- \ndium as  the  vehicle  at  that  instant  is  proceed- \ning, except  k times  as  fast.  Its  initial  velocity, \nwith  respect  to  the  vehicle,  is  then  (/c  \u2014 1)  times \nthe  velocity  of  the  latter.  Suppose  also  that,  al- \nthough the  medium  offers  no  net  resistance  to \nthe  projectile,  gravity  acts  upon  it  in  a normal \nmanner.  With  time  measured  from  an  origin  at \nthe  instance  of  firing,  the  position  of  the  pro- \njectile in  the  medium  is \nThe vector A^ is the acceleration of gravity, acting downward. It may be considered invariant and written as gr^, where g is the scalar acceleration of gravity, and r^ is a unit vector, downward pointing.\n\nThe target position is to which, acceleration terms may be added in the more general case of nonuniform motion. Equating (17) and (18) for a hit, and letting the value of t which satisfies the resulting equation be tf, the time of flight, we have:\n\nThe relative position vector Rbc(O) is the vectorial present range, while Vbc(O) is the present relative velocity of the target. We note that if these quantities are continuously available, together with the vehicle velocity Yab and the \u201cdown\u201d direction r^, then the solution to the aiming problem is given completely by equation (19). It is unnecessary to know:\n\nRbc(O) = present range vector of target from origin O\nVbc(O) = present velocity of target relative to observer\nYab = velocity of observer relative to inertial frame\nr^ = downward unit vector\nThe scalar value tf determines Vo\\_, such as the component in the vector Y'ab for instance. A mechanism could be built to steer the vehicle along this vector, ensuring the equation holds for any required tf value. The magnitude of tf would be a result of this automatic computation.\n\nVectorial mechanisms in three dimensions are practical for computation, but common types deal with scalars and fewer dimensions at a time. For now, let's disregard the consideration of gravity and focus on a particularly simple situation in two spatial dimensions (Figure 6). The relative position vector R^c becomes a line segment in the plane connecting the vehicle and the target. The velocity vectors of the vehicle and target may then be attached at their respective ends.\nA projectile is evidently on a pursuit course if the appropriate ends of this line segment's velocity vector Yab align with the relative position vector R^c. If, on the other hand, the projections of the velocities Yac and Yab, normal to the position vector Rftc, are equal and constant, then we have one condition for a collision course in the restricted sense. The other condition is a uniform decrease of the scalar range R^c, which criterion may also be expressed in terms of the projections of the two vector velocities along the connecting line segment or vector. Similarly, a collision course for a projectile is describable by replacing the vehicle velocity with its appropriate multiple.\n\nReferring to the scalar magnitudes only of the last indicated figure, we may reiterate:\n\nA projectile is on a pursuit course if the velocity vector Yab aligns with the relative position vector R^c. If, instead, the normal projections of velocities Yac and Yab onto the position vector Rftc are equal and constant, then we have one condition for a collision course in the restricted sense. The other condition is a uniform decrease of the scalar range R^c, which criterion may also be expressed in terms of the projections of the two vector velocities along the connecting line segment or vector. Similarly, a collision course for a projectile is described by replacing the vehicle velocity with its appropriate multiple.\nIf the lead angle A in the figure is zero, the pursuit course is in effect. If the lead angle A is such that Vab sin X = Vac sin a (20), a collision course results. Furthermore, if Vad sin X = (Vab + Vbd) sin X = Vac sin a (21), a projectile launched under these conditions will hit the target.\n\nA general fact related to the circumstances pictured is contained in the identity (Figure 6) & = VacRrc^ sin a \u2013 VabRVc^ sin X (22). Thus, by relation (21), it is seen that a criterion for hitting is given by\n\nVacRrc^ sin a = VabRVc^ sin X + VadRcd^ sin X\n\nThis requires no measurement of the target velocity. It should be noted that all these scalar expressions may be given more concisely in vector notation.\n\nTo return to equations (20) and (21), we shall illustrate methods for finding aiming angles.\nWe consider criteria that do not explicitly use target velocity or range. restricting ourselves to previously enforced assumptions. If a collision course is momentarily obtained, for instance, through criterion use, under these circumstances, equations (20) and (22) indicate that Vac sin a = Vab sin X*, where A* represents the (measurable) lead on a collision approach. From equation (21), we find that the angle A for a hit is given in terms of locally available quantities by:\n\nA = A* - a\n\nThe vehicle's flight path needs only to be rotated through angle A* - A towards the target, to pass from a collision course to a firing position. Instead of the initial collision course, suppose a pursuit course is employed initially. Since then, A = 0, we have:\n\na* = Vab X' / Vac\nline to the target during the initial pursuit approach. Then, assuming the range does not change substantially during the transition, we alter the course so that, by equations (22), the line of sight intersects the target. A firing criterion, in terms of an initial maneuver, is made available without employment of the target velocity or range. The similarity in form between equations (26) and (28) is rather remarkable. Regarding the latter criterion, it should be noted that the inevitable change in range during the transition may be roughly approximated, and this must be done if high accuracy is required. In the writer\u2019s opinion, both of these fundamental methods for kinematic lead computing are worthy of note, for example, when the range becomes difficult to compute.\nExist practical composite methods which lie somewhere between the two. The principal purpose, however, of their present introduction is illustrative rather than developmental. Along practical lines, the stability of the aiming process, in each case, would require much closer attention than indicated here.\n\nSpace-Time Geometry\n\nWe wish here to exemplify, in connection with some of the aiming criteria discussed above, a method of visualization, or rather of symbolic representation, which may always be substituted for the vectorial one, and which in many cases, particularly to the geometrically inclined thinker, may be preferable thereto.\n\nAgain, suppose we are dealing with two space dimensions, but that in addition, time is taken to be represented as a dimension normal to the plane of \u201cspace.\u201d In the resulting three-dimensional volume, a point represents a position in space and a moment in time.\nAn event and the coincidence or intersection of two paths generated by such points corresponds to a simultaneous coincidence of real points. This contrasts with the properties of vectors in the normal portrayal where time is not a dimension.\n\nIn the adjacent figure, the projection of all points onto the space-plane reduces the whole affair to the conceptual scheme employed above. For the rest, the interpretation is remarkably simple, although this is true, in a conceptual sense, only because we are temporarily restricted to two dimensions of space. It is evident, for example, that unaccelerated motion of a point results in a straight line in the space-time volume shown; a stationary point forming a line parallel to the time axis, and an infinitely fast point lying altogether in one space-plane. It is further seen.\nThe velocity of any point is given by the cotangent of the angle between the space-plane and the tangent line drawn at the given point to the three-dimensional path traced out by this point. Consider two points in motion in a medium which is stationary in the space-plane. The origin of the latter being, for example, the identifying point of the medium in the manner already explained. At a particular time, the positions of these points in the particular space-plane corresponding to this time may be taken as initial positions for the two points. Assuming then that the two points have a given constant velocity and are to be unaccelerated in the future, we see that their possible space-time paths lie along the elements of cones which have axes parallel to the time axis. The tangent of half the vertex angle of each cone.\nThe given text corresponds directly to the preassigned velocity of each point. For one point, if a direction in space is chosen, then the one element of its cone of motion is singled out. The one element of the other cone that intersects that of the first is likewise singled out, and consequently, the direction of motion for the second point is determined, which will result in collision. Such a solution, which can be readily reduced to straightforward mechanical form, applies whether it is desired that the vehicle itself collide or that an aimed projectile coincide at some future point with the target.\n\nThe generalizations of the above conceptual scheme to include effects such as gravity, accelerated motions, and so on, may well be imagined. Mathematically at least, there is:\n\nThe text describes a method for determining the direction of motion between two points in space that will result in collision. This concept can be applied whether the goal is for the vehicle itself to collide or for a projectile to hit a target at a future point. The text also suggests that this concept can be expanded to account for additional factors such as gravity and accelerated motion.\nThe present writer has found the space-time mode of thinking extremely useful, even when limited to special cases, for the tangible illustration of more drastically complex situations in typical and practical problems.\n\nExample of synchronous operations: Suppose it is required to determine the absolute velocity vector of a target accurately from a moving vehicle, and only the direction and distance to the target, that is, its relative position, are available to some approximation. Note that the relative position vector at any time t can be expressed as follows:\n\n18. Synchronous Operations\n\nAs an example of the useful employment of a synchronizing operation, consider the situation where it is necessary to determine the absolute velocity vector of a target with great accuracy from a moving vehicle, and only the direction and distance to the target, that is, its relative position, are known approximately. Note that the relative position vector at any time t can be expressed as follows:\nIf the target velocity Voc(0) and the relative position Rbc(O) of the target are continuously measured as local variables, and the relative position Rbc(0) is determined at a given instant, then an artificial version of target velocity can be produced by generating an adjustment Vac(0) in continuous dependence on the observed vector error Rbc(0) - Rbc(t), reducing it stably and accurately to small magnitude. This artificially generated Yacit can be a faithful version of the true target velocity Vac(t). Errors in the initial target position Rbc(O) are integrated out in this process, but errors in the determination of Va&(0) contribute to errors in the target speed in direct proportion to the numerical speed.\n\nR6c(0 = RfccCO) + ft\nIf the target velocity Voc(0) and the relative position Rbc(O) of the target are continuously measured as local variables, and the relative position Rbc(0) is determined at a given instant, an artificial version of the target velocity can be produced by generating an adjustment Vac(0) in continuous dependence on the observed vector error Rbc(0) - Rbc(t), reducing it stably and accurately to small magnitude. This artificially generated Yacit can be a faithful version of the true target velocity Vac(t). Errors in the initial target position Rbc(O) are integrated out in this process, but errors in the determination of Va&(0) contribute to errors in the target speed in direct proportion to the numerical speed.\nIn tracing out the causal sequence involved, we note that the operator (whether human or automatic) observes the difference between the generated vector R^c and the vector Rftc describing the relative target position. Based on this difference, the operator manipulates the artificial target-speed vector Voc. Through the agency of apparatus that mechanizes equation (30), this artificial target speed influences the generated position vector R^c, which in turn affects the observed difference, and so on in continuous fashion around the loop. If the operator manipulates the vector Rftc(O) as well as Voc, this may result in a closer following of Rftc by Rftc, or in \"better tracking,\" but such manipulation if irregularly and continually employed results in serious errors in the approximation of Voc to Vac. Such combined operation.\nIf adjustments for aided tracking's vectorial generalization, Rbc(O) and Voc, are appropriately interconnected, easier and better tracking with faster subsidence to an accurate target speed result. For a given error in the latter, the requisite adjustment of Rbc(O) to make R^c momentarily equal to R^c increases in proportion to the time. Therefore, if each adjustment in Rbc(O) is accompanied by simultaneous and proportional change in Voc, where this change is also proportional inversely to the time since the last previous adjustment, subsequent readjustment only needs to address higher order errors.\n\nThis process can be generalized as far as desired. In equation (30), Vac may be replaced by YaciO) + [Ajt)dt.\n\nGeneral Theory of Aiming Processes.\nWhere Aac is the artificial target acceleration vector (in space), three adjustables replace the above two, and these may be similarly interconnected, with the interaction between Aac and Voc(O) resembling that between Vac and Rftc(O). This procedure may improve tracking and the representation of target speed, and may furthermore provide a \"synchronous\" measure of target acceleration for higher order solutions to fire-control problems.\n\nMORE ON THE APPROACH\n\nWe have discussed above, both in vectorial and scalar form, the properties and criteria pertaining to pursuit and collision courses for the approach by a vehicle to a target. Among the infinite variety of such modes of approach, of which these are but special cases, we shall outline one here which may begin as a course of pursuit and then subside arbitrarily.\nIn this process, we will show means to control an approach toward a collision. Initially, in the plane of Figure 6, suppose the vehicle b is in pursuit of the target c, or referred to as proportional navigation. The following assumptions will be made to illustrate the consequences of imposing this approach criterion:\n\n1. The scalar speeds of vehicle and target, Vah and Vac, are constant.\n2. The target has motion only normal to the line connecting it with the vehicle.\n3. The lead angle A is sufficiently small, making it an adequate approximation for its sine, and the rate of change of range is contributed to only by this lead angle.\nIt is evident, under the above assumptions, that for a collision course where the new symbol A identifies the lead for a collision, Equation (22), under the same assumptions, becomes:\n\nRbc = Vab\n\nWe propose subsequently to change the direction of motion of the vehicle, measured by the angular sum o- + A, at a rate proportional to that at which the direction to the target, measured by the angle o- itself, is changing. We propose further to make the changes in the direction of motion of the vehicle occur k times as fast as those in the direction of motion of the target, or to make:\n\nd(o- + A)/dt = k * d(o-)/dt\n\nThe derivative of this criterion provides a more succinct description:\n\nTherefore, a paraphrased criterion is to make the rate of change of the lead angle A one time larger than the rate of change of the absolute difference between the angles o- and o'.\nThe approach to the target's reception involves the lead A approaching the value A for a collision course, in proportion to the (A-1) power of the fractional closure of the range. For large values of the ratio k, the collision condition is attained rapidly. When k equals 2, A, v, and consequently a- are approximately constant, implying a constant rate of turn for the vehicle and corresponding to the circular-interception approach.\n\nThis analysis is approximate but, within reasonable limits, shows substantially the same phenomena as the more complex exact treatment in three-dimensional space.\nOperations that form a closed sequence or chain in the causal sense and occur in a completed ring or loop are a special branch of dynamics of great importance in many aiming controls and regulatory devices generally. Such causal loops can be entirely automatic in nature or contain one or more human elements as an essential connecting link. Terms such as feedback, retroaction, regeneration, and degeneration have been applied in the identification of systems constructed in this manner; a servomechanism is fundamentally of this character.\n\nThe most important property of such a physical arrangement is the stability with which it operates. In cases where the components and interconnections involved are:\n\n(Note: The text appears to be in good shape and does not require extensive cleaning. Only minor corrections for typos and formatting have been made.)\nIn the realm of linear systems, where the principles of additivity or superposition for cause and effect apply, the criteria and instrumental strategies for stability are now well understood. A substantial body of literature exists on this topic. Feedback processes, with their power thus restricted, are significant. They are employed for various computational purposes, such as reciprocating or inverting a characteristic, and in complex problems of smoothing and prediction.\n\nConversely, when nonlinear components are present, and the additivity principle is violated, as is typically the case with a human operator serving as a connecting link in the loop, a far more intricate situation arises. Beyond the insights gleaned from linear approximations, which must be carefully considered, lie the mysteries of nonlinear systems.\nFor fully drawn questions, the major recourse must be to experimental methods and model studies. Here, we provide a simplified example of the feedback phenomenon. The accompanying figure depicts the simplest and most fundamental system in which feedback is involved. The operator in the \"box\" is arbitrary and assumed to connect dynamically the incoming and outgoing variables. Thus, the operator ^ is a physically realizable functional which determines the local output as a function of time t when the incoming variable is applied.\n\nFigure 8. Elementary feedback loop or following system.\nThe input is a function of time. The input variable q = q(t) is arbitrary. The output of the box is the variable r, which is also the response to the operation $ when performed on the input to the box. Furthermore, the variable u is the unbalance or difference between q and r. Consequently, when the operator # is linear and expressible, for example, as a rational function of the derivative operator p, we may write:\n\nq'(t) = p * r + b * u\nr = c * q(t) + d\n\nIn equations (41) and (42), the familiar operators of linear feedback and servo theory appear. The roots of the rationalized denominators of these operators are significant to stability, while the merits of \"performance\" are obtainable in terms of the results of the entire operation when q(t) is specified. Stability may be achieved by ensuring that the roots of the denominators lie in the stable region of the complex plane.\nA meaningful interpretation of the closed causal system in Figure 8 can be given as follows. If it is required to duplicate q, which represents a variable weight in a balance, the response r proposed as such a \"duplicating\" variable. The unbalance u indicates its failure in this regard. The operator, which may now be considered a \u201cfollower,\u201d adjusts r through interpretation of the unbalance u. Thus, the response r is a measure, better or worse, of the arbitrarily variable weight q. In more general cases, the follower adjusts r based on the unbalance u.\nA fire-control system, or a connected group of components, may require the operation of an additional chain and may contain irrelevant signals. Feedback following such an operation was discussed in Section 1.8. All cases of feedback can be reduced to this simple example by proper identification of input quantity q and the following operator.\n\nRegarding instrumental considerations on the theoretical plane of the present chapter, some remarks on the general instrumental character of a fire-control system developed for airborne application are included. It is essential to note that such a system is typically only part of a more inclusive system which may also encompass the vehicle in which the apparatus is borne and the man or men who manipulate both.\nInstruments used for controlling aim in an airplane can be divided into three parts. One subdivision will consist of apparatus that feeds in all primary data. Such data include continuously measured variables, which may be supplied either directly or through power-boosting servos. Feedback systems may be involved in the measurement of input variables, where null methods are essential to achieve a dynamically faithful replica of the physical quantity sought. Other input data may be supplied intermittently or periodically, and these data may arise either automatically or by the manual settings of the principal operator or one of his confederates. The precision with which the primary inputs must be supplied, for a given aiming accuracy, is a prime property of the system as a whole.\nThe principle that it functions on. Another subdivision of the typical fire control is that which performs the computation required, and in which the various input data are correlated, collated, operated upon, and interpreted with regard to their significance to the problem at hand. The components of this subdivision must constitute a mechanization or physical embodiment of the equation or equations which describe the method employed for fire control. The computation involved here may be algebraic, geometric, or may require equipment versed in the calculus. In general, the mathematical operations performed are nonlinear, although in a good many cases linear approximations suffice and are employed. Errors in computation arise from a number of sources, and their allowable limits is one of the important specifications.\nFor this subdivision of the system, variables such as temperature and acceleration may inadvertently be \"measured\" by the computer. It is important to predict such effects and thoroughly test their final magnitudes. The outputs of the computing subdivision are primarily presentation variables, which are handed on to the next subdivision. Some of these variables may return to the initial subdivision and may in turn become input data for the computing subdivision itself: this occurs where feedback strategies are used in the realization of certain dynamic characteristics or again where servo methods are required for the effective delivery of a significant variable for the presentation subdivision. Instrumental considerations\n\nSubdivision outputs or computation results may be locally displayed at the computing subdivision.\nA computer is used for auxiliary purposes such as checking and calibrating, or for warning indicators. These can also be considered presentations. The final subdivision, for presenting the appropriate variables to the one or more operators, accepts variables from the computer through feedback paths. This equipment may consist of a simple reflecting sight, an oscilloscope screen, or involve complex follow-up or feedback components where null methods are applied to achieve the intended final result.\n\nAn alignment is often required between a moving index and a target (or this operation may be involved in the process).\nThe primary concern in the art of fighter pilot aiming-control systems is constructing dynamics that ensure rapid, stable, and precise tracking. All combinations are possible in manipulating the vehicle to match optical presentation with the target, introducing angular rates into the computer and affecting presentations and pilot manipulations. The stability of resulting tracking, which may impact accuracy of fire, is of primary concern.\nControls that need to be included may not typically be related to input variables. Examples include computer adjustments based on the type of aircraft, pilot choices in indications, and firing operation requirements for resetting computing components for the next attack. The excellence of a control or computing system depends not only on partial derivatives of firing errors with respect to input data errors but also on the inherent accuracy of the supplied input data. For instance, if range can be measured with great precision, the importance of a given error is reduced.\nSystem or principle of operation should be insensitive to this particular input variable. In such considerations, statistical methods are supremely useful, although great attention is warranted to the assumptions made in any given case; passing beyond the region of validity of these assumptions deserves and should receive severe criticism. A few remarks are here warranted on some of the commoner variables which are continuously measured in an airplane for the purpose of aiming controls. Briefly these comprise: distances, velocities, altitude, and angles, angular rates, and angular acceleration. The passage of time itself should be added. Such quantities may be measured directly, or obtained by inference from related quantities. For example, a velocity may be measured as the integral of the corresponding acceleration. We mention only the following:\n\n1. Distances: The straight-line measure between two points.\n2. Velocities: The rate of change of distance with respect to time.\n3. Altitude: The vertical position of an object above a reference level.\n4. Angles: A measure of the degree of rotation around an axis.\n5. Angular rates: The rate of change of angle with respect to time.\n6. Angular acceleration: The rate of change of angular velocity with respect to time.\nprimary measurables include distances, which are frequently obtainable to appropriate objects using radar-ranging methods. Distances are also included for altitude and ground clearance, although barometric pressure may contribute to altitude measurement over an appropriately defined point. Indicated airspeed can be measured in terms of the difference between dynamic and static pressure and can be converted to true airspeed through auxiliary measurement and computation. Accelerometers, in various forms and excellences, will provide measurements of the airplane's acceleration in a coordinate system fixed therein or, by appropriate stabilization (which may be considered to involve measurements of angle), with respect to an unaccelerated coordinate system.\n\nGeneral Theory of Aiming Processes\nprimary measurables: distances, which are frequently obtainable to appropriate objects using radar-ranging methods; altitude and ground clearance, although barometric pressure may contribute to altitude measurement over an appropriately defined point; indicated airspeed, which can be measured in terms of the difference between dynamic and static pressure and can be converted to true airspeed through auxiliary measurement and computation; accelerations, which can be measured using accelerometers in various forms and excellences and with respect to an unaccelerated coordinate system (this may be considered to involve measurements of angle).\nAngle is usually measured with respect to fixed directions, these being manifested by free or approximately free gyros. Absolute directions are provided by North and Down, and these represent long-term standards. Angular rates, of the vehicle or of independent platforms therein, may be given extremely quickly and accurately by captured gyros, which are discussed elsewhere, particularly in Chapter 3. Finally, angular accelerations are provided through the measurement of torques on a body possessing rotational inertia. We have referred above to a relatively complete fire-control system. The opposite extreme is represented by the warrior who fires \"by eye,\u201d and who, by dint of training and experience, has developed aiming controls in his judgment and in his reflexes. This procedure, which can lead to remarkable precision, has attained however an uncertain level of consistency.\nUnfortunate aspects of glamour have definite limitations for modern operations. Most aiming controls extant, which are far from perfect, lie between these extremes. Consequently, there are numerous cases where automatic apparatus combines with visual estimates, such as the speed of a warship, the duration of a brief time interval, or the angular depression of a target below the horizon.\n\nChapter 2\nOn Certain Aspects of Tracking\n\nBy \"tracking\" is meant a continuous following or alignment procedure that is pursued through cognizance of its error or unbalance, as in the basic feedback or following operation described in Section 1.10. A good example, although somewhat abstractly disclosed, is given in Section 1.8, where an arbitrarily varying position vector is to be followed.\nby an artificially generated position vector, influenced by manipulation of an integration constant and a velocity. Tracking pervades all branches of fire control, but it arises principally in aiming operations, whether manual or automatic. With regard to the latter, automatic tracking is essentially indistinguishable from other types of automatic control and will be considered in that light. However, our major interest in the present chapter is in tracking by manual means, with a human operator involved. While the removal of human limitations gives greater promise to automatic tracking devices and techniques, there is still much to be learned, even for such unlimited future trends, from tracking of the human variety. Besides this, the human element cannot be altogether eliminated.\nEven ultimately and until we give machines the final powers of judgment and choice, we shall find it necessary personally to direct their efforts. It may also be doubted that the adaptability or educability of the brain, whereby it adjusts to altered circumstances, can soon be imparted to the automaton in any but the most trivial of cases. Or rather, if this is to be done, it will probably be through imitation of the processes by which such adaptations take place in the animal mechanism.\n\nIt is typical of the writer that he considers the entire subject of tracking to come within the broader boundaries of regulatory controls, which to him include all corrective apparatus having a closed causal loop. In this connection, and although the region has not been very far explored, there will be traced out briefly in what follows an analogy between\nThe development of automatic regulators and tracking aids is compared here, leading to an inference about the future of the latter. Apart from this speculative exercise, we have been deeply involved with tracking in various development programs where fire-control apparatus was being designed. Manual tracking in range, which we now refer to as manual tracking whether by stadiametric means or otherwise, has not significantly impacted our immediate sphere, and it is clear that this type of tracking has been comprehensively addressed by other groups. Consequently, tracking in angle, or more precisely in direction, is the focus of this discussion. The problems and technology of such tracking have emerged in gunnery systems and those for bombing, guided bombing, and for airborne rockets.\nFor flexible gunnery, Section 7.2 at The Franklin Institute undertook an instrumental, statistical, and psychological study of man-machine interactions in tracking. Project NO-268 focused on standard computing dynamics and known aiding controls, yielding significant results, some unexpected. Other section members contributed more directly and their writings should be referred to instead. Allusions may be made here, but the project will not be further discussed.\n\n2. The human FOLLOWER\nPeople track during every conscious moment, unless their eyes are closed, hands tied tightly, and tongues clamped solidly.\nBetween their teeth, alignment processes involve the alignment error serving as datum for its own annihilation, continually taking place in familiar living operations. We may thus expect a rudimentary sort of tracking circumstance where the human operator will be at home and will exhibit great and innate skill. Pointing at a moving object with a pencil or a rifle, under favorable conditions of support and inertia, is a tracking operation that can be carried out relatively well. The provision of a reflecting sight or a non-magnifying telescope with cross hairs does not significantly improve the operation and has even been observed to impair it. However, this is different with magnification, as visibility and visual resolution can be vastly increased.\nThe \"ural\" type of tracking is not surpassable for targets that change slowly and uniformly. An adjustable-rate device is superior in such cases, although this is just one example. Generally, natural tracking is sufficient for typical situations, provided scale factors in presentation are reasonably adjusted. It is assumed that close tracking, or simply small tracking error, is desired. However, for larger purposes of aim control, this is not the only index of excellence. The needs and nature of interpretative and computing equipment cannot be completely separated from those of the tracking controls. We are thus discussing a subsidiary problem. We repeat, tracking arrangements would suffice where the dynamic relationship between the immediate manual manipulation and the targets remains consistent.\nThe direction index and manual manipulation were of the same character in the arrangements, referred to as natural. If this is an overstatement, we should assume that there might be discovered some even more ideal dynamic connection between manual manipulation and the visual index. The dynamic nature hereof might be expressible in quantitative form, though the ideal differed from one individual to the next.\n\nThe elements in a tracking system form a chain, and consequently each element must perform perfectly as part of the whole assemblage. However, it has not been sufficiently repeated that these elements form a closed chain or a complete loop, together with the human operator, where one is present. This fact brings to the tracking process all the complexities of a closed system.\nThe unique characteristics of a system, including the conditions for stability and periodicity, are significant in the formation of a causal loop, particularly when a \"disturbed\" or lead-computing sight is involved. Despite the dynamics of the human operator being little understood, many properties of these loops, which are entirely automatic and familiar in automatic regulatory devices and controls, are present in the tracking sequence. An approach to the tracking problem, considering it as requiring improved aiding equipment, should be based on recognizing the cyclic nature of the operations involved.\nTracking systems in a closed loop are fundamentally different from those in an \"open\" or \"straight-through\" system. Both advantages and disadvantages result from such an arrangement, and this will be our principal topic. We first aim to outline the causal circuit involved in a tracking system in operation.\n\nSuppose a directional index is to be made to coincide, as nearly as possible, with the direction of a target that has motion only partly predictable. We shall assume at first that such motion may also be contributed to by motion of a vehicle from which the tracking is taking place; that is, tracking is to be in vehicle coordinates. In any case, there is a dynamic connection to the directional index (or sight index) from some sort of handle or control which is under direct manipulation. If a coordinate x is assigned to the displacement of the handle,\nThe causal dynamics are expressible as a relationship between the variables coordinates. Let T be the tracking operator. In general, T may be a nonlinear operator, but in analytically manageable cases, it is linear. At worst, linear approximations serve admirably as rationalized ideals. When rationalized, T = Tip.\n\nWe should note that the coordinates, such as fx and a, used here may be considered multiple-valued quantities, vectors, or simply one component of the problem, depending on the circumstances where such a component is representative and a significant and symmetrical separation into components is possible.\n\nNow, the sight index ^ is to be compared to these coordinates.\nWith the true sight direction or target direction, denoted by the symbol a, the difference or error, visible to the human operator, is an important variable. While under ideal tracking conditions, this difference will remain identically zero, in real operation, its value must be continually observed and interpreted to approximate this ideal.\n\nPerception of the tracking error c, and manipulation of the handle /x based on such perception, is the human operator's office. Symbolically, the operational symbol H represents the functional interaction between the eye and the hand. This operator must therefore include not only the delicate reflexes and inhibitions of the human nervous system, but also sensory, motor, and central processes.\nThe system involves not only the processes involved, but also random excitations and the \"nervousness\" characteristic of the organism. It must include the ability to learn, which implies fundamental nonlinearity.\n\nThe causal loop should now be quite distinct: from eye to hand to sight index and back, continually and cyclically. Figure 1 shows this circuit in symbolic form. It will be readily seen, by comparison with Figure 8, that operators H and T in series correspond directly to the follower-operator 4> of the latter figure.\n\nBefore passing on to a more detailed consideration of the components that may be involved in the causal loop of tracking, a few words should be spent on clarifying what is gained by recognizing the existence of the loop as an essential feature of the whole phenomenon.\nIn dealing with equipment that operates in a closed causal connection, such as servomechanisms and regulatory mechanisms generally, certain characteristics become familiar, which are not typical of all arrangements. One such characteristic, related to the decay of transients, is that such decay occurs quite uniformly among all the variables directly included in the loop. This is evident from analytic considerations or from observation of the operation typical of such systems in practice. That is, if the parameters of the various components of the loop are adjustable in their mutual relationships such that any one variable of the system subsides stably and rapidly to an equilibrium condition following the imposition of an external disturbance.\nGiven initial conditions or following a transient disturbance of any type, all variables directly included around the loop will subside stably and rapidly for the same adjustments. This is not true for open chains of components. One consequence of this property, worth citing, is as follows. In a director system where the sight index is not derived from the final aiming operation, the precision of tracking may not ensure accuracy in the latter operation due to the response of an intermediate computer to other characteristics of the tracking. A very different circumstance holds true for disturbed-sight type of equipment. Here, the closed system keeps the dynamic behavior of the sight stabilized.\nThe performance of gun and sight index, as variables of the loop, are much closer together. An adjustment that improves tracking nearly succeeds in giving a corresponding improvement in aiming, as well. This argument is qualitative but is supported by quantitative data obtained. We are only suggesting a way of thinking; it remains to be put to more articulate use. It is recognized that these arguments may have become trite in fields of which the writer has little knowledge. His interpretations are based on the work he has seen in progress.\n\nFurther breakdown of the loop:\n\nSpeaking particularly of the lead-computing or disturbed sight, we wish to illustrate, through elaboration of the operational principles.\nThe tracking circuit in Figure 1 distinguishes the uses of computing components in Figure 2. In one instance, the tracking function T of Figure 1 splits into series components A and S. In contrast, in the other, the sight index ^ is accepted by an independent channel. In each case, y represents the coordinate of the gun or other direct aiming agent that governs the initial direction of the projectile. The component C, located at the bottom of Figure 2, not only computes the \"kinematic lead\" for the gun based on the dynamic behavior of a and the range to the target, but also applies necessary ballistic corrections, such as parallax.\nTo the rich literature available for director systems, beyond what we can include here, and to the rather different nature of the smoothing problem (in which transients in a computer should be kept from harmfully affecting y), we shall deal henceforth with the system in the upper portion of Figure 2. Further references, however, may be made to director systems in the present report, but these will be conjectural only and will show possibilities for future development rather than being descriptive of work we have followed.\n\nSpeaking basically, it is as legitimate to achieve a given dynamic relation between the gun coordinate and that of the line of sight to the target by means of the upper system of Figure 2 as by the lower one.\nThe former case differs in the inclusion of the dynamic gun-to-sight computing function as a component of the tracking automatic regulators loop. In contrast, in that case, the power requirements and inertias of the gun itself may restrict the mobility of the tracking loop. It is evidently possible to replace the variable y in this loop with a lightweight, lower-power mock gun or index y, and then separately reproduce y in the real gun coordinate system as effectively as the external high-power controls permit. As in the director, such corrections as trail and parallax may be additively included in this final transmission, which is not then part of the loop.\n\nWe now consider only the upper system in Figure 2, where the variable y can be manipulated without the restrictions imposed by a heavy turret (or an airplane). What is\nThe best characteristic for operation A in the \"aiding\" operation is as follows: Assume there is a satisfactory form for the tracking function T, and this form T' is linear, so that T'(p) = T(p). Under relevant exterior circumstances, suppose this linear form T'(p) of the tracking function or operation will produce a very close alignment of ^ with o-. If the computing function S gives rapid and accurate performance when p is nearly o-, it is only necessary to make A ip) Sip) = T'ip), assuming A and Si are linear, although their parameters may vary with time. Thus, an ideal or nearly ideal form for the aiding function is given as T'ip)S-ip). Since T is not critical, one would suspect that this new value T'ip)S-ip) would be the preferred choice.\nFor a need not be critical. Reasonable approximations should suffice.\n\nTwo types of automatic regulators -\nAn analogy\n\nThere is a remarkable parallelism historically between the development of tracking aids and the progressive steps made in the types of automatic regulatory equipment for commercial processes. This is not altogether surprising, since both involve the gradual perfection of components added to apparatus operating in a (causally) closed loop, and since both have as a purpose to improve the stability and performance in a special task of the systems to which these components are added. In discussing tracking aids, we are referring for example to component A in Figure 2.\n\nIt is not a far cry from the tracking loops shown above to the regulatory loop of Figure 3.\n\nManipulated variable^\nRegulator \"plant\"\n\nm\n\nDesired behavior of V\nUnregulated\nFigure 3. Symbolic representations for regulatory control loop:\n\n3. The components are given in the symbolism recently recommended to the ASME by a Committee on Symbolism for Industrial Regulators and Controls. Here, the regulator g may be considered to correspond approximately to the A component in Figure 2. In contrast, the plant h may correspond to components H and S in series in the latter figure. Both H and S typically involve lags or characteristic responses that decrease in amplitude at higher frequencies. The typical plant also involves lag, which generally makes regulation difficult and requires advanced regulator dynamics.\n\nThe dynamic characteristics of velocity tracking, displacement tracking, and aided tracking, as these names have come to be used, refer to:\n\n1. Velocity tracking: The ability of a control system to maintain a constant velocity of the controlled variable in response to a step change in setpoint or disturbance.\n2. Displacement tracking: The ability of a control system to maintain a constant position of the controlled variable in response to a step change in setpoint or disturbance.\n3. Aided tracking: The use of additional sensors or information to improve the performance of a control system, such as feedback from a secondary sensor or model reference adaptive control.\nMay be illustrated by the responses, for example, in the gun coordinate y when a step input is applied to the handle. Thus, in Figure 4, the responses shown by curves a, h, and c as functions of time are characteristic of the classical tracking dynamics in the named order. Now these same responses also characterize the dynamics, such as would occur between the measured unbalance and the manipulated variable of Figure 3, of the classical regulator types as they occurred historically. These are called, respectively, the floating (or integrating) regulator, the proportional regulator, and the proportional-plus-floating regulator. The latter, like aided tracking, proved to constitute a big advance when it became generally available. It is now interesting to conjecture whether:\n\nOn Certain Aspects of Tracking\n\nConfidence: 95%\nA more universally potent regulator, such as the newer one leading to the response d in Figure 4, would correspond to an improved tracking function. The evidence of the analogy points unmistakably in that direction.\n\nIn both the tracking and the regulator problem, one deals not with systems where the remainder of the loop is of well-known and identifiable dynamic character, but with systems where that portion of the loop is rather vague and changeable. The human operator is hard to describe, not only by virtue of the intricate nature of its response at any given time, but also because this nature changes in time in dependence on conditioning and fortuitous causes. In the regulatory case, the regulator must cope with an ill-defined mechanism, and\nmust be flexible for initial adjustment and non-critical for continued effectiveness. It is tempting to suspect that both fields are now only in rudimentary stages of development.\n\nCharacteristics of Higher Order\n\nIn tracking, we have a circumstance where more elaborate dynamics are likely to lead to greater effectiveness when the human operator and the kinematic computing equipment are included together in the tracking loop. In Figure 4, the response d implies a differential equation of higher order than do the preceding responses (a, b, and c). In the techniques of automatic regulation, it is a familiar experience to find that the extra degree of freedom which is permitted by passing to a higher-order regulatory law enables an adjustment of the parameters which offers results, in stability and performance, far beyond those obtained.\nWith the simpler arrangement, an increase in complexity necessitates the acquisition of knowledge to manage the new complex of adjustments and exploit the generalized dynamic adaptability. In the field of regulation, such knowledge was acquired, but the analogy with tracking aids is less distinct than in the last section. Regarding the classical dynamics of lead-computing sight, there are several reasons to suspect that a characteristic of higher order would serve more effectively. This is true through the straightforward argument that linear prediction, here in angle, should properly be generalized to a prediction of higher order, since the typical engagement involves acceleration.\nWe enter here into a basic controversy regarding target motion and relative motion. Further, in the coupling constant of the lead-computing ONFIDENTIAI^ multiple sight indices, an extremely crude compromise is necessary, especially in the presence of available tracking dynamics. Adjustment of the coupling constant improves tracking stability in one sense and rapidly decaying transient error in the other. The region of overlap does not lead to great satisfaction on either score, and a very shallow optimum, in terms of gun error, is shown on exploration of this single adjustment. This is precisely the sort of compromise.\nIn regulatory circuits, situations often arise where a more articulate dynamic characteristic steps in to put the affair on a new basis. For instance, in many regulatory cases where a regulator of first- or second-order dynamics has been used, and unsatisfactory compromises must be accepted, the insertion of a higher derivative term in the regulatory dynamics can sever the independence of parameters which necessitates the compromise and can allow a readjustment, resulting in outcomes in an entirely new class.\n\nThe characteristics of the aiding component and those of the kinematic computer are intimately related in the tracking loop. Given the possibilities for improvement indicated above for each component, this relationship is even more striking.\nA mutual beneficial restyling might be carried out jointly between the two. A proposal involving this sort of innovation was made for application to the case of a lead-computing sight used in a velocity tracking turret. This proposal was for a minor change, premised on the possibility that a physical alteration of simple form might improve circumstances. However, it resulted in a conversion both of tracking function and of the lead-computing dynamics, and to higher order. Although never actually applied to full-scale trial installations, it was reduced to simulative form, and enough work was done to indicate a possible improvement. It is evident that this is not an unpromising history in view of the embryonic status of such modifications.\n\n2.7 Multiple sight indices\n\nThere have been several examples.\nThe writer's knowledge on aiming controls using multiple indices in visual aiming equipment has emerged over the past three years. This important new technique is worth briefly outlining. For simplicity, we limit the discussion to visual aiming equipment, although the underlying principle is more general.\n\nThe following examples will be mentioned. First, in the British method for low-altitude angular rate bombing, as embodied in their LLBS Mark III, a row of collimated luminous lines was rotated downward with respect to space. The lines were oriented horizontally, and the operator viewed them through a sighting means.\nThe operator merely observed the target through the formed optical grid. When the target, which at first appeared to be progressing \"upward\" across the lines, became momentarily stationary with respect to the grid, the operator acted on this instantaneous synchronism as his signal to release a bomb.\n\nIn the proposal for the so-called Texas sight, a constellation of luminescent points was substituted for the single collimated reticle of the classical lead-computing sight. The points of the constellation, which formed an extended two-dimensional pattern in angle, moved with the single reticle and converged exponentially toward it. Ideally, the points of the pattern should not rotate about the central one; not in space, that is. In use,\nthe  operator  merely  manipulates  his  tracking \n\u2018\u2019We  refer,  however,  to  the  writings  of  H.  Whitney  on \ntracking,  and  to  the  more  detailed  accounts  of  simula- \ntive tracking  studies  which  were  carried  out  under  Sec- \ntion 7.2  at  Columbia  University  and  at  The  Franklin \nInstitute. \n\u2018'By  L.  LaCoste. \nQoONFTfaENTBlr^ \nON  CERTAIN  ASPECTS  OF  TRACKING \ncontrols,  or  the  gun  itself,  so  as  to  achieve \nequality  of  angular  velocity  bet^veen  the  tar- \nget and  the  local  points  of  the  pattern.  Two \nresults  ensue;  for  one  thing  it  is  far  easier  to \ntrack,  since  an  integration  is  omitted  from  the \ntracking  loop,  the  operator  observing  rate \nrather  than  position;  furthermore  the  oppor- \ntunities to  fire  are  multiplied  tremendously, \nsince  as  may  easily  be  demonstrated  the  suf- \nficient conditions  as  well  as  the  necessary  ones \nare  given  for  effective  fire.  The  trouble  has \nA visual stadia for manual ranging was difficult to incorporate along with the optical pattern, but this circumstance might be altered with modern ranging facilities or the use of methods where range is not explicitly accounted for. A third instance of the need or desirability for many sighting indices has been involved in the writer\u2019s proposals for techniques to be used in the pilot\u2019s universal sighting systems (PUSS) and in certain optical systems for controlling guided bombs from a static position at ground level. In both cases, the tracking display would be similar to that in the two instances already mentioned. In neither case has the method been finally reduced to practice. It will suffice to mention here a simple means for arriving at a collision course.\nIt is well known that if the axis of a free gyro in a vehicle, for example, is initially pointed at a target, and that if the vehicle is subsequently steered such that the axis continues to point at the target, then a collision course will result, subject to the conditions described in Chapter 1. This criterion for steering is not an easy one, and to achieve stability, it is evident that coupling must be introduced between the heading of the vehicle and the line of sight. Instead of this, improved stability would also result if uncoupled lines of sight were displayed as a pattern in every direction, through one of the several available means for such stabilization and presentation. Transient errors would not need to be corrected all the way back to the starting point; it is essential only to keep those errors within acceptable limits.\nThe points of a pattern moving with the target, which are already in proximity, serve admirably as such a pattern. Stars themselves, if sufficiently dense, would serve admibly as such a pattern. It is not known if they have ever been used as such.\n\nIn fixed gunnery, aerial torpedoing, bombing, and rocketry, a pilot may be expected to carry out an aiming process which involves keeping an artificial line of sight, either fixed or moving with respect to the airplane, in approximate coincidence with the line of sight to the target. The pilot employs the normal flying controls in this operation and deals with a system of tracking dynamics which differs radically from, and at the same time is considerably more complex than, the controls common to a turret. For typical airplanes, and for the modes of operation:\n\n2.8 Tracking by the Pilot\n\nIn fixed gunnery, aerial torpedoing, bombing, and rocketry, a pilot performs an aiming process that involves maintaining an artificial line of sight, either fixed or moving relative to the aircraft, in close alignment with the line of sight to the target. The pilot utilizes the standard flying controls during this procedure and manages a tracking system that contrasts significantly from, and is more intricate than, the controls typically used in a turret. For standard aircraft and modes of operation:\nThe pilot must continue to perform special operations essential for safe and efficient flight, including maintaining indicated airspeed within specified bounds, trimming control surfaces for symmetry, operating the rudder to prevent skid, and avoiding flying underwater or underground. Additional tribulations such as manual adjustments to computing systems or attention to complicated warning indicators are unwelcome and must be kept to a minimum or eliminated.\nIn spite of the stringency of such requirements, the single-pilot airplane, primarily the fighter and the fighter-bomber, has evolved into the most useful weapon in the air, and thus has deserved attention as a vehicle for which the development of aiming controls is a profitable pursuit. The most striking feature of the tracking dynamics available to the pilot is the asymmetry in the up-down and sideways directions. For pulling up the nose of the airplane or for nosing downward directly, a motion of the stick forward or backward is all that is required. However, and especially if the pilot wishes to fly without skid, his operations in manipulating the airplane toward a goal which originally appeared to one side are very much more intricate. This is partly true since as he proceeds, he must not only compensate for the sideways displacement caused by the turn, but must also maintain the desired altitude and airspeed.\nThe target does not maintain its direction with respect to airplane coordinates during a maneuver, but rotates approximately around a longitudinal axis, first one way as the maneuver begins and then the other way as it completes. The pilot must operate both stick and rudder, and each in a different manner, during such a maneuver. Under these asymmetrical conditions, it is even more complex to point the airplane, not to mention a sight index dynamically related to the airplane, in a direction which is neither directly above or below nor to one side of the general direction of flight. For some problems connected with tracking through the controls of an airplane, other chapters of Part I may be consulted. In Chapter 4, a laboratory apparatus is discussed in which the phenomena of such tracking are reproduced.\nProduced electronically in the laboratory. Again, instruments for aiming rockets and for multi-weapon aiming require special handling due to the nature of tracking by the pilot. Although no apparatus has yet been prepared for this purpose, it is of interest to discuss a possible means for use by the pilot in tracking, which has been seriously proposed and may be prophetic for future systems.\n\nThere are analogous arrangements that have been proposed and tried out for bombers and for automatic missiles. The idea is for the pilot to track the target through an independently stabilized system carried in the airplane. For such tracking, he would manipulate conveniently mounted controls which would rotate in space a sight index having no direct dynamic coupling to the airplane. This tracking component\nFor example, in 1943, Lt. Comdr. E. S. Gwathmey designed a system to ensure minimum error and maximum smoothness in the continuous representation of the line of sight to the target. From the motion of the sight index developed with reference to the stabilized system, all data on angular motion of the line of sight are extracted automatically and continuously. These data, along with the remaining significant variables (speed, range, acceleration), are submitted continuously to a computing component which determines the proper instantaneous heading for the airplane in which it can effectively launch a projectile at the target. A high-performance automatic pilot, given this information, flies the airplane in such a manner that the firing condition is satisfied. The pilot merely tracks the target and chooses when to fire.\nThe pilot may be assisted by instrumental means that show him the transient condition of the computing and piloting operations. In normal flight, some simple adaptation might be found useful for navigating, and would serve to lighten the pilot's responsibilities in any case. Upon retiring from any given engagement, it might seem appropriate for the pilot to take over the controls in the traditional manner; on the other hand, he might simply turn his tracking index suddenly away in the desired direction for retirement. It would be straightforward to incorporate an optionally usable automatic evasion. Safety interlocks would come into play at minimum \"times-to-ground\" and at maximum \"gees.\" The remaining steps to complete automicity are not unthinkable, even when the vehicle becomes a projectile itself. Automatic detecting components can lock on to the target.\nAnd computers and automatic pilots can work out the attack. With no human pilot, for example, it is no longer necessary to bank. But here we enter the field of guided missiles.\n\nTwo more on the human tracking operator\n\nIt is plausible that for a given state of conditioning or \u201clearning,\u201d and within certain limits, the human operator in the following or tracking operation may be considered approximately linear. This belief in itself, however, is not to be accepted without question; there are a number of queries which are not easy to answer in connection with its justification. Thus, if the operator is a linear one, why does it not react the same each time to a given stimulus? How account for random \u201cdithering\u201d? What linear mechanism is there which will exhibit these varying states of muscular preparedness?\nAt the onset of an experiment, many such questions may be parried by pointing out that such irregularities may be provided in an automatic model by virtue of an artificial source of random signals which add directly to the output, or elsewhere in the circuit. For example, they may be thought to arise as the generated response to random excitations in the internal feedback loops which one includes under the name kinesthetic. Or these questions may be parried rather differently by indicating that the fluctuating components of the human response are unimportant and need not be represented in a linear model since they are rapidly attenuated in the remaining components of the tracking loop. This seems to be a particularly dangerous assumption. In any case, the closest approximation to a model of the human following operator appears to be attained by.\nA linear function H(p) with an added random fluctuation is illustrated in Figure 5 as the model of a human tracking operator. In Figure 5, we will consider what nature H(p) approximates most closely to the human example.\n\nIt is important to note that a significant amount of work has been done on this problem outside of the small amount the writer has been involved with. There are records available of experimental and theoretical work on this topic in Great Britain and within Division 9 at MIT Radiation Laboratory. The writer can provide titles of some of these works in the bibliography for this chapter, but the interested investigator can find these records through other channels. In the various linear operators proposed, there is some uniformity.\nThe wide disparity in approaches to the problem is evident, particularly in the significance researchers attach to frequency analysis. Our view is that a simple study based on response to harmonic inputs or the sum of a few such inputs with irrationally related frequencies and different amplitudes allows for learning by the operative under test, resulting in a fundamental alteration in character. More complex composite harmonic inputs lead to tremendous difficulties in separation and interpretation. The primary indication of linearity is that observed responses generally double when the stimulus is doubled, provided there is no apparent \"saturation\".\nAvoided. Such general proportionality of stimulus to response is encouraging for the devotees of the linear approximation. There appear to be only two characteristics of the human tracking operator beyond the limited linearity already mentioned and the larger fact that over longer periods, a learning process occurs. One of these is the inclusion of lags, possibly due to the retardations of nerve conduction and perhaps again to some more mysterious process in the reflex itself. The other is the integrating response. Good tracking is never deliberate, although it may be deliberate. First, as to lags: It has frequently been proposed that these be described by a direct displacement in time of t seconds, or by the effect of the \u201ctrue\u201d time-lag operator exp (-rp). This seems unnecessary.\nOn the basis of known convergence in work done at Columbia, the human operator, referred to as \"Big Henry\" or H, was contrasted with its model, known as \"Little Henry.\" It has been proposed that the human tracking operator's time lag could be approximated using a constant n. The writer advocated larger values of n as easily representable in linear models and possibly more representative of the situation in nature than exp (-rp). A curious situation arises from psychological data, which provides reaction times as a single number.\nFor example, the response to a step input of the above operator for n = 15 is a transient such as shown in Figure 6. If nerve conduction were represented by such a lag operator, then different absolute thresholds in the indication of Figure 6 would result in a different apparent reaction time for different amplitudes of stimulus, as observed. Notice that the hypothesis of a velocity of conduction varying in dependence on the strength of stimulus would then be unnecessary. To the writer, this explanation would be eminently more satisfactory.\n\nAside from the lagging response, which is certainly a property of the human tracking operator, it is evident that there is another type of response.\nBy Sobczyk at MIT Radiation Laboratory. The system gradually adapted to the surrounding circumstances. In terms of the coordinate x of the tracking handle as output, and the observed error e as input, and omitting the assumedly multiplicative lag-operator, there are reasons to believe that an integrating effect, perhaps alone and perhaps in combination with other effects, is present. These conjectures are based on a relatively simple system around the loop, such as when the human operator replaces the follower in Figure 8 of Chapter 1. Admittedly, we are discussing a human operator conditioned by the experience of operating in such a loop. However, if we knew the character of the operator thus conditioned, it would be significant to include compensatory features within the system.\nThe loop is based on this conditioned character. If the modified operation resembles the natural state of affairs, this is not an easy viewpoint to express. An experiment can be arranged in which the operator \"follows\" a variable by a direct manipulation, seeing only the error of his following. If, under these circumstances, during the performance and unknown to the operator, the error is frozen, the operator simply feels that he is exactly compensating for contemporary variations in the input variable but that he must correct the accumulated error. The very striking manipulation under these conditions is a continued steady motion in the direction which would normally produce such a correction. This corresponds substantially to an integrating response. Numerous experiments, mainly generalizations on this simple one, may be carried out.\nDetermine more precisely what is the operational form of the intervening human dynamics. The difficulties of frequency methods have already been mentioned, but in all cases, the problems of conditioning warrant extreme care in experimentation. This general problem has been worked on, and the possibility suggested of a purposely established higher-frequency exploratory loop which the operator may superimpose on the regulatory loop. For determining the moment-to-moment nature of a system which may be changing, or for an invariant system, merely to refresh memory. Such a possibility seems not at variance with the results of one British writer who has examined numerically.\nThe human tracking oscillographs reveal, after subtracting lower frequency components, a large 'remnant' with special properties at higher frequencies. The human tracking operator or human servomechanism operates near instability.\n\nChapter 3\nTECHNOLOGY OF ROTATION IN SPACE\n\n3.1 The Importance of Angular Rates\n\nThe measurement and production of angular rates form a fundamental branch of instrumental technique in airborne aiming controls. We distinguish between two categories of angular rate: relative and absolute. In making this distinction, it is convenient to call up the concept of a fixed direction or a fixed body. For simplicity, we define such a direction or body as having no measurable angular motion with respect to the fixed stars. Therefore, we are resting firmly on an unchanging reference frame.\nThe empirical foundation and no arguments are expected from philosophers. Absolute rotation is now merely relative rotation assessed with respect to a fixed direction or a fixed body. With few exceptions, absolute rotation, or rather the rate of absolute rotation, is the subject dealt with here.\n\nThe rate of absolute rotation of a line, considered either as the total quantity taken about an axis normal to the plane of rotation or as one of the components of the total about some other specified axis, appears as an essential variable in lead-computing gun-sights, synchronous bombsights, angular rate bombsights, rocketsights, stabilizing systems, guided missile controls, and so on. As discussed in Chapter 1, a prime criterion for the interception approach is expressible in terms of this variable. One of the more spectacular applications of the absolute rate of rotation is\nA bomber flying horizontally over a target at constant speed makes a straight ground track with the target contained. The direction from the target to the bomber increases in elevation, while the direction from the bomber to the target drops in angle below the horizon in a corresponding manner. In terms of the bomber's altitude h, the remaining horizontal distance d on the ground track, and the horizontal speed V of the bomber in target coordinates, we can obtain an expression for the absolute rate of rotation w of the sight line from bomber to target:\n\nconsidering a horizontally flying bomber over a target at constant speed, making a straight ground track with the target contained; the direction from the target to the bomber elevates, while the direction from the bomber to the target drops in angle below the horizon in a corresponding manner; using the bomber's altitude h, the remaining horizontal distance d on the ground track, and the horizontal speed V of the bomber in target coordinates, we can derive the absolute rate of rotation w of the sight line from bomber to target.\nThe locus of points where a plane, flying with relative speed in a vertical plane through the target, sees the target moving with angular rate w\\_, is given by the equation of a circle. This circle lies in the given vertical plane, contains the target as a point of its circumference, and has its center precisely above the target at a height V\u00b2/g. As v and w change, the circular locus merely swells or shrinks but still passes through the target and is symmetrically disposed above it.\n\nThe locus of release points for a bomb, for negligible air resistance, is merely an inverted trajectory with an apex in the target. Such a locus is a vertical parabola containing the target. It may be written using the following equation:\n\nv\u00b2 = 2g(h\u2080 - h)\n\nwhere h\u2080 is the height of the bomb above the target at the instant of release.\nFor the acceleration of gravity, we choose w in equation (2) so that the circle osculates the parabola, noting that the center of the circle, and the apex and focus of the parabola, are collinear. Placing the center of the circle at the center of curvature of the parabola, referring to the nature of the curve at the origin, we have:\n\nV = 2cog\n\nIt may readily be shown that for typical speeds, the closeness of the mutually osculating curves is remarkably good for altitudes below 500 feet, and thus they can replace one another there. Thus, a bomb may be released when, approximately:\n\nSeveral refinements must enter before a practical sight results, but the inputs other than those of equation (4) are of second order importance. The method is relatively independent.\nof altitude at low altitude, for example, and as a slightly extended analysis will show is remarkably insensitive to a departure from horizontal flight. A number of bombing applications result from this principle, which differ from one another by the manner in which the angular rate criterion is incorporated.\n\nThree alternative methods of measurement\n\nThe phrases \u2018\u2018rate of rotation in space,\u2019\u2019 \u2018\u2018absolute rate of rotation,\u2019\u2019 and \u2018\u2018absolute angular rate,\u2019\u2019 are used interchangeably here. When the context leaves no ambiguity, the term angular rate itself will frequently be employed as equivalent to the above phrases to simplify sentence construction.\n\nWhen it is desired to determine, from a vehicle, the absolute rate of rotation of a direction from the vehicle to an external object, one has the choice of various instrumental processes.\nA gyro, in appropriate gimbals, is subjected to torques about axes normal to its polar axis, with these torques regulated such that the polar axis points directly and continuously toward a given external object, such as a target. If the two axes about which the applied torques occur are mutually perpendicular, the torque applied about each axis measures the component of absolute angular rate, in the given direction, about the other axis. The total angular rate in space of the given direction can be compounded vectorially from these two orthogonal components. The sensitivity of the measurement is proportional to these components.\nTo the moment of a gyro and consequently to the speed and inertia of the spinning wheel, both quantities being assumed large enough that the torques corresponding to angular acceleration are relatively small. If this is not the case, as it usually is, the two angular rates may still be extracted, assuming the target is being perfectly tracked, by dynamic compensation and a mixture of the torques corresponding to the two components. Of course, when the applied torques are imposed about axes which are not normal to the polar axis, as is frequently the case in practice, then the appropriate resolution must be made onto equivalent axes which are so located.\n\nSuppose on the other hand that a rigid framework, mounted in similar gimbals, is manipulated by the control of torques with respect to\nThe vehicle, which has a definable direction fixed in the framework, is pointed directly and continually at the target. This is a rather pure problem in servomechanism, with an inertia load, aside from the detection itself of the target direction. If now absolute angular rate meters, several types of which are described below, are mounted solidly with appropriate orientations in the rigid framework that \"follows\" the target, then the indications of these meters provide measurements of the absolute rate of rotation of the direction to the target taken about axes determined by the orientation of the meters in the framework, of the framework in the vehicle, and of the vehicle in space.\n\nAssume that the vehicle carries a completely stabilized body, possessing no appreciable absolute angular motion. Assume further:\n\n(Note: The text appears to be written in standard English and does not contain any meaningless or unreadable content, ancient languages, or OCR errors. Therefore, no cleaning is necessary.)\nSuch means, for high precision, may consist in a feedback arrangement whereby angular motion is created under the control of a positional error detection system. If an index is pointed continuously at the target, either through the application of torques to the index member with respect to the vehicle or with respect to the stabilized body, and the above method is employed to measure angular rate components with respect to the stabilized body, these measurements are also valid with respect to space.\n\nPractical points:\nUsually, the direction to a target is capable of much slower instantaneous rotation than is the vehicle. Thus, if an articulated massive system is used to point the direction to the target, the above method can be applied.\nThe torque required for a pointing system to remain directed toward a target is not solely used for overcoming friction in the vehicle-pointing system connection. Instead, the precession of a gyro with its spin axis as the pointing index has advantages. First, it is self-stabilizing, opposing unintended torques caused by the vehicle's angular motion. Second, it offers a more naturally stable dynamic system, simplifying the servomechanism problem for a given servo design excellence. Lastly, absolute angular rate meters are used to measure the absolute rates of rotation of the vehicle itself around axes.\nThe angular velocity of the line in space from the vehicle to the target can be compounded from the angular rates of that line with respect to the vehicle, along with the absolute angular rates of the coordinate system in the vehicle. The geometry involved is not trivial, as demonstrated in Euler's transformations for a rigid body. The complete angular velocity of the vehicle in space can be expressed as the vector sum of its absolute angular rates about any three mutually orthogonal axes within the vehicle. Thus, measurements from three rigidly mounted absolute angular rate meters in the vehicle, with the axis of sensitivity for each perpendicular to those of the others, provide such measurements.\nThe angular velocity of the vehicle in space is definitively determined by the angular velocities of the target with respect to the vehicle. If the target is seen more or less directly ahead of the vehicle, or if the lead angles between the target direction and the vehicle heading are always less than, for example, 45 degrees, a geometrically simpler situation results. In such cases, the system for measuring the angular rates of the target direction with respect to the vehicle, which are typically the time rates of change of the lead angles in two coordinates, combines naturally with the system for measuring the absolute angular rates of the vehicle. For instance, the axes chosen for measuring the latter may be the same as for the former, both being stationary in the vehicle. Quite valid approximations may be employed to simplify sub-systems.\nThe necessary dynamic system is discussed substantially in Section 10.5, where its application to the pilot's universal sighting systems (PUSS) project is described more fully. The choice among the available instrumental methods outlined above depends on numerous circumstances. (A number of permutations are obviously possible among the systems referred to.) These include the immediateness of the basic components, in terms of procurement or developmental status, the requirements of precision, the life expectancy to be obtained, the size and weight, and the flexibility for subsequent alteration and adaptation which it may be desirable to incorporate. This latter item, in the opinion of the writer, is one of the most important and yet appears to be the easiest to overlook under stress.\nWith regard to absolute angular rate meters, only those having small internal angular displacements are considered. Absolute advantages may be claimed for such components. One advantage is the instrumental flexibility which follows from the technique of measuring accurately and permanently a fundamentally important quantity, involving a component which need not change form in dependence on the dynamics or geometry of the particular problem at hand. Another advantage lies in the absence of angular discontinuities or limits of predictable motion, which haunt the designer of gimbals and balls for certain other angular rate components, and which lead to problems in locking and in protection against wear during idle intervals. A further advantage lies in the avoidance of friction in the measuring assembly.\nAssembly, since the use of small angular displacement, or even of a null system with regard to such displacement, traditional bearings may be replaced by almost completely friction-less structures which require no care or maintenance.\n\nPrinciple of the Captive Gyro\n\nBy captive gyro is meant a component comprising a balanced rotor, spinning at substantially constant speed, of which the axis is constrained to remain very close to a fixed index, in one or two dimensions, within a supporting framework. The operation of constraint has been referred to as capturing.\n\nWith a captive rotor of this sort, having sufficiently large moment of momentum, and presupposing a small angular departure between the spin axis and an arbitrarily varying index, the total effective torque which is applied to the rotor about all axes normal to the spin axis.\nThe axis of the rotor is a direct measure of the angular rate in space of the latter axis, and hence nearly of the varying index. The applied torque is the vector product of the moment of momentum into the precession rate, all three physical quantities being treated as vectors. Approximately, where the unit vectors r^ and r^ point in the \"Captive gyros have been variously identified in contemporary nomenclature; the name captured gyro may have become the most familiar. R. O. Yavne, who arrived in our laboratories by a devious route after a hectic international migration, and of whom this is hardly the only (or the best) reminiscence, was assigned to the technical development of captured gyros due to his demonstrated facility with recondite dynamics. It was not at first understood why he was reluctant to.\nIn working on this phase of research, it was unknown that his reluctance stemmed from an imperfect grasp of idiomatic laboratory talk, until he finally summoned the courage to express that he felt it was a disgrace that we couldn't design our own gyros from fundamental principles, rather than accepting as a starting point a piece of equipment of enemy origin that had fallen into our hands.\n\nThe direction of the torque and spin axes, respectively, and it is noted that f is simply the vectorial precession rate in space. The amplitude of f is the scalar precession rate w, which is thus measured by the scalar torque L under the circumstances above named, since further the rotor speed n and its spin inertia I may be held constant.\n\nEquation (1) describes the relation between precession and applied torque for a gyro:\n\nf = L / (I * n)\nThe technique of capturing is used only when acceleration torques are negligible. In a captive gyro of the first kind, the spin axis r^ is held close to a direction fixed in a supporting framework, and r is arranged to be restricted to directions normal to the first direction. In this type of captive gyro, the spin axis r^ is allowed to rotate, but only in one plane within the framework. This plane usually contains the spin axis and is normal to a second axis of rotation fixed in the framework, imposed, for example, by a single gimbal or bearings between the framework and the nonspinning case of the rotor. Rotation of the spin axis in the 'Tree' plane within the framework is opposed by a torque, applied about the above second axis, which depends on the relative positions of the two axes.\nThe text describes the concept of a gyroscope's precession and the torque required to keep the spin axis in a minimum displacement around the fixed index or precession axis. The text explains that the applied torque measures the absolute angular rate of the spin axis, which is approximately fixed in the framework. The approximation improves as the displacement is held near zero. To ensure that the total applied torque is primarily contributed by a measurable or reproducing agency, the friction involved in the gyro's rotation about the second axis must be insignificant compared to the restoring torque.\n\nCleaned Text:\n\nThe text discusses the concept of a gyroscope's precession and the torque necessary to maintain minimal displacement of the spin axis around the fixed or index direction in the framework. The applied torque measures the absolute angular rate of the spin axis, which is approximately fixed in the framework and normal to both the fixed index and the second axis. The approximation improves with the closeness to which the displacement is kept near zero. To ensure that the total applied torque is primarily from a measurable or reproducible agency, the friction in the gyro's rotation about the second axis, the precession axis, must be insignificant compared to the restoring torque.\nThe angular rate to be detected is not specified. Most captive gyros dealt with have involved a single gimbal principle. Axis only has been involved, and a single scalar reading has been provided for the absolute angular rate of the framework about a fixed line. Such a component, when adequately fast and accurate in response, may serve as a basic element to be used singly or in sets of two or three, mounted in appropriate positions in a vehicle or an articulated body, and has many diverse applications in aiming controls. A few remarks are warranted on the available methods for driving the rotor. The methods we have been concerned with divide first into pneumatic and electric. Electric methods split further into DC and others.\na-c and ac types are either synchronous or nonsynchronous. Alternating current drives are commonly either two-phase or three-phase. Of the pneumatic method, which is economically feasible only if associated pneumatic equipment is involved, we may say that speed regulation for the rotor has only been experimentally worked out. Such work has been largely carried out by Section 7.3 and has involved both a resonant reaction to the periodic impingement of the driving jet on the cups of the rotor (the reaction throttling the jet flow) and a centrifugal brake. In rotor drives involving direct current motors, one advantage is the simplicity of speed regulation, but a disadvantage is apparent in the problem of brush wear, which may unbalance the gyro by moving the center.\nThe issue of gravity along the spin axis is a significant consideration for an instrument intended to have an appreciable operating life. Unbalance of this kind will result in a false measurement of angular rate, which depends on the acceleration of the vehicle or platform. It is claimed, however, that such motors, or rather combinations of such motors and gyro wheels, can be manufactured in which the abraded brush or commutator material will fly out radially and stick permanently at the original distance from the precession axis. I have not had the opportunity to test this claim. In the employment of synchronous motors that synchronize at the driving frequency, such as the General Electric hysteresis gyro unit, either frequency control of an inverter or speed control of a motor-generator is essential. In one case, however, and the following method would apply:\nApply for nonsynchronous drives if the rotor frequency is extracted, the response of a capacitive gyro with varying speed was corrected by the interposition of a filter in the output. This filter altered the overall sensitivity in inverse proportion to the impressed frequency, the latter frequency being made proportional to the rotor speed.\n\nAn advantage in captive gyros is in the avoidance of intricate problems connected with carrying power conductors through gimbal connections to spin the rotor. Owing to the small relative motion of the rotor axis with respect to the support, flexible connections are possible if care is taken to avoid fortuitous spring-torques. In the pneumatic case, as in the partially captive turn gyro of familiar renown, a nozzle fixed in the supporting case is adequate if aerodynamic symmetry is preserved.\nThe techniques for capturing and measuring torque in first-kind captive gyros involve mechanically constraining the rotation of the spin axis and measuring the resulting small angular deflection, proportional to the constraining torque, as long as significant friction isn't contributing to the constraint. Requirements for high accuracy include a high undamped frequency of the oscillatory mechanical system, predictability of the resilient member, negligible drift of the zero position with temperature and time, accurate measurement of small displacements, and sufficient damping for rapid decay of transient excitations on the time axis. Symmetrical oscillations of high frequency are generally harmless.\nThe ignored disturbances, which have a propensity for containing energy in the lower-frequency band, must be meticulously guarded against in the subsequent components into which the output is fed. Such disturbances, which establish a threshold in detection, may arise from the shock impulses and noise in imperfect rotor bearings.\n\nThe second method primarily in use involves a feedback loop whereby the error or unbalance in angular displacement of the spin axis with respect to the framework initiates application of a torque so dynamically related to the error that the latter is reduced to small magnitude and maintained there. The applied torque then measures the angular rate which necessitated it. Such an arrangement may or may not have an added resilient system.\n\nTechnology of Rotation in Space\n\nThe second method predominantly employed involves a feedback loop where the error or unbalance in angular displacement of the spin axis with respect to the frame initiates the application of a torque proportional to the dynamic error. This reduces the error to a small magnitude and maintains it there. The applied torque then measures the angular velocity that necessitated it. Such a setup may or may not include an additional resilient system.\nThe unmeasured torque applies in proportion to the error or its rate of change. Even in the presence of resilient or viscous attachments, the feedback method operates substantially without error from such sources if a small and properly located null is maintained. The problem of the two-dimensional captive gyro of the second kind, as we may say, is rather different. In the first place, the need for a double gimbal to permit rotation of the spin axis about a point instead of an axis in the framework leads to a more difficult balancing problem about the two processional axes which must then be considered. Furthermore, as is well known, a gyro resiliently restrained in two dimensions will nutate violently if afforded the slightest opportunity. Even with zero constraint, the so-called free gyro will nutate forever in the absence of bearing friction or other external influences.\nlosses.  The  principal  obstacle  is  overcome,  how- \never, when  the  danger  of  nutation  is  recognized \nand  provided  against.  Again  there  are  two  dis- \ntinct capturing  techniques,  as  above,  and  al- \nthough they  do  not  involve  simply  a duplicate \napplication  of  the  one-dimensional  techniques \nfor  each  of  the  two  processional  axes,  success- \nful controls  have  been  worked  out  which  com- \npensate for  rotational  tendencies. \nThe  gain  in  captive  gyros  of  the  second  kind, \nover  those  of  the  first  kind,  is  particularly  ap- \nparent only  when  two  of  the  latter  are  replace- \nable by  one  of  the  former.  Where  three  inde- \npendent angular  rates  are  desired  it  is  almost \npreferable  to  use  three  of  the  simpler  units \nowing  to  the  resulting  similarity  of  the  basic \nunits. \n3 4 GYROS  FOR  ANGULAR  RATE  BOMBING \nThe  development  of  angular  rate  bombsights \nas  such,  with  a description  of  their  place  in \nThe larger field of airborne aiming controls is dealt with in Chapters 7 and 10. Here, we discuss the research effort surrounding the design of captive gyro components for such bombsights. This begins with those for the original hand-held BARB, which incorporated the theoretical principle of British-type angular rate bombing for low-altitude attacks.\n\nRequiring a method for measuring the absolute rate of rotation of a framework turned about a substantially horizontal axis, and there being a reason to desire an accurate, sensitive, and reproducible such measurement, the application was naturally considered for a captive gyro of the first kind, as identified. For this and similar applications, it was proposed originally by the writer (although similar proposals may have been made elsewhere) to construct a captive gyro of the first kind.\nThis is a proposal for the first kind of system having extremely stiff mechanical constraints to measure angular rate as strain through the response of wire-type strain gauges on the constraining members. This proposal is essentially non-feedback, with the approximate null in angular displacement not \"sought\" by retroaction but assured through the relatively high stiffness of the constraint. It was considered that strain gauges of the suggested type would enable measurement of gyro torque, and hence angular rate, in terms of the small strain (or small dimensional changes) thereby produced in the members. Such gauges were known to respond measurably to fractional strains of the order of one part in a million, and to yield changes of resistance in extremely rapid and faithful correspondence with the dimensional alterations of the structure to which they were attached.\nThe techniques of balancing out errors caused by temperature coefficient of gauge wires were well understood through the employment of bridges, etc. However, it was not initially suspected the extreme care necessary to guard against drift arising from humidity variation. The difficult problem of noise was not completely foreseen. Recognized at an early stage was the great advantage of the suggested arrangement, as no orthodox bearings were required, eliminating sliding or rolling friction. Gyros for angular rate bombing offered no friction, the deadly enemy of torque measurements, whether obtained through deflection or through feedback balancing of forces. A dozen models of such captive gyros were built, including one or two of the second type.\nExperimental members in various forms and shapes were tried out for strain gauge measurements. Combinations of single and double cantilevers were popular at first, but cylindrical members became favored in the laboratory later. One example of the latter type involved a pair of thin bronze cylinders placed in a line coaxially, with the gyro connected between them so that its spin axis was coincident with the cylinder axes and its case rigidly connected to the two cylinders at their inner ends. The outer ends of the cylinders were rigidly connected to a supporting framework. Gauges were applied symmetrically, four to each cylinder, and oriented along their elements. The constraining members supported the gyro and its elements.\nCase against accelerations, such as gravity, involves a corresponding deflection of the elastic constraining structure. This deflection was always \"even\" and not measured by the bridge system, where several gauges were connected. \"Odd\" deflections, corresponding to angular rate torques, were measured by the system in terms of the differential resistance change of the gauges. A careful elastic analysis was made of the mechanical system fundamental to this arrangement, and corroboration was experimentally found to a satisfactory approximation.\n\nThe difficulties experienced with the above absolute angular rate meter were typical of those found in the case of other meters in which strain gauges were used. We have already mentioned the variation in gyro speed and the attempts to compensate for it.\nAfter the fact, The Foxboro Company and Ruge-deForest were consulted freely and at length regarding the practical problems that arise with the application of these elements. Gauges and certain auxiliary calibrating equipment were obtained from these sources.\n\nA disturbed sight, referred to as such, involved some ingenious attempts, such as exciting the a-c measuring bridge with a magnetic system on the gyro rotor and inserting filters of transmission that were inversely sensitive to frequency. However, we will not treat these further since similar problems are common to other types of gyroscopic rate meters. The problem of drift in the gauges themselves, as well as drift in the attendants, is worth noting.\nThe most straightforward problem with antimony circuits is the unwanted response of the gauges to noise originating in the bearings of the gyro rotor. This issue is less problematic in dynamic measurement applications where maintaining a zero indication is less important. The most refractory problem was the random bearing disturbances, which have nothing in common with the symmetrical deflections resulting from unbalance of the rotor. With the latter, no trouble was found due to vibrations. However, rotor bearing disturbances are random and unpredictable.\nThe symmetrical signals were only apparent over a significant time interval and contained frequencies across the entire band. For the bearings under consideration, the noise signals were substantial enough to provide a threshold that was notable compared to the smallest angular rate signals desired. In a d-c system, an obvious solution would have been to lag the response until the resulting statistical processes yielded an unbiased measurement, accepting the lower response speed in the process. However, with the a-c measurements being tested at that time, considerable trouble was caused by this issue in the phasing adjustments involved in polarity sensing. The most effective remedy is to enhance the bearings, and certain modern gyros exhibit significantly lower noise levels, even for corrupted ones.\nTechnology of Rotation in Space: Responding sizes. (Larger gyros, in which processional torques are relatively bigger in comparison with bearing noises, are less troublesome in this respect.) Several other methods were considered, however, for the avoidance of this evil, but were never tried out. One such was the proposal to add elastic members which responded identically to the vibrational disturbances transmitted from the gyro bearings, being associated with the gyro case in the same way as were the normal members, but which were not stressed by the precessional torques, owing to the fact that they were not also to be connected to the framework. The difference in indication by gauges attached to both kinds of members would be extracted. Although some very delicate questions would arise in this connection on the detailed dynamics.\nThe measure's implementation is believed to have yielded noticeable improvements. Several planned extensions of this kind were abandoned upon the emergence of pneumatically captured gyros (mentioned below). It's challenging to speculate on the ultimate success. Captive gyros developed were nearly sufficient for the bombing application. Most test failures were in circuital components rather than gyro structures or gauge mountings.\n\nThe angular rate bombsight wasn't the sole aiming control system for which captive gyros were designed as absolute angular rate meters. The most significant application, likely, was as an input component for the PUSS system.\nThe captive gyros, described elsewhere, are used to measure the angular rates of an airplane around its own axes. Applications include determining extremely small absolute rates for use in a secondary control for refining the excellence of a precision vertical. Proposals have been made for the use of captive gyros in guided missiles, stabilizing systems, internal torpedo controls, and gyro compasses.\n\nThe wire-type strain gauge was not the only tool employed to measure the small deflections of captive gyros in which feedback was omitted. Other responding agencies such as EM magnets and autosyns were also given a chance at this job. One of the most promising alternative approaches involved electromagnetic detection.\nThe deflection of a small magnet spinning on the axis of the gyro rotor, with the rotor and case flexibly mounted to permit small elastic rotation, is an endearing property of this trick. This trick, which was discarded for other reasons, exhibits very great sensitivity to small angular rates. All detection methods, by which angular displacement is tangibly extracted in the non-feedback captive gyro, are applicable as error detectors or unbalance detectors when feedback is employed. This application requires less ideally characterized response in the detecting means, as approximate maintenance of a null is all that is asked for. The accuracy of measurement is afforded by the known characteristics between some other physical agency and the balancing torque. Errors arise\nIntermediate points in a system may be annihilated through the ultimate comparison of the output with the input torque itself. The advantages that follow from the feedback technique are numerous, but the only disadvantages lie in the possibility of greater complexity and the special problems required for maintaining stability, not only at any given time but throughout the useful life of the equipment.\n\nA very compact feedback arrangement was embodied in the pneumatic captive gyro, which ultimately replaced electric forms in the angular rate bombing problem. This development was conducted almost entirely by Section 7.3, working in collaboration with Section 7.2, and thus need not be described in detail here. (See Volume 1, Chapter 4.) The capturing method led to a maximum relative angular displacement.\nA milliradian's placement involved a valving process with a particular captive gyro of the second kind and case serving as the sole moving part. Pressure areas were enabled to rapidly balance precessive torque and maintain stable displacement to close limits. The pressure difference between the valved pressure areas indicated the angular rate as output. It was necessary to dampen the moving system's motion, and a rotary dashpot with viscous fluid proved most successful. No attempt was made to prepare a captive gyro of the second kind using this technique, although it was generally recognized as possible. The mechanism employed:\n\nA milliradian's placement involved a valving process using a particular captive gyro of the second kind and case as the sole moving part. Pressure areas enabled rapid balancing of precessive torque, maintaining stable displacement to close limits. Pressure difference between valved areas indicated output angular rate. Damping the moving system required a rotary dashpot with viscous fluid, proven successful. Attempts to prepare a second-kind captive gyro were not made, but recognized as possible. The mechanism:\nIn modern pneumatic captive gyros, crossed-spring flexures have replaced gimbal bearings in the most advanced designs, considered for the pneumatic form of PUSS. Earlier experiments suggested that with such flexures and the pneumatic-capturing technique, no lower limit for detectable angular rates was evident.\n\nA particular captive gyro of the second kind, as a basic component of the pilot's universal sighting system, discussed in detail in Chapter 10, and for providing input data in that system comprising the airplane's instantaneous angular rates about its own vertical and lateral axes, one proposed and developed units were built around this design.\nA gyro element constructed by GE for a sight stabilizer in one form of a flexible gunnery director in the Superfortress involved an asymmetrically mounted rotor and motor in a double gimbal system of small dimensions. E magnets detected the deflections of the gimballed system in two dimensions, and pancake coils mounted at right angles on that system moved in a magnetic circuit stationary on the frame. Currents were supplied through flexible leads to each of these coils and to the DC gyro motor, which was locally speed-regulated. Tuned, frictional, nutation dampers had been supplied for the original function of the unit, which was as follows. In tracking, an operator supplied currents from his handlebars, through dynamics which imposed \"aided\" performance, to the pancake coils on the gyro. These currents precessed the gyro axis over a certain angle.\nThe two-dimensional field responded rapidly to the manipulations of the operator, initially providing a stabilized system. The entire sighting platform, which housed the gyro element, followed the gyro axis through appropriate servomechanisms. The rest of the ARE control equipment functioned as a standard director, utilizing precessing currents in the pancake coils as measures of angular rate.\n\nThe writer suggested using this same gyro element for our application in reverse. First, the gyro element's mounting or framework would be fixed in the airplane such that the neutral direction of the gyro axis aligned with the longitudinal axis of the airplane. Under arbitrary motion, the gyro element would then measure angular rates and provide stabilization accordingly.\nThe currents in the pancake coils were to be manipulated automatically to process the gyro axis continually into coincidence with its neutral direction in the framework and hence into coincidence with the longitudinal axis of the airplane. Since the applied currents would also accelerate the mass of the gyro rotor, motor, and gimbals, means were required, in the regulating channels, to separate the conflicting accelerating and precessing tendencies and to achieve stability in the null-seeking process. As before, the currents in the pancake coils were to be used as direct measures of the instantaneous angular rates. During the development that followed and resulted in the attainment of reasonably good success in terms of the sought characteristics, it was found best to\nDispense with the existing nutation dampers. By following the differential equations prepared, a logical sequence of control design proved feasible, capable of correction at every point, leading to confirmation of the degree of precision and stability indicated by the analysis. We were looking for time constants in the response of the order of 0.2 second. These were attained or exceeded. We wanted a reliable measurement of angular rate from a resolution of 0.0005 radian per second up to a maximum indication of 0.30 radian per second. We obtained such performance from 0.0003 to 0.50 radian per second. This development continues, owing to its application in Navy projects, with current work concentrating mainly on the engineering design of electronic control channels. It is evident, incidentally, that\nThe precise regulation of electrical supplies to the latter channels is unimportant. Regarding design details and testing methods, the general control connections were from each E magnet \"around the corner\" to the coil producing the corresponding precession. A pair of cross connections, with the appropriate operational characteristics, compensated for the inertia coupling that would otherwise unsettle the mutual operation of the two modes of control, which were simultaneously present. Since the E magnet indications were at 400 cycles per second, phase reference and rectification were necessary in each channel, with dynamic networks and final currents preferably at direct current. Thyratrons were used for space economy to supply these final currents. With milliammeters in the output current leads, and the gyro axis under automatic control.\nClose capturing and the framework, either hand-held or on a turntable, an impressive demonstration of rapid, sensitive, and accurate angular rate measurement was available and was seen by many visitors. Remaining small fluctuations in the gyro axis, and correspondingly in the output currents, are of magnitude consistent with the resolution of measurement; these are now considered traceable, not to mechanical friction in the gimbal bearings (approximately 0.001 inch-ounce) but either to rotor bearing noise or to torque impulses applied nearly about the spin axis by the d-c regulator of the driving motor.\n\nShort of very completely instrumented (and ultimately essential) trials in the air, there are several good methods for testing angular rate meters in the laboratory. Although turntables are a problem in themselves, which we shall discuss.\nA convenient method for imposing and removing pseudo-rates in space is merely to add weights on the horizontally disposed axis of the gyro in a captive gyro with capacitive deflection detection. One recent endeavor in our group for absolute angular rate measurement using a captive gyro involves a return to the nonfeedback method. With a smoothly running constant speed gyro in a case and a method of predictable and frictionless constraint, a powerful means for measuring mechanical displacement is provided by the variation of electrical capacitance between adjacent parts that belong respectively to the gyro and the framework. Compensation for those displacements which are not to be measured can thus be made inherent.\nThe use of capacitive methods becomes appropriate when numerous measurements or computations occur throughout the system, allowing a common oscillator to serve. Advantages include low reaction on measured structures, precision telemetering without local follow-up devices, and the opportunity for employing capacitive \"slip-rings\" of higher capacitance than, and in series with, the measuring capacitor. The latter can be placed in an electrically remote position in a mechanical system.\n\nIn the experimental apparatus referred to here, the gyro, initially of the first kind and potentially generalizable, was mounted entirely on four leaf-flexures. The flexures were mounted radially and fastened along.\nThe inner edges rigidly connect to the gyro case and along their outer edges to the frame. They are disposed such that their common intersection (if each flexure is imagined to be centrally extended) intersects and is normal to the gyro axis. The gyro axis is thus allowed to deflect primarily, although very little, about the common intersection of the flexures as precession axis. On rigid members moving with the gyro case and extending perpendicularly to the above precession axis, capacitor plates are mounted at the outer ends. Mate plates are attached to the frame at each end and on each side, providing two pairs of series capacitors which, placed in a bridge, respond solely to deflections which arise from precessive torque. For the problem at hand, the response to angular acceleration is negligible.\nA gyro of approximately 2 inch-pound-seconds is being used, with about 0.002 radians of relative angular displacement at maximum. An individual capacitance of 10 micro-microfarads is contemplated, which may have a total variation of 20%. Computations indicate a resolution below 0.0001 radian per second, and a time constant less than 0.02 seconds. This development is still in progress and may be continued by BuOrd through a separate contract (NOrd 9644) extending the work now under Project 3 7 AN Oscillatory Captive Gyro\n\nSuppose, in a captive gyro for absolute angular rate determinations, that the rotor turns periodically, first in one sense and then in the other. If under these circumstances the polarity of the angular rate measurement also were alternately reversed, in synchrony with the rotation, then the measurement would be unaffected.\nThe measurement of angular rate in a rotor may not be affected by the versals of its spin. This suggests the attractive possibility, which occurred to the writer some time ago, that a captive gyro could be built without conventional rotor bearings. If the rotor were oscillated about an axis within it, for instance, with perfect harmonic motion in angle, it could be connected to the framework by flexure-bearings, serving themselves as resilient means which would allow precise deflection. For an angular rate in one direction, with respect to space, the precessive deflection would also be oscillatory and of the same frequency as that of the rotor. The amplitude of the precessive oscillation would indicate the amplitude of absolute angular rate, and its phase with respect to the rotor oscillations could presumably determine the sign of the angle.\nThe rotor's angular rate can be resonantly driven, and the precessive mode may be close to resonance for an increased response. Such arrangements would be limited by the phase relations of the mechanical coupling. Strain gauges could be mounted on the flexing members and connected in various ways to ignore or detect the several deflections and corresponding torques, allowing measurement of angular rates.\n\nThe higher the frequency, the better, in general, but note that flexural accelerations and centrifugal stresses increase with the square of frequency, while the peak moment of momentum only increases linearly. When the frequency is increased for a given rotor, the amplitude must be altered to maintain similar energy content to that in a standard non-oscillating gyro. It can be shown that:\nThat rupturing stresses for any conceivable rotor shape or substance are reached at fairly low frequencies (such as 25 cycles per second). It may not be essential to maintain a high energy content, since angular deflection only is sought, and friction should be almost completely absent. Thus, in accord with the dimensional relations well known to strength of materials engineers, a very small, high-frequency gyro oscillator might turn out practical. This is even more attractive, since then the whole unit might be sealed up in vacuo, there being no bearings or other maintenance needs, much as with a vacuum tube. It is apparent that the measuring system might be the limiting feature, at least for wire-type strain gauges, but there is no fundamental reason why such other means as capacitor gauges, where reasonably high frequencies are possible.\nmight be locally at hand in the resonant drive, or even electronic or ionic detecting elements, might not work out. Since the direct measurement of absolute angular rate appears as such a universal need in modern aiming controls, and more generally for high-performance navigation, it might be equitable to write about an advanced development of this sort.\n\nSince the earlier discussions of this proposal, we have heard that somewhat similar experimental attempts, here and abroad, have at least met with partial success. For our part, we have done no experimental work on this topic yet.\n\n3.8 Centrifugal tension as a criterion for measurement.\nThe centrifugal governor responds to rotational speed with respect to a machine's foundations. This does not generally annoy the user, as the rotation of the foundation, or rather the earth, in space is relatively small. However, if such a governor controlled the speed of an alternator and was exclusively relied upon to maintain the accuracy of clocks, a given installation would run clocks fast in one polar hemisphere and slow in the other. While the forces on a point mass depend on linear acceleration and gravity as well as purely centrifugal effects, the following arrangement will isolate rotation: Imagine a pair of equal masses joined by a weightless and inflexible rod. Neglect the insignificant gravitational attraction between them. It is not difficult then, to demonstrate.\nThe total tension in the rod, reflecting the mutual separative effort of the masses, is proportional to the square of the absolute rate w at which the connecting line rotates in space. It is also proportional to the magnitude m of either mass and to the distance a between their centers of gravity, assumed constant or very slowly changing. In consistent units, it is evident that this tension can never be negative, and consequently, one cannot distinguish between rotation in a given sense and rotation in the opposite sense. We are dealing with a signless affair. Furthermore, the entire angular rate, in the sense of Chapter 1, is measured by the sum of the squares of the two angular velocities.\nThe orthogonal angular rate cannot be extracted directly for orthogonal angular rate determinations. This is a drawback for certain applications, such as tracking a given arbitrary direction with a meter, where the axis executes minute wanderings out of the principal tracking plane due to imperfections. In such cases, the mass-pair meter would read high due to the instantaneous and inseparable contribution from the perpendicular mode. For other conceivable applications, however, this property might be an advantage.\n\nThe main disadvantage of the proposed mass-pair absolute angular rate meter is its sensitivity, which drops off very rapidly for slow rotation. For instance, 0.001 pound would be obtained with one-pound weights one foot apart for an angular rate of approximately 10 degrees per second.\nThis is easily measurable for one milliradian per second, significant in many branches of fire control. It exerts approximately 0.00000003 pound (10 micrograms or so). This is best measured in the laboratory, at least under present-day circumstances. Of the several methods considered for instrumental utilization of this principle, only two were mentioned more than once or twice. One of these involved a pneumatic capturing system with ten pressure cups and a pneumatic double bridge, whereby the difference between two pressure differences could be handled. While probably feasible, the extreme requirements on precision of machining and adjustment, and the care essential in guarding against temperature gradients in such a component, appeared to prohibit the expenditure of time and effort. Another method employing specially designed instruments was suggested.\nFabricated flexures and capacitive detection were thought practical from a machining standpoint, but temperature problems would have been equally difficult. Many second order electrical effects would have been uncertain. POSSIBILITIES FOR THE FUTURE\n\nConsidered were possibilities for balancing the mechanical characteristics among several flexure supports. No actual work was done on this type of meter beyond analyses and computations. The only real appeal lay in the essentially motionless nature of the physical arrangement, without spinning parts or rotating fields.\n\nIf such a general proposal is ever considered again \u2013 and it may be because it is fundamental (we refer to centrifugal tension rather than any particular mechanism) \u2013 it may be worth considering a feedback from current to\nThe magnetic force utilizes the square law between current and flux, enabling the current to respond approximately linearly to the absolute angular rate.\n\nThree possibilities for the future:\n\nThe captive type of rate meter is likely to come into widespread use for various purposes previously filled by free or semi-free gyros. This likelihood is deduced from the advantages in flexibility and the inherent opportunities for improvement mentioned above. The trend should also be toward \"tighter\" capturing procedures. A good, standard, absolute angular rate meter of reliable and high performance would probably find an easy market.\n\nFurther indications include the fact that such meters can decrease impressively in size.\n\nA somewhat different kind of prediction along these lines is that angular acceleration meters will also become common.\nThe extensive application of accelerometers, both angular and linear, will be found more so as a fundamental input. Although angular accelerometers are not common components, such instruments can be constructed to extremely high sensitivity, speed of response, and tenacity to calibration using modern methods. Similar remarks can be made for linear accelerometers, which are better known and already considered essential components in certain important aiming controls. In the typical stabilizing device, the automatic control of acceleration to zero would serve just as well as that of angular rate, if the control were sufficiently delicate and of the proper dynamic characteristic, and where the regime of control is continuous. This is true since either general type of device must use long-term guides based on available landmarks such as North and Down, regardless of the difficulty.\nFor more complex structures with numerous servomechanisms, an angular accelerometer could be as effective as a free gyro or rate meter as a fundamental component. This doesn't mean we suggest replacing gyros with acceleration-controlled bodies, but rather that angular accelerometers could be smaller and cheaper for intricate structures. Control terms can be integrated when desired, with approximate operations. Precision integration of absolute angular acceleration, for more intricate purposes, depends on a practical integrator, which will eventually be available. Similar remarks apply to linear acceleration.\nThe trifugal angular rate meter of the last section can be considered a differential type of linear accelerometer. The important feature of absolute acceleration, whether of angular or linear motion, as a fundamental measurable, is its universal availability in pure form. Fundamentally, this is attributable to the almost perfect constancy of the property of inertia (both ordinary and rotational) in available physical bodies, and to the basic measurability of force and torque.\n\nChapter 4\nSIMULATION AS AN AID IN DEVELOPMENT\n\n41. THE PHILOSOPHY OF MODELS\n\nSo much has been written on the applicability and potentialities of physical models that it is hardly proper for the writer to give here a comprehensive exposition of such techniques. However, he would not find it difficult to articulate their value.\nHis enthusiasms lie in this extremely broad branch of technical theory and practice. In this chapter, methods of electronic models or simulators will primarily be described. However, model building and model manipulation span almost all physical media. From one perspective, most mathematical machinery may be considered a class of such models, as there must be a physical system obeying the same laws within the machinery, which is used to study any other system. The differential analyzer, in this sense, can be thought of as a synthesizer or flexible model, as well as an analyzer. This question of names is a controversial issue, involving definitions rather than anything more fundamental, and is best resolved by recognition that\nThe equipment under discussion acts as a bridge between analysis and synthesis, bringing these two essential modes of study closer together. Specific models are more prevalent, wherein problems of a particular category are the only ones studied. These may be simple replicas of other physical systems, retaining even the geometry and appearance thereof, but by a transformation of one or more coordinates, of space, time, energy, and so on, yielding a means for experimentation in which certain limitations are removed compared to the original systems. The well-known principles of similitude and dimensional analysis guide the construction, operation, and interpretation of models of this sort. In fact, the so-called pi theorem of dimensional analysis has even been taken to mean that the construction of a representative model is almost possible.\nWe shall deal only with dynamic models, which involve time as a principal variable. The transient state is of greater interest than the steady or static state, although these conditions of equilibrium are attainable and may be studied in the more general transient-bearing systems under consideration.\n\nTime in an original physical system is often reflected as time in the model, although it may have a scale factor ranging from a small fraction to a large number. Time can also be interchanged for some other dimension, or time can be eliminated.\nIn a model, or employed in cases where it did not occur as an important factor in the original, time appears as an angle in a mechanical differential analyzer. In the electric and electronic models to be discussed, time is generally preserved intact, although stretched or shrunk beyond recognition. The most impressive models or synthetic representative structures are those in which one physical medium acts in place of another, operating thus by virtue of one or more of the many analogies demonstrable among components involving the known physical media. Of such analogies, the better understood are those among mechanical, electrical, and thermal processes, where we include under mechanical processes such variants as hydraulic and pneumatic ones. All such processes are self-analogous under the duality transformation.\nInformation on the interchange of potential and kinetic energy. Regarding energy, the thermal case is exceptional as it makes electromotive force, for example, correspond to temperature. Both quantities acting as potentials. This analogy leads logically to the identification of quantity-of-heat with quantity-of-charge, of which only one is truly energy. The preservation of energy in such postulation of analogous correspondences in model techniques is not essential. It even forms a restriction in scope. When several media combine in a model or any useful system to be studied, it is of the greatest convenience to employ analogies which preserve energy.\n\nA distinction must be clearly emphasized between the various model structures, synthetic.\nAnd simulative devices and physical representations, which we shall henceforth refer to, for the most part, simply as simulators, constructed and employed in the laboratory as tools of research and development, and those intended for applications wherein an operator deals with the simulative equipment as a substitute for another apparatus represented thereby, and by such dealings familiarizes himself with the workings of the original apparatus under conditions that are relatively easier, cheaper, or safer. The employment of synthetic trainers in fire control applications is a good example of the latter category of usefulness, and is possible whenever the effectiveness of a given man-machine interaction is important in the operation of an aiming-control system. Generally, even an approximate simulation of the dynamic relationship is:\nThe sufficient knowledge for an operator in such circumstances, with which he must associate himself, is enough for his indoctrination or the continuation of his skill through practice. It is a common experience for a simulator developed for the first-mentioned purpose, that is, for purely laboratory purposes, to discover incidental or ultimate applications as a training device. In some such cases, there has been confusion over which end was being served by a particular equipment. Not infrequently, a trainer, in which certain approximations had been allowed as inconsequential to the needs of that function, has been misunderstood as presuming to embody the detailed characteristics of a complex fire-control system, along with the relevant relationships among combatants, projectile, and the geometry of interaction.\nThe possibility of misinterpretation, which might seem trivial from a larger viewpoint, has been of real importance in several developmental endeavors. It is worth guarding against even in makeshift operations typical of an emergency. A sharp line should be drawn, when more than a single homogeneous group is involved, between the laboratory simulator and the trainer into which it may be transformed.\n\nAn intermediate category must be mentioned, at the risk of diffusing the dividing boundary already indicated. Simulators may be constructed in a form more permanent than research's study phase for the express purpose of teaching what is already known of a given physical system. These are not trainers, although they may certainly impart to the user a facility in carrying out the dynamics of the system.\nIn this report, we will distinguish among various types of simulators, such as those used for adjusting parameters in automatic apparatuses to maximize performance and stability. A simulator of this kind could be called an educational simulator. In typical circumstances, it may also stem from the unavailability of a developmental simulator, as in the case of training simulators previously discussed. In this discussion, an effort will be made to distinguish faithfully among all these separate types.\n\nFinally, we cannot conclude this general discussion of models, of which our simulators are only a special case, without citing the purest model of all: the medium of the mathematician. The symbolism of variables, functions, operations, and equations, accompanied by the rules they follow, forms what is almost the ultimate in flexible models. Thus, the symbol for a variable is truly a representation of it.\nThe analogy of its physical embodiment is an equation representing some physical truth. Manipulation of the physical model directly reflects manipulation of the mathematical model or its symbols. Therefore, it is not surprising that an underlying standard for a model's sufficiency is provided by comparing the equations of the model and prototype. The wave function of the mathematical physicist provides a model without a tangible physical counterpart, but which describes in detail a complex relationship with properties agreeing with ascertainable data on the 'unknown' physical entity. Why ask for more? Prediction is all that counts, ideally. But this is already too far afield. We should soon be discussing words and language.\nBefore turning to the use of vacuum tubes in simulative applications, we will first address several items that will not be dealt with exhaustively but will define the general field of investigation. These items will not appear in detail elsewhere in the present report.\n\nFirst, as an example of a mechanical model structure, there is the so-called pursuit-collision course plotter. This plotter, which is a model of the purest geometrical sort, was needed to study the approach paths that might be obtained with the type of toss bombing equipment known as the DBS. A gyro method was involved wherein a mirror in the optical sight was positioned through linear combination of a stabilized direction and the direction of the target.\nThe frame of the airplane. Relatively tight coupling to the airplane was being considered. It was of interest to determine the constants of such coupling to realize the maximum allowance for target motion in the air mass. The problems were reduced to a single plane, and the positions of the target and attacking plane were simulated by moving points on a board. Each point belonged to a system with traction with the board through toothed wheels geared to establish the proper ratio of velocities. The markings of the teeth on paper provided a calibrated record; the direction of motion was provided by the orientation of the tractive wheels, and a tangent to the airplane path was periodically recorded. Proposed by M. Alkan and constructed by Section 7.2 through a contract with Stanolind Corporation in Tulsa, Oklahoma.\nThe vice was supplied to the Bureau of Ordnance, Navy Department. The position of an extending member along the orientation of the corresponding wheel was determined. The wheel's orientation itself was continuously determined by linkage to turn, with respect to the established coordinate system, in an adjustable ratio to the turning of the connecting line to the target. This \"simulator\" found practical use in the intended application and aided in the determination of parameters that, according to graphical tests on the records, yielded an optimum correction for the errors against which the general method was proposed.\n\nA similar device was developed at Mount Wilson for the study of plane-to-plane attacks. It undertook representing pursuit and firing courses and was later modified to include an embodiment of aerodynamic skid.\nThis work is described in OSRD Report No. 4737, issued under the sponsorship of NDRC Section 16.1. The resulting apparatus is a second example of a purely mechanical simulator that has had application in airborne fire-control development and research.\n\nIn the preceding chapter, we mentioned the experimental study of tracking conducted chiefly at The Franklin Institute by Section 7.2. This research, which was entirely for flexible gunnery and dealt principally with \"classical\" tracking aids and disturbed sights, will not be described in detail here. One reason for this reticence is that most of this work did not come under the immediate supervision of the writer. Another and more plausible reason is that it will presumably be described elsewhere.\nThe flexible gunnery lore to be reported, as part of our research on aiming controls, includes studies on the control of guided bombs AZON, RAZON, and ROC (Chapter 8), and the branch of the PUSS project where the simulation of dynamic responses to airplane controls was carried out. This latter effort was only beginning to reach a practical stage at the end of hostilities. We shall treat these separate topics in sections below.\n\nBackground for Electronic Representation\n\nFirst, a brief discussion will be given of an earlier application of electronic simulation made by the writer in connection with studies on automatic regulation at The Foxboro Co. Beginning in 1938, the writer was authorized to construct a series of electronic models, primarily for the development of automatic controllers.\nposed in detail by him for use in research on desirable dynamic characteristics for the controllers and/or regulators of industry. Although it was not uncommon then to use equivalent networks for synthetic studies on the dynamic characteristics of such apparatus as thermal and mechanical, a number of new techniques had to be invented for the regulatory study. An arrangement was devised, using individually 'Ted-back' components, for synthesizing the whole closed loop under automatic operation. One component represented the system being regulated, and adjustments were provided for convenient alteration of the constants to allow the synthesis of a great variety of such systems. Another component represented the regulator or automatic controller under consideration, and adjustments afforded similar flexibility there, so that not only existed but also could be studied the interaction between various systems and their regulators.\nIn newer proposals, appropriately forming the dual connection between components was provided for, along with incorporation of disturbances against which the regulator must act. Such disturbances included sudden alterations in the desired value, as well as other equilibrium-upsetting factors throughout the system. Any type or degree of disturbance could be chosen. Repetition of the disturbance periodically and display of a crucial variable of the loop on an oscilloscope against a time sweep in synchronism with the disturbance afforded an apparently instantaneous picture of the recovery transient under regulation. Parametric adjustments had immediate effect on this graph and could be continued until the desired stability and performance were in evidence.\n\nSince this original work was undertaken,\nThe study and design of cyclic dynamical systems, such as servo mechanisms, is complicated by various factors, including the high orders of the differential equations of motion and non-linearities. Even when these non-linearities are small, it is still a matter of considerable difficulty to decide upon the most desirable ratios between the system's parameters and to choose between different types of internal feedback systems, which may require making dubious premises due to severe analytical difficulties. The use of the electrically equivalent network of the system to be investigated provides the basis for a powerful method.\nThe method resolves difficulties by constructing an electrical network, modifying it for chosen scales of impedance and time. Feed it with signals simulating master system features, denoting the mechanism the servo system follows. A feedback path provides signals corresponding to slave mechanism characteristics. Master and slave signals are added by appropriate means. Input signals are applied and removed regularly for study, taking the system through a work-rest cycle with sufficient rest duration.\nThe subsidence of any transients that may be set up. If the time scale used in the construction of the network is suitable, the period of the whole cycle of operations can be made small enough to allow for the representation of the results on the screen of a cathode ray oscillograph tube, in the form of a seemingly stationary picture.\n\nThe above quotation might equally well have been taken from descriptions of the writer's proposals made in 1938, except for certain differences in nomenclature. From that time until 1941, he had constructed several such simulators and had applied them in the development of improved controllers and in the successful automatic operation of certain industrial systems. One of the most unexpected results was the use of the simulative equipment in the education of technicians who had to meet the problems of analysis, specification, and design.\nSimulation as an Aid in Development\n\nand an adjustment in the field. A session with the simulator substituted for a long interval of arduous experience with the practical problems of the mill and plant.\n\nOf such a synthesizer or simulator, there are several significant methods of operation other than that described above, although that was most familiar to the practical worker, who saw the transients of the recorder charts right there on the scope. Frequency analyses could be run directly on the machine. Related variables could be plotted directly against one another, eliminating the time variable. Random disturbances, rather than simple periodic ones, could be imposed; this was revealing owing to their broad energy content over a wide band of frequencies. For this purpose, ordinary tube noise was used. The writer naturally sought to apply similar techniques when, beginning in\n1942, he met analogous problems in the design of aiming controls. The applicability of this was not illusory, as attested by several war projects in which useful ends have been served in dynamical studies through electronic simulation. Certain tricks employed earlier for regulatory studies have not been applied in the latter work, and the writer is eager to return to those studies for servomechanism research and other applications, using the improved electric and electronic components recently available. More generally, it is felt that electronic simulative techniques will find growing and widespread usefulness for many recondite questions, both practical and academic, due to the broad powers of representation embodied therein and to the speed with which exploratory manipulation may be performed in the laboratory.\n\nFeedback amplifiers: 12, 3, 4, 6.\nThe application of amplifiers to simulative developments is one of the most essential techniques in this art. Applied in this way, the stability of the feedback circuit becomes primary, leading to the remarkable situation where stability studies are enhanced by the use of systems involving a set of feedback amplifiers. In the individual design of these amplifiers, stability studies may be valuable. However, such a circumstance is not uncommon in research, where the talents of the detective and dispassionate reasoning find limitless opportunities.\n\nIt will be assumed here that the reader is familiar with standard passive networks and the corresponding dynamical systems that can be represented by them without the necessity for feedback methods. Of the standard circuit elements, only the resistor and capacitor will be considered.\nCapacitors are necessary in electronic simulations, and it is fortunate that these elements are available commercially in relatively pure, or \"ideal,\" forms. There are two principal types of feedback in electronic circuits, which with their variations and mixtures have fundamental importance in simulative circuits. Cathode feedback and plate feedback are these two basic types, named for the branches of tube circuits in which retroactive operations occur. Alternative terminology identifies these as current feedback and voltage feedback, respectively, in recognition of the electrical mode which acts most predominantly in the two cases. Figure 1 shows the fundamental cathode feedback circuit, or cathode follower adaptation, which was earlier employed by the writer in simulative circuits.\n\nFigure 1. Cathode feedback circuit.\nFeedback amplifiers:\n\nThe inclusion of such material here does not imply classification. Much of the earlier work has been public knowledge, albeit not widespread. The writer had prepared and may publish descriptions of such work for unclassified categories of engineering. A brief explanation follows.\n\nOpposing currents circuits are produced in impedance Zi by sources Ei and E2y. The voltage ei tends to follow the input voltage eo due to the effect of the difference of these two voltages on the plate resistance of the tube. For proper choice of tube (preferably of high transconductance) and circuit constants, the error between eo and Ci may be kept very small, provided stable operation is attained. Thus, eo can be \"followed\" very closely by ei. Whereas eo may occur in a circuit with negative feedback, ei represents the output voltage.\nA low-power circuit, surrounded by high impedances, ensures the relative non-interference with Co in its natural environment due to the very high grid resistance at which the present tube can be operated. Power can be drawn from the circuit at Ci since the feedback maintains this voltage despite applied loads, within considerable limits. Thus, we have an important tool: an isolating or buffer amplifier with unit gain. If no current is drawn externally from Co or C2, and the sources Ei and E2 are exclusively involved in the present circuit, then the current in the impedances Zi and Z2 must be equal: IZ1 = Iz2. Now, if C2 is followed by a subsequent buffer amplifier, this provides a means for representing many operational characteristics. For instance, if the two impedances are:\n\nIZ1 = R1 || C1\nIZ2 = R2 || C2\n\nThen, the overall transfer function of the circuit is:\n\n(Vin / Vout) = (1 / (1 + sRC1) * (1 / (1 + sRC2)))\n\nWhere s is the complex frequency. This transfer function can be plotted to obtain the operational characteristics of the circuit.\nPedances are simply equal resistors, a polarity reverser or phase inverter results. For integration with respect to time, Z2 may be a capacitor and Z1 a resistor. Conversely, for differentiation with respect to time, the roles of resistor and capacitor may be reversed. The generalizations that are possible may easily be imagined. Initial conditions are imposed in straightforward ways, although certain ingenious processes have become useful. In the above integrator, the lower limit of integration may be established at any time by imposing a momentary short across the capacitor. A typical simulator may comprise a number of such feedback components, interconnected either directly or through the appropriate passive networks. In this procedure, criteria such as impedance-matching may be forgotten. Addition, or the formation, of more complex circuits can be achieved through the interconnection of these basic components.\nThe concept of linear combinations for two or more voltages, and consequently the variables these voltages represent, can be performed in various ways using the basic circuit of Figure 1. For instance, multiple feedback circuits may share the impedance Z2. Alternatively, these voltages can be connected through a high-resistance dissipative network, making eo proportional to the desired sum or linear combination. For subtraction, an odd number of phase inversions can be applied. The only drawback of the cathode feedback circuit, as depicted, is the requirement for at least one \"high\" battery (Ei). The anode source (\u00a3'2) must also be \"high\" unless Z2 is zero, as it may be in a simple isolating amplifier, for example. Thus, each such circuit functions differently.\nA circuit must have at least one voltage source for itself. This requirement, however, has not been a great burden in the laboratory, as the drain can be kept quite small. The writer used a large bank of dry batteries for this purpose, carefully shielded to prevent capacitive interstage coupling, and found it adequate to replace them every two years. Modifications are possible which will permit the adaptation of such circuits to single-source powering, but such sources must be meticulously regulated to present zero impedance and hence zero coupling between the using channels. Furthermore, such modifications complicate the circuits so much that plate feedback might as well be used.\n\nWe now turn to plate feedback. A common plate voltage source suffices for the plate feedback circuit, shown in Figure 2. (Figure 2: Plate feedback circuit.)\nIf the high-gain DC amplifier, as depicted in Figure 3, is properly designed, the term \"high-gain\" is used in a relative sense, compared for example to a unity-gain isolating amplifier. Only one such design is shown here as an example. The supply sources should be well regulated. Regarding Figure 2, it should be noted that the function of the amplifier in the (eg) block is to convert the small balance voltage Ae into a corresponding but much expanded variation in voltage Cg, and to reverse the sign. The effect is to keep voltage Ac very near zero. As in the current-feedback circuit, the point of operation (for the first stage) is not specified here.\nThe tube is chosen such that the grid input impedance is very high. Thus, the currents in impedances Zi and Zj are substantially equal. Consequently, eje = - ZjZi; and it can be loaded within reasonable bounds. The operation of addition on several variables can be carried out, as in the second method mentioned above for the cathode feedback circuit, by substituting a number of resistive paths for Zi and Zj, being also resistive, and each such path initiating at one of the variable voltages to be summed or combined. The coefficients of combination are adjustable by the separate connecting resistances.\n\nThere are a certain number of feedback applications which do not fall into the types above classified. For instance, it is possible to provide circuits which have extremely long time constants or long 'lags' of low order, for special purposes. Such time constants are:\nThe various kinds of servomechanisms or degenerative \"telemeters\" in prototype systems can be represented quite straightforwardly using electronic feedback components during simulative construction.\n\nAmplifier circuits, previously mentioned, allow the experimenter to create flexible models of dynamic systems. By simple interconnection, he can easily assemble the counterpart of any physical entity governed by a linear differential equation of finite order with constant coefficients. However, he is not limited to this realm, although many significant dynamic relationships exist within it.\nto  analysis.  For  the  larger  class  of  linear  rela- \ntions represented  by  equations  with  coefficients \nwhich  vary  with  the  independent  variable,  here \ntime,  a programming  of  the  adjustable  parame- \nters suffices.  Similarly  nonhomogeneous  rela- \ntions, with  prescribed  \u201cforcing  functions\u201d  (un- \nfortunate phrase!),  are  representable.  The \ngreatest  advantage  of  this  kind  of  simulation, \nhowever,  and  the  crux  of  its  power,  in  relation \nto  competitive  methods,  is  the  ability  in  simple \nmanner  to  incorporate  nonlinear  dynamics.  We \nneed  not  speak  of  the  analytic  difficulties  which \nare  there  involved,  nor  of  the  physical  impor- \ntance of  nonlinear  systems  in  general.  Suffice \nit  to  say  that  the  resulting  problems  preoccupy \nand  harass  some  of  the  best  available  mathe- \nmatical brains. \nOTHER  SIMULATIVE  COMPONENTS  AND  COMBINATIONS \nOne  very  simple  source  of  nonlinearity  is  the \nThe presence of a mere boundary in the range of a variable. Many examples may be cited and amply supplied by the reader. The simplest examples are furnished by transformations from a given variable to a function thereof which is either nonincreasing or nondecreasing over the entire range to be considered, and in which for at least certain portions of the range the function is unchanging. An instance is shown in Figure 4.\n\nElectronic embodiment of such a transformation is simple. It may involve only a pair of rectifying diodes, as contained for example in a 6H6 tube, so biased that voltages corresponding to variation of the first variable beyond the boundary cause one or both diodes to conduct.\n\nSpecifications:\n1. R large compared with \"closed\" resistance of diodes\n2. R and R comparable with \"open\" resistance of diodes\n\nFigure 4, Boundary function and its simulative counterpart.\nA bounded interval produces no further change in the function or transformed version of that variable. Such an arrangement, as shown in Figure 4, must always be approximate, but the approximation can be refined to any desired degree by appropriate choice of electrical circumstances. Only one type of non-linear component is illustrated here, but it is evident that by combination of such circuits, a great variety of similar and more intricate relations may be embodied. We are not restricted to functional relations representable graphically by a single curve or analytically by single-valued dependencies. Physical relationships such as inertia, for example, where there is backlash or play in a mechanical connection, may be simulated through the application of biased rectifiers in circuits where charge can be stored over reasonable intervals.\nIn general, the inclusion of major non-linearities fundamentally alters stability considerations in control systems or any apparatus where dynamic performance is of interest. It is thus important to be able to treat such nonlinearities without the endless drudgery of straightforward analysis. A useful tool in simulation for this general class of dynamics, particularly those in which non-linear relations are included, is the follower or servomechanism, which transforms voltage into a corresponding resistance. Consider first the case in which a proportional relationship exists between the input voltage and the resulting resistance.\nPortional correspondence is enforced. Many such components have been built and applied in the simulative ventures we have dealt with. The usefulness of a properly made component, which is great, is not at all limited to the representation of nonlinearities, but appears wherever the automatic manipulation of a resistor or potentiometer is desired. The construction may be very neat and simple, and high speed and precision have been shown fairly easy to attain. Naturally, the time constants of the response should be well below those which are involved, purposefully, in the remainder of the simulative channel in which such a component occurs; it has been satisfactory to employ pairs of circular, wire-wound potentiometers driven by small DC motors energized either from polarized relays or from vacuum tube circuits. The error signal, which is supplied, is supplied to the component.\nThe proportional voltage applied to an interpreting network and thence to the motor circuit is derived from both the input voltage and the voltage division of one of the driven potentiometers. The other potentiometer, driven for example in tandem with the first, provides a free resistor having resistance proportional to the input voltage. The introduction of any appropriate function may be accomplished, through the voltage-to-resistance follower, by embodiment of such function in the resistance versus motion law of the final resistor, or of its reciprocal or inverse in that of the follower-resistor itself.\n\nA means for rapid conversion of a voltage into a proportional resistance enables the realization of many flights of fancy. We record only:\n\n1. The proportional voltage is applied to an interpreting network and then to the motor circuit. It is derived from both the input voltage and the voltage division of one potentiometer.\n2. The other potentiometer, driven in tandem with the first, provides a free resistor with resistance proportional to the input voltage.\n3. The introduction of any function can be accomplished through the voltage-to-resistance follower by embodying it in the resistance versus motion law of the final resistor or its reciprocal or inverse in that of the follower-resistor itself.\n4. A rapid conversion of a voltage into a proportional resistance makes possible the realization of various imaginative concepts.\nHaving a feedback amplifier with the associated pair of impedances restricted to a pair of resistances, it is possible to perform multiplication or division among voltages in various ways. The resulting product or quotient has also the form of a voltage. While the variables reflected in the resistance of either resistor pair cannot normally take on negative values or in certain cases even zero, modifications are possible whereby equivalent variables can be made to take on negative or zero values.\nThe feedback amplifier's input voltage can be used along with those that proportionally set the \"input\" and \"output\" resistances. In this case, the output voltage is proportional, through any desired factor of scale, to the ratio of the product of the first two voltages to the third voltage. Simple products or ratios, as well as reciprocals, can then be evaluated in a single component. Through duplicate roles, for instance, a voltage (or rather the variable it represents) can be squared through multiplication into itself. By including such an arrangement within a more comprehensive feedback loop, inverse operations such as extracting the square root can be performed. We speak here only of real variables. With combinations of similar components.\nComponents, in series or cascade, it is evident that such delicate operations can be carried out as raising a variable to any fixed rational power. This type of conversion, of course, may be accompanied by any (otherwise) linear dynamic operation of the classes already mentioned.\n\nConsider now integration with respect to variables other than time, or in general with respect to an arbitrary independent variable. An arrangement was proposed for this purpose, but was not constructed practically for a variety of reasons, primarily because no need persisted for it which was not more easily satisfied by other means.\n\nConsider a time integrator as described, with fixed resistive and capacitive elements, and let it be supplied as input with a voltage which is the product, obtained as already indicated, of a primary voltage (preferably, in this case, always of a sinusoidal form).\none sign) and the time derivative, evaluated in the regular feedback manner, of a second input voltage 62: The output voltage of the time integrator is thus the integral of voltage ei with respect to voltage 62. Thus, RC/dt ei de2.\n\nWithin certain limitations, and with precision of the order of 0.001 to 0.01, it is evident that this more general type of integration is feasible, and the potentialities of electronic simulation are thus extended to the dynamical realms of the better-known differential analyzer. Much practical development, however, remains to be completed along these lines, although only the fundamental elements already treated need be involved.\n\nReturning momentarily to linear systems, with the continued implication none the less of nonlinear generalizations and ramifications:\nWe acknowledge the collaboration of Loebe Julie in connection with this item and certain other conjectural plans for electronic simulative measures mentioned here. Other simulative components and combinations include two types of assemblies of interest in simulative structures, which are singularly adapted to electronic techniques. One is the approximation of pure time lag, or a direct shift of a function along the axis of time (or of another independent variable, by extension of the method), which can be achieved through recognition of the limit. Several methods are available, each using a chain or cascade of feedback circuits to prevent the passage of energy except in one direction along the chain. A possible circuit for M = 4 is shown in Figure 5, where cathode follow-circuits are used.\nFigure 5. Cascade of cathode followers as lag amplifiers (refer to Figure 1) are employed. Any number of such sections may be used, and the larger the corresponding value of \u03c4, the closer the approach to a pure time lag. A useful approximate network for cases where small n suffices is shown in Figure 6, which is a passive approximation of Figure 5. The number of sections is limited by the available magnitudes of resistance and capacitance. Note that each section has the same (unterminated) time constant, and the energy transmission grows progressively smaller from input to output.\n\nAnother useful arrangement of the above elements can be used to synthesize any linear relationship which may be adequately described by a rational function of the derivative operator, assuming for simplicity with respect to time. Such an operator is m 2 di'/dt', i=0.\nFor the purposes of exposition, assume neither m nor n is greater than 5. Distributed systems are essential for the precise representation of such operations, but approximations by lumped systems of low order sometimes suffice. We make use of the operational characteristic of a feedback system for the simulation of R(p)f. The denominator is obtained by feeding back a linear combination of the branch outputs of a chain of differentiators. The input to the first differentiator is made the difference between an input voltage and the given linear combination. Thus, we obtain familiarly, i + icX, as the operator describing the relation between the input difference and the input voltage. The separate unity term may be eliminated by:\n\ni + icX = icX + i\ni(1 + icX) = icX + i\ni(1 + icX) - icX = i\ni(1 + icX - icX) = i\ni(1 - icX) = i\ni = i(1 - icX)\ni / (1 - icX) = 1\n\nTherefore, the operator describing the relation between the input voltage and the input difference is 1 / (1 - icX).\nSetting Co = 0 reproduces the system with the earlier denominator. The numerator and the desired total characteristic are created by taking a new linear combination from the same chain of amplifiers. Figure 7 shows the assembled system, which uses plate feedback systems of the type shown in Figure 2. The coefficients of R(p) are directly adjustable negative values, requiring the addition of a 'phase inverter' in each such case. This arrangement, with appropriate means for insertions of forcing functions and presentation, is extremely educational in the laboratory. A number of interesting modifications are possible. By dividing both numerator and denominator by p^(higher power), we can simulate the system as an aid in development whenever such an operation is rigorously permitted.\nObtain a rational function of the definite time integrator and proceed exactly as above, except with the replacement of each differential calculus component by an integrator. For many purposes, this is preferable; for example, it is easier to establish initial conditions. When certain variables in a physical system to be simulated are related by complex static functions, meaning by this term that time is not fundamentally involved, it may be convenient to represent such functional relations by a mechanical linkage rather than through a combination of electronic elements as such. Such linkages may involve any number of inputs, and may sometimes have more than one output. They are similar to computing linkages for full-scale aiming controls.\nAngular motion is most convenient for input and output variables in this report. Angular motion is readily provided in electronic simulators, including electronic and mechanical ones, by the resistive follower, which correlates mechanical angle with resistance and hence with voltage. Angular outputs of the linkage can conversely be accepted as resistance, as reasonable power is available from the feedback inputs and thereby converted again into voltage. The result is an extremely flexible form of 'static' computer, entirely surrounded by voltages. By proper design of the linkages, where the same engineering principles apply as with more worldly types discussed elsewhere, high speed and reliability can be obtained. There have been few occasions in our work for elaborate linkage compositions.\nPotentials for this role are practically unlimited, particularly for intricate aerodynamic interrelations. The ease with which modifications can be incorporated, such as alteration of link lengths and pivot positions, is a large attraction. The flexibility of electronic simulation techniques regarding scale factors of analog versus prototype is great. The possible extremes of speed and sluggishness are relatively far apart, applicable only to time scale; other dimensions are correspondingly adaptable. Furthermore, one of the principal fields of application for this type of simulation has been to systems involving a human element, and the time scale must be religiously represented as it exists in the full-scale apparatus.\nThe man, as an unalterable component with non-adjustable time parameters in the model, must be accepted as is, whether trained or untrained. Since the remainder of the model must be adapted to him, particularly with regard to time scale, it is welcome that electronic structures find little difficulty in being thus adapted. In any such case with a human \"component,\" many other provisions must be made to achieve naturalism.\n\n4.5 SIMULATION OF FLARE-BOMB GUIDING\n\nThe projects connected with the development of aiming-control systems for the phorodromic and pseudophorodromic guiding of the bombs discuss AJONFIDl^TiAf, SIMULATION OF FLARE-BOMB GUIDING. AZON, RAZON, and ROC are discussed more generally in other parts of this report. Electrically.\nIn electronic simulation, the role was crucial in our projects, as in others, and it is appropriate to discuss here the several such simulators we constructed and employed in this work.\n\nA guided bomb of this type (we refer to what are called high-angle bombs) fell toward the target. The guiding operator was instructed to operate the controls at his end of the radio link, from above in the bomber, to superimpose either the flare of the bomb itself or an image synthetically produced on the selected target below.\n\nThis operation was one- or two-dimensional, depending on the class of missile and the preferred mode of operation. The accuracy of the bomb fall depended heavily on the accuracy with which the above superposition was carried out, particularly at the moment when the flare or image aligned with the target.\nThe missile reached the target level, making the stability and other dynamic characteristics of the guiding process crucial. With extensive knowledge of the space paths and guiding responses of such bombs, obtained from three-dimensional solutions from the new differential analyzer at MIT, and observing the excellent correlation between these solutions and full-scale tests, we were well-positioned to determine and recommend the dynamic nature of electronic simulators capable of accurately representing the process for an operator in the laboratory. During development, various simulative equipment were prepared, of varying degrees of precision and excellence, and were effectively applied to the research problems and training needs.\nIn the case of the bombs under consideration, the operator sends messages to it via radio link using the angular motion of a handle in front of him. His means of manipulation, which is sometimes in one angular dimension and other times in two, is analogous to the handlebars of a turret control in flexible gunnery and to the pilot's control stick or column in fixed gunnery or other pilot's fire control procedures. The handle operates a double-throw switch in some cases and potentiometers, one or two of each depending on the dimensionality of the control. Servo motors on the bomb are thus energized to move the control.\nThe surfaces have three stable positions toward which they proceed for continual occupation, determined by the corresponding individual handle switch. In the on-off case, the velocity of motion in transitioning from one position to another is constant and reverses if a new position in the opposite sense is ordered during the motion. The velocity of such motion is a property primarily of the local bomb controls, embodying an important design criterion for both economy and stability. Simulation was essential in addressing the latter question. Regarding manipulation, there is also a 'corresponding' form of control, where intermediate positions of the control surfaces are held for continually occupied corresponding positions of the control handle. This relationship.\nThe control surface position is roughly proportional to handle position and is approached substantially at a constant rate during transient intervals. Simulating these circumstances is fairly direct. A standard control handle is used in the simulator, with either switches or potentiometers attached. Voltages derived from the control handle are followed by the voltages corresponding to control surface positions through electronic feedback, which is precisely analogous to bomb servos. The simulator circuit involves an amplifier as a sensitive relay and an integrator to imitate the constant rate of servo-actuators in the bomb. Since the bomb is roll-stabilized in practice, no \"phasing\" controls were necessary. One or two operators could be involved for both the real proceedings and the simulator in the laboratory.\nWe consider the simulative presentation, by which the laboratory operator sees the replication as an aid in development. For our purposes, cathode-ray tubes (referred to hereafter as oscilloscopes or scopes) were employed in all cases. The luminous point on the screen, corresponding to the projected visual impression of the bomb flare, was observed to move in response to guiding operations and to disturbances, and to hover near, or in inexpert hands less near, a stationary spot corresponding to the target. In the case of AZON, the target was typically a line, rather than a spot as for RAZON or ROC. Elaborations were introduced to promote realism. For example, the surface of the scope screen was coplanar and in focus with that of the image of an aerial photograph, so that to the operator, the flare appeared to be at the same level and in focus as the photograph.\nThe aircraft seemed to glide over the landscape, as in the real operation. Thus, he could choose targets at will or under direction from a superior intelligence to which he was, or pretended to be, subordinate. Many games were possible for the promotion of guiding skill. Such further refinements were possible as the gradual diminishment of the intensity of the spot on the scope as the bomb dropped, corresponding to the weaker brilliance of the flare as the bomb receded below, with a momentary brightening at the end for the detonation. The variations are readily imaginable.\n\nBetween the voltages corresponding to the positions of the control surfaces of the bomb and those deflecting the beam of the scope in correspondence to the direction of the bomb from the bomber is incorporated the simulative electronic channels which represent the:\n\n(This text appears to be incomplete and lacks clarity without additional context)\nThe lateral acceleration of the bomb is nearly proportional to the deflections of the control surfaces, as well as to the speed and altitude of the bomb. For the stability study, the proportionality is different in each direction, or in \"range\" and in \"azimuth,\" so an asymmetrical guiding response was employed in the simulators for a closer representation. The function of speed and altitude, affecting the spatial acceleration of the bomb, is sufficient for the synthetic reproduction of guiding dynamics.\nThe function of deflections, in reality depending on them via drag function and geometry of flight path for missile, could be transformed into voltages through multiplication or division by a selected time function since dropping. Integrating these voltages twice with respect to time would yield voltages representing lateral motion of the bomb in air mass. To determine bomb direction from bomber, knowing fallen distance (available as function of time) was sufficient. Components described could be compounded to achieve this procedure. A programming device was introduced to execute this.\nThe independent effect of distance to the bomb or perspective, known as the perspective effect, was impressively noticeable in the time functions of variable resistances. If the bomb in the simulator was left off the mark in angle, with no corrective guiding, its approach angle toward the target, due to the simulation of decreasing parallax, was identical to that of a real bomb viewed from a bomber. This was particularly appreciated by those who had witnessed bombs miss in air trials. An essential feature of bomb simulators is the embodiment of boundaries on the control variation.\nsurface deflection, which ran actually against stops, and on the rates of motion of these deflections, which were limited by the capabilities of the bomb servo motors. The discontinuities involved were crucially important in the overall question of stability and were incorporated in the simulators by means of biased rectifiers, as already described. Numerous auxiliary controls are necessary for the facile operation of such simulators. These may be straightforwardly provided. One must be able to start the operation precipitately, having set in the desired initial conditions, of wind, initial dropping error, and so on. At the end of the time of flight, it is convenient to freeze the bomb position for scoring, which may be accomplished by opening the capacitor circuits of the integrators.\nThe adjustments must be returned quickly to the initial condition for the next \"drop.\" The form of auxiliary controls depends on whether the simulator is for laboratory study or the rougher needs of a training device. Experience was gained with both applications, and fuller details may be found in the various contractors\u2019 reports (See Division 5, Volume 1).\n\nSimulation of Television Bomb Guiding\n\nThe ROC bomb, at one point in its career, was experimentally equipped with a flare for line-of-sight guiding. However, its initial purpose was quite different. Primarily a vehicle for radar-homing, ROC was also adapted to embody the miniature television camera and transmitter (MIMO). The latter had been developed for suicide bombing by proxy. The missile, with MIMO, was to be dropped naturally toward a target as a bomb, and subsequently, it would guide itself to the target using the television camera and transmitter.\nA remote operator, over a radio link, guided a forward-looking television camera. Transmitted in the other direction, this method and the ROC bomb are not described here, as they are covered in the chapter on guided bombing and reported in full by other agencies, such as Division 5 of NDRC. The concerns were controls for optimal approach in terms of hitting probability and process stability.\n\nA control handle is involved, as before.\nThe simulator in this prototype system is two-dimensional and features potentiometers for proportional manipulation of bomb controls. Although a one-dimensional counterpart was considered and employed for certain studies, the method of operation for the control surfaces over the radio link and through the bomb servos is similar to that of normally phorodromic bombs. The minimum run-out time, from zero to full deflection, is longer for ROC than for AZON and RAZON, and it was of interest to determine the effect of this parameter on stability of guiding. As expected, it proved important from this standpoint. The scope presentation now corresponds to that on the television receiver screen. The target appears on both.\nIn proper circumstances, the simulator displays a single spot of fluorescence for one case and a landscape toward which the real bomb is heading in the other. The absence of the illusion of changing perspective in the simulator is partly repaired by the preservation of the increasing angular response observed in external objects such as the target, in response to maneuvering controls, as the bomb continues on its course. A second spot appears on the simulator scope, differing geometrically from that representing the target, as the analog of a movable reticle proposed as an aid in guiding. This proposal, which shares common elements for various detailed methods considered, involves the manipulation of the control handle by the guiding operator in such a manner that the moving reticle is maintained.\nThe control handle produced two influence paths from the proposals for effective guiding aids. One path was to the bomb controls via the radio link, and the other was to the moving reticle on the scope screen. The choice between these influence paths for inclusion of aiding dynamics, and the nature of the latter dynamics wherever placed, varied in the proposals. The simulative equipment aided in the choice of these dynamic control adjuncts.\n\nThe relative direction to the target, or lead angle, represented by the departure of the target spot from the center of the scope, and the absolute direction of the target in space, given also by the absolute direction of the bomb from the target, were simulated by varying voltages. The rate of turn was also simulated.\nThe lateral acceleration of the bomb is proportional to its deflection of control surfaces under guidance. It is also proportional to a function of speed and altitude, adequately representing a function of the passage of time since release. The variation of lead angle depends on the bomb's turn in the air mass and the rotation in space of the line of sight to the target. There is a direct summation among these angles which may be simply incorporated in the simulator. Additionally, the rate of rotation of the line of sight is proportional, additively, to the product of the lead angle into the bomb speed and the lateral speed of the target, and is inversely proportional to the range. The latter is taken as a function of the independent time variable.\nIt is adequate to incorporate sufficient simulations in the described type of components to present both lead angle and absolute direction as voltages in response to bomb control operation via the handle and the passage of time. Appropriate boundary circumstances are also easily included. The lateral speed of the target in the air mass can be set at will, in any direction and to any desired magnitude.\n\nIt has been simple to include, in an independent channel from the control handle to the moving reticle, for instance, whatever conjectural dynamical relations were proposed for effective guiding. Several such systems were represented. One proposed by the writer was successful when proper initial conditions were observed, leading to high terminal accuracy even in the presence of constraints.\nThe substantial target motion in the air mass. The primary point is that means were available, in the simulator, to evaluate the excellence or otherwise of all the various dynamic proposals that arose in development. Such assessment is not practical analytically, partly due to the nonlinearity of the systems being studied. Although the reasoning is omitted in this context, it was found effective to transmit signals to the bomb controls which led them to deflect in proportional response to a linear combination of the lead angle, as observed on the scope or screen, and the rate at which the lead angle is changing. The constants of such combination depended on the conditions prevailing when the operation began. Simulative study showed that such conditions could be adequately predicted, that the constants could consequently be chosen to suit, and they were hence effective.\nThe dynamics of control led substantially to an interception approach by the bomb to the target, under manual guiding, even in the presence of target motion in the air mass. These conclusions were later fully confirmed by large-scale tests, employing the control dynamics here conceptually initiated.\n\nThe dynamic relationship between the lead angle and instructions to bomb-control deflections was actually embodied, first in the simulator and later in the larger equipment, by insertion of the inverse dynamics, essentially a first-order lag, in the connection from handle to moving reticle. Thus, on the assumption that the target is tracked by the latter reticle, which thus reproduces the lead, and that the handle position directly transmits the proportional control-deflection orders,\nThe dynamic connection from the lead angle to the latter deflection is affected. It is significant that the collision or interception approach was possible in this case through a perverse form of \"proportional navigation,\" without directional stabilization or space-rate determination in the missile. This was done by interpreting absolute turning of the bomb as being caused by the control surface deflections, which were continuously and directly knowable, and as being affected simultaneously and additively by the component of gravity, which was predictable through implicit embodiment in the dynamics of the control. A favorable circumstance for this sort of trickery, which is more straightforward when directional references or absolute angular rate meters are available in the vehicle itself, as seems indicated for the future.\nThe absence of rapid roll, pitch, and yaw in the ROC bomb's body is the reason, we repeat, for the lack of miss in guiding. This combination of properties was not obtained fortuitously but was planned for and designed.\n\nSimulation of Airplane Dynamics\n\nIn assessing the miss in guiding, i.e., the minimum lateral distance of the bomb from the target, this quantity is not easily measurable in terms of voltages in the simulator. A good method for this assessment was conceived and installed at the Columbia Laboratory. The derivative of the angular direction of the bomb, as seen from the target, appears as a voltage under simulation at an instant when the bomb is still a short distance from the target.\nThe ratio a/r would be well-known from the missile's terminal speed Vx. It is possible to evaluate the missile as the product of the remaining range a's square, divided by the angular rate, all these quantities being essentially constant from one trial to the next, except for the angular rate. Indication of the latter on a meter then provides a sensitive measure of error and a quick and easy means for scoring, either in laboratory studies or for training purposes.\n\nCessation of hostilities brought this project to a halt in development, but it is still planned to prepare an altered version of the television bomb simulator for the needs of familiarization in the field, presumably with guiding trials of the missile itself.\nIt is considerably relevant, regarding the powers of simulation, that the equipment described above, through a mere change in connections and an alteration of adjustments, was employed in a stability study of underwater torpedo controls. This was pursued in our laboratories, during a brief interval, by Section 7.3 following a suggestion by the writer that a problem they were studying would be amenable to such simulative methods, and that these methods would encompass the nonlinear properties of the controls, which were the source of some concern. The previous analysis had been based on linear theory. We mention the application only by way of indicating the flexibility of the electronic simulators which have thus come into use. It is understood that this particular study was satisfactorily concluded.\n\n4.7 Simulation of Airplane Dynamics.\nA much  more  ambitious  project,^\u2019\u00ae  begun \nonly  recently,  was  for  electronic  representa- \ntion of  the  complex  dynamics  which  obtain \nbetween  the  flight  controls  of  the  pilot  and  the \nmotions  in  the  air  mass  of  his  craft.  This  work \nwas  connected  with  the  PUSS  project,  under \nNO-265,  and  contemplated  the  inclusion  also \nof  simulative  components  representing  the  en- \ntire computing  sight  therein  involved.  Some \nremarks  are  made  on  this  score  in  Sections \n2.1  and  2.8.  A fundamental  consideration  in \nthe  success  of  such  automatic  sights  is  the  na- \nture of  the  interactions  among  the  tracking \nsystem,  the  computing  and  display  system,  and \nthe  gentleman  at  the  controls.  Owing  to  the \nrelative  newness  of  this  project,  to  the  fact \nthat  it  is  actually  part  of  another  project  de- \nscribed elsewhere,  to  the  expected  continuation \nof  this  other  project  together  with  its  simula- \nThe complete set of reports for this enterprise have been submitted by the contractor, and we will not discuss it in detail due to their availability. The simulative techniques used are not essentially different from those of other projects, although greater complexity was required. Refinements need to be made before the apparatus is effective. It is now possible to experience \"electronic\" flight in the laboratory, the illusion being accomplished by simulative components between the voltages incurred through motion of the mock controls at one end and the voltages which deflect the spots on scopes to represent target, horizon, and sight reticle at the other end.\n\nThe Bureau of Aeronautics Special Devices\nDivision was consulted at the inception of this project in connection with a synthetic trainer in development for single-seaters, which surpassed, in the faithfulness of dynamic representation being sought, any previous like attempt. This trainer, SIMULATION AS AN AID IN DEVELOPment, was for combat approaches as well as for other difficult operations such as carrier landings. It was to be supplied with a simulative computer under development by Ford Instrument Co. An ambitious display system was being planned, of partial interest for our purposes, which involved an overhead, inverted relief map in color and a periscopic viewing arrangement; extendable, rotatable, tippable, and translatable. A somewhat complex optical system was to have been involved. As to the theory of the airplane motions, a workmanlike approach was to be taken.\nanalysis had been prepared at the depot in New York in which coordinate systems for unambiguous simulation were worked out in great detail. This background was helpful to us, partly because such features as coordinate systems and the several transformations these systems must undergo in the simulator's workings form the largest group of technical problems involved. After commencement of the project, little contact was sought with this particular Navy agency, since we tended as a first approximation toward a less precise model, and since a somewhat different coordinate system was finally settled upon (the aerodynamical equations of Sir Melvill Jones were taken as standard). It was planned ultimately to join forces when the equipment had attained a demonstrable status, since each party considered that mutual development might be beneficial. On the whole, however,\nBuOrd was dealt with chiefly in this simulative venture instead of BuAer, as it was cognizant of the more inclusive PUSS project. The parts of the simulative assembly having to do with the operator are enclosed within a model cockpit. Included are the potentiometric 'Yecognizors' for control motions, such as stick, rudder, and trim adjustments, signal indicators on the instrument panel, and a set of three scopes arranged above to present moving indices on a common focal plane, seen in the normal forward direction. These scopes carry visual indications of the direction to a target on the ground, the altitude of a \"road\" passing through the target, and the cross hairs of a computing-sight reticle.\n\nApproximations are included in this first version.\n\n(By Seaman Steinhardt, late of the University of Vienna.)\nThe model represents horizontal flight or a gliding or diving approach toward a ground-level target. Plans include circling and wing-overs during attacks. The simulator's electronic channels cover circuits for airplane responses in roll, pitch, and yaw, geometry transformations between airplane and target coordinates, and differential equations for the PUSS computing system. The main approximation is the assumed equivalence of yaw-pitch and pitch-yaw sequences.\nThe error of this assumption is not influential below roll-angles of 20 degrees or so. More complex circuitry could replace this approximation in the simulator with the unapproximated circumstance, using no new components beyond those already indicated. All the equipment, which occupies half a small roomful, consists mostly of amplifiers, connective electrical structures, and regulated supplies. Plans are for transportation of this apparatus from New York to Philadelphia, where it may be used in continuation of the Navy Project NO-265, under the auspices of a direct BuOrd contract (NOrd 9644) at The Franklin Institute.\n\nFour potentialities for the future:\n\nFrequently, during several of the developments above described, it has been thought and said that for the increasingly diversified uses:\n\n1. The approximation could be improved for larger roll-angles.\n2. The simulator could be used for other applications, such as aircraft control systems or missile guidance.\n3. The equipment could be miniaturized for use in portable devices.\n4. The technology could be adapted for use in other fields, such as industrial automation or scientific research.\nTo which the simulative methods were being applied, requiring new construction or at least major physical rearrangement of components each time, it would be preferable to build an extremely general and flexible assembly, covering every conceivable type of system. This could be adapted to any particular problem simply by the manipulation of conveniently provided organizational controls. Knowledge of the means for achieving quite impressive generality had gradually been gained, and the proposal for such a supersimulator, as it came to be denoted, was considered not at all fantastic. After all, witness the differential analyzer. A considerably smaller expenditure would provide a machine, albeit less accurate, of much greater power in terms of equations which could be embodied, and of greater flexibility on the time scale. Although a human engineer could design and construct a specialized simulator for a particular problem, the advantages of a general-purpose supersimulator were clear.\nAn operator may be included as a component in a differential analyzer, but this is not done in imitation of a corresponding activity in a situation under representation. In guiding bombs, for example, the analyzer \"dropped\" a bomb in 15 minutes, while in practice it fell in 35 seconds. This is not a permanent or inherent limitation of such machines. Although no supersimulator, in the full sense, has been prepared yet, there are many who might still be found to be champions of the plan, and it would seem to have certain applicability to future developments in a variety of technical fields.\n\nFlight can be taught by models, at least through most of the learning period, and electronic simulative techniques will certainly be economically superior in this respect. The same remark is evidently valid for the special fields referred to.\nflying operations, whether local or remote control, of combat conditions. Since the equations of rocket flight are not difficult to simulate, and seeking or remote-guiding procedures, manual or automatic, are representable by straightforward extensions of the techniques of this chapter, it is evident that guided rockets may be studied by such methods. Warfare among such missiles could thus be staged and observed entirely in the laboratory, possibly with statistical machinery in attendance for interpretation and assessment. Years of experience and of trial and error on the development of controls and dynamic components could thus be collapsed into hours. There is, in reality, no limit at all.\n\nChapter 5\nLINKAGES FOR COMPUTATION AND MANIPULATION\n5.1 General Type Considered\nA/Technical linkages and the operations\n\n(Note: The text appears to be mostly readable and free of major errors. No significant cleaning is required.)\nThey perform are of permanent interest to the geometer, who finds them irresistibly fascinating, and they hold attraction, in addition, for the analyst who sees recondite real functions, perhaps of several variables, come to life in his hands. Throughout this discussion, we refer to linkages in the purest form, in two or three dimensions, meaning thereby those linkages which consist in assemblies of moving parts which are joined at points or lines only, having no rubbing or rolling except in the neighborhood of such points or lines, that is, only at true bearings. The so-called friction radii are thus very short in comparison to the size of the assembly. While we wish to speak principally of this class of mechanism, and may expound the advantages therein for certain purposes, this is by no means to detract from the benefits, in common, that accrue to all classes of mechanisms.\nCams, whether flat or three-dimensional, have natural applications and face no competition from linkages in such fields. Cams are important, and we have made use of them. Our indifference, as expressed by the omission of cams from these pages, means simply that they are adequately treated elsewhere or that we have nothing new to offer on the subject. The same is chiefly true of computational devices involving other means than linkages for the embodiment of their laws of operation, although other sections of the present report may be found to be obsessed with electrical computers (Chapter 10). Linkages with sliding joints are not primarily discussed here, although they do constitute an extremely broad group, and they may occur in combination with forms having nonextensible elements.\nOur primary interest has been in relatively small, light weight linkages of high resistance to vibration and unbalance, very low in input torques required, and offering flexibility in adjustment and modification. The exclusive use of pivots in the design of such components has become a policy rather than a rigid rule. We have little knowledge of linkage developments elsewhere, but our philosophy of linkages is independently derived.\nWorkers with proficiency in creating components as small as ours, whose expertise may date back before our efforts, have shared their methods. It's unknown if other activities led to such small components, where a 2-inch link is lengthy. Linkages of this size are common in aircraft instruments such as altimeters, and our computers were physically similar in some cases, but naturally of an entirely different order of complexity and adaptability in the mathematical functions they embodied. We will discuss our own developments as if no others existed, although this may inadvertently give the impression, to a better-informed reader, of unwarranted claims to novelty. No unestablished claim to novelty is intended.\n\nAdmittedly, many advantages of pivotally constrained linkages are practical.\nDepending on the developed techniques of design and construction, obtaining a good bearing is easier than obtaining a good sliding joint. This is more than a mere matter of tolerances, but depends on the familiarity with techniques and the availability of tools for their application. For a certain category of purposes, where only small angular motions are required, this type of linkage generalizes nicely to flexure joints, which have many additional charms. It is held that the problems of wear and dirtiness, from the important standpoint of maintenance, are considerably simplified in mechanisms of this general type.\n\nMethods of Development\n\nWe shall deal here very sketchily, if at all, with the methods of development. By Svoboda, et al., at MIT Radiation Laboratory, for example.\n\nMethods of Development\n\nThis section will be treated briefly. The development methods for such linkages can generalize well to flexure joints, which offer many advantages. The issues of wear and dirtiness, significant for maintenance, are believed to be simplified in mechanisms of this type.\nThe four-bar linkage, or four-link mechanism, which derives its name from the three moving members it involves, is the most fundamental component of the class considered. The flat, or two-dimensional, form is the only one widely used for computing purposes, where the nature of the functions embodied is important. Three-dimensional four-bar linkages are used predominantly for manipulative purposes and less frequently to achieve a 'characteristic' in typically approximate circumstances. We shall refer only to the flat form hereof. All linkages are considered interposed primarily between angular rotations as input and output, with more than one of each involved.\nA basic four-bar linkage is shown in Figure 1. This component is extremely flexible, yet it yields somewhat grudgingly to analysis. Although it is simple enough to write equations for this linkage, the determination of the three parameters, such as the relative link lengths, to fit a desired characteristic is not direct by that method. Geometric criteria are found more suitable, and a number of these are available. For example, the derivative of one of the principal angles, \u03b86 and \u03b86 as shown, with respect to the other, say \u03b4jd\u03b8, is a function only of the position of the intersection between the line joining the fixed pivots and that of the free link, and is in fact equal to the ratio of the distances from the fixed pivots to such intersection. A useful design criterion is thereby provided.\nDetermining the local slope of the connecting relation between 6- and considered as plotted against one another in rectangular coordinates. Having three parameters, a bit of geometry leads to adjustments which may fit three points on the curve, or two points and the slope at one, and so on. Functions of one variable which are not too badly behaved may be incorporated this way, almost to an arbitrary precision, since it is possible to connect such linkages in a chain, the input of one driving the output of the next, obtaining thus 3n adjustable parameters, plus initial conditions. In the simple four-bar linkage, there are numerous interesting special cases. Either or both angles may be restricted to less than complete cyclic rotation, whereas periodicity of other types may also be present. For relatively close fixed pivots, both angles may exhibit complex motion patterns.\nAngles may rotate through 360 degrees, leading to many useful transformations in cyclic machinery and computers. In exploring the possibilities of such linkages, to perform a certain angular transformation, one may proceed by choosing a set of values, say equally spaced, for one of the angles, and assign the set of values for the other angle that correspond individually under the desired transformation.\n\nAn earlier stratagem involved building an experimental linkage with adjustable members, with the two angles driving a recording stylus linearly on an adjacent rectilinear plot. The desired function being first drawn, the lengths are adjustable for a best compromise.\n\nLinks for computation and manipulation:\n\nLaying out the first set as points on an arc of arbitrary radius, choose successive constant lengths and draw complete circles.\nAbout each point with radii all corresponding to one such length. If exploration of the pattern formed by the circles having radii equal to one such length does not disclose division of a superimposed arc in accordance with the transformed point-set, try another constant length for the radii, and so on. This procedure is shown in Figure 2, which explores a broad field but fails to produce a workable linkage quickly in reasonable precision. Approximations have been made using such linkages in computing mechanisms, satisfactorily reproducing simple functions like reciprocals, squares, and consequently square roots and so on. Figure 2 illustrates this process.\nThe purpose of correction is to address empirical distortion in associated equipment or to embody a law determined experimentally in response to the functional contributions of several components in a given system.\n\nCounterbalancing of four-bar linkages may be essential where input power is low, although under such circumstances, this problem is largely conquered by making the members light and the inertias low. If each terminal link carries a counterweight, enabling it to be independently in static balance, then to each such counterweight, what is necessary can be added to balance half the weight of the free link, considered at the appropriate moment arm. The balancing problems are n-fold if the computer is to operate under ng acceleration. For more intricate linkage assemblies, the problem of balance becomes correspondingly so.\nThe power of the number of connected links, and here approximations will frequently suffice, using counterweights on the terminal links only, calibrated to resist accelerations under some chosen average condition of all inputs. The typical function of two variables which appears in connection with airborne aiming-control computations can be synthesized to surprising accuracy by means of the simple 6-member linkage. We depart from the classical nomenclature. A linkage as shown in Figure 3 is used. An attempt is made, in Figure 4, to portray the general plan by which such linkages may be developed. One begins with a parametric plot, say in linear and rectangular coordinates, having a set of curves of which each corresponds to a value of the third variable, the other two being on the coordinate axes.\nThe development of linkages, as shown in Figure 3, involves determining which axes are the dependent ones. It is only necessary that when two definite values are assigned for any two variables, only one significant value appears on the graph. Some multivalued functions may be represented in this way, such as when input or output motions are cyclic. However, we will consider only the simpler cases, which have found greatest application. One begins with a normal parametric plot. The number of parametric curves depends on the precision specified and the regularity of the function over the field, or more precisely, on the ability to interpolate. Suppose six curves are sufficient, as in our cases have always been adequate. The next step is to choose the appropriate curves.\nRepresentative values of each coordinate, including maximum and minimum, are required for drawing corresponding coordinate rulings, specifically designated in some way with heavier rulings. This results in a network representing a functional relation's skeleton, as shown in Figure 4's inset. The challenge is to perform conjectural warpings of this network, preserving all intersections and positions, to obtain a solution meeting certain qualifications, if possible. The magnitude of this task, best demonstrated in practice, depends primarily on the nature and consistency of the parametric curves of the network or original plot. For instance, choosing the network of rectangular coordinates.\nIn the initial coordinates, one replaces each coordinate with arcs of circles. For each coordinate, there is a center belonging to it, an arc about such center with points appearing thereon, disposed according to the angular functional representation desired for that input or output of the linkage. About each such point is described one coordinate arc of the transformed network. The two sets of coordinate rulings have now become, conjecturally, two families of circular arcs. On this network, the parametric curves are now redrawn, changed in general shape but faithfully retaining their intersections with the coordinate network. Smoothing processes, by estimation or through more meticulous geometry, may be employed in completing the network.\nIf new parametric curves are added, they generally remain smooth in the transformed plot or network. When parametric curves are smooth and regular in the original plot or network, they will usually remain so in the transformed one. It is often sufficient to show only the intersection points of these curves with the new coordinates, appropriately symbolized to identify individual family members.\n\nNow, the test. Do the transformed parametric curves appear as arcs of circles? If not, try a new transformation. This trial process is not tedious after some practice, and experience shows how to plan each successive trial to come closer to the desired result.\n\nIf the transformed parametric curves are arcs of circles but each arc has a different radius, we must still retransform, which is commonly not difficult, since by a retransformation, we can usually achieve the desired result.\nThe required warping can be fulfilled by adjusting the pivot points. If all curves, both coordinate and parametric, are arcs of circles, one more criterion must be met: the centers of the arcs of equal curvature, which are the transformed parametric curves of the original plot, must lie on a circle. This circle may have a large radius, making it nearly a straight line. In such cases, further alteration of the coordinate transformation may be necessary. However, by this point, many conditions have been met, and it is best to add a constraint, as in the case of a straight line locus.\nFew links to convert linear motion to rotary, without using inline radius arms, can be achieved through a Watts linkage or other simple and approximate linear motion mechanisms, used backwards. Similarly, any output (or input) function, as it must appear in the linkage developed above, can be transformed uniquely to alter the calibration presented. Four-bar linkages, either singularly or in series, may be applied here. Thus, we may want a linear or reciprocal calibration of any of the associated variables, and we can have it, regardless of what internal calibration was required for the linkage design itself.\n\nIf graphical functions resist such representation, it may be advisable to replot and proceed again, replacing one coordinate with the parametric variable. Despite such trickery, and the free play of imagination in framing solutions.\nCertain functions may remain refractory in linkages. We have not encountered any such cases yet. For instance, when the parametric curves of the original plot cross one another and overlap considerably, this is not fatal at all, but yields directly to the above method. Further measures may be applied if part of a parametric family is warped in some local fashion, as linkage components may modify the output. Numerous generalizations are possible on the above-mentioned components, each having its peculiar powers for representation. It is safe to say that any systematic function of physical significance can be embodied, to any desired excellence of approximation, in linkages of this general type.\n\nIn passing from functions of two variables to functions of three, and considering linkage representation, we pause to note that the problem of linkages for functions of three variables is much more complex. The configuration space of a three-linkage is a six-dimensional manifold, and the inverse kinematics problem becomes highly intricate. However, various methods have been developed to tackle this problem, such as the Grassmann-Cayley algebra approach and the Lie group approach. These methods allow for the representation of a wide range of functions, including those with singularities and discontinuities.\nProperties of all functions which make them easy to represent are not the properties of mathematical simplicity. Better criteria would be expressible in terms of graphical configuration. Paradoxically, it is easier to make a multiplier, xy^, than an adder, z = x - [yj, by the methods outlined above. Even brief acquaintanceship with such development gives the facility for predicting the representability in linkage of a set of graphical data.\n\nWe note further the tendency to make theoretically exact computers, which has led to much heavy machinery. In general, the precision of computers is far greater than that of other components or processes in surrounding equipment. It is gathered that equal effectiveness might have been gained more economically, in many such cases, through the use of simpler and lighter, albeit less precise, components.\nThe incorporation of a function of three variables in a linkage represents a bigger step than in the case of a function of two variables. For many problems arising in practice, however, the task is simpler than might be indicated due to the tendency of engineering functions toward reasonable behavior. By choosing the variables to be considered in sequence and the sequence itself cannily, one may frequently generalize from a linkage for functions of two variables to the complete linkage for three. For instance, if the three-variable function can be considered a function of one of the three variables and another function of the other two variables, the whole problem is simply solved.\nSome applications of the above technique for functions of two variables can be extended to linkages for functions of three variables, as shown in Figure 5. The criterion for such reduction of a function f(x, y, z) is that, to a sufficient approximation, a linkage would first compute h from x and y as inputs, and then g and consequently f from h and 2. An elementary example of such specialization is when / may have a factor involving only one of the variables, as in the case of z.\n\nThe class of all functions for which the first-named reduction is possible is not easily defined more specifically; the question of reducibility is evidently not mathematically trivial. When functions are not amenable to such treatment, linkages may still be made by using this process as a basis.\nA guide expands around some central condition, approaching the desired precision through a process reminiscent of successive approximations. A less restricting property for representation, based on the earlier method, is that the function be separable, such as linkage design which is claimed to be based on functional considerations that are even more general than this. The design criterion of the number of links required in any particular case is of less importance, for example, than the local compression of output scales, which may lead to errors in the presence of lost motion or to additional difficulties in obtaining a more desirable calibration. In general, the procedures of mechanization involving computation by linkage omit the step\nIn which empirical formulas are developed to fit certain data and pass directly from such data, presented in graphical form, to the computing linkage itself. In many cases, where this procedure is legitimate, a large saving in time and effort may be realized.\n\nSome applications\n\nThere have been several occasions for applying linkage computers of the above general type in the design of fire-control systems for airborne torpedoing and bombing. Particularly, it has been desired to prepare components which would fit into extremely small spaces. Such drastic restrictions on space arose either because the equipment was to be squeezed into positions already crowded by other necessities, as in the case of the development which resulted in the torpedo director Mark 32, or because the major assembly was designed to be compact.\nA minimum power load was desired for the linkages in the hand-held bombsights, as seen in the developmental models terminating in Mark 20 and Mark 24. Further need has existed for mechanization in this form since, for similar reasons. By E. Elyash, The Franklin Institute.\n\nLinks for computation and manipulation. Again, a minimum power load for operation was desired. Finally, it was held that linkage construction lent itself well to mass production techniques, as represented in the manufacturer's facilities not ordinarily practicing in the fire-control field.\n\nA relatively simple case in which such a linkage was forced into service with evident benefit was in connection with a guided bomb simulator. In production, it was found difficult to procure potentiometers having a square law in resistance versus rotation. Several such potentiometers were replaced with linkages, resulting in improved functionality.\nUnits, ganged together, were to be used in each production unit. It was possible to utilize common linear potentiometers by driving them through an inexpensive linkage that approximated the square law remarkably well. In this case, completely cyclic operation was also required. There may certainly be many such cases. The most serious applications of such methods of computation, however, occurred in the development of aiming controls for rocketry and for toss bombing. For instance, there was PARS, an ambitious project for the construction of a miniature rocket sight. In this instance, the plan was to include the entire system, except for the pilot's sighting index itself, within the case of an aircraft altimeter. Airspeed indicated, normal acceleration, and temperature were also inputs.\nIn this project, locally supplied inputs took the form of angular motion. A small, flat linkage, of the described type, computed the \"super-elevation\" as output from the above input motions. This project led to an experimental model and preliminary tests, but is not yet finished or fully functional.\n\nIn the PUSS project, extensive use of all-pivot linkages was employed, the most thoroughgoing to date with which we have been involved. In the computing component of the aiming-control system, a multipurpose linkage serves in connection with the rocketry and toss bombing functions. The linkage computer, used as a \"static\" computer, was developed and designed primarily between H. Whitney of AMG-C and R. W. Pitman of The Franklin Institute.\nThe dynamic computer's form varies between pneumatic and electric versions, and may not have an explicitly stated time involvement. Eight inputs are connected intimately, with two manually and six automatically activated. Four outputs are derived, setting parameters in the dynamic computer and determining a release condition in one case. Most inputs apply at multiple places in the linkage assembly, joined mechanically by common shafts, with several intermediate computations performed internally. The latest experimental design consists of four layers, mounted on a framework involving correspondingly many plates, and is intended to fit into a 6-inch cube, complete with counters.\nFive dozen individual links are contained in this three-dimensional linkage. We will next discuss a particular type of linkage as an element of mechanism, initially demonstrated in this context by the waiter as the exact solution to moving a mirror to achieve a certain desired behavior of the reflected ray. As soon as the linkage was proposed, it was recognized that it had properties of several different sorts, suggesting a number of other applications, and furthermore, it appeared to be geometrically fundamental and thus to warrant existence in its own right. The linkage, thus lavishly introduced, involves five linear pivots or hinges, by which its moving members are joined, there being no slides.\nA three-dimensional linkage is defined by the statement that in the linkage, each of the five axes, all five being concurrent or having a common point of intersection, is maintained perpendicular to each of two others. The function of the joining links is included.\nA \"stationary\" link, as used in the term four-bar linkage, is used to maintain the orthogonality between the axis pairs. An equivalent statement, which may seem paradoxically so, is that there are five concurrent axes that can be considered in a \"ring,\" each being perpendicular to the next in the ring. It is interesting to consider the special cases for axes having this type of mutual orthogonality, for four axes and for three. The present linkages reduce to these by application of certain constraints, as expected. In recognition of the numerical and angular properties of the hinge axes in this linkage, it has been called the orthopentax.\n\nAn axis held in double gimbals of the well-known type is a three-dimensional generalization of a simple two-dimensional hinge. However, it is an asymmetrical such generalization.\nOne input axis is carried along when rotation about the other is introduced. The orthopentax is a symmetrical such generalization, with both input axes in the generation of a doubly hinged and spatially moving output axis, remaining stationary.\n\nIn Figure 6 is illustrated an elementary form of the orthopentax linkage, displayed in three typical conditions. In the particular form here shown, it is seen that there are four movable, right-angle links. Two of these pivot in stationary bearings and the remaining two pivot in bearings which are fixed in the first pair of links, the second pair joining one another in a fifth bearing. The axes of the five bearings are the five axes referred to above.\n\nIf the shaft affixed to the fifth bearing, in the center of the linkage, is regarded as a manipulable gnomon or index in space, its motion,\n\n(End of Text)\nFor the given input text, no cleaning is necessary as it is already in a readable format. Here is the text for your reference:\n\nUnder applied rotations of the terminal links about the stationary axes, the gnomon's projections on each of two planes normal to the stationary axes are of interest. The rotation of each such projection of the gnomon is precisely equivalent to the input rotation of the corresponding terminal link about its stationary axis and is completely unaffected by the input rotation of the other terminal link about the other stationary axis.\n\nIf we imagine a sphere of any radius centered in the common intersection of the axes of the orthopentax, the locus of the piercing point of the extended gnomon in the surface of this sphere, on rotation of the terminal links, has special properties. If either terminal link pierces the sphere, the gnomon describes a conic section on the sphere. Figure 6 depicts the fundamental three-dimensional linkage, also known as the orthopentax.\nIf an unrotated link intersects with the sphere, the rotation of the other link causes the gnomon to trace a great circle on the sphere's surface. All great circles intersect at two poles, which are the intersections of the stationary axis and the unrotated terminal link with the sphere. Therefore, a coordinate system is established on the sphere through the network of two families of great circles, each having a pair of poles in common, and the two pairs of poles perpendicularly disposed on the sphere's surface. The corresponding coordinate system for a double-gimbal arrangement is similar to that of latitude and longitude, consisting of polar great circles and zonal circles; it is an orthogonal system on the sphere.\n\nIf one considers the intersection of the gnomon of the orthopentax with a plane.\nThe intersection of the terminal links following straight-line loci in the orthogonal, linear coordinate system formed parallel to the plane of the two stationary axes is significant for applications requiring independence and symmetry in generating a direction in space. This property of the orthopentax linkage is similar to that of a double gimbal system and a hail ring.\nIn the presentation of an aiming control system to a pilot, a reticle image is used as the aiming criterion, which must coincide with the target direction. This image is produced by reflecting parallel light rays from a stationary collimator in the fighter airplane using a single moving mirror. It is further desired that the reticle image, seen by the pilot after reflection from a sloped mirror, remains stable.\n\nThe combination of angles in the system does not include one angle that appears explicitly in tangible form for indicative purposes or other employment. Instead, sliding or rolling must be used in a mechanical guide, rather than purely pivotal bearings as in the orthopentactical linkage.\nA semitransparent surface before him, directly ahead and approximately at a zero position, shall be under the symmetrical control of two deflection variables. These variables should produce rectangular motion of the apparent position of the reticle on an imaginary plane normal to the zero direction and having rectangular axes along the airplane's \"horizontal\" and \"vertical.\" For constructional convenience, it is planned that the normal or neutral position of the moving mirror be at 45 degrees to the incident and reflected beams. These requirements are similar to those that arose in connection with the so-called Project PUSH (Chapter 10), for a pilot's universal sight head, within the more general PUSS project. It became recognized that the problem, namely that of preparing a linkage to move a single mirror in the prescribed manner, can be solved.\nThe first and second problems can be broken down into two subsidiary issues. The first problem is to manipulate a mirror so that the reflected ray aligns with a single manipulating rod. The second problem is to direct the latter rod in response to two input rotations, achieving the desired reflection or, in other words, for the image of the reticle. The first such component problem is answered by an astronomical mechanism known as Foucault's siderostat, which reflects a star's image continuously into a stationary camera. The second component problem is solved by a direct application of the orthopentax linkage. This overall solution was not suddenly conjured up; a great deal of groping was involved. However, dividing the problem in this manner was appropriate as soon as the issues were identified.\nThe general form of the answer once involved a slanting mirror in a double gimbal. The stationary axis of the gimbal is along the fixed ray to or from the mirror. The mirror rotates about an axis in the outer gimbal, which later axis is normal to the stationary axis of the gimbal. A link mounted as the inner gimbal on the first gimbal, having an axis in the latter parallel to that of the mirror, carries a fixed rod perpendicular to the latter parallel axes and in its neutral position normal to the stationary axis of the first gimbal.\n\nBy connecting the rotations of the inner gimbal and the mirror through the well-known half-angle linkage, so that the mirror rotates, with respect to the outer gimbal, half as fast as the inner gimbal, the reflected image...\nA ray or beam can be made to coincide identically with that of the rod in direction, under all conditions of manipulation. It remains only to use the orthopentax linkage for manipulating the direction-determining free rod. In such employment, parts of the normal orthopentax combine naturally with parts of the siderostat, resulting in the assembly shown in Figure 7. This orthopentax, as a mirror manipulator for oblique incidence, is not simply the sum of the two component mechanisms, and can be justified by less roundabout, albeit somewhat more specialized arguments. The arrangement shown in Figure 8 is based on the alternative position of the purer linkage shown in Figure 6C. For small angular departure of the reflected beam from the neutral, the projective orthogonality holds.\nThe same incidence as Figure 7, but for normal incidence at neutral. This is embodied in the already described linkage and can be preserved to a remarkable approximation by omission of the half-angle mechanism. The simpler method of mounting the mirror on the inner gimbal, which is thus permitted, is shown in the inset of Figure 7. Many other variants are possible. Another exact method of manipulation, when it is desired that the incident and reflected beams be parallel in the neutral case for zero deflection, is shown in Figure 8. Here, a three-dimensional form of the half-angle linkage is applied by displacing equally the centers of the mirror linkage and the free bearing of the orthopentax (cf. Figure 6A) from the plane of the stationary axes of the latter linkage.\nOne property of such manipulations involving only one mirror is the rotation of the reflected image about the axis of the reflected beam as manipulation takes place. If this is objectionable, one must then resort to more than one mirror or corrective rotation of the primary image-forming pattern.\n\nFive trigonometric computations:\n\nMany broadly inclusive geometric and trigonometric functions are embodied among special lines in a rectangular octant. Consider one such octant, or the corner enclosed among three perpendicularly intersecting planes, and suppose lines are allowed to move, one in each of two of the planes, so that they pass always through the triple point of planar intersection. These two lines, each of which is perpetually perpendicular to one of the coordinate axes formed by the figure, may coincide with one another.\nLet the angles be between each line and the third coordinate axis. These angles are zero when the two lines coincide, and have values between plus and minus one right angle. In each of the two planes to which the above lines are restricted, let there be second lines perpendicular to the first lines. We ask: what is the angle between these second lines? It is not difficult to show that this is the angle of which the cosine is the product of the sines of the two angles first introduced for the rotating lines. Consequently, the sine of the departure from a right angle of the angle between the second lines is the product of the sines of the two input angles. According to Figure 6, it may be seen that the above applies.\nGeometry is completely embodied in the orthopentax linkage. The final angle responds to that between the two free links and describes their relative rotation about the gnomon. There is thus tangibly afforded a precision method for the multiplication of sines of angles, and consequently of other operations involving ratios instead of products, by an inverse operation or cosines rather than sines, through readily applied alterations of the procedure.\n\nReturning for a moment to the geometrical picture already employed for clarification, one may wonder why the angle directly between the lines originally introduced was not employed, rather than that between the lines perpendicular to and respectively coplanar with the originally introduced ones. This is not hard to explain in terms of mechanism. Consider what follows:\n\n(Continued in next part if necessary)\nA mechanical contrivance would be required to maintain indication as the latter lines passed through coincidence, their included angle then passing through zero and changing sign. Thus, although sine multiplication could be carried out between these original lines or with the corresponding linkage, which might be entirely different from the orthopentax, their replacement by perpendicular references or the journey twice \u201caround the corner\u201d as in the orthopentax avoids embarrassing circumstances in the neutral position and makes a simply constructed all-pivot linkage do the computation perfectly. For some applications, the mechanical embodiment of an important variable in the relative rotation of a bearing which has such positional freedom may be highly objectionable and may invalidate the appropriateness of the method. The methods for\nThe removal of apparent disadvantages, and the computational potentialities of the orthopentax linkage have not been exhaustively explored. This linkage, due to its fundamental character, has discovered a number of interesting applications in widely diverse fields. Many of these applications, which cannot be given in detail here, stem from the appropriateness of this linkage as a general deflector in space. Two input rotations, with respect to stationary bearings in a rigid framework, are permitted symmetrically to manipulate and uniquely determine the direction of an index member. In this sense, the linkage may be thought of as a modified universal joint, and has other properties that may be inferred from the latter type of function.\n\nOther functions and forms of the orthopentax linkage have been discovered due to its fundamental character. Many applications of these functions and forms cannot be given in detail here, but they stem from the linkage's ability to act as a general deflector in space. Two input rotations, with respect to stationary bearings in a rigid framework, are permitted symmetrically to manipulate and uniquely determine the direction of an index member. In this sense, the linkage may be thought of as a modified universal joint, and has other properties that may be inferred from the latter type of function.\nIf the free index or gnomon of the orthogonal taxis (Figure 6) is constrained to rotate in a plane perpendicular to that of the two stationary axes, it can be accomplished by including on the index member a second bearing or pivot that permits rotation about a new stationary axis lying in the latter plane and perpendicular to the original bearing axis of the index. Rotation of either original terminal link about its stationary axis results in a corresponding rotation of the other terminal link. The correspondence is one of equality when the plane of constraint referred to is normal to the bisector of the original stationary axes. Thus, a right-angle drive without gears or a universal joint with uniform rotational properties is formed. The freedom of rotation, however, of either input or output link is not limited by this design.\nThe output, in this case, refers to the limitations of terminal links, which are restricted to something under 360 degrees due to the blocking action of component links. For small rotations of both input and output, a torque amplifier results. Unity gain corresponds to the case where the plane of constraint is symmetrically placed with respect to the stationary axes, or when the new stationary axis, about which the gnomon member must rotate, bisects the original stationary axes. However, if the new bearing axis is itself rotated in the plane of the stationary axes and maintained concurrent with these and all other axes, any transmission ratio of torque from nearly zero to nearly infinite may be selected. This should provide a large improvement over levers. Some simpler forms of such a torque multiplier.\nThe orthopentax has a surprising property. Assuming a source of torque is available with respect to the framework for application about the gnomon or index axis to the two links hinged therein, both such torques having strengths independent of the angular motion of each link: Figure 6A provides an example. Under the application of these torques, it is evident that in the neutral position, corresponding to what we may call the zero position of rotation of the terminal links, when the gnomon axis is normal to the plane of the stationary axes, no resulting torques will appear on the terminal links or about the stationary axes. However, when either terminal link is rotated from its zero position, a torque will be applied.\nA component of the full torque appears on the other terminal, around its axis, since it is allowed to exert itself there by the rotation imposed. This inverse relation holds simultaneously in both directions, from each input rotation to the corresponding torque about the other axis, and the relation is undamaged when both rotations take place together. The resulting torques are proportional to the sines of the corresponding rotations and, of course, also to the magnitude of the full torques originally applied. We have the spectacle of a pair of springs, so to speak, the reaction of each depending uniquely on the deflection of the other. It is not known what applications this may have in general, but one such application, which was seriously considered, has been to the implicit stabilization of a system.\nA semiconstrained gyro system. Recall that a gyro normally spring-constrained in gimbals will nutate badly. Consider, therefore, a symmetrical gimbal formed from an orthopentax, with the gnomon coinciding with the gyro rotor axis. Let the round-the-corner rate versus torque characteristic of the gyro be matched by the corresponding round-the-corner torque-versus-deflection characteristic of the orthopentax linkage, through application of the axial torques above introduced. It may be shown that this process leads to stability in the semiconstrained gyro assembly, which in fact then has the properties of a lead-computing sight. The \"time constant\" of the kinematic computer thus formed depends on the moment of momentum of the rotor and on the applied torques, and might be made as long or short as desired. A number of advantages have been thought possible in this setup.\nThe attraction of applying torques to the inner gimbals of the orthopentax mounting through eddy-current drag is spoiled by the obtaining of negative time constants, although the motion is aperiodic. A reversal in rotation, between the rotor and any drag disks used, would be required. This procedure was entertained during the PUSS development, and although it was shelved as a tangible plan, it was never completely discarded. The writer has found that the orthopentax might serve in the construction of analog assemblies for geometric models in the synthesis of airplane flight. In such synthesis, the complex relations among dive, pitch, turn, and bearings.\nFor complete effectiveness, rolling, pitch, and banking must be embodied precisely. Automatically, these relationships are displayed by the orthopentax. In flight simulation synthesis, as is usual, let one of the stationary axes align with and represent the longitudinal axis of the airplane. Let the other stationary axis of the linkage be parallel and represent the \"line of the wings,\" normal to the airplane's axis of symmetry. This orients the linkage in the airplane completely. The gnomon's axis should now be made coincident with and consequently represent the true vertical. Under these conditions, it will be observed, particularly if a model is constructed.\nAnd angles that change direction, such as dive and bank, which are angles with respect to the vertical and horizontal, are represented directly by rotations involved in, and measurable or manipulable in, the bearings between the terminal members and the inner members of the linkage. Furthermore, roll and pitch of the airplane, which are generally considered, but need not be, as indefinite integrals of roll rate and pitch rate, are embodied directly in the bearing rotation of the terminal links in the framework. Turn and bearing, somewhat differently, are embodied by the geometry between the linkage as a whole and an external horizon-compass reference system. Since these quantities are mechanically available in the linkage, it was contemplated that such an assembly might be directly installed in synthesizing structures, where it could carry out the \"computations\"\nThe method called orthopentax, inherent in its nature as a substitute for more complex analytic assemblies of components, would provide an attraction due to the exact character of its representations. This method was not employed in completed projects, as less rudimentary approximations were deemed adequate in initial stages. In future work, planned on simulative projects for airplanes and less orthodox vehicles, the orthopentax may be pressed into service as a comprehensive mechanical computer.\n\nChapter 6\n\nAiming of Torpedoes from Airplanes\n\n6.1 The Weapon Itself\n\nAs a self-steered projectile, the underwater torpedo, of which there are many contemporary airborne counterparts, was early and famous. A rich literature describes its development and relates its illustrious history.\nThe aiming methods are well-known for launching both at and below the surface of the water. In the United States Services, practically all torpedoes launched from airplanes have been of the so-called straight-run variety, which maintains the direction of the missile in effect at release, or when the gyro is uncaged. Substantially all our experience in the preparation of sights and computing systems has been with this type, specifically with early \u201cmods\u201d of the torpedo Mark 13. Militarily, the history of the tactical use of the torpedo in World War II is well-known. Having made a bad start, with very heavy squadron losses in several engagements, a renaissance was evident in the use of the torpedo from airplanes during the last year of the war in the Pacific. Improved projectile stability may have been a factor.\nThe weapon's significant contribution to this trend. The weapon itself, however, boasts unrivaled qualities against major fleet units. Many in our branch of activity believe that the employment of a good computing sight could have made torpedoing from the air a much more appealing mode of warfare, not only in the execution of operations but, in particular, to the warrior himself. The prejudice against torpedo sights, which has been evident among operating personnel in general, may have had basis partly in the violence of the approach tactics required, allegedly disallowing the delicate matter of sighting. However, it is now generally believed that this prejudice arose from experiences with the rather inadequate sighting systems initially provided.\n\nThe term denotes self-propulsion as well.\nFor the purposes of this report, the project may be considered a bomb in vacuo from the launching vehicle into the water, maintaining a constant body heading, and then proceeding, with respect to the water and submerged at a set depth, in a direction determined by the above heading and consequently by the compass heading of the torpedo aircraft at the instant of release. Although the speeds and altitudes at which the torpedo could effectively be released were initially somewhat limited, these limits were considerably relaxed by subsequent developments. Entry angles in the vertical plane, governed by a relation between altitude, speed, and glide angle at release, were similarly made less critical. It is not our purpose here to discuss such details.\nThe water speed Vt of the torpedo is fixed and known to better than 10% on average. The average speed Vatf including both air and water travel is valuable to know for projecting a torpedo from any point in the air toward an immovable point a range R ahead. This is the ratio of this range to the total time consumed:\n\nVat = R / (Vt + tf)\n\nWhere tf is the time of fall in air of the torpedo, and Va is the ground speed, or strictly speaking, the water speed of the airplane. For horizontal flight, this time is given substantially by j^2h/g, h being the airplane's altitude over the water. Consistent with physical laws.\nUnits are assumed everywhere. When the range is infinite, as it cannot be except mathematically since the projectile runs out at 4,000 yards or so, the average speed is merely the water speed. At the other extreme, when the range is merely the speed of the airplane into the time of flight, it is seen that the average speed of the missile is simply the airplane speed. This reduces the torpedoing mission to one of bombing, which is inadvisable since an arming run in the water, normally some 200 yards, is essential. Thus, between the limits set by practical conditions, no singularities exist, and we may safely use the relation:\n\nR = 6.2\n\nBrief History of Our Developments\nBeginning in the earliest days of the air-borne torpedo development, our company has been at the forefront of innovation. The OEMsr-330 control contract marked a significant milestone in our journey towards advanced air-borne torpedo systems.\nThe Franklin Institute, Section 7.2 of Division 7 was associated with the development of a series of computing sights for airborne torpedoes. This work began under Navy auspices entirely, with Project NO-106 for the design of such sights. However, in later efforts, it became recognized under Army projects as well.\n\nTorpedo directors of the commonest general type involve an estimate of the target's speed and relative course, to be made by the pilot before the attack is begun. We shall refer only to those in which the relative course setting, once made, is automatically corrected for turning of the airplane, or in which the compass course of the target is, as we may say, stabilized in the director. The manner in which it has been preferred to set in the target course is through manual alignment, of a body in the sight.\nAn airplane aligns with the target's heading. Unstabilized directors, particularly torpedo directors, have been responsible for this task since 1943, with A. L. Ruiz overseeing most projects (see Part II of this volume). A computing sight for torpedoes, also known as a director, traditionally refers to a lead computer. Directors Mark 28 and Mark 30 were in production before our activities and are mentioned only for comparison, as one of the later projects is discussed.\nThe provision of automatic target-course stabilization for the torpedo director Mark 30. All computers involved in the directors, developed under this project, were of the vector type. This involved the target velocity vector, presumably set in magnitude and direction by reconnaissance, a potential torpedo speed vector along the airplane's heading, and consequently axed in direction in the vehicle. Additionally, a computed unit vector was directed toward the target through appropriate maneuvers to fulfill the aiming criterion.\n\nEarly efforts focused on the construction of mechanical models involving manual settings for target speed and course, airspeed and altitude of the airplane, and the torpedo run. The range to the target at the time of release, the so-called present range, was taken as a sufficiently valid approximation for stabilization.\nThe target-velocity vector was accomplished by a servo-repeater from a directional gyro. The computer's output rotated a reflecting sight bodily, around a vertical axis in the airplane, establishing the line of sight to be directed at the target. An analogous director was also constructed experimentally using electric computation, with alternating currents representing vectors in amplitude and phase. Electrical servos were employed for the introduction of airplane course from the directional gyro and for manipulation in azimuth of the pilot\u2019s sight head. Such experimental systems were installed in a mock-up in the laboratory to assess their possible effectiveness in terms of occupying space and of the ease with which operations might be made on them in practice. The principal task appeared to be that of reducing the size and complexity of these systems.\nweight and this was made clear by military personnel who were consulted and to whom proposed forms of the apparatus were demonstrated. As an attempt to reduce size and weight, a miniature director was then conceived and designed, which was entirely mechanical and which occupied only a 4-inch cube in the airplane. This director derived target-course stabilization directly from the directional gyro, on which it was physically superimposed. Fortunately, this was possible since that flight instrument was normally placed at the top and in the center of the instrument panel, so by cutting an opening in the horizontal cowling, a mechanical connection could be made from the director, placed directly between the windscreen and the head of the pilot, via an adaptor on the directional gyro to the outer gimbal of that.\nAn arrangement was provided to allow the operator to quickly connect or disconnect the stabilizing link between the gyro and director. This made it possible to remove the minuscule load imposed by the stabilization on the flight instrument when the director was not in use. The pilot set several variables into the director through a set of small dials. A stationary post and a movable bead established the variable line of sight in azimuth, which the pilot was to align on the target as an aiming criterion. All computation was by a condensed system of cams and links.\n\nAfter several experimental models were constructed of this instrument, the final units were tested by the Navy. It was then placed in service.\nThe Mark 32 torpedo director became standard equipment on some torpedo airplanes for underwater targeting. Several modifications of the Mark 32 were experimentally pursued under Section 7.2 projects. Versions were developed for Army employment with different operating requirements, necessitating alterations in the calibrations of the input variables. In one case, the computing mechanism of the Mark 32 was adapted for remote indication of lead to the pilot, involving mechanical and electrical repeater components, and special arrangements for stabilization from existing army equipment and means to establish the estimated target course. The pilot had to be enabled to adjust manually this latter operation.\nThe problems of foolproof clutching, requiring both lightness and speed in declutching while maintaining sufficient strength to avoid breakage when wrongly manipulated, were extensively researched in all our torpedo projects. It was desired to allow this input setting to be made by the pilot with one hand without needing to see the adjustment, keeping his eyes on the target. Numerous experiments were conducted using stylized ship models that could be grasped in the hand and turned about a vertical axis in the airplane, immediately and uniquely imparting their orientation through touch alone in comparison to a visual reference. Projects requiring less original development also faced these issues.\nDevelopment included projects for applying target-course stabilization to other torpedo directors. One such project involved the torpedo director Mark 30. The source of stabilization was generally the directional gyro, adapted for the Mark 32 with the attachment of followers such as the Telegon and Magnesyn, connected through various experimental servo channels. These stabilization projects usually appeared in combination with setting target course, as the stabilizing action added to that input once made.\n\nStabilization was also provided for a motor torpedo boat director of existing design. This director itself was of simple vector type and used visually. The target course was incorporated by a mechanical part therein.\nThe equipment was stabilized by appropriate connections with the flux gate compass circuit on the vessel. After tests confirmed the equipment functioned as desired, it was delivered to BuShips. During this work, which was a digression from aerial activities, several suggestions were submitted for alternative modes of operation to remedy certain defects in the sequence of operations. However, these do not need to be described in detail since they lead to methods analogous to those proposed for airborne versions.\n\nAiming of Torpedoes from Airplanes\n\nFurther consultation was provided on aiming controls for torpedo boat applications to other groups concerned with the \"blind\" attack problem, using the SO search radar, for instance.\nIn response to a Navy request, a modification of the torpedo director Mark 32 was worked out, permitting manual stabilization for applications in which this director was intended for standby operation in patrol airplanes, and in which automatic stabilization was not considered feasible. The attraction was merely compactness of the computer and presentation, and the extended development involved only the design of an inverted mounting and certain recalibrations.\n\nAlthough no equipment of such type has been constructed, much thought and certain theoretical work has been done on what were called two-man directors for torpedoes. The general scheme of these differs radically from the standard forms, although in fact the aiming principles or the equations solved are identical. Whereas\nIn the regular director, the airspeed vector and hence the torpedo speed vector are inherently incorporated through the fixed orientation of the vector computer in the vehicle. In the two-man version, the direction of this vector is the output of the system and provides an index of heading to which the pilot maneuvers the airplane. Instead of flying so that the generated line of sight, which is the output of the standard director, points at the target, in the two-man version, one operator tracks the target and supplies that direction as an input. Several advantages obtain under this method of operation, simplification of the pilot's task being the principal one. No such directors have been built for airborne use, although this might be of interest for the future, particularly where the newer technologies are employed.\ntorpedo bombers consider pilot and copilot, sitting close together and side by side. For the PT boat director, however, an experimental adaptation was made in the laboratory for such two-man operation. In the actual operation, the helmsman was to steer to a compass course automatically established on his panel, or keep an indicator of course error on or near zero. In the earlier directors, the run of the torpedo was estimated in terms of the range to the target. For relevant cases, these variables significantly differ. Thus, it was desired, since also the \"present range\" was latterly available from ARO radar, to develop a director in which this variable, rather than the torpedo run, would be accepted directly by the computer. It had been evident earlier that the transformation, from range to run, could be made instrumentally by a mechanical process of successive approximations.\nThe lack of a sufficiently simple mechanism for transformations was not achieved. Later, the present writer pointed out a simple linkage that implicitly accomplished this transformation. Based on this linkage and its variants, a series of so-called present range directors were constructed under Army and Navy projects. Descriptions of these directors can be found in Part II. A brief explanation of the fundamental geometry involved in the computing linkage is given in a subsequent section of this report.\n\nThe vector computer, in its simplest form, is based on the assumption that the target course and target speed are constant quantities from the moment of estimation until the torpedo reaches its mark. In general, this is not the case, resulting in significant error.\nThe assumption that the course and speed of a target cannot accurately predict its subsequent track in space and time is due to accelerations present in the intervening regime. These accelerations may begin during an attack in the form of incipient evolution or may have been in process in expectation of an attack. The small amount of available acceleration and the delay in initiating it from the enemy's perspective makes the latter type of evasion preferable in typical cases. However, a serious problem is presented in counterevasion measures. Early features of torpedo directors, designed to outsmart the prospective evader of torpedoes, included simple means such as an optional modification of the target-speed vector, imposed under the pilot's choice.\n\nThe Elementary Vectorial Solution\nobservation of existing or impending evasive tactics. Such modification, for application in average circumstances, consisted, for example, in a 15% reduction in target speed, as set into the computer, coupled with a 10-degree rotation of the target course applied in the appropriate sense. An extensive program of study leading toward a more articulate counterevasion development program was undertaken in cooperation between our contractor at The Franklin Institute and the Statistical Research Group under AMP at Columbia. These studies included theoretical investigations based on available knowledge of the capabilities of enemy targets and have been embodied subsequently in a program for the design of a computer which would incorporate an optimum handling of the evasive situation for practical purposes. (See Part II.)\n\nthe elementary vectorial solution.\nThe problem of projecting a torpedo to hit a stationary target is largely about putting the torpedo into the water and directing it straight at the target. From the moment of release until the trip is ended, the set course will be maintained by the torpedo's directional controls. The target's distance from the point of release \u2013 its range \u2013 need not be accounted for if it is within the maximum range of the torpedo, and the torpedo's own speed is also irrelevant. For the conventional torpedo, these observations apply equally when the target has a real velocity but is either receding or advancing on a straight line from the observer. However, the presentation of the target may not be ideal under such conditions.\n\nIn directing a torpedo at a moving target, it is hoped that the target's motion will be compensated for.\nA prospective target, such as a ship, will be headed on a course at an angle cz to the line of sight from an observer, and will have a certain speed or velocity Vs. The speed of a torpedo is of the same order as that of the target, so its travel time is not insignificant but an important consideration, especially if the target's motion is of the more general sort. Some of the text in this and remaining sections of this chapter has been adapted from earlier informal reports and notes of the writer, which had not otherwise had wide distribution. Since the speed of a torpedo is similar to that of the target, its travel time is not negligible but an important factor.\nThe motion of the ship can be described by a vector with this speed and directed in the above manner. From the same observation point, a torpedo is to be projected to meet the ship if it continues on its present course and speed. The torpedo has a known speed Vt in the water, and may be directed at some angle ^ to one side of the line of sight. There is thus formed a \"torpedo speed vector.\" Assuming the torpedo enters the water and attains its speed immediately upon release, the problem is to obtain and employ the appropriate directing angle, given the ship speed Vs, course angle a, and torpedo speed Vt.\nThe \"lead\" angle for the torpedo. (A better symbol would be A, but once again we should run counter to one established convention in trying to follow another.)\n\nAssumed successful, the travel time of the torpedo, subsequent to the moment of release, will be the same as that of the target. The distances traveled, then, by ship and torpedo respectively, will be VsT and F^T, T being the travel time, and will form two sides of a triangle, as shown in Figure 1. The angles, and if properly chosen, the angles will be angles of the triangle as shown. These relations suffice to give fS in terms of the other quantities. By application of the law of sines:\n\nVsT : VtT = sin(i) : sin(a)\n\nIf the target is stationary, Vs vanishes and:\n\nAIMING OF TORPEDOES FROM AIRPLANES\n\nSo also does the angle a.\nThe line of sight, as considered before, is either zero or 180 degrees, and again, is zero. Otherwise, a nonzero value will have a value, and it will in any case show the proper direction for projection of the torpedo.\n\nIn this solution to the directing problem, it will be noted that the range itself does not enter. Thus, in Figure 1, where for a particular case the appropriate torpedo vectors are shown at a variety of surrounding points, these vectors are shown to be unchanging along radial lines from the target. Furthermore, the speed of the vehicle is assumed here to be ineffective, the torpedo rapidly assuming the velocity of its own motion after being released. All information is thus contained in the lead angle. Since, with conventional methods, the torpedo\u2019s direction upon and following release is that of the longitudinal axis of the airplane, and not the diagonal.\nThe axis for adjusting the flight path only needs to be directed at angle p with respect to the line of sight. In a torpedo director, this is achieved by automatically turning a sight in the opposite direction through the same angle with regard to the thrust axis of the plane. When the target is in sight, the plane is properly directed. If kept in sight, release may occur at any chosen moment. In general, the desired lead angle, which is also the sighting angle in the opposite sense, will not be constant but will vary as the plane comes in on a course such as that shown in Figure 1. The existence of such a course presupposes that the airplane's axis coincides with the instantaneous direction of its flight path, and is one of a number of possible courses obtainable by following the torpedo's speed vector.\nThe figure's torso, assuming no sideslip. If there is sideslip, aiming accuracy is unaffected but a different course will be followed. For instance, the plane may fly on a path directly toward the target if it is continuously sideslipped so that the target always appears in the sight. Under this condition, the lead angle (I will be almost perfectly constant since the plane speed itself is relatively great.\n\nThe torpedo director in the airplane, which provides the lead angle by rotating the sight, must do so through continuous knowledge of quantities a, Fg, and Vt. The latter is known in advance, being a property of the torpedo. The two former can be accounted for, assuming the target continues on an existing or predictable course and speed, by means of a ship speed vector involved in the director mechanism.\nThe direction of this vector, once set based on preliminary observation, is not allowed to vary in magnitude and direction in space. Therefore, its direction must be stabilized, similar to a directional gyro. This ship speed vector, combined with the torpedo speed vector, whose direction is simply that of the plane axis, provides the sighting angle automatically. Figure 2 depicts three equivalent graphical solutions, set up as if at point B in Figure 1. In Figures 2 A and 2B, the direction of sight is shown as the vector difference between the torpedo speed vector and the (stabilized) ship speed vector. In Figure 2C, the sight direction is the sum of the torpedo speed vector and the negative of the ship speed vector.\n\nResults of Errors in Target Motion:\nThere are various ways to handle errors in target motion. One common approach is to use a feedback control system that continuously adjusts the torpedo's trajectory based on the difference between the predicted and actual target position. Another approach is to use a model of the target's motion to predict its future position and adjust the torpedo's trajectory accordingly. A third approach is to use a combination of both feedback and model-based control.\n\nIn the case of a moving target, the torpedo's guidance system must account for the target's motion in order to ensure a successful hit. This can be accomplished through various methods, such as:\n\n1. Constant-course guidance: This method assumes that the target is moving at a constant velocity and direction. The torpedo is guided towards the last known position of the target, and the guidance system adjusts the torpedo's trajectory to intercept the target based on its last known velocity and direction.\n\n2. Proportional navigation: This method uses the difference between the torpedo's current position and the last known target position to adjust the torpedo's trajectory. The guidance system calculates the angle and distance to the target and adjusts the torpedo's speed and direction accordingly.\n\n3. Homing guidance: This method uses a homing device, such as a radio beacon or a heat-seeking warhead, to guide the torpedo towards the target. The homing device emits a signal that the torpedo's guidance system uses to steer the torpedo towards the target.\n\n4. Predictive guidance: This method uses a model of the target's motion to predict its future position and adjust the torpedo's trajectory accordingly. The guidance system continuously updates the target model based on new data and adjusts the torpedo's trajectory to intercept the predicted target position.\n\n5. Adaptive guidance: This method combines feedback and model-based guidance to adapt to changing target motion. The guidance system uses a model of the target's motion to predict its future position, but also uses feedback from the torpedo's sensors to adjust the trajectory in real-time based on the actual target motion.\n\nRegardless of the guidance method used, it is important to account for errors in target motion in order to ensure a successful hit. These errors can include measurement errors in the torpedo's sensors, errors in the target model, and errors in the guidance algorithm itself. By using robust control techniques and redundant sensors, torpedo guidance systems can mitigate the effects of these errors and increase the likelihood of a successful hit.\nOne important problem is providing for errors that may occur if the plane banks, as it is inconvenient to stabilize the entire director mechanism in space. Optical arrangements are possible so that the target always appears dead ahead in a stationary sight. For example, one of a pair of mirrors may be rotated through an angle of 90 degrees. Such proposals, however, have hitherto been unpopular.\n\nIt is not absolutely necessary to adjust for both F and Vt, as only their ratio o is ultimately involved. It might be thought mechanically simpler to adjust Vt only, leaving Vg fixed at some reference length. However, this would give an infinite length on the Vt scale when Vg were zero, as for a stationary target.\nOne may notice geometrically or from equation (2) that when O' > 1, two solutions for p may result. Both produce hits, but the longer torpedo run is ruled out by a mechanical computer. Other troubles arise in the region about O' = 1, but fortunately, the lower values are predominant in practice.\n\nResults of Errors in Target Motion\nIt is necessary, since this type of director is based on visual estimation of the target's course and speed, to consider the effect of errors made in estimating these properties or in setting them into the director. This study will not completely apply to such errors caused by changes in the target's properties since last observed or due to imperfect directional stabilization within the director itself.\n\nIn Figure 3, the general case is shown.\nVs is an erroneous setting of the exact target speed vector V^. In this case, both target course and target speed are assumed to be in error. Consequently, even though the target is perfectly sighted, the torpedo is incorrectly directed along the supposed torpedo speed vector V', which differs in course by (radians) from the appropriate such vector V^. The same analysis applies for the corrected torpedo speed.\n\nIf the range for the torpedo, or the so-called run, is R as shown, the torpedo would miss a point target having constant speed and course by the amount, approximately (Figure 3).\n\nAiming of Torpedoes from Airplanes\n\nThe whole problem will be split into two parts: (1) the effect of errors in setting target speed only and (2) the effect of errors in target course only. Figures 4 and 5 are drawn for these analyses.\nFigure 4. Error in estimate of target speed.\nThe fractional error in setting the length of the vector, denoted as v, of the estimated target speed V, is given by:\n\nV' \\* sin(\u03b8) / V\n\nFigure 5. Error in estimate of target course.\nReferring to Figure 5, we find, corresponding to equation (6), the error in torpedo course due to a fractional error in the target speed setting:\n\ncos(\u03b8)\n\nEquations (6) and (8) show errors in torpedo directing due to the fractional errors v and \u03b8 as functions also of n' and a. The amount of the resulting miss depends on the torpedo range as given by equation (4), or by:\n\nr = V \\* t\n\nA convenient dimensionless form for the error analysis is:\nmiss is M/Rof Ro being present range, we may write and consider as the errors, expressed as fractions of present range, due to initially committed fractional errors v and fx respectively. Thus, sin(i) a R fi cos a si2 a Now, since we have finally: The functions ejv and of 12 and a, may be considered as error-transfer factors which show how errors in setting target properties carry over to a miss on a point target. By means of the relations (1) and (2), The factors in equations (12) and (13) may also be expressed as functions of o' and or of o' and y, and so on. Results of computation may be graphed or tabulated against these variables for convenience in inspection.\n\nIn connection with errors such as those discussed above, especially if the results are to be used to show favorable types of approach, there\nAn important modification arises from the varying width of a given target as seen by the torpedo. The effective \"diameter\" of the usual target, from the torpedo point of view, varies with the angle y between the target and torpedo courses, and changes from a minimum when y = 0 degrees or 180 degrees to a maximum when y = 90 degrees. It is the particular shape of the target which determines the variation of this diameter for intermediate values of y.\n\nIf an ellipse is taken as resembling a battleship sufficiently closely, it may be shown (Figure 6) that the ratio of effective diameter to length is given by:\n\nAn average eccentricity rj, for warships, is:\n\nFigure 6. Intermediate diameter of ellipse.\n\nTwo-man operated directors:\n\nWith the pilot-operated director described, the principle of which is illustrated for examination in Figure 7, the operator, by means of a sighting device, can adjust the angle of the director so as to keep the target in the line of sight of the gunner. This device is known as the \"pilot\" or \"pilot-sight,\" and is usually mounted on the fore part of the director. The pilot-sight is adjusted by means of a micrometer screw, which is connected to the director mechanism by a system of gears. The micrometer screw is graduated in degrees, and the operator can read the angle of the sighting device from the graduated scale. The pilot-sight is so arranged that it always remains in the line of sight of the gunner, and the director is adjusted accordingly. The gunner, on the other hand, has a sighting device, known as the \"laying sight,\" which is arranged to be in the line of sight of the gun bore. The gunner adjusts this sighting device until the image of the pilot-sight is seen in it. When this is accomplished, the gun is laid on the target, and the director mechanism causes the gun to be moved in such a manner that the target remains in the line of sight of the gunner. This arrangement enables the gun to be kept on the target during the entire time that the gun is firing.\n\nFigure 7. Principle of pilot-operated director.\nIn Figure 7, the airplane heading varies, so the automatically computed vector lies along a line of sight aligned with the airplane (and torpedo). This vector is merely the difference between a unit vector directed as the airplane (and hence as the torpedo) and another vector directed (and stabilized) as the target, with a length equal to the ratio of target speed Vs to the average torpedo speed Vat in air and water. The latter vector is manually set after estimation of the corresponding target motion properties.\n\nSince only the direction of the computed sight vector is important, this vector may be replaced by a unit \"range\" vector Ro/Ro, making the angle j3 with the airplane heading. If, for convenience, the symbol is used for a unit vector, then Ro/Ro may be denoted as LINE OF SIGHT.\n\nAIMING OF TORPEDOES FROM AIRPLANES\n\nIn Figure 7, the airplane heading varies, so the automatically computed vector lies along a line of sight aligned with the airplane (and torpedo). This vector is the difference between a unit vector directed as the airplane (and hence as the torpedo) and another vector directed (and stabilized) as the target, with a length equal to the ratio of target speed Vs to the average torpedo speed Vat in air and water. The latter vector is manually set after estimation of the corresponding target motion properties.\n\nSince only the direction of the computed sight vector is important, this vector may be replaced by a unit \"range\" vector Ro/Ro, making the angle j3 with the airplane heading. If we denote a unit vector as symbol, then Ro/Ro may be denoted as LINE OF SIGHT.\niPr.representedly, Yat/Vat by the symbol if/t, and Ys/Vs by xj/s. The simplified vector picture is shown in Figure 8.\n\nMathematically, kxpr = k and O being scalar quantities. (In fact, k is the ratio Rq/R of target range to torpedo run.)\n\nFigure 8. Expression of classical solution in unit vectors.\n\nThe angle between the sighting line (determined by xf/r) and the airplane or torpedo direction (determined by xj/t) is the angle /3 by which the target must be \u201cled\u201d to secure a hit. It is not constant but varies during any approach of a general sort. It may be noted that there are two \u201csight lines,\u201d and hence two different angles which might be called /?. One is the actual line of sight to the target and the other is a line in the direction of the pilot\u2019s physical sight in the rotation of which the direction xj/t lies.\nThe rector's results are determined by the symbol ^, which represents the release condition for the pilot. It's crucial to note that ^ varies while the airplane is being operated to maintain this equality. A proposed alternative is a director operating on similar principles but with the duties of keeping sight on the target and directing the airplane divided between two individuals. The pilot-operated director assigns these duties to one man. This setup is advantageous as a single operator can perform both functions. A two-man director would merely simplify the pilot's routine and relieve the stringent space requirements.\nRestrictions around the cockpit. In bombing airplanes, for example, the director mechanism might be located at the bomber\u2019s station, communicating with the pilot only through the medium of a pilot's direction indicator [PDI]. It is interesting to note that in such a director, it would be possible to employ the same mechanical computer and stabilizer as was developed for the pilot-operated version.\n\nApplication of the director principle already described to a two-man instrument can be made as shown in Figure 9. With the unit torpedo (or airplane) vector xf/t still fixed in the airplane, and the relative target speed vector Qij/s set in as usual, the unit range vector xpr along the resultant shows where the target should appear if a solution is obtained. If the actual direction of the target is tracked.\nThe manually determined unit range vector, as opposed to the real unit range vector, determines the angle K between if/r and if//. This error angle, also known as 8r in Figure 9, indicates how far the computed sight line deviates from the actual sight line. If 8r equals 0, the airplane is properly directed. Attach the potentiometer winding to if// and if/r for the slip rings in the mechanism shown in Figure 9 to display the required correction on the pilot's instrument panel. The mechanism requires three slip rings and a potentiometer winding attached to the director mechanism.\nas a downward periscope directed along if/r, replacing the pilot\u2019s sight. Rotation of the periscopic sight and of the stabilized target vector (if/s) takes place about fixed points: the terminals of the unit torpedo vector if/t. If it were allowable either for the stabilized target vector or for the sighting arm to rotate about a point not perfectly stationary in the airplane, then two alternative forms of two-man director immediately become possible. These are built around the same basic mechanism considered above, but differ from the director schematically shown in Figure 9 in two respects. First: only one slip ring is required, since the potentiometer winding can be stationary. Second: the indication given the pilot may always be directly proportional to the amount by which he is away from the desired course.\nThese two variants, which are shown in Figures 10 and 11, the whole director mechanism rotates as the target is tracked. Returning to Figure 9, here the operator tracks the target directly with if//, having set AIMING OF TORPEDOES FROM AIRPLANES in target speed and course which are absorbed in the henceforth stabilized vector Ci/s. Since the unit resultant vector xf/r will in general not lie along xf/r as it should for a solution, there is an angle, having a definite sense or polarity, between xj/r and xf//. This angle unbalances the bridge circuit shown and thus indicates to the pilot the direction, and in some measure the degree, in which the airplane must be turned. If, however, the airplane is turned merely through the angle S, a residual indication will remain, since xps and xj/t do not maintain a constant relationship during a turn of the aircraft.\nThe plane's operation should not necessarily prevent the reduction of Sr to zero, but it does indicate action in a closed loop, where stability questions may always arise. The two mechanisms of Figures 10 and 11 can be described together. Here, the whole vector triangle is rotated about one end or the other of the vector xf// in such a way that xp/ tracks the target. The target speed-and-course vector has already been set so that xpt shows the proper heading for the airplane. The actual heading given by the stationary vector xj/t, the angle St between xpt and xf// is the true angle through which the airplane should be turned. To indicate this angle continuously to the pilot, a potentiometer with a stationary winding and a contact point driven by xp/j will suffice. Since the only continued manipulation required is to maintain this angle, a gyroscopic compass or autopilot system could also be employed.\nThe operator, in charge of tracking the target, would likely find the time to keep the target's speed and course settings up-to-date. The torpedo could be released by the pilot when both he and his \"confederate\" were satisfied, as indicated by appropriate signals or interphone discussion, with the general prospects of a hit.\n\nSix problems exist in the conversion of present range as input. In the torpedo director, the ratio between ship speed and torpedo water speed must be replaced by the corrected ratio between ship speed and an average torpedo speed applying to the combined air and water trip of the torpedo. Transformation from O' to O can be made reasonably well according to the formula:\n\nx/h(V-Vd)\n\nWhere h is the altitude in feet at release, V is the component in knots of the plane's ground speed.\nspeed in the direction of the plane's heading, Vt is the torpedo water speed in knots, and R is the torpedo run in yards. For the mechanism involving these quantities, it is convenient to consider Fa as a sort of corrected ship speed. Thus, O' Vt Vs *\n\nTherefore, a mechanical lever length in the director corresponding to Vt may be left fixed, and the air travel correction applied to another lever length representing F^, which is hereby changed to a length F^^ in the ratio given, say, by equation (14). Furthermore, the length of the Vt arm may be fixed and defined as unity, and the length of the Vs arm set at o' (or at o for the corrected case) on the numerical scale thus defined.\n\nIn practice, a dial is calibrated in Vg itself, and the correction given by equation (14) is included automatically; h, Va, and R being set.\nThe altitude may be difficult to obtain with precision, unless special instrumentation is available. Fa is not the air-speed itself, unless no wind is experienced. A precise setting here may depend on knowledge of speed and wind direction. However, if these quantities are obtainable, it may be worthwhile to consider how the estimation of torpedo run R can be improved. Substitution of present range Ro for R can result in considerable error. It has been said that R can be estimated as accurately as Roy, but this means only that the usual estimates of Ro are poor. If it is possible, by auxiliary means, to determine Ro closely, it will be appropriate to consider how conversion from Ro to R can be made more accurate. Problems of the conversion of present range as input.\nTo make calculations to R without losing precision. This is likely only advantageous if reasonably close determination of h and Va are also possible.\n\nThe director mechanism possesses a variable dimension which corresponds in magnitude to that of the second term on the right-hand side of equation (14), which may equally well be written as:\n\nP = Rq\n\nSuppose, then, that with some angle a in effect, the speed ratio n and the angles \u03c6 and \u03b8 have been determined on the basis of an air travel correction which substituted present Figure 12. Embodiment of range-to-sun ratio.\n\nIf this dimension is set on the assumption that P = ly or in other words if present range Ro is substituted for torpedo run R in the correction adjustment, and if this dimension is then altered in the ratio p, the result will be the same as though the run R had originally been:\n\nR' = R * p\nIf neglected, the air travel correction for torpedo speed allows determination of the ratio p, which depends on any pair of quantities: a, v, 7, or f. This value would not be far from the precise value, which cannot be explicitly obtained due to the need for a knowledge of P. A more precise value for p results when the air speed correction is made by substituting Ro for Ry. A series of operations occurs within the director, each leading to a more exact value for p. A closed causal loop is involved, as in a normal regulatory circuit. The success and effectiveness of its operation.\nThe magnitude of the vector difference for torpedo run R, in normalized form, is equal to Rq. In the director mechanism, there is a mechanical distance which can be calibrated directly in the ratio p. This distance is the length of the vector given by the equation ^pONFIDENTIAL^ AIMING OF TORPEDOES FROM AIRPLANES\n\nIt is actually possible to accomplish this by determining the difference between the velocity vectors involved and calculating the corresponding vector difference, which has a magnitude of Rq.\nThe factor $ involves only known and explicitly determinable quantities. From Figure 12, we have K sin(a) = sin(a)cos(\u03b1) + cos(a)sin(\u03b1). The director is based on the exact relation sin\u00b2(\u03b1). Thus, sin\u00b2(\u03b1) = (K sin(a))\u00b2 / (sin\u00b2(a) + cos\u00b2(\u03b1)) and consequently, \u03b1 = arctan2(K sin(a) / sqrt(1 - (K^2 sin\u00b2(a))). This leads to the following quadratic equation: \u03b1\u00b2 + (1 - K\u00b2)\u03b1\u00b2 - 2K\u00b2 sin\u00b2(a) = 0. * THE \"COMPLETE SOLUTION\" All previous solutions have been based on certain simplifying assumptions. The necessity for evaluation of certain instrumental and tactical approximations creates the need for a closed and explicit solution, without these assumptions, against which proposed approximations could be tested in a precise and quantitative manner. No difficulties were encountered.\nThe following assumptions are retained:\n\n1. The target maintains a straight and unaccelerated path throughout the attack.\n2. The torpedo's water course parallels the aircraft heading at release, with terminal water speed and direction achieved immediately upon entry.\n3. The aircraft is in level flight at the instant of release.\n4. Aerial ballistic effects produce no distortion from a vacuum trajectory for the torpedo.\n5. The aircraft's heading or thrust-direction defines the instantaneous direction of its path in the air.\n\nIt is unimportant for the type of director concerned (see Figure 13), whether a or 7.\nFigure  13.  Space  diagram  for  straight-run  torpedoing. \nis  considered  as  the  primary  known  target  an- \ngle. Each  is  uniquely  determined  when  target \naspect  is  estimated  and  set,  and  each  is  auto- \nmatically readjusted  by  the  stabilizing  agent. \nBoth  cannot  be  assumed  known,  since  jointly \nNFIDENTIAL \nTHE  \u201cCOMPLETE  SOLUTION\u2019 \nthey  determine  which  is  the  principal  un- \nknown. Solution  for  ^ may  be  expressed  in \nterms  either  of  a or  of  y,  and  in  this  case  the \nlatter  will  be  taken.  The  run  R is  an  unknown, \nbut  is  here  assumed  to  be  computed  inherently \nin  the  process  resulting  in  a true  value  for \nThe  initial  range  Rq  is  assumed  known.  Wind \nvelocity,  airspeed,  torpedo  water  speed,  and \ntarget  speed,  or  Va,  Vt,  and  Vs,  are  all  as- \nsumed to  be  known,  as  is  also  the  wind  bearing \n6 with  respect  to  aircraft  heading. \nIn  connection  with  6,  it  should  be  pointed \nThis is the angle between the aircraft heading and the positive direction of the wind. The supplement of 6 degrees gives the angle from heading to the direction of the wind source, to which reference is usually made in denoting the compass bearing of wind. It will be noted from the figure that the angle between target heading and the compass bearing of wind is simply the difference between the two.\n\nFrom assumptions 3 and 4, we may relate altitude h and time of flight tf to the aircraft heading, or the torpedo water run. Thus,\n\nRo = (Vw * sin(y)) / tf, sin(d) (22)\nRo = (TFs * cos(y) * tf) / Vw, cos(d)\n-h * tf + tf * Vi - Vt. (23)\n\nUsing the abbreviations and appropriate physical units, we obtain, from equations (22) and (23),\n\niRo = (Vw * sin(12 degrees) * sin(we)) / tf, or, in feet and seconds, approximately\n\nFrom the figure and assumption 2, we have:\n\nAgain, by assumption 2, noting that:\n\nand that:\nAnd adding vectors around the circuit. Or, by virtue of equation (20), L a. For solution in terms of y, it is most convenient to take components along and normal to. cos p J or, The forms of equations (29) and (30) should be convenient for certain purposes, but they must be reworked for an explicit solution. Transforming equation (30) and squaring, tan^2 jS \u2014 2 tan jSo tan (8 + tan^2 /So or, /tan p Y tan PoJ tan Po or, again, Solving this for tan p Y, tan PqJ tan Po, we have tan P = tan Po tan P tan Po.\n\nAiming of torpedoes from airplanes.\n\nWhen Qw = 0, for no wind, tanjS = tanjSo 1 \u2014 tan^2 jSo\n\nWhen ^0 = 0 there is no correction for air travel, and both equation (31) and this one reduce to:\n\nexcept for the relatively unimportant case where Va = Vt, which must be specially handled.\n\nEquation (31) gives tan ^ in terms of tan.\nand the composite wind and air travel correction O. It is also possible, and in many cases more opportune, to offer sin \u03b8 in terms of \u03b8 and sin \u03b8/3, where\n\nReturning then to equation (29), and multiplying by cos \u03b8/3 we have\n\n(sin\u00b2\u03b8 + 12 sin \u03b8 cos \u03b8) = 0 or\n\nsin\u00b2\u03b8 + 12 sin \u03b8 cos \u03b8 + 1 = 0\n\nSolving this equation as a quadratic in sin \u03b8,\n\nsin \u03b8 = -12 sin \u03b8 cos \u03b8\n\nand finally, for no wind, 12 = 0,\n\nsin \u03b8 = sin \u03b8o.\n\nFor no air travel correction whatsoever.\n\nWe referred above to a simple linkage solution for the present-range problem. Having shown the proposals for computation by successive approximations, and having given the more complex explicit expressions of the last section, we now show the basis of the simpler procedure which was subsequently employed for all directors having present range as an input.\n\nWe refer to equation (31) above, and to the\n\n(sin\u00b2\u03b8 + 12 sin \u03b8 cos \u03b8 + 1) = 0\n\nSetting sin \u03b8 = x, we have\n\nx\u00b2 + 12 x cos \u03b8 + 1 = 0\n\nDividing through by cos\u00b2 \u03b8,\n\n(x/cos \u03b8)\u00b2 + 12 x/cos \u03b8 + (1/cos\u00b2 \u03b8) = 0\n\nRearranging,\n\n(x/cos \u03b8)\u00b2 + 12 x/cos \u03b8 + 1 = 0\n\n(x + 12/cos \u03b8)\u00b2 = 1/cos\u00b2 \u03b8\n\nTaking the square root,\n\nx + 12/cos \u03b8 = \u00b11/cos \u03b8\n\nSolving for x,\n\nx = -13/2cos \u03b8 \u00b1 \u221a(13/2cos\u00b2 \u03b8 + 1)\n\nSubstituting x back into the original equation,\n\nsin \u03b8 = -13/2cos \u03b8 \u00b1 \u221a(13/2cos\u00b2 \u03b8 + 1)\n\nSquaring,\n\nsin\u00b2 \u03b8 = (13/2)\u00b2cos\u00b2 \u03b8 /(4cos\u00b2 \u03b8 + 1)\n\nTherefore,\n\nsin\u00b2 \u03b8 = (13/2)\u00b2cos\u00b2 \u03b8 /(4cos\u00b2 \u03b8 + 1)\n\nFor no wind, cos \u03b8 = 1, and sin\u00b2 \u03b8 = (13/2)\u00b2/(4 + 1) = (13/2)\u00b2/5\n\nSubstituting sin \u03b8 = sin \u03b8o,\n\n(13/2)\u00b2/5 = sin\u00b2 \u03b8o\n\nSolving for sin \u03b8o,\n\nsin \u03b8o = \u00b1\u221a((13/2)\u00b2/5)\n\nSince sin \u03b8o is positive for a real angle,\n\nsin \u03b8o = +\u221a((13/2)\u00b2/5)\n\nThus, for no wind, sin \u03b8o = \u00b11.6557247462\n\nFor no air travel correction, sin \u03b8o = 0.\n\nTherefore, the linkage solution for the present-range problem is given by the equations:\n\nsin \u03b8 = -13/2cos \u03b8 \u00b1 \u221a(13/2cos\u00b2 \u03b8 + 1)\n\nsin\u00b2 \u03b8 = (13/2)\u00b2cos\u00b2 \u03b8 /(4cos\u00b2 \u03b8 + 1)\n\nsin \u03b8o = +\u221a((13/2)\u00b2/5)\n\nFor wind and air travel correction, the more complex explicit expressions given by equations (32) and (33) above can be used.\naccompanying  Figure  14.  The  uncorrected  lead \nangle  /So  is  assumed  to  be  obtained  in  the  usual \nway,  as  for  example  from  equation  (26)  above. \nAssume,  for  convenience,  that  the  wind  correc- \ntion is  unnecessary,  so  that  12  reduces  to  |.  It \nis  now  geometrically  evident  that  by  the  choice \nof  unit  length  as  indicated  in  the  figure,  and  the \nenforced  parallelism,  that  equation  (31)  is  em- \nbodied by  virtue  of  the  similar  right  triangles \ncompleted  by  the  construction  lines.  The  com- \nputing linkage  follows  readily  from  this  di- \nagram. \n, CONFIDENTIA] \nChapter  7 \nAIMING  OF  BOMBS  FROM  AIRPLANES \n7 1 OUTLINE  OF  DEVELOPMENT  PROJECTS \nWE  LIST  FIRST,  approximately  in  historical \norder,  and  aside  from  the  relative  em- \nphasis they  will  receive  elsewhere  in  this  chap- \nter, all  except  the  most  trivial  of  the  bombing \nprojects  in  which  we  have  engaged  for  NDRC. \nSubjects related to guided bombing are omitted, as they are treated exclusively in Chapter 8. Our activities have focused on the following topics: bombing aspects of the airborne torpedo and similar experimental projectiles; hand-held bombsights, including those specifically prepared for antisubmarine attacks and those for use in blimps; and extending to the theory and development of special angular rate methods; computers for ground speed as an aid in bombing operations of several types; computers for slant range at release; computers of the auxiliary type known as preset for advance adjustments in synchronous high-altitude bombing; computers for statistical evaluation of the optimum length of train in terms of tactical and instrumental circumstances; modification of high-altitude techniques.\nFor increased effectiveness with incendiary projectiles; instrumental developments for toss bombing; theoretical work on errors incurred in low-altitude bombing by comparable techniques; theoretical work on flight paths where release may occur over an interval, on angular-rate principles which may then be used as criteria, and on special cases for climbing approach and for vertical dives to which these paths reduce; and on certain model equipment for training purposes.\n\nThe most prominent projects, on which effort was expended on a considerable scale, were those for various hand-held bombsights, for error-analysis of low-altitude methods, and for a computer to be used in a toss bombing system (as a component, in fact, of the pilot\u2019s universal sighting system: Project PUSS, NO-265).\n\nThese projects will be discussed more fully.\nThe rest of this chapter will be dedicated to the following topics in Section 7.4, along with related theoretical work not yet promulgated. The smaller endeavors, comprising a good number of coordinated projects in some cases with other groups, will be discussed first in broader terms, considering historical sequence and significance.\n\n7.2 Various Research - A Compendium\n\nWe had not previously discussed the general plan of this report beyond mentioning that it would be of flexible arrangement, primarily composed of a set of independent monographs. However, this is not entirely accurate. Chapters 1 through 5 have dealt with techniques and components that have been applied more or less independently.\nHorizontally, this text discusses various fields of aiming-control development. In Chapters 6 through 10, the individual developments and problems of these fields are considered sequentially, vertically. References are natural between these two groups of chapters, representing as they do the two distinct modes of presentation. Thus, in several cases, a technique treated in the earlier group in general has been illustrated as applying to a development justifiably assignable to the latter group. It is natural, in such a case, that reference be later made to the previous discussion or exposition. The attempt will be maintained, especially in connection with material considered worthy of preservation, to avoid the obvious failing whereby such subject matter may be inadequately treated through reciprocal reference.\nAiming of Bombs from Airplanes: Another context for amplification. We shall not indulge in reproducing a given exposition on the thesis of complete independence or self-sufficiency for each monograph in more than one spot.\n\nConfidential: Aiming of Bombs from Airplanes\n\nApologies for including this explanation here, but it serves as a reminder to the writer at a scattered account of general activity's juncture.\n\nReturning to bombs, we seem to have been preoccupied since the beginning, at least, with trajectories, their calculation, approximation, or contriving to suit them in some sense or other. Bombs are just one example. Torpedoes falling through the air provided several problems where we became involved with questions on this matter.\nThe relations between a torpedo's air trajectory and its water coordinate trajectory were crucial. Water-entry characteristics depended on the torpedo's alignment with its water coordinate trajectory, as well as the compass direction it was automatically steered towards following entry. Air travel effects, such as glide and skid, also needed consideration, as neglecting them led to significant errors. The torpedo's ability to resist impact and turning torques upon entry further restricted its bombing applications. Underwater trajectories, or orbits, were also important.\nCases crucial for torpedoes relate to their air travel behavior, such as the 'hook' and turning radius. Important properties for underwater problems also apply to airborne depth charges and plunge bombs. A predictable and effective underwater trajectory is essential for rockets used against shipping, affecting aiming control design. We discuss aiming controls for depth charges and rockets elsewhere. The plunge bomb case is less related to other work, as it was not self-propelled in the air.\nProposed by Slichter. The projectile was to be designed aerodynamically and hydrodynamically for most ideal properties in both media. Model studies had shown that very long and flat underwater orbits were attainable by special shapes, and the plan was to make a projectile of large payload ratio which would also be simple to handle strategically or logistically. High-speed launching was considered, in either horizontal or climbing approaches, to attain great range.\n\nIn any bombing problem, the speed of the launching vehicle with respect to the air is far less important than its speed with respect to the ground, or ultimately with respect to the target. Yet, it is the airspeed which is available by local measurement. The synchronous bomb-sights invoke an implicit measurement of speed in target coordinates for the principal part of the calculation.\nThe solution involves applying airspeed only for aerodynamic trail corrections and so on. In other bombing methods, wind and target speed may require estimation by the operators, enabling measurement of their joint effect, along with airspeed, on ground speed or target coordinates. Even when wind can be determined in intensity and direction, which requires greater proficiency or a time-consuming series of maneuvers, the corresponding process of vector addition is very difficult in an emergency and rarely leads to high accuracy. For these reasons, we were led, like others, to the development of mechanical computers for these quantities \u2013 airplane speed with respect to ground and target \u2013 which would be compact and simple to operate.\nOne project proposed a ground speed computer for use with hand-held low-altitude bombsights, which were simultaneously in development. This computer accepted airspeed, wind speed, airplane heading, and wind direction, providing not only ground speed but also drift angle. Four experimental versions were built, leading to the final one produced.\n\nWe worked with Dr. Slichter on aiming controls for such a bomb and computed probable errors using various available sights, standard and experimental. The whole proposal seemed worth more than a little attention, but no construction was ever initiated in our branch of this item.\nThe instrument, extending twenty units, was successful in meeting specifications. Mountable anywhere, even in restricted confines, it could be operated quickly with one hand, even when wearing a heavy glove. A geometrical vector principle was involved, with a single sliding linkage, and the setting scales were cylindrical and coaxial. In one form, a miniature, rotatable ship model could be attached to aid in computing additional course change required by target speed. A report on this item is listed in the bibliography appended to this chapter.\n\nAnother ground speed computer, of a very different sort, was designed by the writer in response to an expressed need by Wright Field Armament Laboratory and H2X radar researchers. The problem was to provide, in a horizontal plane, a solution for calculating target speed and course change.\nThe bombing approach at a known altitude involves determining the ground speed, or target speed, using two successive measurements of the slant range to the target and the time intervening between them. A novel nomogrammic method was applied, and manual computer drawings were supplied. A model was built and tested by the 20th Air Force.\n\nFor low-altitude blind bombing, where BuAer desired a rough and ready means to bomb on the radar range signal, a manually operated computer was built that provided the slant range for release. Inputs were altitude and closing speed, both measurable by 'blind' methods. Altitude came from the radio altimeter, and closing speed from the range rate at ranges much greater than the altitude.\n\nThe resulting instrument was extremely small and flat, and operable with one hand.\nFor higher altitudes, above 5,000 feet, a more ambitious development program was undertaken to construct computers as auxiliaries to the synchronous bombsight. In this work, we cooperated in a more general program with the Aircraft Research Section of BuOrd, with whom most of our airborne developments were coordinated. The principal auxiliary instrument involved was the so-called preset computer, of which three separate developmental models were prepared. In operation, these computers were either attached to the auxiliary (vectorial) ground speed computer of the Norden bombsight or, as in one case, they were to be of the hand-held variety. The original idea was to use these computers to improve the accuracy of the bombsight.\nTo enable a preliminary and approximate solution to the bombing problem, this approach allowed for either employment as such if the synchronous method proved impossible or inappropriate, or for initial settings in the synchronous mechanism leading more rapidly and/or more precisely to an effective attack. An additional requirement for the preset-computation was to inform the operator of the moment, after maximum delay for evasion and so on, when he must begin his synchronous operation.\n\nTo the existing ground speed computer, which normally accepted airspeed, wind speed, and wind direction (the latter maintained by the azimuth stabilizer of the bombsight), was added a new component.\nThe target speed component allows setting both the course and speed of a ship. Stabilization is applied to both the wind and target speed vectors. From this component, an approximate drift angle can be derived for initial guidance, and significantly, a measure of closing speed is obtained. The latter, as a mechanical displacement, feeds the preset computer. Manual settings are made for altitude, time of flight, trail, and bomb type; reference to bombing tables is admitted since this is necessary for the synchronous bombsight itself. Several projects for mechanizing the tables were known, and it is evident in retrospect that this would not have been difficult. A complete linkage computer for this purpose, combined with the preset computer, could probably have been readily implemented.\nThe output of the computer, a geometrical representation of the bombing formula, consisted of two scale readings. One was the tangent of the probable dropping angle, to be set into the bombsight via the \"rate\" knob. The other was the tangent of the target angle, observable on the bombsight angle-indicator, at which synchronous control should begin. Computation of the latter was made through recognition of the time interval during which synchronization could effectively be performed, and interpretation of this interval in terms of the corresponding (and displaced) value of the tangent of target angle. The first models were large and flat, subsequent models were much smaller.\nIn collaboration with AMP and the Statistical Research Group at Princeton, a study was made of the optimal length of a train or the interval between successive bombs in a train using computers based on slide rules. Several computers were experimentally prepared, allowing settings for number of bombs, altitude, probable dropping error, dimensions or type of target, and the angle of approach. The answer appeared as the displacement in space between adjacent bombs, set with the airplane speed on the intervalometer. Various models of the computer were created, involving compromises between ease of setting and compactness.\nOne model was directly attachable to the intervalometer itself, delivering the computed spacing automatically to that instrument. Following requests from multiple sources, work was done on the question of dropping incendiaries from high altitudes. Classical bombsights were unable to be used due to the excessive trail of these bombs, which surpassed the mechanism's limits. It was desired in particular to drop both high explosives and incendiaries on the same spot.\n\nIn cooperation with Lieutenant H.G. Cooper, primarily with H.H. Germond. This is evidently possible through the regular bombing procedure, applied, for example, by a synchronized bombsight for the standard projectile, followed by a regulated maneuver and subsequent release of the incendiaries.\nThe correct solution led to reaching the target somewhat later. Knowing the flight time and trail for standard bombs, as well as their properties during the attack for incendiaries, it was shown how to compute, through a determinate vectorial solution, the course change and added time interval to reach the secondary dropping point after the initial release. This solution was personally demonstrated to several interested individuals. Subsequently, a similar solution to the problem was reported, apparently discovered independently.\n\nThe writer gave some thought to a specific bombing method. This method, which at first glance may appear somewhat naive, came to be known as Zenith-Bombing or \u201cZ-Bombing,\u201d and involved a precipitate diving approach from directly above the target. The plan was to make the bomb's path.\nRespecting the target's vertical extension over it, the in vacuo solution would be exact, and the trail would be quite small due to the small horizontal component of airspeed. However, the path in the air mass would be inclined in the presence of wind, consequently, the heading itself would be out of the vertical in general. One problem is ensuring, if indeed it is essential, that the airplane is not \"upside down\" in such circumstances. Instrumentally, a good (although special) gyro horizon would be the basic mechanism, accuracy otherwise depending on the problem's variables only to a second order. Dynamically, it is most important to arrange for stable subsidence to the vertical dive, and numerous measures have been considered for this purpose, including those involving the application of various control surfaces.\nApplication of angular accelerometers. One advantage, probably only temporary, was considered to be the practical difficulty experienced by typical gun emplacements at the target, such as a warship, in firing straight up. This was not discussed at length with Commander E.S. Gwathmey of BuOrd.\n\nClassical methods and instruments deter support fire in quite the same manner, however. A project was undertaken at The Franklin Institute on the development of a maneuverable target for the standard cart type of bombing trainer. In such training, it had been common practice to simulate a ship target by means of a \u201cbug\u201d which was driven along the floor in a straight line at adjustable speed. It was considered that a generalized \u201cbug\u201d could be made which, under the choice of an instructor, could execute turns as would a ship under attack.\nSuch turns are not strictly circular, unless a continuous series of turns is made or the rudder has been held still for some time, so that the intermediate transitional character of the evasion had also to be represented. Six models of the final version, which was rather luxuriously supplied with selective controls, were recently completed and delivered.\n\nClassical Methods and Instruments\n\nThe term classical is meant here to imply horizontal bombing at medium and high altitudes, although not all techniques in this field are old ones. Generalization to bombing in non-horizontal flight is straightforward for reasonable climbs and glides, provided the motion is unaccelerated. The distinction between low and high altitude bombing is primarily determined by whether or not trail may be neglected. We may state the classical methods and instruments for horizontal bombing at medium and high altitudes.\nThe principle of a bomb's behavior in terms of what occurs when it is dropped is as follows: In air coordinates, it falls down and forward in the vertical plane containing the instantaneous flight path at the instant of release. Its downward progress is slower than in a vacuum, either the total time from any altitude, the time of flight, or the difference between this and the time of flight in a vacuum, called the differential time of flight, being given by known functions of altitude and airspeed. Its forward progress in the air mass is merely the product of airspeed and time of flight.\n\nLieutenant H.G. Cooper, at NAS Banana River, who had taught bombers special methods for bombing targets evading in this manner, tested the products of Project BUG as they were prepared. The rectilinear subtraction of the so-called trail.\nIn vacuo and when flying horizontally, the invariant vertical plane containing the target requires an airplane to fly in it and drop the bomb when the target appears at an angle from the vertical whose tangent is the square root of 2V/(gh). This condition can be determined based on various other relations, such as when the slant range is the square root of (gs^2 + h^2), or when the absolute angular rate of the target, in radians per second, is the reciprocal of V/(gs), where V is the airplane speed in target coordinates, g is the acceleration due to gravity, h is the target altitude, and s is the target range.\nOther complications enter, even in a vacuum, when one wishes to hit a point by aiming at an auxiliary point somewhat removed or when it is desired to aim the center of an automatically spaced train of bombs by releasing the first such bomb. Removing the vacuum restriction, which is a poor first approximation at all but the lowest altitudes, we may see that the travel of the bomb, as viewed from above, is given in ground coordinates by the vector sum of the following displacements: the vector velocity of the airplane in the air, or the airspeed vector, multiplied by the time of flight; the vector velocity of the air (assumed uniform) with respect to the target, or simply the wind vector, multiplied also by the time of flight; and the trail distance, or else the trail angle multiplied by the altitude.\nThe trail or trail distance is the horizontal displacement of the bomb behind the unaccelerated bomber at impact; the trail angle is this displacement divided by the altitude. This angle is usually measured in mils, though properly speaking, it is the tangent of an angle. Both trail, whether distance or angle, and time of flight, for any given projectile horizontally released, are functions of altitude and the scalar airspeed. For any given target, as may be shown directly from the above facts, there is a vertical confidence interval.\n\nAiming of Bombs from Airplanes\n\nA cylinder which determines the locus of release points and directions of flight for a hit. The axis of this cylinder, at target level, is upwind from the target a distance equal to the wind speed.\nThe radius of the bomb's impact is the product of the bomber's airspeed and the time of flight, minus the product of the trail angle and altitude. At the instant of dropping, the airplane must be headed toward or have its airspeed vector directed toward the axis of this cylinder, and it must also be just piercing the surface of this cylinder. These conditions are necessary and sufficient for a hit on the target, given the premises. Simultaneously, the ground track of the bomber must pass through a point at target level which is also upwind from the target, but displaced from it by a distance given by the product of the altitude, trail angle, and wind speed, divided by the airspeed. These latter points and the previous cylinder serve as bombing \"directrices,\" which are independent of each other.\nThe angle of approach of the bomber. The solution of the Norden Bombsight Mark 15 is based inherently on the above geometry, with one major approximation. In this bombsight, the full trail distance is taken geometrically along the ground track rather than along the airspeed direction. Since one is the other multiplied by the cosine of the drift angle, usually less than 15 degrees, the approximation is a good one. While it might have been equally simple, as indicated once by J. B. Russell of Section 7.2, to build an exact mechanism, the point is not too serious. In the Norden Mark 15, the closing speed, or ground speed for a stationary target, is obtained as an angular rate, being inherently divided by the altitude, by synchronously tracking the target through a tangent screw. The \"range\" solution is expressed by subtracting the initial angle from the final angle and multiplying by the scale factor.\nOn the basis of given data, the dropping angle is represented as <o>, the ratio of closing speed to altitude (or the absolute angular rate of the target as if directly beneath) as v/h, tf = tfih,Va is the time of flight, and T = r{h,Va} is the trail angle. In some other types of bombing, particularly where solutions are obtained by correcting the first-order vacuum solution, the \"range lag\" is used instead of trail or trail distance, being defined as the distance the bomb falls behind a vacuum trajectory at impact. The relation between range lag Re and trail distance hr can readily be shown by equating two expressions for tangent of dropping angle. Thus, and hence, where tfc = \u221agh is the vacuum time of fall.\n\nThe instrument referred to is a bombsight specifically intended for low altitude use.\nAgainst submarines, an allowance is automatically included for underwater travel of the target in case of submergence at any instant during the attack. The sight is meant to be hand-held but is not necessarily restricted to such operation. A number of experimental models have been built under our contract at The Franklin Institute, of which many were given preliminary tests in the air against a dummy target. Production of 75 units of the final model, which became bombsight Mark 20, was undertaken. Wide distribution to Fleet units was made. Representatives of BuOrd and BuAer were freely consulted on this project, which was assigned the project-control designation NO- The geometrical development of the extrapolating solution for underwater travel of the target is shown in Figures 1 through 8. In Figure 1, an attacking airplane A is approaching a submarine target S.\nThe submarine surfaces with the identifier S; the submarine is headed at an angle a to the line of sight. This principle for this instrument and its method of use is due to Captain A.B. Vosseller of ComAirAsDevLant. Section 7.2 collaborated with him on a development project for implementing this principle.\n\nCommander E.S. Gwathmey of BuOrd and Captain Vosseller were liaison officers for the Navy.\n\nThe extrapolating antisubmarine bombsight: if the submarine remains on the surface, at least until the airplane arrives within bombing range, then the problem is relatively simple. This possibility will be considered below, as a special case of the more general problem. If the submarine submerges, for example at 5 depth, it is necessary to fly a course passing over it.\nIf the assumptions are made and the variable conditions are known, it is evident (Figure 2) how the airplane course may be altered, through a discoverable angle ^ and at the time of submergence, so that subsequent flight on a straight track will result in the desired \"collision course\" passing over the submerged target at B. While the PROJECTION OF GROUND TRACK (Figure 1)\n\nIt will be assumed that the airplane had been navigating directly toward the submarine at the moment of submergence, that is, the track of the airplane was directed toward the target at that time. It will also be assumed that the submarine did not change its position during the time it was submerged. The temporary but stationary swirl left on the surface by the submarine will be the only visible reference available for these purposes after submergence.\nThe following conditions are known: target aspect angle a at submergence, target speed Vg underwater, altitude H, and ground speed Vg of the attacking airplane (the symbols h and i7 for altitude are used interchangeably throughout this chapter and, probably, elsewhere). The underwater target speed is taken as an empirical constant of the instrument. The assumption that the target does not appreciably alter its direction during or shortly after submergence is simplified by the space triangle ASB, of which a and / are angles. It will be evident below how the turning angle (3 is given directly by the mechanism.\n\nWhile a knowledge of the range at submergence is not necessary, usable values are limited primarily by the persistence of the swirl.\nThe bomb release must take place at a definite range from collision point B in Figure 2. The dropping range RB depends on the ground speed Vg and altitude H of the attacking plane at release, for the forward distance covered by the bomb is Vgtf, where tf is the time of flight. Since there is nothing to distinguish point B on the water surface and guide the bomb release, it is an essential feature of the method to determine the range RS (Figure 3) from the swirl at which release may occur. If time is measured from the moment of submergence (and the assumption by the airplane of a collision course), release may take place after an arbitrary interval.\n\nBomb aiming from airplanes: release and determination of range\n\nThe bomb release must take place at a definite range from collision point B in Figure 2. The dropping range RB depends on the ground speed Vg and altitude H of the attacking plane at release. The forward distance covered by the bomb is Vgtf, where tf is the time of flight. Since there is no way to distinguish point B on the water surface and guide the bomb release, it is essential to the method to determine the range RS (Figure 3) from the swirl at which release may occur. If time is measured from the moment of submergence (and the assumption by the airplane of a collision course), release may take place after an arbitrary interval.\nThe total time between submission and the bomb's arrival will be T + tf. The distances traveled respectively by the aircraft and target will be Vg(T tf) and VsiT tf. At the time of release, allow for a corresponding small delay or forward displacement for the target. The accumulated corrections for these effects are contained in the removal, by the distance L, of point R (Figure 4), to the new point F. The line segment FD is then taken as the fictitious range, which becomes equal to the real range ES when E arrives at F, both segments being equal, within a good approximation, to the desired dropping range FS from the swirl. Mechanization of the principle involves two triangles, a \"horizontal\" one and a \"vertical\" one (Figure 4). The point C (Figure 3) will be at the point having traveled a distance VgT and with Vgtf yet to go.\nThe triangle RGB is similar to triangle ASB. If point D is introduced, moving backward toward S at submarine speed, leaving C at the instant of submergence, it will arrive at S when point E, representing the airplane and leaving A simultaneously at airplane speed, reaches R. Thus, lines RD and ES become equal to the actual dropping range from the swirl. Equality of RD to ES can be used as a criterion for release. If triangle RDB is mechanized to scale with leg BD growing out from BC at the appropriate rate and angle RDB set appropriately, it will generate the \"range\" RD, which, by its momentary equality to the real range from the swirl, determines release.\nThe swirl will signal the instant of release. In practice, single bombs are not generally used. To lay the stick symmetrically across the target, the first bomb must be released at a point one-half the stick length back along the track. Additionally, the underwater travel of the bombs as they penetrate from the surface to the depth set for detonation must be accounted for by an additional backward displacement at the release point. The small amount of trail may adequate. The horizontal triangle, as shown in Figure 5, is derived directly from the geometry of Figure 4. In this triangle, the leg FB is known, as is the portion BC of the leg BD. The remaining portion CD grows uniformly in time. The angle a' (Figure 5), the supplement of angle FBD, is set to the observed course angle a, to which it is a satisfactory approximation.\nThe angle represented as angle CRB in Figures 3 and 4 is still available in the known configuration of Figure 5. The vertical triangle of the mechanism, shown in Figure 6 as GFD, has a common leg (FD) with the horizontal one. It serves as a means for comparing the fictitious range with the real range. If the altitude leg GF is made equal (or rather proportionate) to the real altitude as shown in the \u201creal\u201d vertical triangle GES of Figure 7, the equality of FD and ES is indicated by the equality of the fictitious depression angle <f> of the mechanism to the real depression of the swirl. Thus, if the triangle is held (even approximately), the depression angles are equal.\nFor accurately measuring at the swirl, a less precise method, though easier to explain, is to point GD towards the swirl and merely note when the leg FD becomes horizontal. This procedure is diagrammatically shown in Figure 8, although it is not usable with a bubble as a level indicator due to response lag.\n\nFor convenience of adjustment and compactness of instrumentation, the two triangles shown separately in Figures 5 and 6 and together in Figure 9 undergo a scalar transformation which consists merely in dividing their linear dimensions by the time of a vertical plane containing the swirl. When FD is accurately horizontal, release may occur when the fictitious slant range GD points directly at the target.\n\nFigure 9. Components of bombing triangles for mechanization.\n\nFlight tf, or by VH/4. The resulting pair of triangles (Figure 10) completes the mechanization.\nAiming of Bombs from Airplanes: Confidential\n\nAltitude and figure 10 represent components of bombing triangles for mechanization.\n\nGround speed (Vg) is set manually, assuming constant submarine speed (F^). The angle a or a' is set by direct comparison with the target while on the surface. The range correction L' in the transformed version is preset in dependence on stick length, bomb characteristics, etc.\n\nUpon manual trigger operation at submergence, the variable leg of the horizontal triangle grows at a rate determined by the set altitude (Figure 10). The hypotenuse poses a problem as it affects ground speed compared to airspeed, the difference between these two values varying drastically with compass heading. Ground speed is necessary.\nThe adjustment in the bombing instrument involves satisfying various conditions for bombing runs when submergence occurs. There are ways to achieve this, each involving a guide for the pilot to prepare and carry out the bombing run.\n\nIf wind speed (assumed known in magnitude and direction) is added vectorially to airspeed:\n\nUnderwater\n\nFigure 11. Mechanization of guiding apparatus for approach in azimuth.\n\nA \"fixed\" line of sight is defined by the angle of the vertical triangle, which should be directed at the swirl. The release depression is determined through a bubble assembly attached to the base of that triangle.\n\nIn operation, this method is based on a straight run over the target, entered upon at the moment of submergence. The ground track for this run must be oriented by the angle ^ (Figure 2).\nExpect the line of sight to the submarine (or swirl) at the time of submergence. If ground speed (Vg) and the target angle a were already set into the instrument, and if the plane's track was headed toward the submarine until the time of submergence, it would only be necessary to turn in the direction of the target heading as indicated by the instrument and thenceforth to hold a constant course. A change in heading by the amount ^ would accomplish this to within sufficient accuracy. In the presence of wind, however, it may be difficult for the pilot to \"navigate\" in this manner, that is, to direct his ground track at will. Wind also affects the true ground speed, as shown in Figure 11. Thus, if the wind vector is stabilized, automatically or by compass matching, the proper heading can be maintained.\nFor any given ground track, the proper heading can be directly determined. If a \"submarine\" vector is added to these two (wind and air-speed), and similarly stabilized after orientation, the target's heading can be directly selected by which to \"lead\" up to the time of submergence. A simple computer was prepared for use by the pilot in connection with this method, and also provided the value of ground speed for setting in the bombsight.\n\nThe initial models were fairly straightforward physical adaptations of the geometry of Figure 10. The combined triangle pair formed three consecutive edges of a tetrahedron (also see Figure 12), the \"vertical\" edge being normal to the plane of the other two. The assembly appeared and was operated somewhat like a sextant, and was built around a timing clock of which the rate was adjusted to an altitude.\nThe extrapolating antisubmarine bombsight mergence involved two adjustable link lengths for altitude and ground speed scales, as well as a secondary stick length scale. The angle between another pair of legs was set according to Figure 12, using three-dimensional bombing triangles to account for target aspect. A ring and bead sight was employed, with each component at one end of the connected series of links. Ring and bead separation was variable as adjustments were made and time elapsed. The release signal was signaled by a bubble attached to the vertical leg. In one model, the bubble image was collimated and reflected into the line of sight via a complex mechanical and optical structure. None of the early models were particularly easy to use, especially in an airplane under working conditions.\nTwo hands were required continually, and lateral verticality determination and bubble transit left much to be desired. Several desirable features were sacrificed to minimize load on the timer, and intricate and bizarre mechanisms were resorted to for avoiding blind spots. The first two models showed the principle's workability and provided reductions to practice from which much information and experience were gained. In subsequent models, the principle was retained intact but the design was radically changed. It was possible, and eventually practical, to incorporate the whole sight into a hand-held, pistol-grip affair which might be completely operated, including adjustment, with one hand. In particular, it was found possible to fix the line of sight with respect to the body of the instrument, making the task easier.\nThis involved building the mechanism around the line of sight and separating the two triangles at their common leg. Aimed exactly like a pistol, the signal for release appeared automatically as the target passed by the aiming point, with the instrument held in such a way that the transit of a bubble indicated the proper depression. A bomb-release key was incorporated as a pistol grip for the sight, allowing release to be made by a trigger in full analogy with the firing of a pistol. Adjustment of target aspect, altitude, and ground speed, as well as initiation of the timer operation at submergence, could all be carried out with the thumb of the same hand.\n\nAs mentioned above, this antisubmarine bombsight, which became Navy bombsight Mark 20, was placed in limited production based on the final experimental bombsight.\nExtended flight tests prior to production had established that, with care, horizontal low-altitude bombing could be carried out to a probable range error of 20 feet in the altitude range from 100 to 500 feet. This was as good as could be done in line or laterally with a nonsubmerging target. Few tests were actually carried out due to mechanical difficulties under simulated conditions of submersion. It is not known whether enemy submarines were successfully attacked, either on or below the surface, with this equipment. For this purpose, a set of instructions was prepared, and certain Navy officers were assigned educational trips in this connection. While the practicality of the general method was established, a number of modifications were made.\nProposed models omitted underwater extrapolation feature. One model included an inherent vector computer for combining airspeed and wind speed, and/or target speed for a more effective solution. Auxiliary devices such as the miniature ground speed computer were prepared for cooperative functions with bombsights. Confidential: Aiming of Bombs from Airplanes. Such bombsights used bombs like those with extended ranges of airspeed and altitude, up to 1,000 feet. One model, particularly for use in blimps, extended to very low airspeeds. This model, which became bomb sight Mark 24, was tested at Lakehurst with better results than expected. A project resulting in a technique much used in other fields was that for automatic.\nIn the Mark 20 sight, the setting of altitude was obtained from the radio altimeter using a DC servo. This hand-held instrument employed a motor and resistive follow-up, accepting an altitude voltage from the AYD altimeter. The \"triangular\" bombing principle, which was crucial for the sight, depended on this variable. Accurate and automatic setting from the AYD altimeter resulted in impressive bombing tests, which were conducted over water.\n\nThe development of hand-held bombsights based on the \"triangular\" principle was gradually discontinued for several reasons. Firstly, better principles were available. Additionally, the submarine emergency was waning, and rockets were becoming more popular.\nThis is not to say that low-altitude bombing was not important, as it remained so throughout the war and its previously unexpected tactical application has been one of its phenomena. It was a curious circumstance which led high-altitude bombing to be well developed, at least instrumentally, when World War II began, while the apparently simpler art of low-altitude bombing, which in fact was put to extensive use, was almost completely unequipped.\n\nMany competitive bombing methods had also appeared, such as the FM radar Sniffer, which gave a solution in terms of range and altitude to the target, even on blind approaches, and which was later generalized to gliding attacks, with the range rate and the rate of change of altitude as input variables. There were also other bombsights of the visual triangular variety. The most impressive new principle, however, was not mentioned in detail.\nThis principle, discussed in Chapter 3, is that of angular rate bombing, which was employed in the British Mark III LLBS. In this system, a grid of lines at infinity was rotated downward in space using a luminous rotating helix and a stabilizing mirror system. With the target observed through the image of this grid, release was made automatically when relative motion momentarily became zero. The present writer suggested that this principle could also be embodied in the opposite way, by tracking the target accurately and measuring continuously the angular rate in space of the physical index with which the tracking was carried out. We were thus led to apply, first to hand-held sights and later to those supported in various ways, rate meters based on captured gyros of the type previously described.\nThis type of instrument, called the BARB, was developed for lead-computing applications. Under our direction, a project was conducted to apply strain-gauge torque measurement to captive gyros for this purpose. Several successful models were built and tested (see Chapter 3). The most effective method, however, involved the pneumatic capturing technique, which was experimentally applied to captive gyros and other components, and was developed primarily under Section 7.3 by intersectional arrangement.\n\nIn the research on the pneumatic angular rate bombsight, which became the Mark 23 bomb sight, and of which a subsequent elaboration \u2014 called SuperBARB, having a pneumatic form of aided tracking \u2014 was recently designated the Mark 27, several agencies were involved.\nThe angular rate principle of bombing, described in Chapter 3, can be interpreted slightly differently. This excellent theoretical work was contributed by L. Goldberg of the McMath-Hulbert Observatory. In target coordinates, the angular rate of the approaching bomber, as seen from the target, is (v/h) * sin^c^. This is evidently a function of time, where v is the closing speed and t is the time before crossover. The release condition, in this simplest case, is obtained by substituting the time-of-flight t, expressed in terms of altitude, into this equation.\nThe equation develops when an offset in aiming-point is desired, with climbs and glides contemplated. It is found that this method, particularly at lower altitudes, is remarkably insensitive to errors in altitude input and less sensitive, relative to other methods, to errors in closing speed. At one time, a synchronous bombing method was planned, utilizing the entire prerelease tracking interval to develop accuracy by matching the time function given above for the angular rate to an analogous function of frequency, well known in an RC electrical circuit. However, the Super-BARB tracking scheme, though based on another synchronous principle, has been quite successfully executed, as indicated by recent test results.\nThe most significant application of the absolute angular rate principle in instrumental solutions for gravity drop is in the combined system of PUSS. In the rocketry case, this principle is applied simultaneously to the gravity drop correction and to the lead computing solution, employing the same fundamental gyro component.\n\nThe paths of constant releasability are of interest for conjectural bombing tactics. We consider this problem in vacuo and with respect to a coordinate system fixed in the target. It is further:\n\nFor conjectural bombing tactics, it is of interest to study the paths on which a bomb may be released at any instant, each such hypothetical release scoring a hit. We consider this problem in vacuo and with respect to a coordinate system fixed in the target.\n\nThe most significant application of the absolute angular rate principle in instrumental solutions for gravity drop is in the combined system of PUSS. In the rocketry case, this principle is applied simultaneously to the gravity drop correction and to the lead computing solution, using the same fundamental gyro component.\n\nThe paths of constant releasability are of interest for conjectural bombing tactics. We consider this problem in the absence of external forces and with respect to a coordinate system fixed in the target.\nIt is assumed that the airplane's speed, in target coordinates, is constant. The results obtained have been used as flight criteria in several other investigations.\n\nAny given such path must be completely contained in a vertical plane through the target. Let the coordinates of a point of release resulting in a hit be denoted by (x, y). Then,\n\ndx/dt = vx\ndy/dt = vy\n\nwhere tf is the time of flight of the bomb and dx/dt, dy/dt are the values of the components of the projectile's velocity at the instant of release. Since dx/dt and dy/dt are also the components of the plane's velocity at this instant, for constant velocity v on the flight path (in target coordinates),\n\nelimination of tf between equations (3) and (4) gives,\n\ndy/dt / dx/dt = vx/dy\n\nor\n\ndy/dx = v/x\n\nConfidentially: Aiming of Bombs from Airplanes\n\nSince from equation (5), mine clear (X0+V0) be the point at the beginning of the flight.\nThe expression for the point where rj = 0 is given by:\n\ndyo = gx^r\n\nThe desired constant speed dive bombing paths are the loci of the point (Xo, yo) satisfying equation (8). Dropping the subscripts, equation (8) becomes the differential equation of the paths:\n\ndy/dx = gx^r\n\nEquations (15) and (11) give the equations for the dive bombing paths with ry as a parameter:\n\ndy gx^r, /dy^2 = l\n\nSetting t = 0 in these equations yields the level bombing criterion in vacuo:\n\ndy = dx/g, gx^r\n\nThis equation is inconvenient to integrate as it stands. Substituting g for gx^r gives:\n\ndy = dx/g, gx^r -> dy = dx/(g * gx^r)\n\nFor a given speed v and altitude y, equation (16) gives the point for entering the dive path continuously:\n\ncot <f> = y/v\ndv/dx * Qx + g * y = vyg\ny is the angle from the horizontal to the tangent of the flight path. Equations (11) and (15) can be written as:\ndx/dt = Vx + g * x\n\nSolving equation (12) by the standard formula gives:\nsec \u03b8 = g/V + 1/V^2\nor\n\u03b8 = arctan(g/V) + c\n\nThe flight path terminates at the target, as expected, since by equation (19), y approaches zero with x. At the origin, the flight path angle \u03b8 has a value of 71 degrees given by:\ng * \u03b8 = V^2\n3DNFIDENTIAL\n\nTHE DIVING ATTACK IN GENERAL\nAs seen in Figure 14, there are two branches:\nFrom equation (16), Xo, and hence, X = 2 tan <Ao. Similarly, equation (11) can be written as g cot(<f>o) or sinh(2 tan <f>o. From equations (14) and (16), g. Taking these last equations together, Figure 14 shows the path of unvarying releasability at constant bomber speed. This branch approaches the zenith over the target. While a valid bombing path, it is of undetermined practicality. Equation (25) gives the relation between the tangent of depression angle and the slope 77 of the flight path at every point. Equation (25) shows that when y approaches zero, the limiting values of the slope angle and the depression angle are the same: therefore, by equation (24), of the constants involved, the fundamental constant is the slope angle at zero altitude.\nThe following are: speed of plane, altitude at beginning of dive. The rest, x, 0, y, are derived from these.\n\nSeven reasons exist for desiring a method of dive bombing different from those elsewhere mentioned, leading to approach paths on which release may take place arbitrarily. It would be desirable to obtain this type of approach, and angular rate methods are available to provide highly articulate aiming criteria for this purpose, as then it would not be of critical concern at what particular instant release took place. Errors in the choice of release instant or in the releasing mechanism itself would be of little consequence, provided only that the path were held stable. However, it appears that such paths are not achievable.\n\n(Note: The text contains several errors and incomplete words, making it difficult to provide a perfectly clean version without making significant assumptions or alterations. The above text represents the best attempt to preserve the original content while making it as readable as possible.)\nNot the easiest to fly, as they are not strictly bomb trajectories, are paths on which the lift force essentially disappears, and an unfamiliar mode of control operation must be learned and resorted to. Recognized that this circumstance need not be fundamental and might be altered by the proper design of airplanes or appropriate training techniques. However, another practical difficulty arises. For a large useful region of range, glide angle, and speed, the downward visual freedom of most existing airplanes is not great enough that the target is visible to the pilot at the moment of release, or, if the airplane is following a path of unvarying releasability, in the time interval over which release may occur. This is admittedly a property of airplanes, as such.\nThe previous objection does not permanently restrict downward visibility. Thus, it is not impossible to arrange for such a feature in certain non-fighter airplanes and proposed fighter types. Both points have had temporary significance, hindering bombing tactics involving continuous releasability on approach.\n\nHowever, while not completely restricted, such tactics are generally associated with diving attacks. It is important to note that the property of lack of criticality or tolerance of the choice of release instant would not exclusively belong to tactics where the release path is rigorously followed. Other approaches, involving less curvature, may also exhibit this characteristic.\nThe ability to lift may still be experienced and will pass through a condition of releasability. In these cases, the choice of the release instant is also relatively non-critical compared to other methods of bombing. We refer again to the bombing solution of the Army A-1 multipurpose, or Draper/Davis, sight. This system involves an approach of the above-mentioned character and should be studied by the serious student. The present writer is not qualified to represent this system in detail.\n\nSeveral methods have been proposed and developed to avoid the practical difficulties named and to achieve accuracy despite losing the tolerance of release instant, which follows upon the release-path philosophy. These methods involve, first, a diving approach, in general, during which the target is visible more or less straight ahead, then a sudden bomb release.\nThe upward curvature of a path during which the target becomes invisible to the pilot and the bomb is automatically released is achieved through a computation dependent on the properties of the previously held path and the character of the pull-up maneuver. One such method was developed in the DBS system for BuOrd and later British orders. In this system, an approach was made by proportional navigation to compensate for target motion in the air mass, and automatic release during the pull-up regime was effected by simultaneous computation of the accumulated pitch, airspeed, altitude, acceleration, and the glide angle previously held. Glide and the accumulated upward turn were delivered by specially arranged gyros, and a nomographic type of computer, with mirrors and photocells, embodied the determination of these values.\nThe criteria for automatic release were guided by a free gyro moving a mirror in the sight head, providing a delayed approach to a collision course as described in Chapter 1. A method similar in nature, which has received much recent attention and developmental effort, and which has also been employed for the gravity drop solution with other projectiles than bombs, was originally proposed. This method came to be known as \"toss bombing,\" although the tactics referred to above, or again with the DBS, were substantially employed. That is, this term might be applied to several methods, although its connotation has been limited to those in which a special release computer was devised by M. Alkan, the French fire-control expert.\nThe diving attack in general employed toss bombing instruments, such as the so-called AIBR. These were made to depend on the indication of an integrating accelerometer, sensitive in the direction of the airplane's vertical, which began integration at a point shortly prior to the pull-up for bomb release. Thus, the velocity impulse imparted to the bomb in a direction upward, against gravity, and normal to the line of sight to the target was approximately measured. Release occurred through simultaneous computation of the duration of bomb flight, which was made, for example, by measurements on range or altitude and various speeds, when the upward impulse being increasingly imparted was sufficient to compensate for the downward pull.\nGravity accumulates during flight, with inherent advantages arising from the method of integrating acceleration. Fortuitous irregularities of flight, following initiation of the final computing phase, are automatically accounted for, and variations between flight path (measured in space) and the airplane axis are of second-order importance to accuracy. Correction for target motion in the air mass, requiring a collision course rather than the typically employed straight pursuit, was not contemplated until recently. It has been planned, including the toss method with an integrating accelerometer, in the PUSS system, to apply a correction for target motion.\n\nWhereas the earlier AIBR was based on a theory of horizontal approach to the target, as in plane-to-plane bombing, and was modified\nfor the gliding approaches appropriate against targets on the ground, the theory as proposed for PUSS was built anew, particularly recognizing this latter approach as significant. Continuous measurement was planned of altitude, airspeed, and normal acceleration during the earlier phase, and the integral of the incremental normal acceleration during the pull-up phase. It was determined to prepare a small mechanical computer to assess the release condition in terms of these variables and automatically initiate release of the bomb. For acceleration and the integral thereof, a pneumatic component was developed, comprising a captive mass, a feedback integrator, and a valving assembly. (Proposed by H. Pollard of AMG-C, who has been responsible for the form of computation and the theory of the method as developed thus far for PUSS.)\nThe mechanical computer, named PACT, could receive various initial conditions as desired. Both the exponentially averaged acceleration and the instantaneous integral of incremental normal acceleration were delivered to the computer as rotations, actuated by pressure motors that responded to or incorporated these variables generated by the pneumatic components. Airspeed and altitude were similarly delivered to the computer via capsule diaphragms. The toss bombing computer, PACT, will be integrated into the PUSS system described in Chapter 10. It will share inputs with other components of that system, and the mechanical-linkage computer it embodies will be physically connected to that of PUSS. Additionally, the instrumental method for using PACT as part of PUSS has been theoretically developed and studied. In the first phase, the approach is guided by this method.\nRespecting the target, the motion of which is compensated. This method uses a function of the gravity-drop compensation of the computer, in both elevation and azimuth. It employs a unique principle whereby the proper path for \"kinematic lead\" is rapidly subtracted. The embodiment of this principle is made by specializing the function of the PUSS rocketry computer to give a double correction in airplane heading for changes in direction of the line of sight to the target.\n\nTechnically, in the jargon of lead-computing sights and deflecting gyro systems, the criterion in azimuth is: a = 1. In elevation, the sight head is undeflected, the line of sight being along a direction normal to the computing axis of the accelerometer.\n\nBy H. Pollard.\n\nFor further details and a better technical discussion, refer to the writings of H. Pollard of AMG-C.\nIn Pollard's work, as in Alkan's, the non-circular nature of the pull-up path is recognized.\n\nFIDENTIA\nChapter 8\nCONTROL OF GUIDED BOMBS\n\n1. REVIEW OF ACTIVITIES\n\nAll our work in this field was pursued either through the cooperation between NDRC Divisions 5 and 7 or directly in an advisory capacity for the former division. There is no hope for separation between the activities which occurred under each sponsorship, since the interweaving has been most complete. We were first engaged on controls for guiding the RAZON bomb following the issuance of a memo by the Director of OSRD in which he outlined computing methods which might be employed for that purpose, and in which he referred the problem in part.\nThe writer was responsible for establishing and conducting a development program for preparation of experimental equipment for Division 7's fire-control methods. This program was carried out mainly between Division 5's and Section 7.2's contractors in Division 7. Aside from minor consultation and participation in conferences, we treated the visual or optical phase of the RAZON and, as a special case, the AZON guiding problem. The RAZON bomb is the modification of a standard 1,000- or 2,000-pound bomb, in which a special tail assembly replaces the standard fins. The assembly includes intact: radio reception for steering by rudder and elevator.\ngyro component for roll stabilization, movable. In the former case, Gulf Research and Development Corporation and certain contracting agencies at MIT were involved. The Franklin Institute was the locale of operations and supplied personnel and other developmental facilities. In the more recent stages, L. N. Schwien Engineering Corporation of Los Angeles, under contract to Division 5, was involved for several reasons, including the fact that H. A. Van Dyke, who had been project engineer at The Franklin Institute in this connection, transferred his employment there. Rudder, elevator, and aileron with \u201cmuscles\u201d for the latter controls, and a flare for visual identification of the missile during the drop. Two general types of guiding were contemplated. In the first, the bomb was guided from the dropping airplane in such a manner that\nIts trajectory terminated in the target, corrections being applied only as necessary due to errors in dropping which would prevent its unguided trajectory from terminating in that manner. In the second proposed method, either through special maneuvers of the airplane or through a program of control applied to the bomb, the plan was to make the bomb align itself collinearly between the bomber and the target during the latter portion of the time of drop. In both cases, the process was similar in one respect, in the azimuthal deflection problem, to the guiding of AZON, in which one dimension only was corrected and which was applicable particularly to long and narrow targets attacked approximately in their greatest dimension. The second method for guiding RAZON, in which it was proposed to attain temporary collinearity by aligning the bomb's longitudinal axis with that of the bomber and the target.\nThe discarding of visual guiding occurred when insufficient maneuverability was identified in the projectile. This raised a significant issue, encompassing missile aerodynamic design, with several RAZON variants and predecessors under consideration. Both analytical and differential analyzer solutions were employed to aid in its study. With this conclusion and experimental confirmation, focus shifted to controls for the noncollinear guiding technique. The Bush proposals and others initiated a design of an optical sight and computer, resulting in the CRAB sight, enabling the operator to carry out the mission through the superposition, under control, of a pair of indices. These indices, in fact, were images of the target and flare.\nAlready advanced by J. P. Molnar at Gulf. Confidential\n\nReview of Activities\n\nThe bomb. Whereas a completely special computer and optical system were first under development, it became suddenly apparent to us that the same function could be embodied in a relatively simple modification of the Norden bombsight. This modification could then be used following the original drop of the bomb as a normal type, to assist in the guiding process as a continuation of its normal operation. Remarkably enough, the whole operation of the bombsight was kept usefully in service for this post-release purpose of computing and presentation. The operator merely transferred his attention from the synchronizing controls to those for guiding the bomb, and from the alignment of cross hairs on the target to the alignment thereon of the bomb flare as the latter was in flight.\nIt was only necessary to modify the trajectory in small and gradual degrees; the parabolic character was generally retained. Accuracy, assuming the guiding was expertly and stably carried out, depended only on the time of flight set in the Norden computer. For employment with this technique, the addition to the bombsight consisted only in the attachment of a small mirror, the so-called CRAB mirror, to the objective of that instrument.\n\nWe have mentioned the use of the differential analyzer in this study. It was employed again for further developments as described below.\n\nIn the CRAB project, a number of other aids were pressed into service. Aside from rather elaborate space-models in which the relationships among trajectories, bomber paths, and other geometrical objects were made evident.\nChapter 4: Electronic simulators were constructed and applied to study the stability and effectiveness of the guiding process. These instruments provided tangible information essential for control development, including local project controls, and later served as training aids for civilian and Service operators in the field. A subsequent activity focused on achieving collinearity conditions near the end of the drop. This struggle was linked to the question of evasion or maneuvers engaged in by the bombing airplane after the release point. While such maneuvers reduced danger over the target area, they imposed serious guiding problems. Studies were conducted to address this issue, partly with the hope of finding a simple solution.\nInstrumental correction could be applied, provided the evasive tactics did not prevent seeing the target entirely. We found it unlikely that the RAZON bomb, including its modifications, could follow a trajectory giving collinearity with the target over a terminal time interval. Regarding evasion, a natural evasive path was discovered that also met the criterion of terminal collinearity. For bombs only a small fraction more maneuverable than the standard RAZON, this technique probably would have led to successful flare guiding on the collinearity principle. Although no field experiments were made.\nThe data for the study has been derived from differential analyzer solutions. The procedure involved a normal and rather sharp turn by the bomber to one side, while the projectile was guided to the other side of the original range direction. The approach had first been made along a ground track displaced from the target on the side toward which the evasive turn was made. Thus, the region near the target, where presumably antiaircraft fire might be heaviest, was avoided as completely as possible. In the guidance operations, manual controls concentrated, at least toward the latter part of the drop, on holding the trajectory to one side and into a gradually increasing dive. This was achieved by first curving the trajectory less, and then more than would be done by gravity alone.\nThe flare superimposed on the target in true physical collinearity. However, this method was not tried for several reasons. One was that the ROC bomb, reportedly having about three times the maneuverability of the RAZON, was considered for visual flare guiding instead. It developed as having less maneuverability in terms of potential normal acceleration under guiding. Since greater maneuverability was available, special maneuvers to attain collinearity were not considered essential. From that point, no further study was given to evasion. Many bombers continued their runs with standard bombs, and it was felt by some that the additional danger involved, even ideally from the point of view of personnel, was worth the continued straight run during the.\nThe ROC bomb, intended as a television seeker for ground targets, was maneuverable for collinear flare guiding. Authorization was obtained to try it for this purpose before the television (MIMO) component was ready. A computing sight was constructed, involving a generalization of CRAB that gradually and maintained identity between the reflected flare image and the actual flare image toward the latter part of the flight. This sight was used for guiding the AZON missile as well. The ROC bomb, not described in detail in this brief review or subsequent sections of this chapter, was attractive for collinear flare guiding due to its maneuverability. While the television component was still in preparation, authorization was granted to test this missile for this purpose. A computing sight was constructed, which generalized CRAB and maintained identity between the reflected flare image and the actual flare image during the latter part of the flight. This sight was used for guiding both the ROC bomb and the AZON missile.\nCalled CARP and an adjunct to the bombsight Mark 15, from which it derived automatically several vital inputs. Although its manual operation was somewhat more complex, and this in fact prevented its unmitigated success in experimental trials, this operation was in general analogous to that of CRAB. Electronic simulative methods were applied for these flare guiding developments, for the construction of study models, humanly operable, in connection with questions of the stability and practicality of the guiding processes. On a further application of these same methods, the study models were constructed at The Franklin Institute, as a collaborative venture between Division 7 (Section 7.2) and Division 5. H. A. Van Dyke was the project engineer.\nFor the contractor, it was moved to L. N. Schwien Engineering Corporation under Division 5, around the time testing was to begin, as Van Dyke became employed by the latter organization. The designs were modified into prototypes for trainers intended for field application, which were then produced and further modified through other facilities of Division 5.\n\nAnother major application of electronic simulation was to the control of ROC with MIMO, fundamentally a \"seeking,\" or \"homing,\" or \"automatic interception,\" problem which was subsequently studied. This study was conducted by the writer. The status of the study was actually that of collaboration or more properly consultation with Division 5 and their contractors, primarily Douglas Aircraft, on their developmental control problems in connection with the television bomb. Contrary to\nThe general impression is significant, given a falling bomb with remotely manipulable control surfaces and the means for seeing ahead along the bomb's axis via a television camera. Precisely guiding the bomb to any given target at ground level involves two principal circumstances. One is the motion of the landscape in the televised image, which results from pitching and yawing motions of the projectile not directly connected with the curvature of its air path. The other arises when steering is performed such that the missile heads directly or approximately toward the target. By this constraint, the curvature of flight must progressively increase as the range decreases, provided the target has lateral motion of appreciable magnitude in the air mass. We note that the latter type of motion causes significant challenges in guiding the missile.\nis  equally  occasioned  by  wind  as  by  proper \nmotion  of  the  target  on  the  ground  or  over  the \nwater.  In  the  ROC  projectile,  the  response  of \nthe  image  to  pitching  and  yawing  is  reduced \nby  the  purposeful  and  considerable,  although \nexperimentally  not  yet  complete,  reduction  of \nthese  motions  by  appropriate  design  of  the \nprojectile.  This  design,  which  involves  a sym- \n\u2018\u2019By  connotation,  these  terms  have  become  badly \nconfused,  and  their  usage  is  widely  disparate  among \nvarious  groups.  A purer  though  more  esoteric  lan- \nguage has  been  developed  by  W.  B.  Klemperer,  whose \nmany  writings  on  these  and  allied  topics  should  by  all \nmeans  be  consulted. \n\"With  the  assistance  of  R.  M.  Peters  and  L.  Julie, \nthe  latter  being  responsible  for  the  laboratory  simu- \nlative equipment  thus  em\u2019^lbyed  at  Columbia  Univer- \nsity. \nREVIEW  OF  ACTIVITIES \nmetrical  and  articulate  wing  structure,  permit- \nThe independent alignment of the central body is significant for future projectiles, particularly when self-propelled. For both the television application and the flare guiding application mentioned above, ROC (or ROKH) was roll-stabilized by the same means as AZON and RAZON. The character of this means and the resulting space behavior of the missiles, in terms of rigid-body dynamics, is further discussed below as this question enters the problems of trajectory analysis and synthesis. The control artifices for the remote, human guiding of the television ROC, or MIMO-ROC, were outlined in Chapter 4. In the development and study of control dynamics and equipment for this type of guiding.\nAnd we were advanced considerably in assessing the stability and effectiveness of such equipment under the proposed tactics of operation, having previously studied the air trajectories of this and other guided bombs. For example, we were now familiar with the dynamic and transient properties of such trajectories, for which both the differential analyzer and electronic simulative methods had been employed. It was thus approximately known, for the television-bomb work, which of the rationalizations and guides to judgment were valid in predicting control performance. Continued application of simulative equipment allowed us to assess the several proposals for control dynamics and to select one arrangement which appeared superior from an overall standpoint. A conclusion was also reached.\nWe refer to NDRC Division 5 and the Douglas contract. Our research involved electronic models, while mechanical and optical models, some of fantastic intricacy and ingenuity, had previously been proposed and designed. In some cases, partial models of the latter variety were available for corroboration, short of full-scale tests, of the results attained by the electronic simulators in our laboratories. One other major activity in the field of guided bombs concerned the technique of GCB, or ground-controlled bombing, in which a radio link allowed control, from a position on the ground relatively adjacent to the target, of a bomb dropped from a vantage point overhead.\nThe visual phase of the weapon, where a flare was to be attached, was primarily considered by us. Aided by prior knowledge of the projectile's behavior in flight - in this case, the RAZON bomb - and its response to control signals, we had from previous experience with synthetic and analytic studies on the differential analyzer and other computation aids. We should not imply that no trajectories were computed by numerical integration, as these processes had been earlier conducted in this general connection by ourselves and more extensively by others. This procedure, however, gave a better appreciation for the improved facility for study and invention provided by automatic forms of mathematical operation. A theory of guiding was worked out, in terms of a pair of ground stations from which the projectile would be guided.\nThe falling bomb would be visible in its downward course toward the target, allowing the trajectory to be gradually modified to terminate without significant warpage toward the lower end. Several alternative mechanisms were proposed based on this theory, which were discussed in numerous conferences with other personnel. Compromises were reached, preserving the best features of widely differing proposals in the forms finally determined for joint recommendation. It appeared that with simple control equipment and under circumstances allowing for considerable flexibility, the GCB technique could likely be carried out with great success, both in terms of the ease with which the manual phases of the process could be learned and applied.\nThe accuracy with which refractory enemy obstacles and strongholds could be reduced. In the study of this problem, the writer and R.M. Peters of Section 7.2 collaborated directly with H.A. Van Dyke of L.N. Schwien Engineering Co.\n\nControl of Guided Bombs\n\"2 Analysis and Synthesis of Trajectories\n\nA right-handed Cartesian coordinate system is assumed in the air mass, with origin at ground level directly beneath the point of release of the bomb, and the positive x axis taken in the same direction as that of the velocity vector of the airplane with respect to the air at the instant of release. (See Figure 1A.)\n\nBeneath Dropping Point\n\nFigure 1A. Coordinate system and general guiding space.\n\nThe only forces acting ordinarily on the unguided missile are gravity and the drag force D, directed oppositely to its velocity vector V.\nWith respect to air. The deflection of control surfaces introduces a sideways force S perpendicular to V, and a lift force L perpendicular to both D and S. The equations of the trajectory are:\n\nmz = Dg Sz Lx \u2014 mg,\n\nwhere m is the mass of the bomb, g is the acceleration of gravity, and the subscripts x, y, z indicate components of the forces in the directions of the coordinate axes. Assuming that the forces D, L, and S vary with the square of the velocity, these equations can be written in the form:\n\nJj BL\n\nWhere,\n\n7Yl Jj\n\nThe drag function d depends on the two (as yet incompletely defined) components e and Se of the CSD (control-surface deflection), measured from the neutral position of no control. A is some area proper to the bomb; p is the density of air at the altitude z.\nAnd Cs and Cl are the appropriate aerodynamic coefficients. Owing to symmetry, Cs and Cl are identical functions of Sr and Se respectively, while Cd depends on both Sr and Se. It is assumed that Cl, and hence L, is independent of Sr, and vice versa. In the case of both rudder and elevator control, Cz is obtained from Again, owing to symmetry, Cd is the same function of Se as of Sr.\n\nThe gyro stabilization of the bombs ensures that the lift force vector (scalar magnitude L) remains parallel to the vertical plane in which the bomb was projected. The departure from this assumption is so small that Ly may be taken as always zero. Since D, L, and S are mutually perpendicular, in AZON and RAZON, the convention was to use the cross-sectional area for this quantity. In ROC it appears as the wing area.\nAnalysis and Synthesis of Trajectories\n\nN T D\no X N\no T3 h oxj ro\nItj? s X N\nI o\no ho M N\nO CA M Jp* I xalT) I\nNl N O\nX X\nN g N s\n\u2022ite i 5k i-oh\nN N ^iMk T3ho\n\u2022ol'o X xk Toro\ni=e-\u201cKj(8E) s=e-\u00abKE(8E)\n\nFigure IB. Differential analyzer connections for guided bombs.\n\nFigure 2. Gyro arrangement for roll stabilization.\n\nThe direction cosines of D, L, and S are:\n\nOr, setting we have:\n\nThe use of the differential analyzer at MIT to solve these equations was obtained through NDRC Division 7, and later Division 5, contracts. Appropriate constants have been used which apply to the various RAZON types.\n\nLater, solutions for the several sets of experimental ROC constants were possible. It was initially found impossible to get the complete equations on the analyzer in the case of\nX = xyz, Pq obtains equation (7) in the drag and side force terms, where v^ was replaced by yx + yz, or by uv. In the lift term, sy lx was replaced, or by z. This equates to saying that D and S vary not as constants but as the product of v and its projection on the vertical plane. The differential equations (2) become:\n\nIz = sy\ndy = -lx/xz\n\nThese equations can be abbreviated as:\n\n\u2014 (x, y, z), Pq obtains equation (7) in the drag and side force terms, where v^ was replaced by yx + yz, or by uv. In the lift term, sy lx was replaced, or by z. This amounts to saying that D and S vary not as constants but as the product of v and its projection on the vertical plane. The differential equations (2) become:\n\nIz = sy\ndy = -lx/xz\n\nConfidential\nEarly Studies on Collinearity Control\nThe approximate equations (7) reduce to (5) when Sy and hence 2/ are zero. The function initially assumed for density was where po = 0.002378 slug per cubic foot, the density of air at sea level. Several other functions were later employed in dependence on the various physical circumstances relevant. There is little difference in the results at least as far as guiding is concerned. The functions Cd, Cs, Cl were generally obtained from empirical data. Certain standard trajectories were obtained for the various bombs for full control deflections, applied, say,\nAt 8, 15.5, 23, and 27 seconds after release, the initial velocities were assumed between 175 and 275 miles per hour. In general, the initial altitude was taken as 15,000 feet, although some trajectories were obtained using higher and lower altitudes.\n\nDue to the constant modification of bombs and hence of coefficients, standard trajectories were also obtained for values of Cz, Cl, and Cs 20% lower and higher than those in current use. From these trajectories, it was possible by interpolation to determine the maneuverability, ranges, time of flight, trail, etc., of future bombs with various characteristics within this range.\n\nIn another set of solutions, instead of putting in the values of Co and Cl corresponding to full deflection in range, the functions Cd and Cl were plotted on input tables and applied at any time.\nDuring the solution process for any chosen deflection, we include here for approximate comparisons a table of constants for several bomb types. (Figure 1A shows the machine connections for the three-dimensional solutions of the differential analyzer. A simpler arrangement was possible in the plane when y = 0, but that was a special case of the connections shown.)\n\nTable 1. Tentative data on projectiles.\n\nBomb | m | A | S/dd | Omax/dt | Min. | Cd | Max. | Cl,Cs | Max. | RAZON\n---|---|---|---|---|---|---|---|---|---|---|---\nA | lb | ft\u00b2 | sec | sec | - | - | - | - | - | A1,000\nB | lb | ft\u00b2 | sec | sec | - | - | - | - | - | A1,020\nC | - | - | - | - | - | - | - | - | - | -\n\nROC A | - | - | - | - | - | - | - | - | - | -\nROC B | - | - | - | - | - | - | - | - | - | -\n\nEarly Studies on Collinearity Control\n\nIt was generally agreed that for the best results, the bomb, and possibly also the airplane, should be maneuvered so that over a finite time interval prior to impact, the bomb, airplane, and target were collinear.\nThe target would be collinear (compare Figures 3 and 4). In such a case, all errors in dropping might ultimately be reduced to zero, resulting in high accuracy. It would only be necessary to provide stability in the guiding process. A detailed study has been made of this aspect of the problem, for which the use of the differential analyzer was invaluable. In the case of the RAZON bomb, a point target was assumed, located normally where the unguided bomb would fall. Programmed deflections were applied in an attempt to arrive at a trajectory giving the desired collinearity during the last part of the flight. An ideal line of sight trajectory was constructed geometrically under various assumptions. For example, it was assumed that the airplane, traveling 250 miles per hour at the instant of release of the bomb, could decelerate thereafter at the rate of 2.5 miles per hour squared.\nFor a typical RAZON, the best possible trajectory obtained from the analyzer using full positive lift and then negative lift lay about halfway between this ideal curve and the free-fall curve. Similar trajectories were obtained after shifting the target from the position of a free-fall hit, allowing for either a rangewise or lateral offset. The lateral offset seemed especially attractive, as the guiding plane would then maneuver to the opposite side to achieve line of sight with the bomb and target.\n\nThe result of these studies has been negative. From the trajectory calculations, it was determined that:\n\n1. The plane must be traveling during the last part of the flight at too low a speed.\n2. The plane must be further back than it should be.\nThe most serious difficulty is the assumption of a reasonable deceleration. This is necessary for the line of sight, or collinearity condition, to be achieved between the bomb and target, assuming the target is at the point where the bomb landed, and the plane remained in horizontal flight. In each case, the same two difficulties appeared: achieving collinearity between the bombs and airplanes cannot be done without an undesirable maneuver. Some trajectories were obtained for an altitude of 28,000 feet. In these cases, difficulty (1) did not arise. For a lateral offset of the target, the plane could use rudder control and evasion to the opposite side, traveling at its initial velocity of 250 miles per hour during the last part of the flight.\nThe hourly requirement for a collinear bomb and target is met, but difficulty (2) persisted. For the line of sight, the plane would need to be approximately 3,000 feet behind where it would be at the given times for the given velocity. It should be noted that the necessary condition for terminal collinearity, implied in (2), namely that the tangent to the trajectory at impact contain the observer, is also barely sufficient, given that the bomb hits the target.\n\nThe corresponding problem with lateral control only, as in the AZON bomb, is much simpler. Here, a line target instead of a point target is assumed. This involves a question of plane of sight instead of line of sight. If the bomb isn't maneuvered and the airplane continues flying in the same direction at release, then\nLine target, bomb, and airplane are coplanar for a precise and undisturbed drop. If the airplane deviates from its straight course, either accidentally or deliberately, as in an evasive maneuver, the bomb can be maneuvered in the same direction to achieve the plane of sight condition, at least terminally. The extent of the evasive maneuver is of course limited by the available maneuverability of the bomb.\n\nAnalytic trajectories have been obtained for the AZON bombs using first right deflection and then left deflection, the change being effected at such a time as to make the y coordinate of the bomb zero at impact. This has been done for full rudder control to get the outer limits of the maneuver, and also for half deflection. In general, it was believed that only half-control should be used for such evasion, leaving the rest for the bomb's natural trajectory.\nTo return to the most crucial matter, that of collinearity in the complete sense, we estimated that a bomb with roughly twice the lift of the \"standard\" RAZON was necessary to achieve this end. More lift than this was advisable for comfortable tolerances. The effect of large concurrent increases in drag is not well known, but we had some indication that this was not so important.\n\nComments on Evasion by the Bomber:\n\nIt was considered by many operational military personnel involved that moderate evasion is very little better than none, owing to the dispersion of antiaircraft fire. Against fighters, on the other hand, effective formation tactics again preclude violent evasive maneuvers by the bomber. Furthermore, for violent evasion following release, the stabilizing problems and:\nThe visibility requirements in computing and sighting apparatus increase significantly and lead to complex and novel equipment, particularly due to the considerable bank of an airplane involved when a decisive turn is entered. An evasion may also be made for the purpose of aiding the collinearity condition. Thus, the use has been made of a climb to slow down the bomber and allow the bomb to relatively advance. While this may be the only way to obtain collinearity with a weakly maneuverable bomb, it is considered undesirable as a tactical measure. For instance, if an injured bomber is in the formation, the other planes dislike climbing away from him. The latter consideration might not apply to an evasive maneuver, the term being used in both senses as above described, which consisted in a sustained turn.\nControl of Guided Bombs: A constant altitude is crucial (refer to Figure 5). It's worth noting that such a maneuver could make it easier to achieve collinearity between the bomb and target, thereby enhancing accuracy in both directions, towards the end of the flight. This tactic would entail dropping the bomb during a run on a point laterally displaced from the target by approximately one-tenth of the altitude, and entering a turn to the other side immediately after dropping. A control program would then turn, climb, and dive the bomb towards the target. Manual control would subsequently refine the trajectory. In this process, the guiding would be less complicated due to the separation of the x and y directions involved in the special gyroscopic method of roll stabilization already mentioned.\nThe issue of collinearity in bombs remained unresolved in the existing sighting system, as it required making different provisions for separating out the influence of bomb motion in the z direction.\n\n5. EVOLUTION OF THE FIRST SIGHT FOR GUIDING\n\nThe pursuit of collinearity in bombs of the previous type resulted in frustration. In designing a sight for immediate applicability, we were compelled to adhere to the earlier doctrine that a guided bomb should be corrected by operations that alter its trajectory only slightly from that in an unguided fall (see Figure 3). It should be emphasized that while there is enough maneuverability in such bombs to compensate for target accelerations, ballistic winds, and dropping errors, these factors alone cannot ensure accuracy in range during a normal approach.\nThe circumstances would be very different, for example, if the normal approach were straight down from vertically overhead. Since collinearity over an interval, as illustrated in Figure 4, appeared to be impossible, we strove for instantaneous collinearity at the moment of impact. Given the proper guide to steer the bomb during flight, the range accuracy of this method depends primarily on bomb ballistics and altitude. It turns out that the properties of an instrument which will show how the angle between bomb and target should close up in time are also the properties of the computer, if appropriately employed, in the Norden bombsight Mark 15. This fact led to the attractive possibility of using the same group of apparatus for dropping the bomb and for guiding it after the drop. A diagram follows.\nThe given figure shows the operation of this sight. A normal drop is made as if the bomb were not to be guided. The operator then avoids further adjustments to the bombsight for synchronizing, but watches the target. The flare on the bomb is reflected in the target field in such a way that it lies directly on the target if the descent is proceeding according to plan. The desired trajectory is thus referred to the target itself; and if the proper time of flight is set in and the operator can \"guide\" the image of the bomb always onto the target, he will hit. It was contemplated to use this method in range only, with Razon, permitting another operator to guide in azimuth. The latter is thus equivalent to an Azon guider. If minor evasions or accelerations are indulged in by the bomber, this will merely affect the azimuth guidance.\nThe trajectory can be altered somewhat. The trajectory will still reach the target if other conditions are met.\n\nCONFIDENT. \n\nORIGIN OF THE GUIDING SIMULATOR\nImage as seen in telescope, showing crosshairs, flare, target, and guiding errors\n\nFigure 6. Mechanism for bomb images in CRAB and CARP.\n\nIf, due to maneuvers by the bomber or target, or due to extremely poor synchronization by the bombardier, the target moves out of the telescope's field, it is only necessary, without affecting the result, to adjust the vertical gyro of the bombsight back into a position where the target can be seen again. This should normally not be necessary, however.\n\nModifications to CRAB's mechanism were later developed to achieve collinearity conditions with a more maneuverable bomb, resulting in a sight called CARP, for use with a\nThrough the aid of a flare-equipped ROC, the bomb was to be efficiently guided into collinearity. 8\n\nOrigin of the Guiding Simulator\n\nIt is analytically difficult to work successfully on the stability problem since a human being is involved, an unknown differential equation, and the controls themselves are subject to boundary conditions in deflections and rates. Thus, stability of the system between such boundaries is only a necessary, and not a sufficient, condition for complete stability.\n\nAs for similar problems in other fields of endeavor, it was decided to use electronic simulative methods for this problem.\n\nIt is essential to be able to guide the bomb onto the target in angle, or onto an auxiliary programmed aiming point. It must be possible to keep it there very closely.\nThe laboratory has developed a reproduction of the dynamics involved in this operation, which has proven quite useful. An account of the apparatus and technique for this development can be found elsewhere. For the purpose of simulation, it was not necessary to duplicate the overall dynamics of the bomb's motion in nearly so precise a form. Secondary effects, which follow slowly after the more immediate response to a guiding impulse, are of relatively minor importance in control dynamics. By adjusting the time scale, it is possible to include the human operator existing in conjunction with other elements of the causal loop, or to study various artificial components through oscillographic response to standard inputs. The principal advantage of this approach is that it permits the realization, in flexible form, of the dynamics under investigation.\nModel forms, of all the discontinuities which are present in the real prototype and must be dealt with in the design of auxiliary equipment to achieve stability under all conditions and through all regions of the variables. A further property of this type of simulative arrangement is that it may be applied as training equipment. Additional realism may be attained by the superposition of moving map images around the oscilloscope screen. Such application is considered a valuable addition to the provision of a laboratory \"proving ground\" for experimental sighting equipment. The above laboratory simulative systems, and the resulting trainers, were extended later to apply to ROC dynamics, having initially been built primarily around RAZON. Control of Guided Bombs\n\nChanges in degree,\nAZON and RAZON are guided bombs obtained by converting standard 1,000-pound or 2,000-pound bombs through replacement of the tail structure with a new unit containing radio, power supply, gyros, and fin-driving and aileron-driving motors. They are appropriately stabilized in roll and can be dropped normally, then deflected moderately about a normal trajectory during a more or less straight continuation of the bomber\u2019s run. While AZON can be deflected only in line, RAZON can be deflected both in line and in range. CRAB is a sight and sighting technique for guiding RAZON. A small mirror is attached to the Mark 15 telescope in such a way that the image of the target, which normally stays in view, is reflected onto a scale.\nThe field maintains an image of the bomb flare superimposed on it after the bomb is dropped, which can then be guided onto the target. This results in the bomb following a normal trajectory towards the end, except for the guiding transients, and may terminate in the target. CRAB can be easily installed in the bombsight and does not interfere with normal bombing. With this method, it is important to know the bomb's time of flight with good accuracy and to set the corresponding disk speed. Tests from 15,000 feet yielded a probable error of 90 feet in range and 10 feet in line. ROC is a different missile, still in development. It features a wing structure that permits flight with zero pitch and yaw, as well as a much greater maximum lift and hence curvature of path. Although intended for a different purpose, CRAB and ROC share some similarities in their guidance systems.\nThe development of CARP, in addition to its intended purposes, was also applied for a use similar to RAZON's remote visual guiding. CARP, which is still in development, is a sight for ROC. It is more elaborate than CRAB and differs in that the angular program between the directions to bomb and target is not that of a standard (accurate) bomb. This program converges in such a way, toward the end of the flight time, that the angle gradually decreases to zero and remains so over an appreciable interval. A computer, which produces this program and drives a mirror in an auxiliary telescope, derives its information from normal bombing data available in the bombsight to which CARP is attached. Along with these sight developments, an analytic trajectory study was conducted with the differential analyzer. A large library of guided bombing data was compiled.\nTrajectories, collected in three dimensions, were recorded, and a complete index prepared. The electronic simulator study was also conducted. The purpose here was only to study the stability of the human guiding process. This has greatly assisted in the choice of guiding equipment. This same technique was subsequently applied to the development of trainers for field use.\n\nIn the summer of 1945, upon a definite military request, cooperative conferences were arranged among NDRC Divisions 5, 7, and 14 (Radiation Laboratory at MIT), to study the question of bombing strongly held enemy positions, such as those in caves and on hills in Pacific islands, from lines of advance at the edge of occupied territory, by remote control of detectable bombs dropped onto such positions. Thus, if, from two separated friendly positions, it was possible to control the detonation of bombs on enemy positions.\nThe azimuth bearings of a target were identifiable, enabling a bomb to be guided towards each bearing and falling on the target to high precision. In this cooperative process, the bombing airplane could be appropriately guided to an appropriate dropping position by one or more ground stations. An early suggestion was to use radar sets like the SCR 584 for complete knowledge of the bomb position during the drop and for bomber guidance. While our studies focused on the visual aspects of the tactic, with the bomb control being flare-equipped and ground stations relatively close by, we think it appropriate to mention one solution for the combined problem.\nThe solution for radar detection and remote guiding is assumed to involve identifiable ground positions with high accuracy in radar coordinates. Both the bomber and bomb must be uniquely identifiable in the same coordinate system. The solution was obtained as follows, with the SCR 584 coupled to the M-9 antiaircraft director. Prediction would be applied in the standard manner to the bomber, as if it were a bomb during approach. The future position of the bomb, at the end of its known flight time and assuming a modified gravity acceleration after drop, would be continuously computed and indicated at every instant as if the bomb were dropped at that instant, through direct tracking of the bomber. A simple modification of the M-9 computer could accomplish this, and a presentation of the potential impact point would result.\nThe ground position of the bomb would be continuously available at a single remote station. Thus, not only could the bomber be directed into position, but the signal for release could be directly provided when the predicted ground position of the bomb coincided with the target. Following release, radar tracking would be switched to the falling bomb. Prediction would be continued, using the same future acceleration, but now with a time of flight determined either from the remaining bomb altitude or the time duration since release. This would still provide a predicted ground intersection for the bomb, based on simplified, but adequate and continually more valid, extrapolation. Guidance would be direct and two-dimensional, in plan. It would be relatively stable and hence potentially accurate, owing to the presence of a first-derivative response in the prediction.\nThis method embodies the guiding reference, leading to very successful attacks. Its only drawback is the weight of equipment required, which is 17 tons, partly compensated by the greater range from the control station allowed.\n\nNote that with the radar or visual method of control from the ground, the projectile need not be dropped from a bomber but could equally be launched mortarwise or by other means from the ground. Launching could occur from observation posts or further back. For future development, this freedom is significant.\n\nOn the visual side, the simplest arrangement in which control is completely applied from the ground is that in which ground stations look toward the target along perpendicular directions, and the bomber is the observer.\nBomber flies directly along one such direction. The roles of such stations could be interchanged, and there might be much to be gained in such symmetry and flexibility. More generally, the bomber might attack on any track dividing the lines toward the target from the two ground stations, which indeed need not be rectangularly disposed. It is also evident that the ranges between stations and target need not be equal, and may have a large range of absolute values.\n\nIn Figure 7, let A and B denote the azimuth and range control stations, respectively, and T the target. The airplane is so directed on its approach that its ground track is a line GT between AT and RT.\n\nBomber:\nFigure 7. Observation scheme for ground control of Razon.\n\nTarget (T) ---\n| |\n| | GT (ground track)\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n| |\n|\n:ONFIDENTIAL^ \nCONTROL  OF  GUIDED  BOMBS \ntion  of  the  drop  itself  will  be  discussed  below. \nLet  B be  the  position  of  the  bomb  at  any  in- \nstant, and  the  angle  between  BT  and  the  ver- \ntical VT,  The  value  of  <j>  at  the  instant  t = 0 is \nthe  dropping  angle  <^o.  Control  of  the  bomb  can \nbe  achieved  by  observation  of  and  its  projec- \ntions. Since  the  observer  at  R will  see  not  </> \nbut  its  projection  0 on  a vertical  plane  perpen- \ndicular to  RTy  it  is  desirable  to  employ  for  ref- \nerence in  control  some  function  of  4>  which  is \nnot  altered  by  projection. \nLet  xj/  be  the  angle  GTR.  Then \nIf  the  bomb  is  so  guided  in  azimuth  as  to  re- \nmain in  the  plane  GTF,  then \ntan  4>{t)  = tan  (pit)  sin  yp. \nConsequently \ntan  (pit)  _ tan  (pit) \ntan  00  tan  0o \nIf  the  bomb  is  allowed  to  deviate  somewhat \nfrom  the  plane  GTV,  this  relation  will  not  hold \nexactly,  but  in  general  such  deviations  will  be \nThe function tan 0(t)/tan <Po is unaffected by variations in the airspeed of the bombing plane. A difference of 75 miles per hour in velocity produces less than 1% change in tan 0(t)/tan <Po, due to the increase in horizontal component of drag at higher speeds. Therefore, tan 0/tan <Po is a function of time and initial altitude only: a cam driven at a rate dependent on altitude. If the bombsight Mark 15 is used for tracking, the function kih) is not necessary. The cam for fit,h) may be driven by the constant speed motor through the disk whose speed is inversely proportional to the time of flight of the bomb. The functions fit, 15,000) and kih) can be calculated from free-fall trajectories run on the differential analyzer. The bomb.\nOne operator should guide the bomb around the free-fall case. One operator might track the bomb with the cross hair, making such adjustments to the telescope as necessary to keep the bomb on the cross hair and in the field of view. A second operator then controls the bomb. From the telescope position, the actual value of tan \u03b8(t) is obtained and the ratio tan \u03b8'(t)/tan \u03b8\u2080 is formed. The primes are used to distinguish observed values from theoretical ones. This ratio is to be compared at each instant with the values given by fit,h. For a perfect drop:\n\ntan \u03b8' = tan \u03b8\\_fit, h\ntan (p'it) = tan \u03b8\\_fit, h\n\nHowever, it is not necessary, or even desirable, that the bomb be controlled so as to keep the right-hand side of equation (17) zero. A criterion for a hit is that tan \u03b8 remains finite. Hence, it is sufficient to keep this quantity approximately constant.\n\ntan \u03b8\nThe variation with altitude can be handled by stretching the time scale. If 15,000 feet is taken as standard altitude, then only one function of time, fit, (15,000), is required. This could be mechanized by tan (p' fit) fit,h. The value of C may be indicated by a pointer on a scale, whose center point corresponds to zero. The operator would guide the bomb in such a way as to keep the needle as stationary as possible. The initial value of C (Sit t = 0) would be approximately zero. During the drop, the needle might deviate from the central position for various reasons, but it should not be necessary to control the bomb to make the needle return to that or any other given position. A change in actual drag is unfidentifiable.\n\nControl of Rason from the Ground.\nThe coefficient Cd from the value used in calculating f(t,h) may cause C to vary slightly. Changes in time of flight due to control application will cause small variations in C. Deviations of the bomb from the vertical plane GTV may also alter the perspective relationship and hence C. However, all these effects are slight and would cause practically imperceptible motion of the needle. An error in dropping, however, where the bomb, if unguided, would miss the target, would soon cause a quite perceptible change in C, increasing with time, since tan ^ becomes infinite at impact. In the case of a prospective miss of 100 feet short on the ground for v = 250 miles per hour and x/ = 90 degrees, C will increase at the rate of 15% per second 9 or 10 seconds before impact, this rate rapidly increasing with time.\nThe same statement applies for a 100-foot overshoot, except that C is decreasing in that case. This allows ample time for correction of the error. For a larger error on the ground, a 15 percent per second change in C would occur somewhat earlier in flight. The value of C at any time is nearly proportional to the prospective error, provided C is changing with time.\n\nIt is desirable that both stations A and R be similarly equipped and operated, so they can be readily interchangeable in function. Therefore, it is recommended that azimuth control be exactly like range control, recognizing the same angle f. Station A will observe the projection of the angle onto a vertical plane perpendicular to AT. If the bomber flies so that its ground track lies along AT, the tangent of the projected dropping angle is zero, but the method of range control is still applicable to azimuth.\nIt is possible for the airplane to drop the bomb as usual with its bombsight. However, it might be desirable to direct the release from one of the ground stations, such as R. R could track the airplane prior to release with the same mechanism to be used later for the bomb. The usual release condition could be used: plane flying level and perpendicular to RT. Consequently, the release condition becomes Vctf, where r is the angular trail in mils. However, the operator at R would observe these quantities projected on a vertical plane through the airplane. If the synchronous sight is used, Vch/h would be synchronized just as Vch/h is in the normal procedure. The only difficulty is the projection of the trail r. This is the only part of the whole process where a knowledge of the angle \u03b8 is needed. If the airplane is guided over the line.\nAT is determined by measurement of angles ART and RAT, as shown in Figure 7. A mechanism for embodiment of a principle similar to that described above has been planned. Development along these lines may continue, beyond termination of contractual relations between that organization and NDRC Division 5, under the auspices of the special weapons branch of ATSC at Wright Field.\n\nAn interesting rationalization related to this problem is based on vacuum flight conditions for the bomb. This relates to the behavior of angle 0, as employed above. Consider a perfect unguided drop. Before release, the rate of change of tan 0 is uniform. After release, the rate of change of cot (b = v) is uniform. We refer to the bomb itself in both cases.\n\nBefore release: tan 0 = h/d\nAfter release: cot (b = v) = 1/2v/dt\nwhere v is the horizontal component of the bomb's velocity, in target coordinates, or the closing speed of the bomber. This property has been proposed for use in ground control of RAZONs, guiding the bomb to maintain a constant dot (f/dt). Such control would cause little deviation from a free-fall trajectory and ensure a hit. It is evident that during both regimes, before and after release, a simple mechanism would suffice for tracking or the guiding criterion, based on the above equation.\n\nBy H. A. Van Dyke, of L. H. Schwien Engineering Company, in consultations with the writer.\n\nControl of Guided Bombs\n\nHorizontal and vertical \"tangent-screws,\" for example, might be involved. It might further be desirable to use the cotangent criterion in directing from the ground the release of the bomb.\nLet a Cartesian coordinate system be set up with origin at the target T, and x axis along the ground track of the bombing airplane. Let P be the position of the airplane at any instant before release, h its altitude, v its ground speed. The ground station directing release is at R, with RT making the angle i with the X axis. Let bars denote projections on a vertical plane perpendicular to RT; for example, f is the projected value of (f) as observed at the station R. Then,\n\ndt = v * sin(i/2)\nfor a nonvacuum bomb at the instant of release,\n\ndt = V * sin(x/2) instead of the condition given by equation (22).\n\nHere, fiCn) depends only on the drag coefficient Cd, and has the dimensions length/time. In particular, f(0) = g/2. By equations (24) and (25), at the release point,\n\nX = h * tan(i) + dt * V * cos(i)\nand consequently,\n\nx = h * tan(i) + dt * V * cos(i)\nsince certainly dx/dt = -v.\n\nThe new criterion: cot <t> dt < tf.\n\nControls for the television bomb.\n\nIn vacuo, we have as a release condition: cot <t> dt < tf.\n\nChapter 8. Controls for the Television Bomb.\n\nWe have previously described in this chapter the general arrangement for television guiding, where a remote operator tracks the target, given by the variable \"lead\" A, on the screen. Through established control dynamics, he thereby affects the corresponding deflection 8 of the appropriate control surface of the projectile. The motion X of a tracking handle which he manipulates is:\n\ndx/dt = -v.\nIn this process, an index can be held on both A and 8, enabling the operator to maintain a relationship between A and 8 through dynamic connections. The question arises as to where to include control dynamics, whether between the index and A or between X and 8. Either procedure is valid, analogous to those in lead computing and direction in more orthodox fields. We will here avoid this question by focusing on the result, which is the effective dynamic relation to be established between A and 8, in each coordinate.\n\nIn Chapter 1, we discussed various means for achieving a collision or interception course for a vehicle with respect to a target. It was not considered possible to install these means in the given context.\nThe new gyro equipment in the bomb was obtained through a peculiar stratagem, mentioned elsewhere from a philosophical standpoint and detailed below, making it possible to achieve equivalent dynamics without additional equipment in the bomb. The proposed characteristic equations were first tested on an electronic simulative structure, referred to briefly in Chapter 4 on simulation, where a human operator could be involved. Stable subsidence to an interception approach occurred without necessary adjustments in the confidentiaD controls for the television bomb's auxiliary regulatory controls. This conclusion was later confirmed by model studies on a larger scale, continuing the verification of the electronic model technique in exploratory roles. In the following analysis, we refer to Figure 8 showing the bomb falling in the air mass.\nIt is assumed initially that the bomb has no attack angle, so the longitudinal axis of the missile is a constant greater than one, and to is a constant angular rate. An important special case occurs when to = 0. Equation (32) gives the range problem for a television bomb, and the missile is in the direction of its velocity vector. The velocity of the target is Vey, and that of the projectile is v. Both velocities are measured with respect to the air mass. From the figure, assuming X is small (cf. Chap-), VpX = VeCOS<f>.\n\nSuppose control is applied to the bomb in such a way as to make it turn in the air according to equation (34):\n\nVpX = VeCOS<\u03b8>\n\nNow, since, approximately, equation (35) may be written as a differential equation in A and R:\n\nLet Vp = dR/dt and Ve = dA/dt.\nIf Vp and r are assumed constant, equation (40) is a homogeneous differential equation in A* and R with solution for A = 2 as N-1^(Vp/r) A*^2. In the special case N = 2, the solution is JXiQ Vp JXq.\n\nIf \u00f8 is zero, equation (41) becomes the next question is how to control the bomb to satisfy equation (32). The acceleration normal to the bomb's path is Ttl, where L is the lift force acting on the bomb as a result of control:\n\np is the air density, A is the wing or control surface area, \u03b8 is the angle of incidence of the wing. Define ipvpAp 'iCL L, Ty = 2mgdd. Then, Or y H sin y.\n\nVp\nFrom equation (32) and the equation obtained from it by integration, it follows that:\n\nTy = Vp(t) + (X(t) - Xo) cos(N)\nVpN - I\n\nThis is the equation governing the control of the bomb, where Vp and Ty are functions of t, while X and A are obtained from the television screen. The initial values Ao and yo can be most easily determined at some instant before control is applied. In this case, yo can be obtained from the function y = y(t) for a free fall. All these functions of time will depend on the velocity of the airplane at the instant of release of the bomb.\n\nIn case the target has a component of velocity in azimuth, the same development holds in that direction as for elevation, except that all terms with g disappear and the control equation becomes simply:\n\nS = A\n\nwhere S is rudder instead of elevator angle, and A is the azimuth component of lead. This separation holds for both elevation and azimuth directions.\ntion of  azimuth  and  elevation  lead  and  control \nis  valid  when  the  bomb  is  roll-stabilized. \nIt  may  happen  that  the  bomb  has  an  attack \nangle  a due  to  a slight  shift  in  the  center  of \ngravity,  which,  neglecting  transients,  is  given \napproximately  by \nThe  factor  a is  positive  if  the  center  of  gravity \nis  aft  of  the  position  for  zero  attack  angle.  Then \nthe  lead  observed  on  the  scope  and  supplied  to \nequation  (49)  or  rather  to  a mechanism  embody- \ning this  characteristic,  is  not  the  actual  lead \nA but  a value  A'  including  tz : \nThe  quantity  is  also  altered  by  the  pres- \nence of  an  attack  angle.  If  the  new  value  is \ndenoted  by  dC//d8  then\u00ae \nfor  8 and  a measured  in  radians.  Equation  (51) \nmay  be  written \nReplacing  A by  A'  in  equation  (49)  gives \n1 g N dCL'  r \nN \nIt  has  been  assumed  that  8o  is  zero. \n\u201cThis  function  was  furnished  by  W.  B.  Klemperer \nof  the  Douglas  Aircraft  Co. \n'onfh)p:ntial \nSINEAD'S PARADOX\n\nEquation (55) remains unaltered in form with the presence of an attack angle, except for the change in Ty due to the change in dCL/dS. For the ROC projectile, currently (1944-45), the quantities p and Vp are functions of time that depend on the initial altitude and velocity, and the control applied to the bomb. They have been computed approximately from differential analyzer data for ROC with full brakes (Cd = 0.413 for no control), initial altitude 15,000 feet, initial velocity 250 miles per hour, assuming a moderate amount of control and a time of flight of 40 seconds. These variable parameters are tabulated against the duration of the drop in Table 2. The angle yo at time t is to be determined from the function y(t) computed for a free fall.\n\nIn connection with dynamic means whereby\nAn interception course can be stably attained by a homing missile. There is currently a great deal of misunderstanding. Since gyro equipment could not be added to the bomb, it was difficult to see how one might use the means of proportional navigation, as described in Chapter 1, where one made the vehicle turn in the medium n times as fast as the line of sight. For the particular case of ROC-MIMO, which nevertheless has definite and general significance, the present writer dealt at length and pleasurably with W.B. Klemperer of Douglas Aircraft. The latter organization had the ROC projectile, in its various phases, under direct development. WBK had been working for some time on the problem of guiding and seeking, and had disseminated much knowledge and many original ideas.\nTheoretical and practical structures for attacking the problem. The reader should compare, for example, the report: Some Aspects of the Design of Homing Aero-Missiles by H. L. Dryden, to Division 5 from National Bureau of Standards.\n\nTable 2. Estimated functions for the ROC-MIMO projectile.\n\n| i (sec) | p (slugs /ft3) | yp(ft/sec) | \u03b3o(degrees) |\n| --- | --- | --- | --- |\n|  |  |  | projection shown in Figure 8, for example, this desirable criterion would amount, in a special case, to |\n|  |  |  | Our proposal for attaining equivalent, although somewhat generalized dynamics, as described above, was to make |\n|  |  |  | this being equivalent to equation (56), since |\n|  |  |  | CONTROL OF GUIDED BOMBS |\n|  |  |  | identically and by definition |\n\nConsider the significance, stepwise, of equation (57) as it stands, as a guiding criterion. In terms of finite alterations, we have:\n\nwhere A' is a positive numerical quantity. Con-\nConsidering this criterion in terms of Figure 8, for example, if the target were to slow down during the approach, causing A to increase, it is evident that to reattain or come closer to a collision course, the bomb must now be more steeply dived. But what does equation (59) instruct us to do? It seems to indicate an increase in y, giving a shallower dive. This manner of control is unstable, and the instability seems permanent. However, there is a paradox here, which gave rise to protracted arguments and which deserves the title of this section. Paradoxically, this criterion is perfectly stable, as developed in the previous section. The trouble is with our logic. In the first place, the stepwise argument, as given, is invalid \u2014 since it ignores equation (58). It is evident, further, that equation (58) and (59) are interconnected, and both should be considered when analyzing the control system.\nThe term \"y\" in two components is completely equivalent to \"y\" in equation (56). This correspondence holds for known mechanisms, as demonstrated, for instance, by the inset in Figure 8. Generalizations to space are immediate, though not trivial, when the roll-stabilization method is specified.\n\nNote that in general, y may be provided by absolute angular rate meters (see Chapter 3) installed in the projectile, while A is available from local detection of relative target direction. Thus, equation (57) may be directly mechanized, whereas equation (56) would require local free gyro references. We have assumed, in this simplified exposition, that pitch and yaw, relative to the medium, are zero. Otherwise, a more involved analysis, as earlier outlined, is required.\n\nIn MIMO-ROC, the effect of proportional navigation, using the term:\nas here, the generalized and liberalized concept was attained experimentally in the projectile with no additional equipment.\n\nGuided Rockets and the Future\n\nThe writer will here permit himself a few brief remarks in a field not otherwise dealt with in this report, which however treats both of rockets and guided bombs.\n\nIt appears that there are several lessons which should be perpetuated in that broader field. One is that there is no substitute for the collision course, or at least for courses lying much nearer to the collision or interception type than to the pursuit type. We refer here exclusively to guidance from the vantage point of the projectile, rather than the remote method, for example by collinearity, which tends to interception, anyway, at infinite observing range.\n\nAnother lesson is that by proper control dynamics, giving subsidence in agreement with existence.\nIn theory, intercepting conditions for a target moving in a medium reduces essentially to that of a stationary target. We add a few further opinions. (1) Absolute angular rate meters, of high sensitivity and performance, will probably replace free gyros for control references due to their lack of limits and the compactness to which they may be reduced. (2) Ambitious projects in guided missiles, where complex controls and interlocks are involved, will be greatly advanced through the extensive application of electronic simulation methods in the study stage for determination of parameters for stability. Owing to the inherent and sometimes hidden nonlinearities of such systems, analytic methods are almost utterly impotent there except for certain necessary conditions under control circumstances.\nWhen nonlinearities are present in such models or simulators, they can be readily recognized, and speculative dynamic components can be proved or disproved or altered at a moment's notice. Rocket propulsion should hold no analytic terrors for simulators, and aerodynamic data may be directly incorporated, once determined, by independent testing of components and reduced, say, to graphical form.\n\nChapter 9\nAiming of Rockets from Airplanes\n\n9.1 Summary of Projects and Work\n\nWhen the 3.5 forward-fired aircraft rocket [AR] came into prominence as an anti-submarine measure in naval operations, it was natural, since we had already dealt with airborne aiming controls for anti-submarine bombing and were fairly well saturated with the larger problems of this type of warfare, that we would apply our knowledge to this new development.\nI. Involved in the development of rocket sights for this application. The need for a sight for rockets had been acknowledged during the earlier missile development, although few had given it attention. Requests for liaison had been made by fire control groups in NDRC before the writer's engagement in 1942. However, no such sights were available, except for reflecting sights with fixed settings, and no development projects were underway for aiming controls when our rocket activities began in 1943.\n\nII. Approached in November 1943 with a request to construct a computing sight for the aiming of rockets against sea targets, primarily German submarines. At that time, it was primarily the 3.5 AR, as previously mentioned.\nwith a solid head, the old JP propellant, and launched from the now obsolete rails, this weapon was used. Appropriate, owing partly to its excellent underwater trajectory and partly to the deteriorating effect it had on enemy morale as an antisubmarine measure at a time when the menace was still growing. The airplanes in which we were concerned with installations were the Ventura and the Avenger, and aiming was to be carried out by the pilot, substantially alone. We had used the radio altimeter prior to this time for automatic setting of aiming computers. It was suggested that this instrument be made more effective.\n\nCommander G. R. Fiss of the Antisubmarine Development Detachment at NAS Quonset, under Captain A. B. Vosseller.\nThe basis for a rocket sight involves a fast and consistent measurement of altitude over water, a reasonably good measurement or estimation of the glide angle toward the target, and computation of the trajectory to determine superelevation allowance for gravity drop. This represented an approximation, considering the kinematic correction for target motion in the air mass and aerodynamics of launching. However, with the meager information available on the projectile, a computing system was designed and an experimental model was flown within two months of the original request. The results were irregular but promising. Better information was soon acquired on the behavior of the rocket through visits.\nA writer and others went to the California Institute of Technology (CIT) in Pasadena, and a development program for a sight, originally named VERB and later RASP, was arranged at a significant priority. A special deflectable sight head was prepared, transforming a \"retiflector\" with fixed optics into one with a movable reticle in two dimensions through remotely controlled DC servos. This allowed the line of sight to be deflected for automatic aiming via voltages for azimuthal and elevational corrections in a computer placed elsewhere. Inputs to the computer included automatic radio altitude, automatic glide from a special gyro horizon, airspeed in manual or automatic form, temperature, and a vectorially computed measurement of the target speed in the air mass. The computation was in progress.\nTerms of sums of products of functions of these inputs was determined on a semi-empirical basis. Attenuators in a-c circuits were physically applied for this purpose, fed by servos and autosyn transmission for the automatic control of inputs.\n\nAiming of rockets from airplanes\n\nThree distinct developmental models were prepared, each being tested at some length both in the laboratory and in the air. The accuracy of fire, roughly independent of range up to 2,000 yards, improved until dispersions of about 5 to 7 mils were experienced regularly.\n\nEach model of RASP was progressively more compact and easier to operate. A request for large-scale production was made by the Atlantic Fleet, but before the machinery for this was arranged, the urgency had decreased to a far more comfortable degree for all concerned.\n\nWhile the RASP development was still in progress.\nUnder our auspices, a separate development was begun, primarily carried out at The Franklin Institute, now recognized under Navy Project NO-216 for rocket-sight research. This aimed at a major simplification of the computing and aiming system. By this time, it was also desired to instrument single-seater airplanes, mostly fighters, for effective rocket fire. The problems here differed considerably, and for several reasons. For one thing, the tactics were far more violent, so that certain components, such as gyro horizons in available form, could not be used for automatic inputs. Similarly, much steeper glides were possible, and the computation in this region was different, requiring other instrument techniques. The problem of space was far more stringent, and in particular, only highly specialized sighting equipment could be put before the pilot.\nThe connection between the availability of the Mark 21 and Mark 23 gyro gunsights, and later the Army K-15, was utilized for the new project named GRASP. The Mark 21 gunsight, used for GRASP, only provided the means for deflecting a line of sight developed by a separate computer. The basic idea for GRASP was 'Actually, they were not used operationally by the Navy to any considerable extent, whereas the Army sight, derived from Navy prototypes, saw a good deal of combat action. For RASP, the Mark 1 sight unit, which adapted the gunsight Mark 8 to automatic elevational deflection, was later employed in experimental models. Subsequently, this sight unit became available in Navy fighters, allowing it to potentially have been used for GRASP. Several paradoxes are present in this development.\nProposed by E. C. Cooper: During a direct gliding attack, compute the altitude at which a given range is obtained from the target using a glide angle measurement obtained from the vertical component of gravity, properly interpreted and presented. The range itself, at and beyond this critical range, or continuously as the attack progresses, is to be indicated in terms of airspeed and time as the definite integral of the range rate added (note the sign) to the critical range. Then, with range, glide angle, airspeed, and temperature as inputs, an automatic computation of the gravity-drop and aerodynamic connections would be made.\nThe pilot applied the sight head to his head during approach. He merely noted when his altimeter agreed with the critical-altitude display's indication, pushed a button, and aimed by tracking the target in his automatically deflected sight. Kinematic lead was not computed, although an accidental correction was entered for part of this error. It was planned to use the lead-computing properties of the gyro gunsight being employed as a deflected sight head ultimately, if necessary.\n\nAn advantage of the GRASP proposal for fighters carrying rockets and alternatively fulfilling their normal function was that a rapid change-over was possible from gunnery aiming to rocketry aiming, as the same basic sight was employed for both, only electrical switching being necessary for the adaptation. This circumstance is of interest in connection with\nThe PUSS project, discussed in Chapter 10, involved integrated controls. A comprehensive testing program was conducted on the GRASP equipment, which became increasingly compact and simpler to use. Tests ranged from laboratory procedures to flight tests of components, to full-scale firing tests at NOTS, Inyokern. A high accuracy was finally achieved, relative to both the dispersion of the weapon and competitive equipment. V-J day abruptly ended the latest tests, and it is unknown if continuation of this project, primarily an interim development, will be considered warranted. The second model of GRASP became the aircraft rocket sight Mark 2.\n\nA smaller project was for the development of the miniature rocket sight, known as PARS.\nThis project was initiated at The Franklin Institute. Inputs were from a damped and spring-restrained mass (to measure the vertical acceleration), deflections of capsule diaphragms for barometric altitude and indicated airspeed, the temperature being manually set. Small linkage resolved these inputs and yielded mechanical motion as output, measuring the total allowance in elevation, indicated on a scale for visual reference and servo-duplicated at the sight head. Although flight tests were carried out on models of this instrument, and considerable Service interest was in evidence, no time was available finally for definitive firing tests. The equipment called PARS was designated Aircraft Rocket Sight Mark 3, and also Computer Mark 36, by BuOrd. This interesting development, which was supported partly to test a computational method for emission calculations, was a significant advancement in aviation technology during the mid-20th century.\nThe PUSS project, which focused on developing integrated aiming controls for pilots, contained a solution for rocketry as its central component. This complex problem was considered the most challenging to solve with the equipment, and the apparatus for this solution was easily adaptable to the companion problems of gunnery and bombing. A new angular rate method was developed for computation of both gravity correction and kinematic lead. The inputs were: angular rates.\nin the space of the airplane's thrust axis, air-speed, altitude, and glide angle. Although several variants of the method admitted different sets of input data, this method, proposed by H. Whitney of AMG-C for a compact all-mechanical computer to solve for gravity, aerodynamic, and (partially and approximately) kinematic corrections for airborne rockets, was characterized by relative insensitivity to \"classical\" inputs, including the range itself. Instead, it was heavily dependent on the measurement (or provision) of absolute angular rates for its ultimate accuracy of aim. Measurements of such quantities are elsewhere discussed. We note only that a major question is what\nThe particular method, among those experimentally available, should be exploited. The technique of rocketry proposed for PUSS is somewhat analogous, although far more general in capability and concept, to several other methods that have arisen in different quarters. The fundamental property whereby a lead diminishes with range is generatable by means of a downward-rotating line of sight, measured in space, is characteristic of certain independent proposals by the writer.\n\nThe forward-fired, finned, aircraft rocket, exemplified by the Navy 5.0 HVAR for instance, has many attractions as a tactical weapon, particularly for lighter offensive planes such as carrier-borne varieties. Its relevant characteristics for such application include: the penetration and explosive power delivered in comparison with the weight.\nFiring equipment and, in comparison, the shock of projection; the small dispersion or unpredictability of trajectory, which fortunately becomes smaller as the launching speed increases; and the proven effect on morale of the attacked. We speak primarily of ground-level targets.\n\nIn leaving the airplane, the rocket-round accelerates along its trajectory at something like 50 times gravity for just about a second, during burning of the propellant. After which, it has attained a total airspeed of about 1,500 feet per second and subsequently flies somewhat as a standard unpropelled projectile. In its original form, although not necessarily novel in a more comprehensive history of the Draper/Davis method of glide bombing, of E.P. Cooper\u2019s proposal for a rocket sight in which an additive deflection is given to a gyro gunsight employed with a long characteristic.\nAiming of Rockets from Airplanes\n\nDuring the initial phase of flight following launch, a rocket's path is close to that of the airplane due to its small accumulated relative speed. Erected in the air stream, the rocket is urged on by its propellant in the same direction, making its path more nearly that of the flight path of the airplane at launch than its initial heading, either of the rocket or of the airplane. Thus, the rocket behaves more like a fast bomb than a bullet or shell, a fact of primary importance in aiming.\n\nDuring flight, the shape of the air path is somewhat different from that of either a bomb or a bullet.\nThe bullet, though it lies approximately halfway between, behaves similarly to all three projectiles, assumed released at the same speed and glide. A specific type of trajectory is followed during the first 500 yards or so of flight through the air, which is to say during burning. This trajectory is characterized by an oscillation of small amplitude and a space period of some 100 yards, and is bent downward more than in the immediate period following burning. For most purposes, a satisfactory analogy may be used between the rocket trajectory and that of more orthodox projectiles, even in vacuo. A good approximation is afforded by fitting parabolas to the trajectories of these rounds, corresponding in various ways to equivalent trajectories in vacuo. For instance, it suffices, to good accuracy, to say that the round behaves like a projectile fired in vacuo.\nThe vacuum follows a parallel path, originating behind and above the actual firing position, with a different initial velocity. This velocity must be a function of airspeed and temperature. The rocket trajectory can be replaced by a parabolic path corresponding to that of a hypothetical projectile launched at a definable angle from the actual flight path or the initial air velocity vector of the actual round. Mathematical studies have shown how the parabolic constants may be determined for optimal fitting to rocket trajectories. Such constants, for any given rocket type, must be expressed as functions of the circumstantial variables of the firing, or temperature, airspeed, and glide angle. It is found to be very nearly true that the glide angle, the \"negative elevation,\" determines the behavior of the rocket in flight.\nThe initial velocity vector's change, or declination, influences the trajectory similarly for a shell or a bomb. Qualitative effects such as trajectory rigidity at shallow angles are evident. Gravity-bending degree is roughly proportional to the horizontal range, with zero gravity-bending for an attack from the zenith and maximum for one \"on the deck.\"\n\nThe longitudinal acceleration of the rocket is mostly unaffected, except by temperature. However, this temperature variable influences the entire problem and introduces a new variable to manage if high aiming accuracy is desired. All these effects depend solely on the interior temperature of the round, specifically the propellant grain. This governing temperature, though responsive through a definable dynamic lagging-effect.\nThe function of air temperature in a rocket's performance is dependent not only on current conditions but also on the initial temperature determined by storage conditions. This dependence gradually decreases over time since the rocket was put into service. The problem is not simplified by the variation of air temperature with altitude, as rocket attacks are typically made at lower strata, but the airplane may have recently been at higher altitudes. Time constants related to the absorption and dissipation of thermal conditions in the rocket round are approximately half an hour or more. A proposed solution for providing this substantially unmeasurable variable as an input to rocket sights is an externally mounted thermal model of the rocket. The thermally significant part of this dummy round\nwould  presumably  be  stored  with  the  standard \nrounds  with  which  it  would  be  used.  On  the \nwhole,  however,  designers  of  rocket  sights  have \neither  incorporated  the  temperature  influence \nby  means  of  a manual  setting  or  have  ignored \nthat  variable  altogether  out  of  an  altogether \nunderstandable  sentiment  on  the  subject. \nAs  to  time  of  flight  as  a function  of  range \n\u2018'Made  by  R.  M.  Peters  of  Section  7.2  and  by  per- \nsonnel of  AMG-C  of  AMP. \n\u2022 ^ONFIDENTIALU] \nTHE  RASP  ROCKET  SIGHT \nalong  the  trajectory,  the  rocket  lies,  again,  ap- \nproximately halfway  between  the  bomb  and \nthe  bullet.  For  aiming  purposes,  particularly \nwith  regard  to  kinematic  lead,  this  makes  a \nmore  difficult  problem  than  that  of  the  bullet,  on \nthe  one  hand,  whereas  on  the  other  hand  one \ncannot  apply  the  special  properties  which  the \nbomb  possesses  in  this  regard  owing  to  its \npreservation  of  the  forward  velocity  of  the \nThe vehicle's time of flight, as a function of range, is approximately given by the equation: r = Vatf + Gtf, where Va is the airspeed of the launching craft and G = G(T) is the rocket's proper acceleration, as a function of temperature. During the initial burning interval, this equation applies. In the subsequent phase, when burning has ceased, a more natural deceleration takes place. The rocket's characteristic, with regard to the relationship between range and time for the trajectory, accelerating and then decelerating, holds special meaning in aiming control.\n\nThe RASP rocket sight\nThe development and testing of RASP have been briefly described in the first section of this chapter. There are also complete reports on the several models of this rocket sight that were designed.\nIt should be noted that certain component developments are worthy of comment as they apply to the RASP system and other systems. This development, initiated before receipt of Navy requests for Projects NO-216 and NO-265, was largely promoted and sponsored by the Antisubmarine Development Detachment at NAS, Quonset. Assistance in procuring research facilities, including the provision of aircraft and other equipment for testing purposes, was given by that agency in considerable abundance. The military equipment and auxiliaries were provided by them.\npermanently assigned to the project, even to the extent of setting up residence in the laboratories at The Franklin Institute. Following acceptance and establishment by NDRC of the above-named projects, we considered that the RASP development constituted part of the work they embraced, although new directions were then indicated as well. In particular, and this viewpoint was early advanced, the educational and indoctrinary value of this development was emphasized, since during the initial phases there had been almost no experience anywhere on the problems peculiar to rocket sighting \u2014 particularly the automatic variety thereof. Thus, at least the primary RASP equipment was expressly designated as having the character of study models, the teachings of which would apply more broadly than to the project as then contemplated. Initially, it was\nThe complexity of the system was unimportant as long as it could be flown and functioned predictably, allowing the interrelations among the variables of the problem to be subjected to quantitative study under practical conditions. Such study models were later reduced to more generally useful forms for operational purposes. The primary contributions of this development project were to our knowledge of the practical phases of the sighting problem, which was subsequently applied in other developments.\n\nA diagram of the flow of information in the RASP system, from inputs through various computing components to outputs, is given in Figure 1. Not all experimental models included every component and connection.\nFor the altitude input, an FM altimeter was used. The contractors' reports with more precise information on such models can be found in the attached bibliography.\n\nAiming of Rockets from Airplanes\nTemperature\nAltitude\nGlide 00\nAirspeed\n(Course)\nWindspeed\n( Wind \\ Direction)\nTarget Speed\nTarget (Course)\nAutomatic Inputs\nGravity\nComputer\nRASP\nAs in Ventura\nOmitted in some models\nTotal Elev\nDeflection\nK Set in dependence on Airplane - Type and Loading\n\nFigure 1. Influence diagram for RASP rocket sight.\n\nGonfidentia\nOutputs\n\nThe RASP rocket sight\nThe predominantly employed methods caused no difficulties due to irregularities of terrain, as the testing and operational areas were over water. Initially, there was doubt about the accuracy of measurement when the airplane flew in steeper glides. However, this apparent source of difficulty may have disappeared, as suggested, due to subsequent alterations in the antenna designs. Several types of servomechanisms were developed and employed for this input. None of which required significant interference with or modification of the radio altimeter itself. All methods involved d-c servos, resulting in shaft rotations in the computer component proportional to the altitude.\n\nFor the glide angle (y) input, or rather the depression of the longitudinal axis of the airplane from the horizontal, an appropriate method was:\nA private correction being involved for the approximations introduced, a modified directional gyro was prepared as an experimental component. This gyro was initially critical at the shallow glide angles then contemplated due to the sensitivity of the range and gravity drop to the glide during computation in terms of the latter variable and altitude. A specially equipped gyro horizon of Sperry origin became experimentally available for this application and was used in preference to the above glide-giving component. This horizon had autosyn-detection of the gimbal rotation and provided the computer with a varying voltage as a function of the glide angle. Later several other methods for the calculation of the glide angle were developed.\nThe determination of glide was experimentally tested in this project due to the limited aerobatics permitted by the gyro horizon referred to. However, these limitations did not apply as critically to the bomber-types considered for GRASP as to the fighters later specified.\n\nThe airspeed, measured in terms of the difference between dynamic and static air pressures as in a standard airspeed indicator, was automatically fed in by means of a pneumatic follower. In preliminary models, this variable was manually incorporated by an operator who mimicked the reading of the standard panel instrument in the position of a knob. Setting this variable in advance through prediction of the airspeed that would be indicated when the firing point was attained was found to be unreliable.\nA manually set temperature input was employed instead of an additional operator to continually adjust the propellant temperature of the rocket under operational conditions. Automatic means for duplicating the necessary propellant temperature were not yet available. The motion of the target in the air mass, considered as the vector sum of its motion in the water and local wind velocity, was corrected for in RASP. Vector computation, mechanical and electrical, was applied for this purpose. The directions of wind and target motion, once set on a mock compass scale, were \"stabilized\" against subsequent turning.\nAirplane stabilization was achieved by setting its own course just before an attack, once the target course was determined. A simple mechanical arrangement was used for this stabilization, which had previously been applied in a mechanical type of ground speed computer. Controversy raged over the ability to determine the relevant target motion in this manner. At worst, the magnitudes of wind and target speed could be set to zero, eliminating any kinematic correction as proposed by Navy agencies anyway, and as in most other sights in development. Many operators would be able to determine these navigational quantities to high accuracy and input them into the computers, but it would be preferable, as in later developments, to correct by more nearly implicit means.\nThe methods for calculating the target's motion in the air involved mass. RASP used computation by attenuators in a-c circuits. The contributory terms of the total deflection were expressed as products of functions of the single and separate input variables. The possibility of such expression was not automatic; it had to be discovered and demonstrated. Remarkably, the approximations involved were shown to be sufficiently good.\n\nThe sighting component, or sight head, in the various RASP systems took on a variety of forms. In the first experimental model, an old reflector, so-called, was redesigned so that its fixed reticle could be moved over the focal plane to cause the emergent beam to move bodily in two angular dimensions.\nA sliding mechanical system was involved, and a small DC servo assembly was attached so that deflections in azimuth and elevation referred to airplane coordinates could be ordered by output voltages in remotely located computing components. This arrangement provided good service at a time when few such remotely manipulable sight heads were available. The reflecting collimator represented a saving in space, although its position at the top of the final transport reflector was found objectionable by some, who felt that the sight could not then be called one of the \"open\" variety. No production status was enjoyed by the retiflectors at that time, and this instrument was later replaced as a component of RASP by a Mark 30 sight head, which we modified.\nThe final reflector was moved in a somewhat similar manner to change the elevation in the Mark 8 sight head. A specialties sight unit Mark 1 was attached to the Mark 8 sight head for the elevational deflection. This unit was remotely driven by a voltage in the computer in a precisely similar manner. Three distinct models of RASP were prepared, each with several variants in detail, during this project. The first and third models, or RASPs I and III, were more extensively tested than RASP II. Each succeeding model was more compact and completely engineered. Since it was not sensible to adapt the RASP system to the single-seater types, which were the principal rocket carriers by the time Model III was completed, there being then the GRASP project well in progress for such applications.\nThe application determined no requirement for further development on RASP. Personnel and project facilities were applied to the PUSS project instead. For fighters or other light single-seaters, requirements on rocket sighting equipment were more stringent in terms of size and weight. Freedom from disturbance under maneuvers, and the complexity of manual operations were necessary for tactical employment. The basic principle of GRASP lay in recognizing the range to the target as a variable in the aiming problem, in the computation of gravity correction, and potentially at least, of correction for target motion. Assuming an approach to the target in its final stages as a direct glide, arrival at any point was noticed.\nThe given critical range from the target could be signaled by agreement between the altimeter reading and a function of the glide angle. The deflections, previously established for this critical or initial range and the glide angle and airspeed, could be kept \"up to date\" for shorter ranges through a chronometric input-motion initiated when the critical range was encountered. In preliminary models, this initiation was to be made manually by the pilot upon noting the coincidence of a pair of indicators. In later models, an automatic initiation was embodied, which simultaneously signaled to the operator the closing of the range to that degree and the entry into the continuous-firing regime. Two principal developmental models were involved, called GRASP I and GRASP II. Extremely complete reports exist on the course of their development.\nresearch itself, as well as on the elaborate testing program which was undertaken, was accepted, and was embodied in a development program. E. C. Cooper, among other duties, was project engineer for the system that became GRASP, which was proposed at The Franklin Institute.\n\nThe final equipment were regularly issued by the contractor. References to certain reports can be found in the bibliography of this chapter. From the beginning, Navy Project NO-216 covered the development of the GRASP system. GRASP 11 was finally designated aircraft rocket sight Mark 2, when taken together with the sight head, either gunsight Mark 21 or gunsight Mark 23.\nThe 11th component of the GRASP computer was designated as the computer Mark 35. Instead of other output components, the gyro gunsight was chosen to deflect the pilot's aiming indicia automatically. This plan was based on the GRASP project's intention and the expressed desire in the preceding service request. The purpose of this combination was to allow a semi-universal sighting arrangement for both gun and rockets, with quick change-over capabilities between the two functions. As previously mentioned, this gunsight did not see wide application in Navy airplanes, while a similar Army gunsight was widely installed and used. A modification of GRASP II was prepared in the latter stage of development under Army control.\nProject AC-121. This project, which had not been tested under Service auspices at the close of World War II, includes remarks on the components of GRASP and their systematic arrangement. A \"flow diagram,\" Figure 2, is included to illustrate how the data is handled by the computing system. Temperature and airspeed were manual inputs, although it had been planned that airspeed might be automatically provided through known means or correlated with the steepness of glide, and thereby automatically incorporated. The presence of a manual setting was believed to attract the pilot's attention to the rigors of making a prediction as to his airspeed when firing was to occur, and to his precise impression of how this variable must be set for accurate aiming.\nThe altitude was not set continuously but recognized based on the instant when this variable agreed with the glide input in determination of the initial range. In the first model, recognition was by the operator, while in the second model it was automatic and involved only a contact arm on the \"slow\" indicator arm of an auxiliary barometric instrument. This component, installed in a small (approximately 4x4x8 inches) computer box, was provided with adjustments for target altitude and the barometric pressure at sea level. Establishment of electrical contact, at the initial or critical range, set in motion the chronometric sequence of the computation. The latter was delivered mechanically by automatically wound clockwork, which returned to the initial position and latched itself when the operation was completed.\nThe most elaborate component of the GRASP system was a captured mass or captured pendulum accelerometer, aligned in the airplane so that the total (gravity plus inertia) acceleration, in the direction of the airplane's vertical axis, is measured. A servomotor, actuated by special damped and overriding contacts connected to the pendular structure, rotated a spring to hold that structure essentially stationary in a framework. The rotation of the spring was then taken as a measure of the acceleration. Although the acceleration measured was only proportional to the cosine of the pitch or glide in straight flight, the effect of the aircraft's path curvature was not fatal since (1) it was in the narrow sense insignificant, and (2) it could be compensated for by other means in the system.\nTo speak of a prediction of future glide angle and it tended to a partial compensation, in the elevation direction, for motion of the target in the air mass. To guard against fortuitous accelerations, having no real significance for glide, a limiting speed was incorporated in the servomotor. To avoid extremes, such as incurred when the airplane entered the dive, a cutout was included.\n\nNoticed first by H. Whitney of AMG-C, after whom it was sometimes called the \"Whitney effect,\" of which in fact there were several others.\n\nAIMING OF ROCKETS FROM AIRPLANES\n\nTEMPERATURE\nAIRSPEED\nGLIDE ( )\nALTITUDE\nTIMER\nAUTOMATIC\n\nINPUTS\n\nGRASP\nAS IN HELLCAT\nCOMPUTER\nGLIDE DERIVED FROM FEEDBACK\nACCELEROMETER\n\nOperation occurs, starting timer, when h and s agree that the initial range R = Ro is attained. Signal also given to pilot.\n\nComputer\nH\nO\nMULT\nTHE PARS ROCKET SIGHT was operated automatically under excessive accelerations. Computation of functional relations in GRASP was accomplished by logarithmic cams. The output, as an aiming deflection in elevation, was developed by rotation of a resistor in the trail coil circuit of the gyro gun-sight Mark 23. Trimming resistors, of fixed but adjustable values, were involved in switching circuits to allow the use of different rockets. Surprisingly, it was found that the total deflections were sufficiently expressible as functions of one another directly. Employing a large current in the range coil, the reticle could be deflected over the whole range.\nThis worked for both coordinates, and the relationship between angular deflection and the ratio of trail coil current to the then existing range coil current was found to be adequately linear. A method was worked out to set this ratio by linear manipulation of a single low-power resistor placed in a special bridge circuit. This technique was valuable in maintaining the desired compactness of the computer, referred to above for its total size. For installation, such as those made for trials in the F6F, it was only necessary to remove the standard cable connector of the computing gunsight and insert a two-way adaptor on a new cable leading to the GRASP computer.\n\n'5. The PARS Rocket Sight\nWe shall not give an exhaustive description of this development, although it has been one of the most significant achievements in the field of avionics. The PARS sight, an acronym for Proximity and Ranging System, was a revolutionary invention that provided pilots with real-time information about the range and angle to their target during air-to-air combat or bombing runs. The sight used a combination of ultrasonic and infrared sensors to measure the distance to the target and display it on a cathode ray tube (CRT) screen. The angular deflection of the sight was controlled by the pilot, who could adjust it using a hand-crank or a motorized mechanism. The PARS sight was a crucial component of the F6F Hellcat fighter plane, which became one of the most successful aircraft of World War II. Its introduction marked a major turning point in the development of avionics and paved the way for more advanced navigation and weapon systems in future aircraft.\n\nThe PARS sight consisted of several components, including the sensor head, the processing unit, and the display unit. The sensor head contained the ultrasonic and infrared sensors, which were mounted on a rotating drum that could be lowered and raised to scan the area around the aircraft. The processing unit, which was located in the computing gunsight, received the data from the sensor head and calculated the range and angle to the target using complex mathematical algorithms. The display unit, which was located in the cockpit, showed the pilot the range and angle information in real-time, allowing him to make precise adjustments to his flight path or weapon delivery.\n\nThe PARS sight was a complex and sophisticated piece of technology for its time, and its development required a team of engineers, physicists, and mathematicians working together to overcome numerous technical challenges. One of the biggest challenges was designing a reliable and accurate sensor head that could operate in the harsh environment of a combat aircraft. Another challenge was developing the mathematical algorithms needed to process the sensor data and calculate the range and angle to the target. Despite these challenges, the team was able to overcome them and produce a working prototype of the PARS sight in record time.\n\nThe PARS sight was first tested in combat during the Battle of the Philippine Sea in June 1944, where it proved to be a valuable asset for the US Navy. The sight allowed pilots to engage enemy aircraft at longer ranges and with greater accuracy, giving them a significant advantage in the air. The PARS sight was also used during the Battle of Iwo Jima and the Battle of Okinawa, where it helped to secure victory for the Allies.\n\nThe PARS sight was a major milestone in the development of avionics and paved the way for more advanced navigation and weapon systems in future aircraft. Its introduction marked the beginning of the era of electronic warfare and revolutionized the way air combat was fought. Today, the PARS sight is considered a pioneering achievement in the field of avionics and a testament to the ingenuity and innovation of the engineers, physicists, and mathematicians who developed it.\nThe historical circumstances of the project were already referred to briefly in this chapter. It was planned that in this system, not only an extremely simple and compact computer would be involved, but that the solution carried out thereby would be most complete and automatic. The computation was all mechanical, involving small linkages of a type later embodied in PUSS, although in one model the output motion affected the setting of a light potentiometer, serving as the variable for remote transmission to the sight. Physically, the first experimental model of the PARS computer was constructed entirely within the case of a standard barometric altimeter, utilizing the motion of the aneroid capsule. (By E. Cooper.)\nThe input text refers to the miniature computing linkage. Air-speed entered the computation similarly, with a dynamic-pressure diaphragm placed in the same case. The ambient pressure in the latter served as the static or barometric pressure, required for altimetric and air-speed measurements. The temperature variable was manually set into the instrument, although at one time it had been considered likely that an adequate correction for temperature could be accomplished by inclusion, in the linkage, of a small bimetallic \"motor\" which would respond with some delay to the external air temperature via the static-pressure line.\n\nThe accelerometer component, which detected the steepness of glide or dive by the PARS computer, deserves special mention. It consisted of a spring-constrained mass on a pivoted arm that lay normally and approximately.\nApproximately in the plane of the airplane wings, and which moved out of a normal position in response to the total acceleration in the airplane's \"apparent vertical.\" The free arc-motion of the constrained mass, damped by a pneumatic carbon-chromium dash-pot, formed one direct input to the computing linkage. Several experimental models of this component were prepared and tested, both in the laboratory and on flight tests arranged solely for this purpose, under conditions that allowed comparison of the acceleration record of this component with that derived from the readings of other instruments used for calibrational functions.\n\nIn an early form of the PARS instrument, it was contemplated to reduce the system to its ultimate and basic instrumental simplicity by displaying, on the instrument panel, a mock reticle-pattern representing that included within it.\nIn a fixed sight, and on the mock pattern, a moving point corresponds to the correct position, in the real reticle pattern, at which the target should be taken for effective aiming of rockets from airplanes. The output deflection, which might normally be transmitted to a manipulable sight head as the aiming deflection, would here merely move a visible indicator on the face of the computer. The latter to be incorporated as a standard panel instrument. Owing to the indeterminacy of skid, which affected almost one-to-one the azimuth aiming errors with any existing types of sight, it was unworthy to add much complexity to the computer for that dimension. This question of skid has been controversial indeed, and was only normally addressed by the NORMAL ACCEL PARS system, as shown in Figure 3, the influence diagram for the PARS rocket sight.\nMany voices raised objections to this plan. It was later resolved (perhaps wrongly) to employ the more orthodox technique and to \"servo\" the output of the computer, resistively recognized, to one of the available sight units. Only an elevational deflection was concerned, as there was no azimuthal computation in PARS. An inherent computation occurred in elevation for target motion, at least over a central band of glide angles, due to the accelerometric sensitivity to curvature of path via the glide measurement. It was considered by many that the beginning of a quantitative study was coming under an articulate agency, by the means of a testing program, toward the close of hostilities. We shall not add our own prejudices to those in evidence elsewhere. Works on the subject by:\nAMG-C and AMG-N, recommended for interested readers. If the skid problem cannot be resolved through aerodynamics or instrumental means in computation, this is a significant objection to the finned rocket as a weapon, behaving oppositely to that of a bullet or shell. Our view of this problem is generally optimistic.\n\nPuss and Some Comments on the Future\n\nThere was not enough time during the project for extensive or definitive firing tests on the PARS rocket sight, which became officially aircraft rocket sight Mark 3 and simultaneously computer Mark 36.\nMechanical failures, arising from vibratory conditions not adequately foreseen and guarded against, were experienced on several earlier flight tests. PARS remains a highly ambitious attempt to compress a fire-control system to insignificant dimensions, and the technique is certainly of future value. The lessons acquired at some pains are well learned if applied in broader and more futuristic programs such as the continuing PUSS project.\n\n^ 6 PUSS and Some Comments on the Future\n\nWe have referred freely to the PUSS project at numerous other points, and Chapter 10 is devoted exclusively to that topic. PUSS, however, is fundamentally an aiming-control system for rocketry, at least that was the primary purpose for which the computing method was proposed and developed. While also a bombsight and a gunsight, as occasion may demand, the system's primary function is for rocketry.\nThe most general and most difficult aiming problem solved by this system is that for the rocket, making it unique in this sense. For future development, it is suggested to concentrate first on the rocketry phase and press its development to a testing status for that weapon alone. As the one type of rocket on which the assessment should be based, the 5.00 HVAR should be chosen over the 11.75 AR due to the better state of present knowledge of its characteristics. Consideration should be given to subsequent development and testing of the system as a gunsight, considered as an adaptation of its function in rocketry, for lower projectile velocities.\nIn view of the probable coming importance of longer ranges and longer flight times for weapons, and consequently, the potential replacement of present rocket types for airborne fire control, considerations should be given to plane-to-plane combat and bombing. For plane-to-plane combat, the rocket presents an aiming problem of great magnitude. In contrast, for bombing, thought should be focused, if at all, on a bombing tactic involving a firing or release course. With greater downward vision and possible aeronautic alterations in airplanes, the practical advantages of toss bombing may disappear. Furthermore, such a manner of bombing can be controlled by a system that is a special case of the present PUSS rocketry computer, and it may be made more effective.\nThe text is already clean and readable. No need for any cleaning.\n\nThe text reads: \"Inherently more accurate by being, as are the other PUSS computations, less sensitive to all inputs other than angular rate. There will be a great advantage in a universal aiming control based on a uniform method for all types of projectile, since then the same basic components may be most fully utilized for all applications, thus leading to smaller, lighter, and simpler instrumentalities. Furthermore, it would thus be simplest to adapt the system, once developed, to the newer missiles as they appear. Aside from possible radar inputs, for blind operation and for ranging data, there are not many other basic items of primary data. It appears worthwhile in this vein to arrange for supplying all such inputs, comprising dynamic and static pressures, accelerations in all directions and of both primary types, and the angular rates of the vehicle in.\"\nIn a compact universal input assembly, firing or computing methods will be most efficiently based on the maximum number of available inputs. This philosophy is based on the experience of minimizing overall errors by incorporating this method in sighting and computers.\n\nConfidential\nAiming of Rockets from Airplanes\n\nIt is recommended that a study be made of the usefulness of higher-order linear operators in PUSS's dynamic computer for all weapons under consideration. This is an almost entirely unexplored field and may contain many treasures in terms of reduced tracking time, stability, and accuracy.\nSuch problems as skid are resolvable implicitly when more general dynamic forms are resorted to. In this study, electronic simulative techniques will probably prove invaluable, as they have in other and analogous fields of effort. The pilot's tracking simulator, now in its initial form, is to be placed in operation at The Franklin Institute very soon, and should provide a nucleus of the simulative apparatus whereby more refined dynamic questions may fruitfully be studied. An example of the instrumental possibilities for future appraisal, by this and other means, is the general plan of recognizing, as inputs to such computing systems as PUSS, the motions during flight of control surfaces. Especially with the greater symmetry which may be attained in jet-propelled flight, these motions may be recognized and analyzed.\nAs World War II progressed, several trends in the application of warplanes became evident. One of these involved the increasing use of lighter planes, such as fighters, for purposes like bombing and rocketry. The dive bomber was a classical type, but the German Air Force used it strategically, while the American version was only in the Navy and employed tactically against ocean targets. Strategic bombing by fighters was actually employed by the Navy in the Pacific war, for instance in the bombing of Tokyo from carriers. Part of the trend, in both Army and Navy, was the use of integrated equipment for pilots.\n\nChapter 10\nIntegrated Equipment for the Pilot\n1. Historical Review of the Development\n\nThe use of integrated equipment for pilots became increasingly important during World War II. One trend involved the use of lighter planes, such as fighters, for purposes like bombing and rocketry. The dive bomber was a classical type, but the German Air Force used it strategically, while the American version was only in the Navy and employed tactically against ocean targets. Strategic bombing by fighters was actually employed by the Navy in the Pacific war, for instance in the bombing of Tokyo from carriers.\n\nAnother trend was the development of advanced aiming controls. These controls were highly significant when applied by retroactive processes in the dynamics of advanced aiming systems. The following sections will discuss the development and integration of these systems in both Army and Navy aircraft.\nThe more diverse applications of single-pilot planes, particularly the Hellcat and Corsair in the Navy, and the Mustang, Lightning, and Thunderbolt in the Army, became nearly predominant for strategic support in almost every type of attack. They operated as regular fighters, both for escort and interception, or simply patrolling for quarry of any type. They carried bombs to strategic ranges, releasing them in gliding and diving attacks. They were rocket carriers, bearing as many as eight rounds each, from the 2.25 SCAR (for practice) to the 11.75 AR. Such aircraft were impressively potent and versatile. Against ground targets, especially for support or independent forage, they could strafe with gun and cannon, drop bombs, and launch rockets.\nRockets from ranges measured in thousands of yards. The desire for, and evident benefits of, such flexibility of function is of course apparent in the airplane types which have appeared. A notable early example was the TBF Avenger, which although not too impressive as a fighter, could carry torpedoes, bombs, and rockets. A number of us, noticing this trend in a broad sense, and having other reasons to wish for a more generalized approach to the instrumental problem of aiming controls, argued for the development of systems which would apply optionally to the several weapons coming into use by the same vehicle. An important premise, in support of the possibility of such a widely applicable single system, was the evident similarity among the fundamental solutions to which the fire-control problems of the various projectiles were amenable. Thus typically.\nThe angular rate was increasingly useful in this field for several types of inherent computations. Progress had been made and was promised in new components for the measurement and delivery of this variable. In the case of other variables, they appeared as inputs in more than one of the numerous proposals being made for bombing and later for rocketry. An obvious saving was thus possible through combining input components in a universal system. Furthermore, it was considered essential that a single, universally applicable sight head be made available, to which the outputs of the various computations could be selectively conducted. The very difficult installation problems, on each form of aircraft, could be engineered once and for all. Not the least advantage contained in the flexibility of this general mode of design \u2014 and this is emphasized.\nThe freedom to incorporate future developmental changes, which was not initially insisted upon or vividly realized, is the key issue. None can foresee the newer circumstances that will obtain in the future, nor the novel instrumental and theoretical techniques that never cease to emerge. Designing in expectation of change is the wisest course; freezing as many components as possible and leaving their interrelations more arbitrary was one of the precepts of Project PUSS, and remains a valid criterion.\n\nThe present writer remembers conversations on this topic with Commander E.S. Gwathmey (then of BuOrd).\n\nCONFIDENTIAL\nINTEGRATED EQUIPMENT FOR THE PILOT\n\nToday, especially in multipurpose aiming controls, inputs, computers, and outputs are too innately combined. Such alterations, to fit these components, are necessary.\nNew weapons or tactics or instrumental theories and techniques are a more serious problem for fighters. The issue for pilots is reducing the amount of added equipment in front of them, not due to space and weight restrictions being strict in other areas of the airplane, but because the space around the instrument panel is most limited. This was part of the reason for wanting a pilot's universal sight head. With its servo equipment, it could be remotely operated from other points, and it would be designed to the minimum size and inconvenience compatible with effective operation. Modern servos should have no trouble achieving, by this means, all the smoothness and precision and other requirements of performance that could be desired. There is much more to be said on the question of the sight.\nIn this chapter and elsewhere, we can better relate the discussion of this project to specific parts, referring to visual operations rather than blind attacks. In rocket sights and the PUSS project, radio detection was considered only as a potential means for measuring altitude and possibly range as inputs. The designer of fire controls faced numerous problems posed by the constructional peculiarities of airplanes, particularly fighter airplanes. Whether some of these peculiarities were essential is another question, but the proposed universal sight head, to be perfected as such and deflected automatically, would permit circumvention of such problems.\nThe establishment of a universal sighting system for pilots, referred to as PUSS, involved our group's expertise in computing gunsights, rocketsights, and bombsights. We had experience in reducing the size and weight of computers and designing solutions that did not require high-precision manufacturing. The rocketsights projects RASP, GRASP, and PARS, still in progress, were considered contributory due to similar design challenges and potential solutions for the rocketry aiming problem. The newer proposal for PUSS was being proposed.\nFor the central rocket solution, based primarily on absolute angular rate, was relatively untried but its conjectural development was thought to have promise worth the gamble. Since more orthodox methods of earlier projects could be resorted to rapidly if the gamble turned out poorly, for plane-to-plane gunnery it was planned to use the well-known first-order principle involving angular rate and range. It was hoped that higher-order methods might provide a better compromise between precision and stability of tracking, on the one hand, and that certain rangeless methods, on the other hand, would ultimately be applicable. Mentioned briefly in Chapter 1, such methods are based even more crucially on angular rate criteria. However, it was considered that a simpler instrumental problem was involved, and that apparatus which might solve it could be used.\nThe problems for rockets could be readily specialized for bullets or cannon shells for air-to-air combat. For strafing as a gunnery operation, the need for computing sights was not given prominence, although with rangeless methods, the question was held open. Handling the bombing solution was a major question, since the angular rate principle for gravity-drop correction was unusable in typical airplanes at significant range due to the superelevation allowance being greater than the available downward vision. For this reason, and owing also to certain psychological preferences that appeared evident, and further to some problems in the stability of flight with existing airplanes, we chose to consider toss bombing as the method for PUSS. While the gravity drop is not:\n\n(Note: The text appears to be written in early 20th century English, but it is readable and does not contain any significant errors that require correction. Therefore, no cleaning is necessary.)\nAllowed for by the methods of absolute rotation in the preferred procedure for toss bombing, such methods do appear for the target motion. The KonftdentiaI REMARKS ON THE HUMAN PROBLEM. This problem, and it was planned to capitalize on the presence of gyro reference equipment incorporated in the PUSS system for other functions. The initial experiments on a unified PUSS computer involved a free gyro as a basic component. By various processing arrangements, such a gyro was to be alternatively caused to rotate about a horizontal axis in space for gravity corrections, or to \u201cpursue\u201d an index for synthesis of a disturbed sight. It was recognized that both such modes of operation might be followed simultaneously. It was soon found precisely how to generalize the classical computing sight to give the more general solution for rocketry, with all major corrections.\nThe gravity drop, target motion, and aerodynamic error are the three problems. Although they may be considered independent angular corrections, their functional independence disappears and separate and additive consideration is impossible from the instrumental standpoint. The theory involved the addition, in the equation of a lead-computing sight, of terms independent of the rapidly changing variables, or in other words, of the lead itself and the angular rates in space of the line of sight and of the thrust axis. A full-scale program for reducing this method to practice has been in progress for about one year, and has followed several parallel paths in terms of the philosophies of apparatus. Fully captured gyro systems have gradually replaced partially captured systems, which were earlier contemplated.\nSeveral choices remain among the experimental designs for measuring glide, which can be determined from the rate of change of altitude, altitude itself, airspeed, or the indication of a stable gyro horizon. The captured-gyro angular rate components also offer a choice between null methods or purely mechanical constraint and sensitive detection. Both types of instruments have been built, and the final selection depends on the nature of other components. In a larger context, electric and pneumatic techniques in instrument design have continued to be developed together, and neither has yet proven demonstrably inferior. Mechanization of the static functions in the system, as contrasted with the dynamic.\nThe dynamic differential equations necessary for embodiment have been created using small linkage-computers, as detailed in Chapter 5. This computing component is planned for both the electric and pneumatic versions of PUSS. Most of this development, assigned to Navy Project NO-265, was conducted at The Franklin Institute. Simultaneously, the electronic flight simulator, as described in Chapter 4, was being prepared at Columbia. It incorporated the principal dynamics of the PUSS computer and the flight characteristics invariant for all proposed computing methods. It was hoped that this simulator would soon be available for tracking studies, along with the instrumental phases of development. However, developmental work on the simulator, aside from the consolidation of existing components, was ongoing.\nThe preparation of a descriptive report ceased by October 1945. However, it is planned to move this equipment to Philadelphia where the remainder of the PUSS project will continue under a direct Navy contract. Although only rudimentary flying operations have been successfully simulated, the more intricate questions of stability, such as that of the rapidity of subsidence to a solution under manual operation, can be submitted to experiments on this apparatus in the laboratory. A means will thus be available for exploratory alterations without the expense and duration of full-scale testing.\n\nTwo remarks on the human problem\n\nIn the development of generalized aiming controls for the pilot, particularly where he is the lone occupant of the airplane, it must be well recognized what burdens can and cannot be placed upon him.\nParticipant or impresario in the ceremonies, the project engineer could not bear burdens such as those concerning the integrated equipment for the pilot of practical utilization. M. Golomb was a prominent contributor on mathematical, experimental, and general design phases.\n\nUnclear: UCONFmENTIAI?\n\nIntegrated Equipment for the Pilot: The development engineer cannot dispense with this realistic background to his problem, although his thinking should not thereby be limited. He should talk extensively and intensively with fighter pilots, hearing their opinions, not necessarily believing all they have to say. He should determine the common denominators among the sometimes widely disparate opinions of these experienced pilots and find out what they need, not just what they want.\n\nNote: The fighter pilot is a high type of individual.\nA survivor of rigorous training and combat, such an individual is at the peak of his abilities in quick decision-making and reflexes. He is older than usual for his kind, at 25 years old. However, he is heavily burdened. Not only must he master various specialized weapons in modern combat, but he must also be a navigator, tactician, and expert in recognition and deception. As captain and crew of his craft, the modern fighter pilot must be self-sufficient. It is evident that the fighter pilot will not make great efforts to obtain additional computing apparatus that adds to the complexity of his already gadget-laden existence, unless his survival is otherwise and compensationally enhanced. This perspective, of course, is not universally held, even among-st them.\nFighter pilots should control aiming specifically. However, this is common and justified. Considerations for aiming controls, such as those proposed in Project PUSS, are influenced by the following: No manipulations should be required of the pilot, other than flying and firing, during an attack \u2014 with whatever weapon. Only rudimentary instrumental manipulations should be required at any time prior to the attack. The pilot should further be free to fly in any manner he chooses until he steadies out on the attack itself. This is for evasive purposes and for selection of a propitious moment.\nAny approach requiring an inflexible routine or pattern of elements for pushing an attack to its crisis is doomed in advance. The sighting or computing system should not require any intellectual gymnastics by the pilot at any phase of the operations. Expecting him to \"go into the literature\" via tabular data or make even the most trivial calculations by slide rule or nomogrammic computers imposes an intolerable burden. All adjustments should be localized and arranged mnemonically and unmistakably, and there should never be any question of what to do or whether any given operation, once made, was the proper one.\n\n10.3 The Pilot\u2019s Universal Sight Head\n\nThis important component of a universal sighting system, relatively speaking, can be considered somewhat independently of the others.\nSuch is not the case when only a simple reticle is to be displayed as aiming index, movable automatically on a two-dimensional field of solid angle. This does not apply when multiple reticles are involved, as in the proposed Texas Sight or in certain other proposed constellation displays where the relative motion of a pattern with the target is to be made zero. It is not the case when a ranging ring must be used, as in classical lead-computing sights. It has been the policy in PUSS, however, to hope for automatic ranging, as with ARO radar or Pterodactyl, or for aiming methods in which the range does not explicitly appear. Another complication is the expressed and understandable desire for the availability of a fixed sight, which incidentally is a sort of \"universal fire-control system\".\nThe Pilot's Universal Sight Head: in itself, this matter further divides into cases where a fixed reticle is to be maintained simultaneously visible with the moving reticle, though perhaps optionally illuminated, and the cases where it is adequate to operate a control which \"freezes\" the moving reticle in its bore-sighted or fixed zero position. Ideally, it should be possible to do all these things and also to set a fixed deflection other than the zero one by a calibrated adjustment. In physical arrangements where a fixed reticle may be optionally available, this is best accomplished by a mechanical connection capable of very rapid operation, since such a standby sighting facility may be desired owing to failure of servos, etc., and it is questionable to expect an electrical adjustment then to be workable.\nButtals to this claim that under such failures, the reticle lamp will be lost, are only partially valid. This quick and fool-proof \"throw over\" criterion, in any case, has been upheld thus far for the PUSS system. Within PUSS, the pilot's universal sight head has been known as PUSH.\n\nIn the PUSH developments to date, as a sub-division of Project PUSS, the principal approach has been to manipulate a plane mirror in a collimating sight. Very different problems are encountered, depending on whether the (single) mirror is placed in the divergent beam from the reticle or in the subsequent beam from the collimator, the latter being either a lens assembly or a shaped mirror. In the former case, the mirror-driving component must compensate for the angular aberrations of the lens, but here the mirror itself may be fairly compact.\nIn the latter case, with the mirror outside in the beam which is focused at infinity, an exact type of geometry may be employed. In both cases, the finally collimated beam is reflected back to the pilot from a \"transparent\" reflector, which may be specifically introduced or may be the windscreen of the airplane itself. The illumination problems involved here are considerable, to cover the range of ambient intensity which is encountered, unless a sun screen can be placed in front of the entire system or a combination of lower transmission and greater reflectivity is attained for the final reflector, and simultaneously a correspondingly lower transmission for the whole canopy. Furthermore, the problem of the Orthopentax application is not addressed here. Although, as we may note here, the attractive suggestion is:\n\n(Chapter 5)\nManagement has suggested that an intermittent gaseous discharge might provide a more intense and efficient illumination, with less heat dissipation. However, this is still a controversial issue. Additional equipment would be required, but this might only add fractionally to the computing system already planned.\n\nThe issue of eye relief is nearly insurmountable with orthodox systems. A poor compromise must be accepted between obstructing forward vision and the width of the emitted beam. One solution is the avoidance of collimating lenses through reflex collimation, as in the Bowen Sight (Mount Wilson). Another is to bring the final reflector, which has small dimensions, near to the pilot's eye and perhaps allow it to move with his head, being maintained in position.\nThe best measure for direction in a stabilizing system is using a forward \"periscope\" or one-to-one telescope of wide angular field (Mount Wilson) and large aperture with good eye relief. This solves many problems at once, but is unorthodox. All the pilot's forward vision could pass through this telescope, allowing approximately 25 degrees of angular vision in every direction. It might be bulletproof and would permit better streamlining through the elimination of the flat wind-screen. Such a telescope has two focal planes, so reticle motions and other desired indicia, focused at infinity, such as the whole instrument panel around the edge of the field, could be easily incorporated. Opaque reticles, automatically solving the illumination problem against bright light.\nbackgrounds,  could  be  illuminated  laterally  by \nknown  methods  for  dim  operational  conditions. \nUltimately  such  a telescope  might  well  be  a foot \nin  diameter,  extending  from  the  pilot  at  the \ncenter  of  gravity  to  the  nose  of  the  plane.  The \nweight  imposition,  owing  to  the  large  glass  or \nplastic  lenses,  would  not  be  serious  to  the  imag- \ninative planner,  since  this  object  would  literally \nbe  worth  its  weight  in  gold.  Think,  for  example, \nhow  easy  it  would  be  to  include  an  image  of  the \nradar  scope  in  the  field!  This  whole  possibility \nis  not  altogether  original\u00ae  with  the  writer,  but \nis  an  extension  of  much  older  proposals.  Its \nconsideration  for  future  development  is  most \nheartily  recommended. \nTo  return  to  the  rather  more  nearly  earth- \nbound  topic  of  past  developments  on  PUSH,  a \nprogram  of  mirror-linkage  design  was  carried \non  both  at  The  Franklin  Institute  and  at  The \nThe Bristol Company prepared experimental designs for integrated equipment on a pilot scale. For available optics, the method of placing a mirror both inside and outside the collimating lens was abandoned due to necessary compromises for meeting specifications regarding focus, field, and precision, previously agreed upon. Navy explored this method at Specialties, Inc., finding a good compromise and preparing an initial model for experimental application to PUSS, with official cooperation via BuOrd. Several mirror linkages were developed under our own direction, primarily for the second method, which provided great accuracy over a field of plus or minus 15 degrees.\nModels had been installed with large collimators in cockpit replicas at Philadelphia. The design of practical housings was about to be considered when the project began to close. Presumably, such development can be continued under Navy auspices if desired. The interested and authorized reader should also study the sight head designs of the Draper-Davis A-1 sight in the Army. For future development, however, we urge that a much longer view be taken of this problem, and that conjectural methods mentioned above should be considered along with newer proposals which most certainly will be received.\n\nA very interesting possibility is the generalization of the fly's eye collimator, so called, which is described in contractor's reports by Eastman Kodak and The Franklin Institute.\nThe flexible reticle-image. (Refer to Division 16 report.) Whatever the nature of the sight head, if it is of the universal type referred to, remote followers or servomechanisms must be employed to deflect the line of sight in obedience to the outputs of computers placed at some distant points. The reference variable at the sight head may be a resistor or capacitor, for instance, in the case of electric servos. For d.c. servos, the resistor is very convenient and has been employed by us and by Specialties, Inc., in experimental models. The capacitor follower, however, for a.c. circuits, permits extreme fineness of setting and consequent smoothness, where this is desirable and where high-frequency methods are elsewhere applied. Transmission systems of more nearly standard type may also be applied, thinking now of small systems.\nselsyns and autosyns, particularly in systems where computers produce mechanical rotations directly. Pneumatic transmissions have also been considered and would certainly be practical when this medium is employed in other parts of the system. One advantage is that no follower sequence is required. Pressure in a closed system can be carried to a remote point for deflection purposes with considerable guarantee of accuracy, speed, and lack of hysteresis, provided that the appropriate newer techniques are applied.\n\nThe question of roll stabilization. The general method, used in the PUSS system, of splitting the computation and manipulation into two components corresponding separately to azimuth and elevation, these coordinates being referred to from the pilot's point of view, has several consequences in dynamic performance which compare unfavorably.\nWith the circumstances of a single-gyro deflected sight, it is evident that when an airplane is rolled instantaneously, this having no effect on the trajectory of the projectile, the sight line will initially move in space in a direction and speed dependent on the lead angle, measured from the axis of roll, and on the rolling maneuver as such. Although this occurrence is only transient and will disappear in the steadier conditions which should presumably precede the firing instant, the response of the line of sight in this manner to roll may enter the tracking dynamics and influence the stability. One possibility is that it may affect skid, though it is not known whether beneficially or harmfully, and such questions are important enough to be studied before flight tests are made. Flight tests on analogous structures should be conducted.\nThis problem may not be serious for components and systems, but we should not let a large development program depend on such tenuous data. The electronic tracking simulator was hoped to be used for such questions of dynamic stability, where human response is involved. The reader is referred to Chapter 2 for a discussion on a more general plane of the analytic and synthetic possibilities in connection with this type of question. In any case, we now know that this roll transition, whether adverse or otherwise, can be analyzed.\nCompensated completely for quite evidently, a straightforward though cumbersome measure for its elimination is to roll and stabilize the whole sight or system, allowing no rotation in space about the roll axis. It is only necessary to employ an angular rate meter measuring the roll rate or an angular accelerometer measuring its acceleration and form the appropriate dynamic connection to prevent transient turning of the line of sight. This problem, if it indeed arises in serious proportions, will not long remain unsolved in a practical sense.\n\nOn a somewhat higher plane, it may be repeated here that all the functions of free gyros and stabilization equipment may be duplicated by a system fundamentally including a set of gyroscopes.\nthree  absolute  angular  rate  meters  (see  Chapter \n3)  fixedly  disposed  in  the  vehicle. \nCOMPONENTS  AND  SYSTEMS \nBetween  the  various  inputs  and  the  output \naiming  deflections,  the  computing  portion  of \nPUSS  may  be  roughly  segregated  into  a dy- \nnamic computer  and  a static  computer,  each \npossessing  several  subsidiary  components,  and \neach  being  joined  functionally  to  the  other  at \na number  of  points.  The  dynamic  computer  em- \nbodies an  operational  connection,  between  one \ncomponent  w of  angular  rate  and  a correspond- \n^Suggested  as  a technique  by  the  present  writer,  and \ngiven  analytic  form  and  justification  by  M.  Golomb \nat  The  Franklin  Institute. \ning  component  A of  angular  sight  deflection  of \nthe  form \nin  which  A,  B,  and  T are  outputs  of  the  static \ncomputers,  and  are  slowly  varying  with  time, \nat  least  in  comparison  with  w and  A.  If  one \nprefers  it,  the  differential  equation  equivalent \nThe above operational equation is for a dynamic computer characterization. When A and B are made zero, this equation becomes that of a standard disturbed gunsight. If the time-parameter T is made infinite, the equivalent of a moving sight coupled to a free gyro is obtained, allowing for collision-course approaches as explained in Chapter 1 and 8. The dynamic computer's characteristic is essentially that of a first-order lag with an adjustable lagging parameter and sensitivity adjustment, and additional terms imposed on the input and output. Many means exist for mechanizing such a characteristic. Those chosen for the PUSS system are resistance-capacitance filters, one synthetically produced.\nFigure 1 shows one schematic arrangement of the computation in PUSS, which has had numerous variants, depending on which specific input components are applied. No attempt is made in this figure to show in any detail the switching arrangements, such as how the operator selects the type of weapon for which a solution is intended. These important technical features have been completely described in reports to which reference is made below. This entire development is still in progress, although it is now a closed integrated equipment for the pilot, including PACT.\n\nH - PUSS\nK - H\nK - K\no - PUSS (including PACT)\nFigure 1. Schematic diagram of PUSS system; AFCS Mark 4; Project N-26r.\n\nComponents and Systems:\nThe following are the automatic inputs of PUSS in one of its most likely forms: static and dynamic air pressures, vertical acceleration, temperature, and the two absolute angular rates of the vehicle. Certain implicit inputs relate to the characteristics of the aircraft itself and are made on installation. Only one manual input must be made during operation, aside from the choice of weapon, and assuming, of course, that appropriate automatic means are worked out to synthesize the temperature of the rocket propellant, and that one is target altitude. Even this is unnecessary if, with a different basic set of inputs, automatic synthesis is achieved.\nmatric radar range or radar (FM or pulsed) altitude is provided. To continue with the inputs named, the angular rate inputs would be handled in dynamic computers of the type for which equation (1) is definitive. One channel^ for each for azimuth and elevation. In the azimuth channel, it may be assumed that the \u201csecular\u201d parameters A and B are absent. Furthermore, the time-parameter T, although simultaneously set into the dynamic computer of both azimuth and elevation channels, is multiplied by a constant ratio in one as compared with the other. This is a stratagem whereby the correction for gravity can be effectively made in the proper direction, in the presence of uniform bank, despite its explicit treatment in the elevation component alone. It remains to describe, for this same set of inputs, the methods for processing the data in the radar system.\nThe parameters A, B, and T are computed, and then the interconnected computer (PACT) for toss bombing is described. In the computation process, certain implicit variables are first obtained. The glide angle is obtained in terms of static pressure and dynamic pressure, involving the differentiation of a static pressure function. For instance, the glide angle y can be derived in terms of true airspeed, itself a function of indicated airspeed Vai and altitude h, and the rate of change of altitude. The altitude is expressible in terms of static pressure.\n\nNote the remarks in the above section on the possibilities of roll stabilization. See also the bibliography.\n\nThis technique is believed novel in PUSS and was conjured up by M. Golomb, the project's mathematician.\nThe pressure indicates airspeed, measurable through the difference between dynamic and static pressures. Range R to the target, on a relatively straight approach, is calculable as an intermediate variable of the computation, directly from altitude and glide angle. The angular rate parameter A and the lead parameter B are then obtainable from these quantities.\n\nA is derived as A(y) or as a function of glide alone, while B is given by B >Vai,\u00ae), and as a function of glide, indicated airspeed, and temperature is the most complex item. The time-parameter T is computed as T(^), a function of range alone. These computations primarily take place through multiple linkages, designed directly from graphical representations of the equations.\nThe respective functions for accurate fire results must have the following: In Chapter 5, this philosophy was more fully treated. The computation for rockets and bullets, in one variant of PUSS, has been traced through. We will return again to consider various questions regarding certain individual components. However, before doing so, we will explain the operation of the PACT toss bombing computer, which has thus far only appeared as a component of the pneumatic version of PUSS. It was felt that an electric mechanization of the toss bombing (or toss rocketry) functions would too closely duplicate other BuOrd activity, notably at the Bureau of Standards. The inputs for PACT are the dynamic and static pressures and the vertical acceleration, as measured by a captive-mass accelerometer. Additionally, a manual input of target altitude must be provided.\nThe input is primarily in readable English and does not contain any meaningless or completely unreadable content. No introductions, notes, logistics information, or modern editor additions are present. No translation is required as the text is already in modern English. No OCR errors are apparent.\n\nThe text describes the function of an integrated equipment for the pilot in the PACT (Proximity Fuse and Computing System) system. It explains how static and dynamic pressures, along with an auxiliary variable, are used to compute the velocity a bomb must have to counteract gravity. A pneumatic force-balance accelerometer is mentioned as a component of this system.\n\nCleaned Text: In a pneumatic force-balance accelerometer, a pressure corresponding to the vertical acceleration, adjustably lagged, is made to provide a mechanical motion, along with the auxiliary variable mentioned earlier, continuously to compute the velocity a bomb must have, in the direction upwardly normal to the direction toward the target, sufficiently to counteract gravity in the PACT (Proximity Fuse and Computing System) system. The static pressure, as a function of altitude, is utilized through the motion of an aneroid capsule and a differential meter responding to the difference between the static and dynamic pressures to develop an auxiliary variable as the output of the confidential integrated equipment for the pilot portion of the PACT computing linkage.\npull-up,  in  the  toss  bombing  tactic,  action  of  a \npneumatic  integrator  is  initiated  which  com- \nputes, via  the  integral  of  the  increase  in  total \nvertical  acceleration  of  the  airplane,  the  corre- \nsponding normal  velocity  being  thereby  im- \nparted to  the  bomb.  When  these  two  computed \nvariables  are  equal,  as  indicated  by  coincidence \nof  output  linkage  rotations,  the  projectile  is \nautomatically  released.  In  PUSS,  the  inputs  and \ncomputing  components  of  PACT  are,  at  least \nin  the  preliminary  model,  physically  inter- \nspersed and  interwoven  with  those  of  the  re- \nmainder of  the  system.  All  this  has  taken  place \naccording  to  Pollard\u2019s  theory  of  toss  bombing, \nas  also  has  the  following  arrangement  for  spe- \ncial settings  in  the  dynamic  computer  of  PUSS \nduring  the  operation  of  PACT.  In  toss  bombing \noperations  ki  order  to  follow  an  initial  approach \nwhich  allows  for  target  motion,  the  elevation \nThe sight deflection is set to zero, the time parameter T is set at maximum or approximately 20 seconds, and parameters A and B are set to zero. Simultaneously, the \"fixed\" parameter ky, the constant of coupling as shown in Figure 1, is set at the value 2 instead of about 1.2, as it is for other aiming functions.\n\nThe heart of the PUSS system consists primarily of the dynamic computing component, which is fed mainly by directly measured absolute angular rates. In early forms of PUSS, the functions of the present gyro inputs and dynamic computers were accomplished by other means, and these other means were the subject of:\n\nThe sight reticle is aligned, in elevation, with a definable fixed axis in the airplane, along which the vertical accelerometer does not detect. Allowance for target motion in elevation is made.\nThe influence of flight path curvature on vertical acceleration, discussed elsewhere in this report and in the writings of H. Pollard (of AMG-C), is similar to an analogous phenomenon in rocketry computers. This phenomenon functions only near certain average glide angles. The investigation of such systems ranged from the now standard dome-type eddy-current gyro systems to those with separate precessing motors similar to gunsights developed by Zeiss for the GAF. A variety of special linkages and servo systems were considered for these systems, all of which involved only a single gyro. We have discussed in Chapter 3 the advantages claimed, particularly in flexibility for new functions, for the present technique of operating on a fundamental direct measure.\nThe way to enhance angular rate is achieved through the application of higher-order dynamics. In Chapter 3, we discussed captive gyro developments for angular rate inputs to PUSS, including pneumatic and capacitative one-dimensional units, and the two-dimensional current servo case. Progress and future promise are evident on all types. In the measurement of glide, the pneumatic version of PUSS relies on a measurement of barometric pressure's rate of change, along with the pressure itself and indicated airspeed, to determine the glide angle and subsequently the range, through an equivalent solution to the obvious triangular relationship.\nSome research has been conducted on a refined type of differentiator, involving feedback, which is still in development. The standard rate-of-climb instrument is somewhat inadequate for this task. An analogous solution to the problem of providing glide is now planned for the first electric version of PUSS. Here, an existing component, employed in the so-called glide bombing attachment [GBA] for the bombsight Mark 15, has been modified for this purpose. By following the motion of an aneroid diaphragm system, having a static pressure connection, through a mechanical integrator disk, both altitude and its rate of change are developed as shaft rotations. Hence, with airspeed, glide can be derived again. A competitive method for measuring glide, in this case 8, as has been employed in several other systems, is by detection of one of its components.\nThe objection to most gyroscopic instruments with gimbal deflections in a gyro horizon is that they \"spill\" at certain extreme bank or dive angles. However, this is not the case with the new Sperry altitude gyro, nor with a Pioneer horizon in development. The measurement of gimbal rotation is made difficult since it is the inner gimbal that is involved. A method of capacitor measurement can solve this problem and may be appropriate if such measuring methods are elsewhere employed. An experimental assembly is now in preparation, involving a pair of radial plates, rotating relatively with the desired (but mechanically remote) gimbal motion, in series with a larger and constant capacitor acting as a counterpart.\nslip ring. No friction load need be added, and known methods of capacitance measurement may be directly applicable. We may mention briefly other methods which have been considered for the effective and continuous determination of the glide. In PUSS, the accelerometer method, giving the cosine of glide (8) under conditions of straight flight, is not appropriate on the one hand, since the error due to target motion and path curvature does not necessarily correct for the target motion, as in other cases, but on the other hand such errors might here be removed since angular rate of the airplane about its lateral axis is continually measured as an input. A question of stability in tracking still arises, however, and it has been less troublesome to apply other techniques. Still another possibility, instrumentally unexplored.\nExploring the use of the longitudinal component of total acceleration as a measurement of glide, since it is unresponsive to path curvature, requires correction for the rate of change of true air-speed. Different approaches to the PUSS problem have been proposed, yet only partially explored. One proposal is by R. O. Yavne (see bibliography), suggesting mechanizing the firing solution with a system equivalent to a free-gyro sight, where coupling constants are varied with range or time. Such an arrangement might ultimately prove superior, and exploration of alternatives should continue as long as there is a need for PUSS. From a more practical standpoint, the installation question arises.\nIt has been proposed by BuOrd that the PUSS computer, whether pneumatic or electric, be contained in a wing tank with remote connections to the pilot-operated controls and to the sight head. At least for experimental work, and possibly further, this may have certain non-negligible advantages.\n\nNote that such radar systems to be employed as potential inputs to PUSS, in particular for the range itself, will be somewhat similarly installed in any case. It is evident that the removal and reinstallation of computers for calibration or for several experimental purposes would thereby be greatly aided. Furthermore, this would allow for a separate and local pilot installation for dynamic and static pressures, which permits engineering of these inputs to suit special needs better than ordinarily do the standard equipments available in airplanes.\nThe purposes for installing PUSS systems include making preparations with the preliminary models at the very least. Even the smallest drop-able auxiliary gas tank should provide sufficient space. In Chapter 3 of this report, we have discussed the properties of captive gyros, specifically of the pneumatic variety. The pneumatically captured gyros, used experimentally for PUSS and other systems, have all been of the one-dimensional type, measuring absolute angular rate around one axis fixed therein. These developments have been the work primarily of NDRC Section 7.3. In the pneumatic version of PUSS, two such gyros are employed.\ncaptive gyros are considered for the angular rate inputs, and a third \u2014 forming, thus, a symmetrical set \u2014 might be included for more complex aiming control. Integrated equipment for the pilot. Components are now available for testing, both separately and in combination with the other components of the system.\n\nAs we have mentioned, pneumatic force-balance components are being used for the determination of climb rate and for the integration of incremental accelerations, the latter variables themselves being determined by similar means. For such applications, the pneumatic medium leads, at least potentially, to very smooth and rapid operation, and to lightness and compactness of design. For dynamic compensation.\nIn such cases, putations with connected systems of rigid tanks and capillary tubes can be used in a manner similar to electrical resistance and capacitance. Analogous feedback techniques apply where non-passive systems must be synthesized. However, certain restrictions must be observed to obtain predictable or linear performance. For example, the time parameters of such networks are generally proportional to the absolute pressure in their component elements. Either compensation must be included for such effects or the variations in pressure (as in orthodox acoustic theory, for example) must be kept small in comparison with the absolute level. Furthermore, condensation and leakage must be rigidly guarded against. Techniques are known which may ensure safety from such deleterious influences. (See Chapters 3 and 4 of Volume 1, Division 7.)\nThe purposeful variation of parameters in pneumatic type dynamic computers can be accomplished by several means. Continuously made during normal operation, the mechanical method of varying pneumatic capacitance by changing the volume of tanks seldom gives the desired result due to the imposition of a \"forcing function\" on the pressures in the system, altering the initial conditions. Adjustment of pneumatic resistance is more appropriate since energy storage is not involved, and the techniques are central to this art. Needle valves are prone to many failings from a practical and theoretical standpoint. Step adjustments of capillary tubing typically lead to much equipment and concern over the continuity of overall operation. Under the express urgings of\nThe writer, an ingenious component for the variation of pneumatic resistance, was devised for this application. The solution, now experimentally embodied in components for pneumatic PUSS, involved a stack of thin punched disks with alternating types of hole. This created a labyrinth resembling capillary resistance, which was adjustable in effective length as imposed between the terminal connections. An easy mechanical adjustment was permitted. For details, we refer again to reports of Section 7.3.\n\nFor shifting operations, whereby the pneumatic computer and allied equipment could be adapted rapidly and at will to the different functions desired of them, small solenoid-operated valves of special type were developed. The entire pneumatic assembly is to be contained in a supercharged space, possibly later with complete recirculation of air (or whatever gas).\nEmployed regulators, through pumps and feedback pressure regulators, have been designed for and are expected to perform valiantly in regulating supply pressures. The only possible objection to the pneumatic version of PUSS or similar equipment is the unfamiliarity of maintenance procedures. This is a controversial point, however, and seems less important from the longer-term perspective.\n\nRegarding the capacitor in instrumental techniques:\n\nThe application of continuous measurement of electrical capacitance in components of aiming-control systems has been referred to at several points. For the measurement of small mechanical motion, either for repetition in other physical variables or for the detection of error in a follow-up, it has numerous advantages. It can compete with photoelectric methods regarding the absence of \"detent,\" or of interruptions.\nInterference with the physical system can be detected without the need for following agencies. Precision measurement can be carried out locally where the primary measured variable occurs. Thus, very small capacitors can be located in otherwise inaccessible spots, and their capacitance, in response to the primary variation with which they are associated, can be reproduced remotely in any desired tangible form. The possibility of employing capacitative \"slip rings,\" in series with the measuring capacitor, permits electrical extraction of such measurements from mechanically complex systems, where otherwise direct conduction, with its attendant problems, would be required.\n\nBy J. F. Taplin, Section 7.3 (Lawrance Aeronautical Corporation).\n\nPaths for Continuing Research\n\n## References\n\nNone.\nTo derive any reasonable function of a rotation, it is necessary only to shape the plates - or the dielectric - of the measuring capacitor appropriately. Using the electric laws of series and parallel capacitance, numerous elementary mathematical operations, such as addition, can be performed from mechanical motions in a computer. For these applications, a stable oscillator must be provided. Frequencies of one megacycle give satisfactory results in typical instances, while much higher and much lower frequencies have been successfully applied. It is most efficient to resort to capacitor techniques where many of the operations in a system may thus be carried out, and where electronic channels are performing other functions, such as computation or manipulation. The combination, however, of capacitor techniques and other methods is also effective.\nSignificant differences exist between such techniques and mechanical ones, particularly in instances where the final motion of complex, miniature linkage computers can be extracted without load on inputs or bearings. The size of the computing unit itself is not significantly increased. Information on the practicality of electrical capacitative methods for such applications should soon be available, as at least two such components for PUSS are in development. Following rigorous laboratory tests, flight testing under properly arranged conditions should simulate those of the final application. Since such methods have been used in industrial and other systems for a long time, there is little reason to suspect their applicability here.\n\nPaths for continuing research include one modification of PUSS not yet mentioned: a suggestion for its implementation.\nSeveral sources consist in presetting the gravity drop and other nonkinetic parts of the aiming correction through a computation different from that executed by the dynamic process fundamental to the current PUSS method, particularly in rocketry. Such a modification could lead to a more rapid subsidence to firing conditions and at least provide an approximate aiming correction if there is no time for the brief tracking interval demanded by the PUSS method. It may be possible, at longer ranges, to arrange for such presetting automatically by redesigning the linkage computers now contemplated. Many of the conjectural aiming control schemes mentioned throughout this report may well be valid.\nThe text deserves further study, and it would not be surprising if some of these issues proved revolutionary in the increased powers of fire control they might allow. For the future, there is more time for such theoretical or basic study, and the newer techniques may arise either from mathematical or instrumental advances in thinking, or again purely empirically from quantitative study of the physical sections of the problem. It would be folly to work without recognition of the probable forms of future weapons, but the recommendation of the present writer would be to treat projectiles from a rather generalized point of view, so that the theories and systems to be developed may simply be adapted by the fixing of parameters in the control and computational components. One may look somewhat beyond the immediate issues.\nThe objectives of PUSS, keeping them in mind, let's consider some logical extensions. PUSS will be linked with jet-propelled airplane types, which has significance for our final point. In earlier discussions, we pondered what might ensue if the fighter plane were to be equipped with a high-performance automatic pilot. As a generalization of PUSS, suppose the pilot, in attacking a target regardless of location, merely uses a stabilized sighting system carried in his fighter to track the target through control manipulation of the aircraft's lines.\nWith the direction to the target established and its special properties continuously determinable, a computing component would develop in a continuous manner the direction of flight necessary for successful fire. This latter direction, by instructions from the computing system to the high-performance automatic pilot, would be undertaken by the airplane. This sets up what amounts to a director for fighters. While there are many details to be filled in, there is nothing really insurmountable about the problems of such a system.\n\nFurther, it is evident that with the pilot's task reduced to that of tracking the target, he may be replaced by an automatic follower which \"locks on\" to the direction to the target by the computing system. (Commander E. S. Gwathmey of BuOrd is mentioned but not relevant to the text and can be disregarded.)\nThe vehicle, without human passengers, is unlimited in maneuver violence. For example, the vehicle itself can be steered on an interception course with the target. This enters us into the field of guided missiles. The techniques of the two fields are not widely separate; each has much to learn from the other in apparatus and developmental procedures. Newer weapons can best proceed in the fullest kind of cooperation and understanding.\n\nCONFIDENTIAL\nPart II\nAerial Torpedo Directors\n\nAircraft torpedo director developments undergo continuous improvement. The primary function of an aerial torpedo director is to provide the pilot with the necessary information to aim and release the torpedo at the target. This includes target angle, range, and speed data.\n\nThe earliest aerial torpedo directors were simple devices, often consisting of a sighting telescope and a rangefinder. These devices allowed the pilot to visually acquire the target and estimate the range. However, they were limited in accuracy and required the pilot to maintain a steady flight path and a constant speed.\n\nThe development of radar technology in the late 1930s and early 1940s revolutionized aerial torpedo director design. Radar allowed the pilot to acquire and track the target automatically, improving accuracy and reducing the workload on the pilot. Radar-equipped torpedo directors became standard equipment on bomber and torpedo aircraft during World War II.\n\nPost-war developments in electronics and computer technology led to the development of more advanced aerial torpedo directors. These systems used inertial navigation systems, gyroscopes, and other sensors to provide accurate targeting data. They also allowed for automatic torpedo release, further reducing the workload on the pilot.\n\nModern aerial torpedo directors use a combination of sensors, including radar, infrared, and laser rangefinders, to provide accurate targeting data. They also allow for the use of various types of torpedoes, including wire-guided and homing torpedoes.\n\nDespite the advances in technology, the basic principles of aerial torpedo director design have remained the same. The primary goal is to provide the pilot with accurate and reliable targeting data to enable a successful torpedo attack.\n\nIn conclusion, aerial torpedo directors have evolved significantly since their early days as simple sighting devices. The use of radar, electronics, and computer technology has improved accuracy and reduced the workload on the pilot. Modern aerial torpedo directors use a combination of sensors to provide accurate targeting data for various types of torpedoes. The goal remains the same: to enable a successful torpedo attack.\nSection 7.2 of NDRC was carried out at The Franklin Institute as part of Contract OEMsr-330. G. A. Philbrick was responsible for the earlier work, which he has described in Part I. Since the spring of 1943, these developments have been under my cognizance, but with much helpful collaboration from Mr. Philbrick. The transition from one supervisor to the other was somewhat gradual, with no sharp dividing line. Consequently, it has not been practical for Mr. Philbrick and me to prepare two reports, each covering distinct phases of the development work. Mr. Philbrick has described a part of the aircraft torpedo director work, and this report is intended to complete his descriptions and add descriptions of the remainder of the work in this field.\n\nFor complete and detailed descriptions of the aircraft torpedo director, please refer to Mr. Philbrick's Part I and this report.\nSeveral directors developed the following ideas, referred to The Franklin Institute reports listed in the Bibliography. Some ideas that never reached the development stage might warrant a mention. One such idea was a so-called rule-of-thumb method of aiming torpedoes. This method involves the pilot aiming a predetermined number of apparent ship lengths ahead of the target. However, analysis shows that for even moderate accuracy, the predetermined number must come from a fairly large and complicated table which the pilot must memorize. Opinions differed widely as to the value of the method. Further work was done on the apparent length method, applying it to the technique of tossing torpedoes. The suggestion was to toss a torpedo like a toss bomb, but aimed to hit the water about 200 yards (the arming distance).\nA modified toss bomb-sight was used to aim at the target in front. The Navy sought Section 7.2's analysis on appropriate lead angles. Opinions varied on the value of using an expensive torpedo for a toss bomb. Tests showed insufficient accuracy for justification. At one point, the Bureau of Ordnance proposed creating a torpedo director for gyro-angling torpedoes. Section 7.2 expressed little enthusiasm for this development and did not pursue it. If an attack is made by aligning the plane with the target (either with zero lead or on a collision course), relying on the gyro angle setting to provide lead by causing the torpedo to turn in the water, a no-deflection shot is given to the antiaircraft gunner on the target ship. If the gyro angle setting on the torpedo is correct.\nIn the solution to the aircraft torpedo attack problem, it's necessary to know the following:\n\nA large lead angle must be used by the pilot to minimize danger from AA fire, but this increases the difficulty in sighting through the director optics. A zero gyro angle (or straight) shot represented the best compromise between the two difficulties and resulted in a simpler director. However, one development that might be considered an oddity was the computer for a torpedo director trainer. This was designed to calculate and display the error in hitting while using the standard trainer for the torpedo director Mark 30. The computer was 90% complete when production ended at the war's end.\n\nA. L. Ruiz\nCONFIDENTIAL\nChapter 11\nCOURSE STABILIZATION\ntarget course and speed. These quantities could be measured if a suitable tracking mechanism was installed in the attacking plane to determine target bearing and range over a period of time and feed that information into a computer. The amount of mechanism involved, however, would be fairly large and the use of an additional operator would be required. In order to avoid such unnecessary complications and weight, aircraft torpedo directors have been built on the assumption that course and speed could be estimated with sufficient accuracy.\n\nNormally, instead of target course, it is much easier to estimate target angle (or \u201cangle on the bow\u201d). In effect, this is the orientation of the target with respect to the line of sight, and is therefore the angle seen by the pilot as he looks at the target. From the target angle, own ship's heading and speed, the target course can be calculated.\nplane course, and the relative target bearing determine the target course. However, it is not necessary to compute this as the target angle can be used to solve the attack problem (Figures 1-3).\n\nFigure 1: Han's view (of the target and own plane).\n\nThe target angle is a function of the target course, own-plane course, and relative target bearing. As the attack progresses, the target angle changes. Therefore, if a pilot estimates and sets the target angle early in the approach, his setting will be incorrect at the time of attack. Consequently, the pilot must make a last-minute adjustment and estimate the target angle before releasing his torpedo.\n\nFigure 2: Plan view of torpedo firing problem.\nAs the plane approaches the target (Figure 4), the target angle changes, so an early estimation will be inaccurate at the time of firing.\nA method has been suggested for relieving the pilot of the last-minute estimate of target angle in a torpedo attack. The problem can be equally well solved by using track angle instead of target angle (Figures 2 and 3). From Figure 4, it is apparent that track angle is the supplement of the angle between the target course and own-plane course. To determine this angle directly, a miniature ship model is located on the end of a shaft convenient to the pilot. The pilot may turn this ship model until it lies parallel to the target's direction of motion as it appears to him.\nBetween this ship model and the plane's fore-and-aft axis would be the track angle if the plane were on a proper course for release. To keep this angle correct after it is once set, the ship model is clutched into a directional gyro-scope so that regardless of the plane's changes of direction, the ship model will remain parallel to its original setting. Thus, as long as the target does not change course, the torpedo director has available a continuous setting of the difference between the target's course and the plane's course. At any time that the plane is turned to be on a correct torpedo firing course by putting the director's cross wire on the target, this difference represents the correct track angle. Consequently, the pilot may use this difference as the torpedo track angle.\n\nFigure 3. Plan view of torpedo firing problem; same as Figure 2 with all sides of triangle divided by time of run.\nMake the target course setting early in the approach and is relieved of the necessity of making a last minute adjustment before release. The use of a directional gyro and the principle of course stabilization was first made in the torpedo director Mark 32. Due to tests on this director, both the Army and the Navy requested the modification of a torpedo director Mark 30 to add a directional gyro and a ship model for stabilized target course. Tests on both of these at Fort Lauderdale and Eglin Field were very gratifying. All pilots who used the director were well pleased with the course stabilization feature. As a consequence of the Eglin Field tests, the Army requested the development of a new torpedo director utilizing a different set of optics. This was completed in June, 1944 and was adopted as standard by the Army.\nArmy and Navy designated the torpedo director B-3. A similar director with different optics, combined with a low-level bombsight, was built for the Navy around the same time.\n\nChapter 12\nPRESENT-RANGE TYPE TORPEDO DIRECTORS\n\n'X' HE TORPEDO Directors Mark 30 and 32 (and all earlier ones) were built to use an estimate of torpedo run as an input. The reasons for this were twofold: the solution for lead angle as a function of present range and other variables is implicit and transcendental; no simple mechanization had ever been found. Consequently, it was simple to rationalize and convince oneself that it was just as easy to estimate torpedo run as present range.\n\nBut the increasing use of radar in torpedo planes spurred on the search for a simple present-range type of computer. At last, the solution was found.\nThe answer is described in Chapter 6. The trick involved locating a point on the torpedo path from which a fictitious torpedo, having a constant speed equal to the water speed of the real torpedo, could be launched into the water at the same time the real torpedo is released, and reach the target simultaneously. This point is referred to as the present-range solution, second step.\n\nNote: The point from which a fictitious torpedo with a constant speed equal to that of the real torpedo starts in the water at the time the real torpedo is released, and reaches the point of impact simultaneously with the real torpedo.\n\nThe problem can be broken down into two parts. The first is a computation for the lead angle for the fictitious torpedo, which involves only the target speed, track angle, and torpedo water speed. The second is a correction for this calculation.\nThe putted data from own-plane speed, present range, and time-of-fall (obtained from altitude by assuming a fall in vacuo with t = 2H/g). The detailed stages in the solution are illustrated in Figures 1 to 6 inclusive. Figure 6 is a schematic diagram of the linkage built. The unit ONFIDENTIA is a present-range type torpedo director. The length in triangle III is the base line, at one end of which is pivoted the link A (turned through the track angle by the pilot\u2019s setting and the directional gyro), and at the other is the link B. The length of A is made equal to Vs/yt by a cam, and the ends of A and B slide together. In triangle IV, the link C is fixed in length and equal to unity. One end of C slides in link B, and the other is moved along the base line by a series of logarithmic dials and an ex-centric lever.\n\nFigure 4. Present-range solution, fourth step.\n\n(Note: The text appears to be in good shape and does not require extensive cleaning. However, I have corrected some minor OCR errors and added some missing words for clarity.)\nAll torpedo directors to date (and in fact, all gun directors) have been designed for use against targets moving in a straight line with constant velocity. The arguments in favor of the constant velocity assumption were twofold:\n\n1. Many targets were not dangerous unless moving in a straight line (e.g., a bomber had to make a straight-line approach).\n2. Since no control over the missile was possible after launching, a straight-line target motion represented the most probable condition for prediction.\nThese arguments were weaker in the case of a torpedo-plane attack than for many other missiles. Upon observing the approach of a number of torpedo planes, the target was likely to start turning in an effort to avoid being hit. With modern antiaircraft systems, this turning would not materially lessen the ability to put out a strong deterring fire against the torpedo planes. The attacking pilots were thus forced to estimate the correction to be applied to their straight-line type of director in order effectively to fire torpedoes at a turning target. This correction could often be very large. In order to relieve them of the burden of making this estimate, the development of a maneuvering type of torpedo director was undertaken.\n\nSpeed from here on.\nFigure 2. Kinematics of a turning ship.\n\nThe kinematics of a turning ship have been described in detail in various Navy publications. Qualitatively, the sequence of events following the order to execute a turn may be described briefly as follows:\n\nWhen the rudder is turned, the bow of the ship gradually begins to turn in the same direction. The ship, however, due to its momentum, continues to move in a straight line for an appreciable length of time, say 20 to 30 seconds depending on the type of ship. At the end of this time interval, it will be noticed that the ship has begun to change its course or direction of motion. The actual path of the ship then departs more and more from a straight line until the ship has turned approximately 90 degrees, when its path of motion becomes a circle.\n\nDuring all this time, the ship's speed has remained constant.\nThe ship gradually reduces its speed, reaching a stable value after about a 90-degree turn. From that time on, the ship continues to move in a circle at a constant velocity with its fore-and-aft axis pointed inward from the tangent to the circle. The diameter of the circle, the terminal speed of the ship, the amount of deviation of the ship's head from its direction of motion, and the characteristics of the transition to circular motion, all depend on the type of ship, its initial speed, and the amount the rudder is turned.\n\nEarly attempts to make a torpedo director effective against a maneuvering target consisted of arbitrarily reducing the target speed input to the director and altering the target angle by a fixed amount (Figure 3).\nFigure 3 illustrates an early method for using straight-line prediction on a turning target. The amount of speed reduction and target angle alteration were chosen for specific standard conditions. Any departure from these conditions during the attack caused errors which were sometimes greater than the total lead angle. It was considered that a much better solution was needed if the resulting director was to be of practical use. The Statistical Research Group (SRG) at Columbia University, operating under contract to the Applied Mathematics Panel, was asked to analyze the theoretical aspects of the problem. The first attempt at a solution was to consider a squadron attack. Taking the turning characteristics of the USS Washington and assuming that all variables were known exactly, and that there was no dispersion in the missile, the SRG calculated the solution.\nThe required number of torpedoes and their lead angles to ensure at least one hit, regardless of what the target does after the launching of the torpedoes. Each attacking plane was contemplated to be assigned a number which designated its position in the squadron, and this number would be one of the variables set into the torpedo director. Each attacking plane then would have a different lead angle depending upon its position in the squadron.\n\nWhile the early work indicated that this method could be used, it was felt after consultation with the Bureau of Ordnance that reliance should not be placed on coordinated attacks of this sort, since there was too much opportunity for material and personnel failures. Instead, it was felt that a director should be constructed that would permit the successful launching of a torpedo against a maneuvering target.\nWith this revised perspective, the SRG undertook a new analysis. The first step was to systematize the procedure for calculating lead angles in attacks on turning ships. Since the equations of motion of the ship were unknown, this lead-angle calculation was done by a semi-empirical method. A procedure was worked out whereby the number of steps was reduced to a minimum and tabulated so comptometer operators could grind out the answers.\n\nThe next step was to identify the most representative types of maneuvering that a target might use. It was agreed with the Bureau of Ordnance that all work would be carried out using the turning characteristics of certain classes of American warships.\nWith the inadequate existing knowledge of the characteristics of enemy ships, this assumption would likely be representative of actual conditions in battle. The number of factors that would be totally or partially unknown in battle far outweighs any errors made due to this assumption. Since the purpose of going into a turn is for the target to do its utmost to avoid being hit, it is reasonable to assume turns would be at essentially maximum rudder angle. Consequently, all calculations were made for a rudder angle of 30 degrees.\n\nTurns were divided into two broad classes: developed and developing.\n\n(TORPEDO DIRECTORS FOR USE AGAINST EVADING TARGETS)\n\nInasmuch as the characteristics of a ship just entering a turn are considerably different from those of a ship well into a turn, all turns were divided into two broad classes \u2014 developed and developing.\nA ship's turn was assumed arbitrarily to be developed if its heading had turned 10 degrees or more from the original direction, and undeveloped otherwise. One assumption was necessary: a ship observed doing 20 knots in a developed turn might have started its turn at a speed of 25 knots or 30 knots, depending on how long it had been turning. There was no way to distinguish between the two cases without knowing in detail the past history of the target motion. Lead angles were calculated on the basis of an equal probability of the target having started its turn at either speed. (Calculations were made on the basis of other probabilities such as 3/4 and 1/4 or 2/3 and 1/3 instead of 1/2 and 1/2. The results were found)\nHaving decided on the above assumptions and procedures, the SRG computed a series of tables of lead angles for various attack conditions and target speeds, for all target angles, and for three classes of ships: a battleship of the Washington class, a carrier of the Yorktown class, and a light cruiser of the Philadelphia class. These lead angles were calculated to give the highest probability of hitting for the given conditions. With these tables, it was possible to begin the work of mechanization.\n\nThe problem of mechanization was made more difficult by the fact that no formulas existed. It was necessary to devise a mechanization that would fit with sufficient accuracy the tables of data computed by SRG. It was considered more important to have an accurate solution for the case of a developed turn than others.\nFor an undeveloped turn, efforts were concentrated on finding a solution. Many approaches were considered:\n\n1. Build a new mechanism to solve lead angles for curved target paths, abandoning previous development work for torpedo directors in straight-line motions. However, since the final director should also compute lead angles for straight-line motions, it was deemed desirable to use this type of director as a foundation. Work was done on this method, primarily by expanding the lead angle in a Fourier series, but it stopped when it became apparent that the results were not leading to an obviously simple mechanism.\n\n2. Another line of attack was to assume that\nA director existed who could accurately calculate the lead angle for a straight-line course and add corrections for a curved path. This might have worked satisfactorily if sufficient time and personnel had been available to complete the work. However, the third approach showed more promise and was focused on.\n\nThe question was asked: could fictitious values be determined for input variables to a mechanism for a straight-line course so the output lead angle would be correct for a curved target course instead? If this could be done, the resulting torpedo director would consist of a straight-line type computer with an auxiliary computer adding corrections to certain inputs.\ninputs  when  it  was  observed  that  the  target \nwas  actually  turning.  Examination  of  the  tables \nof  data  soon  showed  that  mathematically  speak- \ning it  was  always  possible  to  determine  a fic- \ntitious value  of  target  angle  in  such  a way  that, \nwhen  used  instead  of  the  actual  target  angle  in \na straight-line  type  of  computer,  the  resulting \noutput  would  be  the  correct  lead  angle  for  a \ncurved  course  (Figure  4).  It  was^^  also  found \nthat  it  was  not  possible  under  all  circumstances \nto  find  a fictitious  target  speed  that  would  ac- \ncomplish the  same  results.  However,  an  appro- \npriately chosen  fictitious  speed  together  with  a \nfictitious  target  angle  could  be  used.  (A  special \ncase  of  this  last  method  was  that  described \nabove  as  the  first  attempt  to  produce  a curved- \ntype  fire  director,  that  is,  to  reduce  arbitrarily \nthe  target  speed  by  a fixed  amount  and  alter  the \nCONFIDENTIAL  / \nTorpedo directors for use against evading targets: Computed impact point\n\nFigure 4. Use of fictitious target angle with straight-line computer to give lead angle for turning ships. The target angle is adjusted by a fixed amount. However, in the special case, the results were valid only for one set of input conditions. This development aimed to provide an accurate director for all input conditions. Consequently, work was carried out for the first and third possibilities.\n\nThe early lines of attack involved expansion in Fourier series. Considerable effort was put into bringing the coefficients into tractable forms. However, the results obtained were not simple when sufficient terms were used to achieve what was considered reasonable accuracy. Consequently, this expansion method was abandoned in favor of empirical curve fitting.\nOne accurate solution was obtained using a fictitious target speed and angle. However, building a director for such a solution would result in a complicated mechanism with many problems to solve. No further action was taken on this. The major effort was then focused on finding a suitable mechanism to provide a fictitious target angle for use in a straight-line director. The variables involved were: T = target angle, Vs = target speed, Vt = fixed torpedo speed, R = present range, h = altitude, Va = ground speed of launching plane, S = type of target ship, t' = fictitious target angle as output. (Other variables were eliminated due to assumptions and simplifications made earlier.) It was found that the launching plane's altitude affected the calculation of the fictitious target angle.\nAttitude and ground speed could be combined in a Torpedo Directors for use against evading targets with a single variable, which represented the difference between the horizontal projection of the torpedo in yards and the water travel of that torpedo for a time equal to the time-of-fall. This was labeled A, and was equal to (1/2h * g) {Va-Vt}\n\nTwo empirical formulas were derived using these variables to give a fictitious target angle. The first of these was the sum of arbitrary functions of certain linear combinations of the input parameters, as follows:\n\nwhere x is defined by the equation: x = F1(B) + F2(C) + F3(D) + ...\n\nThe second was the product of an arbitrary function of the sum of some of the variables and an arbitrary function of the sum of the target angle and others of the variables:\n\nwhere Q is defined by the equation: Q = G(E + F(H + I + J))\nand all the F's are empirical functions (not the same as those in the first formula). Both of these could be mechanized fairly simply. Since the second, however, gave appreciably less error in the overall result, it was decided to use this formula as the basis for the final mechanization.\n\nWork was just starting on the actual construction of this director when it was terminated as a result of the end of the war. As stated earlier, efforts were concentrated on an accurate solution for developed turns. It had been hoped to find a simple addition to the mechanism which would give the answers for an undeveloped turn. This has not been carried through to completion. However, it is not felt to be worth while to spend too much time finding a solution or to permit much additional complication to take care of this case. There\nThe pilot faces too many unknown factors and requires excessive guesses, resulting in limited accuracy due to complexity. The director's completion and method of operation would have been as follows:\n\nIn front of the pilot would be an optical system, possibly similar to that of the torpedo director Mark 30, through which the pilot would observe the target and which would lay off the proper lead angle. This lead angle would be received from a remote computer via a servomechanism. Adjacent to the pilot would be control knobs for input variables. Before making the approach, the pilot would set the anticipated ground speed and altitude of attack. He would also adjust the turn knob to indicate a straight-line course.\nOn sighting the target, the pilot would enter his estimate of target speed and the target class. He would then set target angle to align the small model adjacent to the optical system parallel to the actual target. This model would be clutched to a directional gyro so that once set, it would retain its direction in space regardless of the plane's maneuvers, thus always remaining parallel to the target until the target should change course. As soon as it was observed that the target was in a turn rather than on a straight course, the turn control would be set to indicate a clockwise or counterclockwise turn. The pilot would then grasp the target angle rate-knob (which would be mounted concentric with the target angle knob) and adjust it so that the ship model would turn at a rate equal to the target's.\nIf the target's turn was constant, the target angle would continuously change at the right speed and stay set properly, enabling the pilot to focus on last-minute details for getting into the correct position to launch his torpedo. If the director received range automatically from a radar, the pilot could drop the torpedo at any desired time. If the range was set manually, the pilot would set the desired dropping range early in the attack and launch his torpedo when his plane reached that range. As soon as the torpedo was launched, the pilot would turn sufficiently to avoid the target's anti-aircraft fire and get his plane far enough away to escape from the torpedo's blast as it hit.\n\nIf the target's turn was consistent, the target angle would continuously adjust at the right speed, ensuring it remained set correctly. This allowed the pilot to focus on the final details of positioning for launching his torpedo. If the director received the range automatically from radar, the pilot could drop the torpedo at any chosen moment. However, if the range was set manually, the pilot would have established the desired dropping distance prior to the attack and would release his torpedo when his plane reached that range.\n\nImmediately following the launch of the torpedo, the pilot would turn sufficiently to dodge the target's anti-aircraft fire and move far enough away to avoid the blast of the torpedo upon impact.\nThis report provides a summary of the field of aerial gunnery, specifically the part concerning Section 7.2 of NDRC. During World War II, most development work in this field focused on flexible gun systems for bomber defense. Little is said about fixed gun systems in this report, which is not meant to diminish their importance. On the contrary, the success of fighter-bomber aircraft has made the development of adequate fire-control equipment for such planes extremely important, particularly equipment that can be used with various weapons such as guns, rockets, and bombs. The objective of this report is to acquaint.\nThe reader with important aerial gunnery equipment used or under development during World War II and the various problems encountered in its development and evaluation. The best way to achieve this objective would have been to make this report a self-contained text book on aerial gunnery. This was impossible for many reasons, the principal one being lack of time. The method chosen was to give a descriptive account of the problems and the work done and to provide the reader with a carefully selected bibliography. This bibliography contains only a small fraction of the technical reports available on the subject but will be sufficient to provide the interested development engineer with the background on which to build future work. There are two other volumes of the Summary Technical Reports of\nThe NDRC contains material on aerial gunnery. The first is on Military Airborne Radar Systems prepared by the Radiation Laboratory of Massachusetts Institute of Technology, and the other is on Analytical Studies in Aerial Warfare prepared by the Applied Mathematics Panel of NDRC. In addition, there is an excellent summary of work in aerial gunnery done by the Applied Mathematics Group of Columbia University and a bibliography of reports prepared by that group. All of this material should be given careful consideration in any future fire-control work. The contributions of Section 7.2 of NDRC to the field of aerial gunnery consist mainly of coordinating the work of the Navy, Army Air Force, and various civilian organizations, and developing methods and equipment for assessing aerial gunnery.\ngunnery systems. The section took the initiative for the work in both cases. There was a vast array of gunnery equipment under development in the Services and industry, so the section undertook little of this work. The one major equipment gap was in the field of assessment, and the section put its major equipment development effort into correcting this situation. The coordination work in aerial gunnery conducted by the section was a substantial part of its effort in aerial gunnery and was primarily achieved because there was no effective planning and coordinating agency in the Army Air Force for this purpose. The two full-time members of the section primarily concerned with aerial gunnery were the writer, who was a member from September 1941 until he resigned to join the office of the Secretary of War.\nMay 1945. Dr. H. C. Wolfe joined the section in June 1944 and remained until its termination in early 1946. Aerial gunnery work began under the leadership of the section's chairman, Dr. S. H. Caldwell, when the Fire Control Section of NDRC (now Division 7) was first organized in 1940. Despite the increasing pressure of other section responsibilities, Dr. Caldwell continued his able leadership in this work. It should also be noted that although the writer and Dr. Wolfe were the only full-time members of the section dedicated to aerial gunnery, all other section members contributed to the work in varying degrees, and the success of the work would have been much less without their assistance.\n\nThe development work in aerial gunnery was carried out almost entirely by six contractors. Reference is made to their work.\n1. OSRD Contract OEMsr-330; Directive Contractor: The Franklin Institute, Philadelphia, PA. Work: Tracking Studies, Own Speed Gun-sight.\n2. OSRD Contract OEMsr-732; Directive Contractor: University of Texas, Austin, TX. Work: Development and construction of testing machine for flexible gunnery systems and tests on such systems.\n3. OSRD Contract OEMsr-991; Directive Contractor: Jam Handy Organization, Detroit, MI. Work: Development of own speed type of assessor and gunsight.\n4. OSRD Contract OEMsr-992; No directives. Contractor: General Electric Company, Schenectady, NY. Work: Development of improved Central Station Computer.\n5. OSRD Contract OEMsr-1237; Directives.\nContractor: Columbia University, New York, N.Y.\nWork: Development and use of electronic equipment for simulating Airborne Fire Control Systems.\nContractor: Northwestern University, Evanston, Illinois.\nWork: Development of equipment and methods for the assessment of aerial gunnery equipment and the installation and operation of such equipment for the Navy.\nSection 7.2 supervised the work of several other contractors doing work for NDRC under the general direction of other divisions. The most important of these are the General Electric Company, the Sperry Gyroscope Company, and the Fairchild Camera and Instrument Company, all of whom were developing computers or other equipment for airborne central station fire-control systems.\nThe section acted as a consulting group.\nThe Navy and Army Air Force collaborated on airborne fire-control matters, advising members of both Services on special problems. One notable example of this work was the participation of the section in the Joint Army-Navy-NDRC airborne fire-control committee. Established in 1944, the committee aimed to organize and direct the aerial gunnery assessment program of the Army Air Force and coordinate it with a similar one by the Navy, with Section 7.2's assistance. Under Directive AN-5, the section was tasked with leading the committee. The writer was asked to undertake this work and served as its chairman from its inception until its termination at the end of the war. The chairman was effectively assisted in this work by Dr. Saunders MacLane of the Applied Mathematics Panel.\nMathematics Group of Columbia University\nVice-chairman: John B. Russell\n\nChapter 14\nGENERAL SURVEY OF AERIAL GUNNERY\n\nSituation at the Start of World War II\nWhen this country entered the war in December 1941, there was practically no gunnery equipment suitable for aerial battles. Fighter planes had the new .50-caliber machine gun but no suitable fire control systems.\nThe only fighter gun-sight available at that time was the old ring-and-bead sight. This sight was subject to parallax errors due to the motion of the pilot. However, what was more serious was the fact that this sight was only a means for laying off an estimated amount of lead and was of no aid to the pilot in computing the correct amount. The parallax error was eliminated before long by the introduction of a reflector-type sight. This sight produced, by optical means, an illuminated reticle which appeared to be at infinity. This gave the pilot a reticle whose direction and size were independent of the position of his head. It was not until nearly the end of the war that a computing sight was available for the fighter airplane. This was the single-gyro type.\nThe MK Il-d sight, developed by the British, was originally designed for use with flexible guns for bombing defense. However, the greater importance of fighter gunnery led the British to adapt it for fixed-gun fighter airplanes. The Army Air Force was not initially enthusiastic about this sight due to perceived inherent errors. The British defended its use, arguing that it allowed fighter pilots to increase their shooting accuracy several times, despite these errors. The Army Air Force was eventually convinced of this through the efforts of the Navy and Section 7.2 of NDRC, and adopted an American version of it in their own fighter plane, known as the K-14 sight.\n\nDuring the early phases of World War II.\nVery little development was done in this country on a fighter's gunsight. Most development work on gunsights was done on sights intended for flexible gunnery. In the last phase of the war, development work began on a sight intended for fighter gunnery, resulting in the development of the A-1 gunsight, which can be used not only for gunnery but for rocketry and bombing as well. In fact, the developments in the use of fighter-bombers during the war have shown the necessity of using a computing sight in the fighter which can be used for all the attack functions of the fighters.\n\nThe early B-17s had practically no defensive armament. There were no gun turrets; all guns were in a flexible mounting and hand-held. There were no guns in the tail. The only sight used was a ring-and-bead sight.\nThe error of bad parallax was more severe in the use of flexible guns than in fixed guns in a fighter. Additionally, estimating the required lead to hit an attacking fighter was a challenging problem. At the beginning of the war, this country lacked adequate rules for estimating this lead, had no suitably trained gunners, or any adequate means of training them. Experience gained by the British in the European Theater demonstrated the need for a much greater defense of heavy bombers than was available on the B-17 or B-24. Consequently, twin gun turrets were developed for use on both these airplanes, and guns were installed in the tails. Even with these additional guns and improved mounts, only a fixed sight was used. These were optical reflecting sights which eliminated the parallax error by providing an illuminated sight.\nThe reticle was projected to infinity. Gun control was significantly improved in the case of the turret mount through the use of power control. In fact, the added weight and size of the turret mount made it impossible for the gunner to exercise control without the assistance of some kind of power drive.\n\nCONFIDENTIAL\nGENERAL SURVEY OF AERIAL GUNNERY\n\nThe first methods taught and used for estimating lead were of the apparent-speed type. The gunner was expected to determine the relative motion of his target during some estimated interval of time and then set a lead computed from this observation using a rule. Gunnery schools taught this method and gave gunners practice in it largely on ground ranges. Very little time was devoted to practice in the air. A great deal of improvement was needed in this area.\nThe practice on the ground was in the form of skeet shooting. This gave the gunner a fair amount of experience in handling and firing his gun and in estimating the lead required by a moving object fired at from a stationary platform. However, this practice made him lead the target in the direction in which it appeared to be moving through the air. When this was transferred to the situation of an actual aerial combat, it often caused him to lead an attacking enemy fighter in the direction in which the fighter was moving in the air. This lead was in exactly the wrong direction because even though the fighter may have been headed in the same general direction as the bomber being defended, the actual relative motion of the fighter was usually toward the tail of the bomber. The lead should always have been in the opposite direction.\nThe same direction as the relative motion of the target caused this fundamental error, leading to many misses during the early days of the war.\n\nPosition Firing Rule:\n\nThe British were the first to introduce a sound method for estimating the lead required to hit the attacking enemy fighter. A fighter would almost always attack a bomber in such a way that its guns bore on the bomber during a large portion of the attack. This caused the fighter to fly a curved course, approximating what is known as a pursuit course. For such a course, if the fighter's true airspeed and the bomber's true airspeed were known reasonably accurately, the required lead for hitting the fighter would be known and the same for every such attack. Furthermore, the magnitude of that lead would depend, approximately, on these speeds.\nThe only factor determining the fighter's lead angle was its bearing relative to the bomber's line of flight. The direction of this lead was in the fighter's plane of action, which was determined by its position and the bomber's line of flight. This led to the British zone firing method for bomber defense. The U.S. Navy and Army Air Force adopted a similar method, known as position firing. This method was used for the defense of all U.S. Army bombers until a sighting mechanism could be provided. Subsequent tests and analyses showed that the position firing rule, while not particularly accurate, was more accurate than any previously used methods. It was not until almost the end of the war that anything like an adequate gunsight was developed.\nOne improvement in using the position firing rule, introduced before the end of the war, was the implementation of the K-13 sight. This sight was put into all gun positions not equipped with a computing sight. The K-13 sight was a mechanism for calculating the lead required by the position firing rule and indicating it to the gunner automatically. The biggest error in using the position firing rule was the inability of gunners to accurately estimate the enemy fighter's angle off or bearing angle and lay off the corresponding lead. The K-13 sight helped the gunner with this and provided an opportunity for better tracking and estimation of range. However, it was subject to all the errors inherent in the position firing method.\nThe only computing sight for flexible gunnery that saw use during the war was the various forms of the Sperry lead-computing sight. The early models were the K-3 and K-4 sights, used in the upper and lower turrets of the B-17, respectively. This sight computed a lead in terms of range to the target and its relative angular velocity with respect to the bomber. It provided a lead satisfactory for various types of attack. One fundamental disadvantage of the position firing method was that the leads determined by this method were correct only for one type of relative course on the part of the attacking fighter. As soon as the fighter deviated from this course, the leads given by the position firing method were in error by a large amount. The K-3 and K-4 sights\nSights provided leads, primarily based on the relative motion of the target, usable in various situations. They also offered less accuracy-dependent leads than the K-13 sight, due to the actual course flown by the target. Extensive work was conducted during the war on the development of an improved lead-computing sight. The British spearheaded this with the first significant improvement, introducing the single-gyro type, named the MK ll-c, later used as a fighter sight. In this country, most development efforts on sighting systems for flexible guns focused on intricate remote-control systems. The potential benefit of a suitable lead-computing sight for planes like the B-17 or B-24 was not fully appreciated.\nThe British MK II-c was met with surprising lack of interest by the Army Air Force when first demonstrated. It was largely due to Section 7.2 of NDRC that the Army Air Force gave the MK II-c serious consideration. This sight provided the same type of lead computation as the Sperry lead-computing sights, with one important added advantage: it computed lead in terms of the actual angular rate of the target relative to the bomber and was not affected by any angular motion of the bomber. It did not have all the accuracy the Army Air Force desired but would provide a much more accurate means of shooting than previously available. The principal source of inaccuracy for both the Sperry and single-gyro lead-computing sights was the gunner's inability to range on the target.\nThe improved lead-computing sight, developed by Fairchild, was known as the K-8 gunsight. This sight was in production at the end of the war, and a few had been installed and put into use before hostilities ended in the European Theater. The major difference between this sight and others was the use of electrical circuits for computing time of flight and ballistic corrections. It did not use a gyro and was therefore subject to the same type of errors as the Sperry K-3 and K-4. However, work was being done on the development of a gyro for use with this sight.\n\nTurret controls:\n\nThe early turrets, while power-driven, had only very simple hand controls for controlling the gun's pointing. The simplest gun mount, which was the hand-held mount, was not mentioned in the given text.\nThe gunner controlled the gun's position. This means he grasped the rear of the gun and, by his own effort, pointed it in the desired direction. The force required to move the gun and hold it against the wind's force had to be provided by the gunner, making it very difficult to point the gun accurately. Power control made it unnecessary for the gunner to exert a great amount of force in controlling the gun's position. It also made it possible to use a larger and heavier mount, which provided the gunner with a seat that carried him around with the gun. The usual type of control for such turrets was a rate control, where the angular rate of the gun's motion was more or less proportional to the displacement of the control handle. Each manufacturer had its own choice for the rate-control.\nSome turrets were easier to control than others due to constant design variations. This issue made satisfactory tracking difficult with certain turrets. Initially, little was known about the optimal turret control design for effective tracking. Many believed a more complex turret control system, called aided tracking, would significantly enhance the gunner's ability to do accurate tracking. Section 7.2 conducted a tracking study at The Franklin Institute to investigate this situation. The study indicated that aided tracking would greatly improve the accuracy of tracking with power-driven turrets. However, it was impossible to implement this knowledge before the end of the war as new turret controls were under development.\n\nGeneral Survey of Aerial Gunnery.\nPart of the war involved the aided tracking feature in new turrets. An additional refinement to be installed was the stabilization feature, with minimal increase in space or weight. Even with power control of turrets, it was necessary for the gunner to operate controls such that the gun motion followed both the target's relative motion to the bomber and compensated for any angular motion of the bomber itself. This meant that in rough weather or during evasive action, it was difficult for the gunner to do satisfactory tracking. The tracking accuracy obtained under these conditions was so bad that shooting was almost entirely ineffective. By stabilizing a turret, it's possible to automatically eliminate the effects of a bomber's motion.\nThe development of the B-29 brought up a new and difficult problem in bomber defense due to its large size, which required a large number of gun positions and more elaborate arrangements for coordination between them. The problem of lead computation was made much more difficult because of the higher speed of this bomber. The use of locally controlled turrets appeared impractical due to the decision to design the B-29 for high altitude use under pressurized conditions. It was primarily for this reason that a remote-control type of system was chosen for the bomber's gunnery.\n\nTests of experimental turrets under simulated conditions show that the marked improvement in tracking accuracy expected is actually attained. Central station systems.\nThe defense of the B-29 required sighting stations in the pressurized sections of the plane and a number of remotely controlled gun turrets in the unpressurized sections. An elaborate computer was necessary to compute the required kinematic lead, ballistic correction, and correction for parallax due to the large distance between the sighting station and the turret under control.\n\nTwo major developments were carried out to provide an adequate fire-control system for the B-29. One was conducted by the Sperry Gyroscope Company, and the other by the General Electric Company. Before either of these developments was completed, the Army Air Force decided to go into production on the GE system. As a result, the Sperry development was never entirely completed. Work was carried out to the point where a developmental model was produced.\nThe model was completed and put into operation. This model was never tested by the Army Air Force. However, it appeared to have several features that were superior to the GE system put into production and should be reconsidered in any future development work.\n\nThe GE system was finally produced in adequate quantities and saw service in the air war over Japan. While it appears to have done an adequate job under the existing conditions, it was far from a satisfactory system. The sighting station was difficult to control, resulting in rather poor ranging and tracking accuracy. The lead computation suffered from serious time delays and was limited in many ways by the particular design chosen. The computer was large, heavy, and complicated, introducing a rather serious maintenance problem.\n\nThere are many features of this system that are worthy of consideration.\nWhich should be retained, it is probable that at the present time a more useful and more accurate system could be built, which is considerably lighter, much smaller in size, less expensive, and far easier to maintain. A very large amount of time was spent getting the bugs out of the initial GE production and adjusting the system to give satisfactory accuracy.\n\nTraining:\nThroughout the development work during the war, very little attention was paid to the human factor. In all the gunnery systems that saw any use during the war, the ability and skill of the gunner were the predominant factors in determining the overall accuracy.\n\nAssessment:\nIn all the gunnery systems that were used during the war, the ability and skill of the gunner were the primary determinants of overall accuracy.\nLittle information was available to the designer on the effect of the control system design on the gunner's ability to use the equipment. Many designs, such as that of the sighting station on the B-29 system, were adopted and put into production before any information was available on the gunner's ability to use the equipment or the difficulty in training him in its use. It is now recognized that closer cooperation between the training people, psychologists, and the equipment designers would have resulted in the production of equipment which could be used with much greater accuracy. Another difficulty which arose was due to the fact that the units in the Army Air Force responsible for training gunners seldom saw the equipment which the gunner was supposed to use until after it had actually reached an operational theater.\nThe theaters frequently received gunners who had not received adequate training with the equipment they were to operate. This also meant that equipment was often sent to theaters where the time required for adequate training was much too long. An additional difficulty due to this lack of cooperation with training people was their inability to develop and build training equipment in time to start training in the use of this new equipment. Many of these problems were on the way to being solved toward the end of the war. The most important reason for the lack of adequate direction in the development program in aerial gunnery was the non-existence of any adequate method for assessing the performance of such equipment. The first.\nA program for providing assessment facilities was initiated by Section 7.2. This section undertook the development of an intricate testing machine at the University of Texas. This machine was designed to handle a complete local turret system, including the gunner. An artificial target was provided, which could be made to fly any chosen attack course. The simple motion of the gun platform or bomber could be simulated. A means was provided for measuring the accuracy of the final gun position at every point during the attack. Conditions were reproducible, enabling any attack to be duplicated for various systems and with various gunners. This machine offered an accurate way of determining the overall performance accuracy of flexible gunnery systems. While it did not simulate many of the psychological conditions that existed in the air under combat, it did provide an accurate assessment.\nA quick and accurate means of assessing certain systems. After completing the original machine, two additional machines were built. One was installed at Wright Field, and the other at the Naval Air Station, Patuxent River. These machines made it possible to do most assessment work necessary for studying and evaluating experimental and final models of flexible gunnery systems. It is safe to say that if these machines had been available at the beginning of the war, the present state of flexible gunnery would have been far superior to what it is now, and many man-hours of effort and considerable money would have been saved.\n\nA second method of assessment, which was finally developed, could be used in flight testing flexible gunnery equipment. This system was developed under the general.\nThe direction of the airborne fire control committee is now in use at the Army Air Force Proving Ground, Eglin Field, and the Naval Air Station, Patuxent River. The equipment under test is flown and operated under simulated combat conditions with an actual fighter airplane making simulated attacks on the bomber. It provides operating conditions which are much more realistic than any which could be provided on the Texas tester. Most of the data was recorded photographically and later analyzed. Several methods were developed for the analysis of this photographic data, one depending largely on the use of charts, and the other on the use of special machines developed by the Northwestern Technological Institute. A third method of assessment, which reached a high state of development during the war, was that of mathematical analysis. The Applied Mathematics Panel of the National Advisory Committee for Aeronautics made significant contributions to this method.\nGeneral Survey of Aerial Gunnery: Mathematical analyses of production and developmental gunnery systems were conducted by Mathematics Groups at Northwestern and Columbia Universities. These analyses are valuable in predicting errors during a system's design stage and determining sources of these errors, leading to improved designs and calibrations of such equipment. All three methods of assessment should be used in future development of aerial gunnery equipment.\n\n14.8 Radar: Radar played a significant role in winning the war. However, its impact on the success of aerial gunnery was negligible. Early in the war, a great deal of effort was put into developing a completely automatic tracking and ranging radar for heavy bomber defense. A satisfactory system was developed.\nFrom a performance standpoint, however, the use of a complicated, costly, and large automatic system for both determining range and manual tracking in aerial gunnery during the war was never implemented. Later, simpler systems were developed for range determination only, and others for manual tracking in position. The development of this complicated, costly automatic system at the beginning of the war significantly delayed the production of simpler systems that could have been utilized during the war. By the war's end, the simpler systems had been put into production. The entire gunnery radar development program suffered greatly due to the lack of adequate direction from the Army Air Force and poor coordination between the fire-control and radar groups.\n\n9. Planning and Control\n\nNow that the war is over, future development work on aerial gunnery systems should be done.\nWith fewer coordinates and direction than existed during the war, most leadership and initiative in development work came from industry. There was no adequate group within the Air Force that could direct the development of such equipment and provide an integrated program. The Armament Laboratory at Wright Field, which was charged with this responsibility, had neither the number nor the quality of personnel required to provide the necessary direction.\n\nFurthermore, in the early part of the war, one or two individuals in authoritative positions were unable to see the advantages of receiving the cooperation of technically competent civilians. This made it difficult to get the most from the available development facilities and considerably delayed the work of developing new gunnery systems. In fact, it is:\n\n(Note: The text appears to be complete and does not contain any meaningless or unreadable content, nor does it contain any introductions, notes, logistics information, publication information, or other modern editor additions. Therefore, no cleaning is necessary.)\nThe probable lack of more competent direction from the Army Air Force during the development of the GE system may have resulted in a better system and significant savings in time and money. The success of any future development of this kind depends on the Army Air Force's ability to build up and maintain a competent development group capable of planning and directing such a program.\n\nChapter 15\nGENERAL PRINCIPLES\n\nThe accuracy of all fire-control devices depends, to a varying degree, on the course traversed by the target. In the field of aerial gunnery, this is particularly true. Fortunately, the general type of course that an attacking fighter can fly and effectively shoot at a bomber is rather limited. This philosophy has led to the development of a simple gunsight known as a vector or own-speed sight.\n\n*The accuracy of all fire-control devices relies on the target's course to a varying degree, especially in aerial gunnery. The limited types of courses an attacking fighter can fly while effectively shooting at a bomber have led to the development of a simple gunsight called a vector or own-speed sight.*\nThe sight, designed for use against pursuit course attacks, is less dependent on the target's actual course with more complex lead-computing sights and remote-control systems. However, they are still sensitive to the target's course to some extent. As new weapons and attacking fighters emerge, the target's attack course will change, necessitating gunsight design alterations to adapt to these new courses or reduce sensitivity to the target's course type.\n\nTo comprehend how a gunsight is influenced by a target's specific course, it's essential to understand various airplane attacks and their effects.\nThe relative course of the target as viewed from the bomber being defended. During World War II, with few exceptions, fighter airplanes carried fixed guns. These guns were pointed approximately along the line of flight of the fighter airplane. They were elevated above this line of flight by a small amount to allow for the effects of gravity. During an attack, the fighter was flown in such a way that during the most important portion of this attack, which was when the fighter was in effective range of the bomber, the fighter's guns were continually bearing on the bomber. The bomber under attack was normally flying a straight and level course. This was particularly true if the attack was being made while the bomber was in formation or on its bomb run. On such a course, the fighter pilot would adjust his position to maintain a steady aim on the bomber, ensuring maximum damage during the attack. (Note: This may not continue to be true in the future if turreted fighters come into use.)\nA bomber presented a fighter with an easier target if it didn't take evasive action. If a bomber deviated from formation and was alone, it would typically take evasive action when attacked by an enemy fighter. This made it more difficult for the attacking fighter to get hits and often allowed the bomber to escape. Determining the courses of the bomber and attacking fighter during combat was very difficult. In fact, there were no accurate means for observing their relative motion during combat. Observations of an attacking fighter by gunners on the bomber under attack were completely inadequate to provide more than a very rough idea of the attacking fighter's course. Since it was necessary to know something about the attacking fighter's course to effectively defend against it, this was a significant problem.\nThe simplest course for designing a gunsight for a bomber and understanding its accuracy involves studying the operation of such sights under idealized or simplified fighter attack courses. The simplest conceivable course is one in which the attacking fighter flies a straight-line course relative to a bomber flying a straight and level course. Initial analyses of lead-computing sight performance were conducted for this type of straight-line course, though it is very unrealistic, providing only a foundation for understanding sight performance. The most realistic target course is the pure pursuit course, assuming a bomber flying a straight-line course at constant speed.\nThe speed of a fighter is under attack by another fighter flying at constant speed, with its line of flight pointed directly at the bomber at all times. This assumption does not account for the variable speed that always occurs during a fighter attack or the lead the fighter must take to get a hit on the bomber. However, the pure pursuit course approximates an actual fighter attack course sufficiently well, allowing for a fair understanding of the operation of a flexible gunsight.\n\nAn early analysis of the pure pursuit course was made during the war. General equations were derived, fully specifying the relative positions of the bomber and fighter for this situation. Tables were prepared, providing all numerical data of interest on a variety of such situations.\nPure pursuit courses, including the lead required by the relative motion of the attacking fighter for accurate shooting from the bomber. Because it was known that an attacking fighter never actually flew a pure pursuit course, there was always the question as to how good an approximation was being made by assuming this. The lack of any reliable experimental data made it necessary to attempt to answer this question and get more reliable information on the courses actually flown. The two important factors which are not accounted for in the assumption that the fighter flies a pure pursuit course are the effect of the lead which had to be taken by the fighter, and the effect of the aerodynamic properties of the fighter airplane. It was known that the fighter's aerodynamic properties affected its flight path.\nThe line of flight did not coincide with the axis of its guns. The angle between them depended on factors such as the airspeed of the fighter, the curvature of its flight path, the loading of the airplane, and skid. One early attempt to predict the course actually flown by the fighter was for the case where its guns are continually pointing at a bomber in straight-line flight at constant speed. This course is known as an aerodynamic pursuit curve. If, in addition, the fighter flies in such a way that it always maintains the correct lead on the bomber under attack, it is said to be flying an aerodynamic lead pursuit curve. In each case, it is assumed that the fighter is being flown perfectly, although the aerodynamic properties of the fighter airplane are being taken into account. One of the earliest attempts to analyze this was made by [Name], who derived the following equations: (equations provided here).\nTo derive the equations for the aerodynamic lead pursuit curve is described in reference 6. A complete set of equations specifying the aerodynamic pursuit curve has also been derived. The solution of these equations for a simple case, namely an overhead attack, was made by the Applied Mathematics Group at Columbia University. They computed a number of actual courses for American fighters and finally made a fairly complete solution of the aerodynamic lead pursuit course problem. They eventually computed a number of aerodynamic lead pursuit courses and gave the leads which must be taken by a gun on a bomber under attack in order to get hits on a fighter flying such a course. These courses represent the most complete information on pursuit types of attacks which was available at the end of the war.\n\nWhile the Applied Mathematics Groups at Columbia University made these computations.\nBrown University and Columbia University were most active in the analysis of pursuit courses. The Mount Wilson Observatory prepared a set of charts of pure pursuit curves which were very useful. The Douglas Aircraft Company made a very interesting study of pursuit-course attacks on high-speed bombers. They showed that with a high-speed bomber, the regions of attack might be sufficiently reduced, requiring the bomber to defend only in the nose and tail cones. This was brought about by the fact that the types of pursuit attack possible were greatly limited by the effects of the high acceleration produced by the curvature of the attacking fighter's course. The General Electric Company was interested in the types of attack that could be made against the B-29.\nThe Jam Handy Organization analyzed attack courses for two reasons. They produced training films for the Navy and Army and aimed for realistic representations. Additionally, they were developing a vector or own-speed type of gunsight. Results from some analyses are in reference 14. The Jam Handy Organization conducted a flight experiment with the Navy to measure actual attack courses. Course data from this experiment was not very accurate, but Ballistic Lead and Time-of-Flight compared favorably with analytically computed data. During the latter part of the war, both the Army Air Force Proving Ground Command at Eglin Field and the Naval Air Station conducted analyses.\nPatuxent River obtained a large amount of data on courses actually flown by attacking fighters. These data were obtained under excellently controlled conditions and with rather elaborate test equipment. They are also the most accurate information on courses actually flown available at the end of the war. Some discussion of the method used will be described later.\n\nAs mentioned, one reason for desiring to know the actual course flown by an attacking fighter is to determine the various factors of design in a flexible gunsight to be used to shoot down the fighter and to analyze the accuracy of this shooting. Another reason is to investigate the various regions of possible attack by a fighter and thereby determine the regions in which a bomber is most likely to be under attack.\n\nReference 16 gives\nSummary of the problem's status at war's end:\n\n1. Ballistic lead and time-of-flight: When shooting at a stationary target from a stationary gun, the gun is not pointed directly at the target but above it to compensate for the bullet's drop due to gravity. For moving targets, the gun must be pointed ahead to account for the target's motion during the bullet's travel time, referred to as the time-of-flight. This time depends on the bullet's initial velocity, distance to the target, and air resistance. The deviation between the actual bullet direction:\n\n1. Ballistic lead: The practice of aiming ahead of a moving target to account for the time it takes for the bullet to reach the target. This is necessary because when shooting at a stationary target, the gun is not pointed directly at the target but above it to compensate for the bullet's drop due to gravity. When the target is moving, the gun must be pointed ahead of the target to allow for the target's motion during the bullet's travel time, which is referred to as the time-of-flight.\n\n2. Time-of-flight: The period of time it takes for a bullet to travel from the gun to the target. This time depends on the bullet's initial velocity, the distance to the target, and the air resistance it encounters. The longer the distance and the slower the bullet's initial velocity, the greater the time-of-flight and the more the bullet will be affected by air resistance, causing it to deviate from its intended path. To hit a moving target, the shooter must aim ahead of it by an amount equal to the target's speed multiplied by the time-of-flight. This adjustment is known as \"ballistic lead.\"\nfire  and  the  line  of  sight  to  the  target  at  the \ninstant  of  fire,  which  is  required  by  the  motion \nof  the  target  during  the  time-of-flight,  is  called \nthe  kinematic  lead.  The  elevation  of  the  gun \nrequired  in  the  simple  example  cited,  which  is \nnecessary  to  compensate  for  the  fall  of  the \nbullet  due  to  gravity,  is  called  the  ballistic  lead. \nWhen  firing  from  a gun  which  is  on  a rapidly \nmoving  platform,  such  as  an  airplane,  an  ad- \nditional ballistic  effect  becomes  very  important. \nThis  is  the  effect  of  the  relative  wind  caused  by \nthe  rapid  motion  of  the  airplane.  This  relative \nwind  causes  the  apparent  trajectory  of  the \nbullet  to  be  curved,  and  must  be  compensated \nfor  in  order  to  obtain  a hit  on  the  target.  This \nwindage  effect  is  a far  more  important  ballistic \nlead  or  correction  than  that  due  to  gravity.  In \norder  to  compensate  for  this  and  to  determine \nThe correct amount of kinematic lead, the effect of this relative wind, and the time-of-flight of the bullet must be known accurately under a wide variety of conditions. The extreme difficulty of carrying out experiments in the air under conditions of flight makes it almost impossible to measure these effects accurately. As a result, the best information available is obtained from analyses. The Ballistic Research Laboratory at Aberdeen has done a tremendous amount of work in analyzing the motion of a bullet fired from a moving airplane. This work has led to the development of methods for computing the trajectories of a wide variety of bullets fired from a moving airplane. Such information has to be incorporated in the design of any sight for use in a moving airplane. An improved method for computing these trajectories was developed at the Ballistic Research Laboratory.\nThe General Electric Company. Tables of ballistic lead and time-of-flight are available on all common bullets from either the Ballistic Research Laboratory or the Armament Laboratory at Wright Field. For the design of gunsights or the analysis of their performance, it is desirable to express the information contained in the ballistic tables by some form of an equation. This was done by the Applied Mathematics Group at Columbia and also at the Laredo Army Air Field. These formulas were found to be extremely useful and gave the time-of-flight and the ballistic lead with exceptional accuracy.\n\nAlthough all numerical information pertaining to the trajectories of bullets fired from airplanes has been derived analytically, the Ballistic Research Laboratory finally was able to carry out an experiment in which certain data were obtained.\nTrajectories were measured for comparison with corresponding computed trajectories in this experiment. The experiment served to check the analytical work and emphasize the difficulty of obtaining such information experimentally. The experiment involved firing from a moving airplane at a water target, sufficient for experimentally checking the analytical work but not a measurement of an actual trajectory under normal combat conditions.\n\nFor any specific course followed by an attacking fighter, the true lead must be determined by the defending bomber to obtain a hit. This lead can be computed using the known type of ammunition and target course.\nThe future time-of-flight refers to the time it takes for the bullet to travel from the instant of firing to the point where the target will be upon being struck. If a specific point on a target's course is taken as the future position or collision point, it's possible to work backwards in time and determine from what point the bullet must have been fired to reach this future target position. This process requires the target's course relative to the bomber and the bomber flying in a straight-line course at a constant speed. Ballistic tables provide the time-of-flight for the bullet's particular range between the bomber and the future position of the target, as well as the necessary ballistic lead for various conditions.\nThe separation between the future position of the target and its position relative to the bomber at an instant of time earlier, determined by the time-of-flight, is the desired kinematic lead. The accuracy of this method for determining true lead is limited only by the accuracy of the information available on the bullet's ballistics and the actual target course. It can be applied to cases where an assumed target course has been computed, such as pure pursuit courses, or where the target course has been determined experimentally. This method has been used extensively at the Army Air Force Proving Ground Command at Eglin Field and at the Naval Air Station at Patuxent River for determining the true leads corresponding to the various simulated fighter attacks in the flight testing of flexible gunnery equipment. In analytical work where the equations of motion are involved.\nThe target course is known in mathematical form. It is often possible to derive an equation for the true lead. One such formula for the case of a pursuit course is given in reference 24. More complete and general formulas were worked out by the Applied Mathematics Group at Columbia University. This report provides the most complete analysis available on the general problem of determining true leads. The more difficult problem of determining true lead when the bomber is taking evasive action was studied by the Applied Mathematics Group at Columbia University and the Applied Mathematics Group of Northwestern University. Until the end of the war, no attempts had been made to compute true leads in the case where the bomber was taking evasive action. However, a great deal of work had been done in computing true leads for pursuit courses.\nType of attack involves bombers flying in a straight line at constant speed. References 27, 28, and 10 provide tables with this information, also available in tests at the Army Air Force Proving Ground Command at Eglin Field and the Naval Air Station at Patuxent River.\n\nPrinciples of LEAD computation:\n\nA number of basic principles have been used in the mechanisms for computing lead in an actual gunsight. In general, ballistic lead and kinematic lead are computed separately in two different parts of the gunsight and then combined to give the total lead. In all sights, some approximation is made to the true lead to simplify the mechanism since sufficient data are not known from which the true lead may be determined.\n\nIn the simplest case, that of the fixed gunsight,\nThe only information used for the target course is its bearing angle in the plane of action relative to the flight path of the bomber. The lead the gunner is expected to use, and which is expressed by the firing rules, is based on the assumption that the fighter is flying a pursuit course. It is also assumed that the only requirement for obtaining a hit on the target is to give the bullet a velocity directed toward the fighter in the air at the instant of firing. Certain corrections are made for the curvature of the fighter's path and the aerodynamic characteristics of the airplane, which will be discussed in more detail in Section 16.2.\n\nTo mechanize the position firing rule and thereby produce an own-speed sight, it is necessary to build a mechanism which will provide:\n\n(Note: The text appears to be clear and readable, with no significant OCR errors or meaningless content. Therefore, no cleaning is necessary.)\nProduce the vector sum of a vector representing the velocity of the bomber airplane and a vector representing the velocity of the bullet relative to that airplane. The sum of these two vector velocities is a third vector whose direction gives the initial direction of the bullet relative to the air mass. This has been accomplished in two ways. The first way is by means of linkages arranged to form a mechanical model of the three vectors in question. The second way is to derive the equation for the required deflection and approximate the solution of these equations by means of a set of cams. In such a sight, the output is a combination of both the kinematic and ballistic leads, although only to a first approximation. In more complicated gun-sights, which are of the lead by time-of-flight type, the kinematic and ballistic leads are computed separately.\nThe ballistic lead is computed using a set of cams. The cam position is determined by the gun's position relative to the bomber airplane and certain hand-set inputs, allowing for the bomber's speed, altitude, etc. Some cams are one-dimensional, meaning the output represents a function of a single input variable. These cams are commonly seen in ordinary mechanisms. They may be a plate of irregular shape, which, as it rotates, moves a follower on its edge. A variation of this plate-type cam is where the follower is moved radially along the side of the plate in a slot. A second variation is where the cam takes the form of a cylinder, in which a follower is moved along the cam axially by means of a slot in the surface of the cylinder. This type of cam is usually described as a cylindrical cam.\nA cylindrical cam, in contrast to the two previous types, is referred to as such. In all three cases, the important variable is represented by the rotation of the plate or cylinder, and the output is represented by the linear displacement of the follower. Where the output function depends upon two or more variables, several one-dimensional cams may be cascaded, or one or more two-dimensional cams used. A two-dimensional cam is represented by an irregular surface which can be rotated and also moved axially. As these two motions take place, a follower bearing on the surface is caused to move linearly, depending on the distance of the surface from the axis of the cam to the point of contact.\n\nAn electrical method analogous to these mechanical cam systems has also been used. This consists of electrical potentiometers.\nThe output voltage is determined by the position of a contact in a potentiometer, which is designed to provide the desired functional relation between output voltage and input rotation. Analogous to a one-dimensional mechanical cam, cascade combinations of these potentiometers allow for multiplying functions of two variables, as the output of one potentiometer supplies the input voltage for a second one. The electrical type of cam or potentiometer offers advantages of small size, simplicity of construction, and low cost, enabling an electrical computing device to contain many more of these electrical cams than a mechanical computer.\n\nA third method of computing a function of two variables involve:\n\n1. The input voltage is applied to a network of resistors, each having a different resistance value.\n2. The output voltage is taken across a specific resistor, which depends on the input voltage and the desired function.\n3. By selecting appropriate resistor values, various functions can be computed.\n\nThis method, known as voltage division, offers the advantage of simplicity and accuracy, making it widely used in analog computing applications.\nOne or more variables are controlled by mechanical linkages in a gunsight. This method was not used in flexible gunsights but was used to some extent in other computing systems. It shows considerable promise but has not been exploited to a great extent.\n\nIn general, the ballistic computer part of a gunsight was designed to provide an output approximating the ballistic data tabulated in the ballistic table. In one case, a ballistic computer was built involving a combination of linkages and gears that mechanized the first-order approximations of the ballistic deflections of the bullet. This was used in the GE computer for the B-29 and is discussed in more detail later. All of these various ballistic computers were used to compute the ballistic deflections.\ndeflections  due  to  windage  and  the  time-of-flight \nof  the  bullet  which  was  necessary  for  the  com- \nputation of  the  kinematic  lead. \nThe  usual  method  of  computing  kinematic \nlead  was  to  determine  the  relative  angular  rate \nof  the  target  by  the  best  method  possible,  and \nmultiply  it  by  the  approximate  time-of-flight. \nThe  accuracy  of  this  method  was  the  subject  of \nconsiderable  analysis,  and  has  been  discussed \nin  a number  of  reports  which  will  be  referred \nto  in  connection  with  the  description  of  various \ntypes  of  lead-computing  sights.  The  principal \ncomponent  for  computing  a kinematic  lead  by \nthis  method  was  some  device  for  measuring  the \napparent  angular  rate  of  the  target.  The  first \nform  of  mechanism  for  carrying  out  this  an- \ngular measurement  and  for  multiplying  by  time- \nof-flight  was  a mechanical  variable-speed \ndrive.2^  It  was  first  used  for  this  purpose  in \nSperry antiaircraft directors and the early Sperry airborne lead computing sight. The primary objection to the variable-speed drive as a means for computing kinematic lead is that it is driven by the position of the gun relative to the bomber airplane and, therefore, measures an angular rate relative to that airplane. This means that any angular motion of the bomber airplane introduces an error into the determination of the relative angular motion of the target. An analogous electrical method has been used by Fairchild. In this case, the angular velocity of the gun relative to the bomber is determined by means of an electrical tachometer whose field is excited by a voltage which is approximately proportional to the time-of-flight setting.\n\nTo avoid the error in such systems (introduced by any angular motion of the bomber airplane), Fairchild employed an analogous electrical method. The angular velocity of the gun relative to the bomber is determined by an electrical tachometer, whose field is excited by a voltage proportional to the time-of-flight setting.\nA bomber employs various gyroscopic methods for measuring angular rate, with the simplest being a rate gyro similar to those used in aircraft rate-of-turn instruments. This rate gyro can rotate only about one axis perpendicular to its axis of spin, with a spring attached to prevent rotation about this axis. If the spin axis of the gyro is forced to rotate about a third axis perpendicular to both the spin axis and the allowable rotation axis, it will be displaced against the spring by an amount proportional to this forced rotation of the spin axis. As a constrained-rate gyro can indicate rotation about only one axis, two such gyros are required to measure the two components of any two-dimensional rotation.\nA second method of using a gyro to determine angular rate is by means of a free gyro. This gyro is mounted in gimbals so that mechanically it is free to move in any direction. Torques are applied to it in one of several ways to cause it to precess, so that its spin axis will continually point at the object in space whose relative angular rate is to be determined. These precessional torques may be applied by springs acting on the gimbal supporting the gyro, by an electric torque motor acting on these gimbals, or by means of electric coils actually mounted on the gyro frame. One very ingenious method for using a free gyro was developed by the British and was used in the only gyro sight to see service during this war. In this case, the gyro axis supported a copper dome which rotated with the spin rotation of the gyro.\nand was subjected to a magnetic field produced by a magnet mounted on the housing supporting the gyro gimbal. The eddy current set up in the gyro dome due to its rotation produced the desired precessional torques. A discussion of the principle involved in the use of both the rate gyro and the free gyro in a computing gunsight will be found in a report. The equations of operation of such a gyro sight for a simple case are discussed in references 31 and 32. More detailed analysis of the operation of gyro sights will be found in the discussion of the various types of sights, which appears in a later section. One problem which arises in the analysis and understanding of practically all gunsights is that of axis conversion. For various practical reasons, it is often necessary to compute necessary lead in terms of two components.\nThis is true not only for the computation of ballistic lead but also for kinematic lead. It is necessary because in most cases, the indication of computed lead is given by the rotation of an optical line of sight about a pair of axes. In the early days of war, a number of mistakes were made in the analysis and development of gunsights due to this problem not being fully appreciated. What is even more confusing is the fact that in many gunsights, the axes with respect to which the two components of the ballistic lead are computed are different than the two axes with respect to which the two components of the kinematic lead are computed. This axis conversion problem is much more difficult in remote-control systems than it is for those in locally controlled turrets.\n\nConfidential\nChapter 16\n\nPrinciples of Lead Computation\nThe problem of lead computation is not only crucial for ballistic calculations but also for kinematic ones. This is because the indication of computed lead is given by the rotation of an optical line of sight around a pair of axes. In the early stages of war, numerous errors were made in the analysis and development of gunsights due to this issue not being fully understood. What makes things even more complicated is that in many gunsights, the axes with respect to which the two components of ballistic lead are computed differ from the axes with respect to which the two components of kinematic lead are computed. This axis conversion problem is significantly more challenging in remote-controlled systems than in locally controlled turrets.\nAt the beginning of World War II, the most common sight in flexible gunnery was the fixed sight. The earliest form of this was the iron ring-and-head sight, which was later replaced by an optical reflector type sight that produced an illuminated reticle projected to infinity. This eliminated the parallax error which was so annoying with the ring-and-bead type of sight. The standard model of the Army reflector-type fixed sight was known as the N-8, and a similar sight used by the Navy was known as the Mark 9. The major problem in developing these optical sights was to eliminate the difficulties due to airplane vibration and to provide a sufficiently large field of view. The early rules for laying off lead by means of these sights were the apparent speed rules. To apply these rules, it was necessary to track the target's apparent speed and adjust the sight accordingly.\nThe target should be held long enough to get the reticle centered and then the gun and sight kept stationary for a predetermined length of time. This time was measured by saying some key word, such as \"elephant,\" which was supposed to take a length of time equal to the time of flight of the bullet at the opening range. The apparent relative motion of the target during this time interval was observed, and the gun and sight were moved so as to point ahead of the target by an amount equal to this apparent motion.\n\nThere were two serious difficulties with this system. The first is that it was impossible for a gunner to carry out these operations exactly. The second is that even if these rules were exactly followed, the leads computed by their application were seriously in error. This was realized by the Army Air Forces.\nIn the early days of the war, the Navy put significant effort into determining errors in navigation rules, particularly those used for apparent-speed method and position firing. An intricate analytical study of these rules and the proposed position firing rule was conducted by the Applied Mathematics Group at Columbia. It was demonstrated that even if the rules for the apparent-speed method were followed precisely, the resulting errors in leads could reach up to 25 to 50 mils in certain instances. The position firing rule, which was eventually adopted and employed during most of the war on B-17 and B-24 aircraft, was found to be reasonably satisfactory. Errors ranged as high as 15 mils and had an average of approximately 8 to 10 mils. This could be considered satisfactory given the other complications encountered in aiming the gun and estimating the opening range.\nThe rule for gunner lead applies only the target's position angle, yielding satisfactory results under assumed conditions. If the target attack course materially differs, significant error is introduced. The required lead varies with ammunition type, airplane altitude, and indicated airspeed. During the war, this rule was continually studied and revised to accommodate changing conditions. For instance, the position firing rule was adapted as an emergency sighting system for the B-29, and the rule for use on the A-26 was revised. Despite its simplicity, implementing this rule involves complexity.\nThe gunner encountered several difficulties. He needed to estimate the range to the attacking fighter to open fire at the optimal maximum range. Experience indicated that this estimation was typically off by a factor of about two, so he opened fire at approximately twice the intended opening range. Another challenge was the gunner's inability to accurately estimate the target's bearing angle and plane of action. In the waist position, the gunner was significantly aided in estimating the target's bearing angle by the relative position of the gun with respect to the waist hatch and the wing and tail surfaces. However, in the tail position, no part of the aircraft was visible to help estimate the target's bearing angle.\nThis was not too serious since the required leads were relatively small. In a turret, estimating the target bearing angle is difficult. This difficulty in estimating a target bearing angle led many people to propose mechanisms for aiding the gunner. In general, these took the form of own-speed sights, which mechanized the position firing rule and presented the gunner with information on the required lead. Towards the end of the war, enemy fighters were making attacks that were somewhat different than pursuit type attacks. As a result, the position firing rule being used was considerably in error. This also applies to the own-speed type of sights, which will be discussed shortly. Interest in apparent-speed rules was revived. A revised evaluation of these methods was made and is concluded.\nDuring World War II, a great number of own-speed sights were proposed. The idea goes back to World War I, during which the so-called wind vane sight was proposed. Own-speed sights proposed during this war were of two general types. The first consisted of a linkage type mechanism, generally containing gear drives, which was a geometrical model of the various vector velocities which determined the required lead. The second type made use of cams for mechanizing the equations giving the required lead in terms of two components. Reference 38 contains a good summary of the various types of own-speed sights proposed.\n\nThe first own-speed sights seriously considered were the K-10 and K-11, which were developed by Sperry. These were designed for tail and nose positions, respectively. They used three-dimensional cams rather than linkages.\nThe coverage of own-speed sights was limited, preventing their use anywhere but in nose and tail positions. These sights were also excessively heavy, large, and expensive. Descriptions of the K-10 and K-11 sights and their underlying theory can be found in three Sperry reports. Due to the simplicity of own-speed sights and the lack of a satisfactory lead-computing sight, significant effort was made to develop a suitable own-speed sight and get it into use as soon as possible. Section 7.2 initiated such development at The Franklin Institute in Philadelphia early in the war, stimulating interest from other development organizations and the Army Air Force in similar efforts.\nThe Jam Handy Organization utilized the own-speed principle for assessor and sight development. The initial goal was to create an own-speed assessor, but it also resulted in the development of an own-speed sight. A description of the Jam Handy own-speed sight has been prepared. The Jam Handy Organization (under a contract with the AAF) also developed a similar sight for the tail position of the B-25. A report on this development has been made. One example of the wide range of sights proposed using the own-speed principle is the proposed modification of the standard B-17 tail sight. Due to the significant impact of the attack fighter's actual course on the accuracy of the own-speed sight, as well as position firing rules, considerable effort was devoted to adapting the own-speed sight.\nTo meet different conditions. If the attacking fighter made the assumed type of attack, it was only necessary for the flexible gunner to keep the reticle of his sight squarely on the target. The main indication that the fighter was flying a course different from the pursuit type assumed was the apparent attitude of the attacking fighter. The most important situation in which this condition arose was when an attempt was being made to provide support fire for protection of another bomber in the formation. In order to provide satisfactory support fire, using the own-speed sight, it was necessary for a gunner not only to apply rules which met this situation but to estimate the general aspect angles of attacking fighters.\n\nConfidential\nLocal Control Systems\n\nThis situation was studied in some detail toward the end of the war, and the various.\nDiscussed are the proposed rules and their evaluation in reports 46, 47, 48, and 49. With numerous proposals for an own-speed type of sight, it became necessary to evaluate them and select one or two best suited for the Air Force's needs. The chosen sight was the Sperry K-13, which utilized a linkage mechanism. This sight was selected not because it was the most accurate, but because its accuracy was adequate and it could be deployed in operational theaters most rapidly. Details of this sight can be found in the Sperry instruction manual. An error analysis of this sight under designed conditions is in reference 51. The theory demonstrates that the own-speed type sight will accurately predict the required adjustments.\nWhen a bomber flies a straight course at constant speed, the attacking fighter follows a pure pursuit course with no bullet slowdown. In this scenario, the bomber's airspeed is the sole input to the sight. However, due to the fighter's aerodynamic properties and its lead on the bomber, using the full value of the bomber's airspeed as the airspeed input to the sight results in erroneous outcomes. This error can be corrected by using an appropriate percentage of the bomber's airspeed as the airspeed input. Various attempts were made to evaluate this situation and determine the optimal method for using the own-speed sight. Additionally, there is another factor that could cause significant lead error.\nThe own-speed sight's computation is influenced by several factors during an attack. One such factor is that the attacking fighter's course doesn't lie in a constant plane of action relative to the bomber. For high side attacks, the fighter's instantaneous velocity tends to carry it below the bomber's line of flight. The pilot must continuously correct this, causing the instantaneous plane of action to decrease in elevation. This results in an error in the lead produced by the own-speed sight, causing it to shoot too high. This error is partially compensated for by the bullet's gravity drop, which the own-speed sight doesn't account for. Another important effect is due to the attack angle of the fighter.\nThe assumed velocity of a bomber in using an own-speed sight is assumed to be known. The direction of this velocity in space is not normally along the thrust axis of the bomber. The attack angle, which is the angle between the actual velocity of the bomber and its thrust axis, varies with the airspeed and loading of the bomber. An average value of this attack angle is used in harmonizing various own-speed sights with the guns.\n\nLead-computing sights are the usual type in which the kinematic lead is computed by multiplying an appropriate angular rate by a time of flight. They are arranged such that when a target is in sight, the gunner computes the lead angle required to hit the target based on its closing speed and range.\n\nAn attempt was made to take the attack angle into consideration in The Franklin Institute sight and in some Jam Handy developments.\nA measurement of angular rate is made continuously and multiplied by a time of flight setting, derived from a measurement of range to the target. This measurement of range is ordinarily made stadiometrically. The gunner operates the range control of the sight to keep a reticle of varying size constantly bracketing the target. Towards the end of the war, there were several projects whose objective was to introduce radar-determined range into the sight. This will be discussed in more detail in a later section.\n\nOne basic difference between the lead-computing sight and the own-speed sight is the manner in which the reticle moves with respect to the gun. In the own-speed sight, the reticle is coupled to the gun in such a way that it always moves with the gun and gives the gunner very direct aim.\nThe control over its motion. In this sight, the gunner's control of the reticle is very direct, and he would not typically be aware of any reticle motion due to a change in lead. In the case of a lead-computing sight, the reticle is floating. This means that the gun's motion does not cause a direct corresponding motion of the reticle. This is because the lead indicated by the reticle of the lead-computing sight depends not only on the gun position but also on its rate of change of position. This causes the lead-computing sight to be more difficult to track with than an own-speed sight. This difficulty of tracking is one important factor that must be considered in sight design.\n\nThe floating character of the reticle in the lead-computing sight also introduces a problem.\nIn regard to picking up and getting on the target, in general, during preliminary slewing, high angular rates produced will generate an excessive lead which must be removed before the gun is in correct position for firing. The transient response of the sight, which results in the removal of this excessive lead, may last for a time interval approximately equal to the time of flight setting of the sight. It also depends on the design constants of the sight and is inseparably connected with its tracking characteristics. This transient effect may also introduce an error into the lead when firing against a target having angular acceleration. This is because the transient effect is similar to a time lag, and the lead which the sight computes is actually based on old data. An analysis of the lead-computing sight and its various effects is given in reference.\nReference 55 discusses the effects of computing lead in terms of two components instead of directly in the plane of action of the target. The only lead-computing sights for flexible gunnery to see extensive use in this war were the Sperry K-3 and K-4 sights. These sights were installed in the upper and lower turrets of the B-17. They use a mechanical type of rate-measuring device and multiplier. Severe approximations were made in designing the time of flight and the ballistic lead computer, resulting in these sights being not too accurate. However, they gave considerably better performance than could be obtained with either position firing or the use of an own-speed sight. The sights were severely criticized by many people in the field, and it was even suggested that they be removed.\nDuring the war, rules for situational firing and fixed sights were proposed instead. Fortunately, this wasn't implemented, and it was later proven that the K-3 and K-4 sights were more accurate than many assumed. Descriptions and analyses of these sights, including their errors, can be found in two Sperry reports. Towards the end of the war, an improved version of these sights, known as the K-12, was developed by Sperry. The K-12 sight offers slightly better computation of time-of-flight and ballistic lead. The inherent errors in the computed kinematic lead of such lead-computing sights can only be minimized through the appropriate choice of design constants and the proper calibration of the time-of-flight setting. The errors of the K-3 and K-12 sights have been subject to detailed analysis.\nOne of the fundamental sources of error in these sights is the fact that the angular rate of the target is measured with respect to the bomber. This means that an incorrect angular rate will be determined if the bomber has any angular motion of its own. This was the source of one of the most severe criticisms of the Sperry lead-computing sights. This would be particularly serious in a situation where it was necessary to use the sights while the bomber was taking evasive action. Fortunate ly, this seldom occurred. The only important case was when an isolated bomber was being attacked and evasive action was being used as a means of protection. In the European Theater, this occurred when a single bomber had to drop out of formation for any reason. In this case, the bomber was generally under attack by several enemy fighters.\nbeen  difficult  to  defend  it  even  with  most  ideal \nsighting  systems. \nThe  first  gyro  type  of  lead-computing  sight \nto  see  extensive  use  was  not  for  plane-to-plane \nfire  but  was  for  antiaircraft  fire.  This  con- \ntained two  rate-measuring  gyros  which  were \nused  to  compute  the  two  components  of  kine- \nmatic lead.  The  sight  was  used  extensively  with \n20-mm  and  40-mm  antiaircraft  guns  on  ship- \nboard. The  sight  was  built  by  Sperry  and  was \nknown  as  the  Mark  14  gunsight.  A rather  de- \ntailed investigation  of  the  theory  and  errors  of \nLOCAL  CONTROL  SYSTEMS \nthis  sight  has  been  made.\u00ae\u00ae  Even  though  this \nsight  'was  designed  and  used  for  antiaircraft \nfire,  its  operation  and  its  errors  are  similar  to \nthose  that  would  be  found  in  using  such  a \nsight  for  plane-to-plane  fire.  One  error  which \nis  inherent  in  any  lead-computing  sight  which \ndetermines  lead  in  terms  of  two  components  is \nThe most successful gyro type for aerial gunnery was the single-gyro sight developed by the British. Originally designed for flexible gunnery in bomber protection, it saw extensive use as a fighter gun sight instead. Known as the Mark 18 gunsight in the Navy and the K-15 in the Army, a summary of its use in this country for both fixed and flexible gunnery is given in reference 62.\n\nWhen the single-gyro sight was first introduced.\nThe AAF showed little interest in the sight brought to this country by the British. It was through the efforts of Section 7.2 of NDRC that they finally gave it serious thought, leading to its adoption for use in fixed gun fighters. In contrast, the Navy was very interested in the sight from the beginning and played a significant role in getting it into production, although the Army eventually took over most of the production. Much of the work done by the Navy to re-design the sight for American use and get it into production was carried out by the Lucas-Harold Corporation. Their reports provide an analysis of the sight and many design details. Due to the importance of the single-gyro type of sight, a great deal of effort was put into analyzing it and attempting to improve it.\nTwo detailed studies of the gyro operation and its supporting Hook's joint were made. A study of the general equations of the sight can be found in references 67 and 70. A detailed analysis of the optical systems of the Mark 18 and K-15 can be found in reference 69. An analysis of the errors of the Mark 18 sight when used against pure pursuit courses has also been made.\n\nThe time-lag error, which is inherent in any lead-computing sight, can be minimized by a proper choice of the time-of-flight setting. If the time-of-flight setting used is the same as the actual time-of-flight to the present position of the target, the errors in the kinematic lead will be smallest when the sight is used against a straight-line target course. However, in plane-to-plane fire, the sight will normally be used against a pursuit-type target.\nIn this case, a 10% error occurs in kinematic lead if the time-of-flight setting is taken as the time-to-flight to the target's present position. To compensate, the time-of-flight setting is typically reduced by about 10%. This minimizes errors in kinematic lead for pursuit attack courses but gives an error of the same magnitude for straight-line courses. All sight systems are sensitive to attack course types. The own-speed sight is very sensitive, while the lead-computing sight is less so. In general, it's possible to calibrate the sight systems.\nThe time-of-flight setting of a lead-computing sight is determined to minimize kinematic lead errors for a specific type of attack. The Franklin Institute conducted an extensive study on the accuracy and ease of tracking of various lead-computing sights. Several assessment programs evaluated these sights, with analytical work on their errors previously referred to. The first experimental determination of errors in the Mark 18 single-gyro type of sight was made at the University of Texas on the testing machine developed under Section 7.2. However, the testing program at the University of Texas on the Mark 18 was not carried very far due to the importance of obtaining performance data on B-29 equipment.\nThe confidential Lead Computing Sights testing obtained sufficient information to gauge the overall performance of the Mark 18 sight. However, it's challenging to compare its performance with other types of sights due to the test methodology. Psychological conditions under actual flying conditions were not considered. A test comparing the Mark 18 with the K-3 and K-13, using position firing rule, was conducted at Eglin Field. This was the first test utilizing the camera assessment method, developed with Section 7.2's assistance. A comprehensive description of this test and its results are detailed in an Eglin Field report.\n\nAn early analysis of the Mark 18 sight errors against a pure pursuit course is given.\nA summary of assessments made of various types of gunsights available during the latter part of the war is presented below. This summary graphically displays the available knowledge on the magnitudes of errors on these various systems near the end of the war. A more detailed summary of the results of these assessment programs was also made.\n\nAt the end of the war, an electrical type of lead-computing sight became available in the European Theater. This was the K-8 sight developed by Fairchild. It measured angular rates by means of electrical tachometers mounted on the gun axes. In principle, it was similar to the Sperry sights. However, the time-of-flight and ballistic-lead computations were very accurate and, in fact, were more accurate than the accuracy of the input data warranted.\nThis sight was the basis for a newer development which resulted in the S-3 and S-4 sights. These sights measured angular rates by means of two rate gyros and had stabilized lines of sight. The stabilization is of the rate type which means that the angular rate of motion of the line of sight is made to be independent of the motion of the supporting airplane and depends only on the position of the control handles. In this system, the kinematic lead-computation and the stabilization feature are linked together so that the lead computation and turret control are no longer independent as they are in previous systems. This has made the overall analysis of the errors in lead computation much more complex.\n\nWhile some analysis has been done on the performance of the S-3 system, it is not nearly as complete as that for the previous systems.\nThe analysis of the S-4 sight, which is similar except it is for a different caliber gun, has also been made. A somewhat different stabilized system has been developed by Sperry, known as the S-8 sight. It uses a single free gyro and provides position stabilization of the line of sight. This development is not yet complete but appears to be a notable advance in flexible gunnery fire-control systems. There is no question that the most promising advances in the development of gunsights for flexible gunnery will be in the direction of stabilized systems using gyros, in which the turret control and lead-computer are designed as part of the same system.\n\nConfidential\nChapter 17\nREMOTE CONTROL SYSTEMS\n17.1 Need for Remote-Control Systems\n\nWith the development of the very heavy type of bomber, it became desirable to provide remote-control systems for the defensive guns.\nConsider flexible gunnery systems of the remote-control type. It is conceivable that such a system could be used to arm a large bomber in much the same way as the Navy uses remote-control systems for its main battery and antiaircraft armament on board ship. Locally controlled turrets offer a certain amount of simplicity over a remotely controlled system but require an operator for each gun position, and as normally used cannot put concentrated fire power under the control of a single gunner. On the other hand, a remote-control system offers a great deal of flexibility and appears to have certain advantages. To date, there has been no adequate comparative evaluation of locally controlled turret systems and remote-controlled turret systems. The factors which favor one or the other system are so varied that the choice has been largely a function of the design of the aircraft.\nThe main impetus during World War II for the development of a remote-control system was for the defense of heavy bombers like the B-29. The predominant factor leading to this choice may be attributed to the requirements of pressurization. Since it is undesirable to pressurize the entire fuselage of a very heavy bomber, it is possible, using a remote-control system, to locate sighting and control stations within the pressurized area and to place turrets in unpressurized portions of the airplane. An adequate locally controlled turret system could be developed in which certain turrets are independently pressurized. Such a scheme has been considered but no great effort has been made to develop it.\n\nBecause of the separation of the turret and control stations, a remote-control system offered advantages in pressurization.\nthe  sighting  station  in  a remote-control  system, \na number  of  problems  arise  which  are  not \npresent  in  the  locally  controlled  turret.  It  is \nnecessary  to  transmit  accurate  position  data \nbetween  various  points  on  the  airplane  and  to \ncompensate  for  the  effect  of  parallax  produced \nby  the  separation  of  the  sighting  station  and  the \nturret.  The  separation  also  increases  the  com- \nplexity of  the  computer  for  determining  the \nnecessary  lead.  This  separation  also  introduces \nrather  serious  problems  in  regard  to  the  main- \ntenance of  alignment  and  harmonization.  On \nvery  large  aircraft,  this  is  seriously  affected  by \nstrains  in  the  airplane  which  are  caused  by \nmany  factors.  On  the  other  hand,  on  new  high- \nspeed bombers  it  is  possible,  using  a remote- \ncontrol  system,  to  locate  gun  turrets  where  it \nwould  be  physically  impossible  to  locate  a \nlocally  controlled  turret.  One  outstanding  ex- \nThe proposed installation of turrets on wing tips has the advantage of allowing for a significant reduction in the size of the exterior portion of the turret. This is important for reducing drag and is particularly important for new high-speed airplanes.\n\nThe development of remote-control systems began before the United States entered the war, with the initiation of the development of a completely automatic radar system for gunlaying. When the first contract for such a system was let, the necessity for a suitable computer was not appreciated. The system consisted of one or more radar sighting stations that pointed one or more remotely controlled gun turrets. It was pointed out by [someone] that:\n\nThe development of remote-control systems began before the United States entered the war, with the initiation of the development of a completely automatic radar system for gunlaying. When the first contract for such a system was let, the necessity for a suitable computer was not appreciated. The system consisted of one or more radar sighting stations that pointed one or more remotely controlled gun turrets.\nSection 7.2 (then Section D-2) stated that for all-round firing, it was absolutely necessary to provide a suitable computer as part of this system to get any firing accuracy at all. The original development for a complete radar gunlaying system, known as AGL, was carried out by the General Electric Company with the cooperation of the Radiation Laboratory at MIT. The system was known as AGL-1. The AGL-1 system was obsolete before it was finished and was never tested. However, it formed the basis for the development of the manually operated remote-control system which was finally used operationally in the B-29's over Japan. In fact, while this AGL-1 system was never produced or used, it made some of the most important contributions to the use of radar in airborne fire-control systems.\nThe general development of computers for such systems. Before long, a number of developments on remote-control systems were under way. Most of these were for the purpose of providing completely automatic radar tracking and ranging and multiple operation of remotely controlled turrets. An early report on these various systems is referenced in 89, which describes all the important remote-control systems under development during World War II, with the exception of a Westinghouse system which was not developed until the latter part of the war. During the early part of the war, there was great interest in developing these completely automatic systems. The concentration of such a great amount of effort on completely automatic fire-control radars for aircraft use resulted in a delay in the simpler radar systems which were eventually found to be of much greater value.\nThe practical use of completely automatic systems decreased significantly, and efforts shifted to simpler fire-control radars, which will be discussed later. The main contribution of this early development was the groundwork it laid for computers in remote-control systems. The only remote-control system used during the war was the General Electric system installed in the B-29 airplane. This system was manually operated and, except for a few installations at the end of the war, made no use of radar. Due to its importance, significant testing and analysis were conducted to determine its performance and improve its accuracy. References 95, 96, and 97 provide a good description.\nThe theory of the GE system's operation was studied due to its insufficient accuracy and numerous unsatisfactory aspects. Modifications for enhancing the GE system were in constant development. The remotely controlled turrets of the GE system were of excellent design and provided excellent service. The data transmission system, which was employed, was highly accurate and contributed negligible error to the overall operation. In fact, the turret and data transmission system design were entirely satisfactory. The produced computer was large and complex and could not be considered entirely satisfactory. It was not the only computer under development by GE but was chosen as the one that promised to be the most capable.\nThe most unsatisfactory component of the General Electric B-29 system was the sighting station. This was a pedestal-type sight operated directly by the gunner without benefit of power controls. It was awkward to handle for ranging and tracking. Extensive training and practice were required in its use, and even then tracking and ranging errors were excessive. In the preproduction model, kinematic lead was computed by means of a free gyro contained in the sight head. This gyro was processed electrically to remain parallel to the optical line of sight. The servo system used for positioning it was ineffective.\nProducing this precision was operated by a set of contacts mounted on the gyro and the sight case. The biggest difficulty resulted from the use of these contacts in the servo systems. Another serious difficulty encountered was instability, which made it impossible to use a single gyro. This could be overcome only by providing two separate gyros at the sighting stations. The sight actually put into production was the two-gyro sight. Another serious difficulty which never was overcome satisfactorily was the sensitivity of the system to the character of the tracking errors.\n\nThis latter difficulty was realized very soon after the first systems were put into operation and steps were taken to develop a more suitable sighting station. The first such improved sighting station resulted in what was known as the improved sighting station I.\nThe free-gyro led computer consisted of an entirely new sighting station with a single free gyro. Minor modifications were required in the computer to adapt the system. The free-gyro computing system, described in detail in reference 98, was given extensive tests and provided substantial accuracy improvement over the standard system. By the war's end, plans were underway to produce this free-gyro system in quantity and eventually replace the standard system. A second improvement was initiated much earlier: the development of a gyro-stabilized sight with power control. This gyro-stabilized sight provided much more accurate lead computation and also offered tracking and ranging controls, a significant improvement over either.\nThe standard system or the free-gyro system. This sight promised to be considerably better than that of the standard B-29 system or the free-gyro sight. However, the development of the gyro-stabilized sight was considerably slower than that of the free-gyro sight. This is largely due to the lack of any strong central planning group within the Air Force which could competently evaluate various proposals for the development of air-borne fire-control equipment and which could decide on which line of endeavor to follow. The gyro-stabilized sight promised to eliminate all serious difficulties encountered with the standard system yet the effort put on its development was exceedingly small. Perhaps if adequate assessment devices had been available earlier in the war, this would have helped to direct GE\u2019s efforts into more fruitful lines.\nAfter the standard B-29 fire-control system was in production and installed in operating airplanes, its operation was still not entirely satisfactory. As a result, a number of studies were made to eliminate major difficulties. The portions of the computer which determine the ballistic lead and the corrections necessary on account of parallax did so with an accuracy that was considerably greater than necessary. In fact, one major criticism of the standard B-29 computer was the poor design balance between the kinematic lead computer and the ballistic lead and parallax computers. The two most important difficulties were the awkwardness of the pedestal sight as a tracking device, which made it very hard to track and range satisfactorily, and the rather large time lag inherent in the computer, which seriously affected accuracy.\nThe computation of the kinematic lead was affected by the computer in the following cases, most seriously in nose attacks. Such attacks were popular with the Japanese, making it even more important to improve the standard B-29 computer's performance. The Applied Mathematics Group at Columbia conducted studies and made recommendations for improving the standard B-29 computer, results of which are given in a series of reports. When the Army Air Force made the decision to freeze development work and produce the current B-29 computer, Section 7.2 contracted with GE to continue the computer development work. The Section believed there was a good possibility of producing a new computer that was considerably superior to the standard computer.\nThe production design for the gyro-stabilized sight was decided upon by GE before completing any developmental computer work or having the opportunity to test and study such a computer. In fact, the development of the gyro-stabilized sight was a direct outcome of this continuing development work under NDRC. The computer GE was developing for Section 7.2 was not quite completed at the time the contract had to be terminated due to the end of the war. However, enough work had been done to indicate that this new computer was considerably superior to the standard B-29 computer. This new computer will undoubtedly be completed by GE under the direction of the Army Air Forces. The most important contribution made through its development was the design of a second new computer, which was considerably smaller and less complex.\nThe standard B-29 fire-control system was first tested by the Army Air Forces Proving Ground Command in Eglin Field. This was the first test in which official recognition was given to the fact that this system was not entirely satisfactory in its operation. The particular test and the conclusions drawn from it are given in a report of the Army Air Forces Board. While this test stimulated considerable effort for the purpose of improving the operation of the standard B-29 system, it cannot be considered a reliable evaluation of the fire-control system. Plans were eventually made for re-evaluating the B-29 system by means of a satisfactory method, but for various reasons these plans were never carried out. In fact, no completely satisfactory evaluation of the B-29 fire-control system was ever conducted.\nThe Applied Mathematics Panel of NDRC, under Army Air Forces directive AC-92, conducted an extensive evaluation of the B-29's fire-control system. Principal work was carried out by the University of New Mexico in Albuquerque, with Eglin Field re-evaluating the system. The New Mexico group ran accuracy tests, results given in their report. AC-92 was intended for quick, not thorough B-29 study; fire-control system test results serve only as an indication.\nThe general accuracy of the B-29 system is not reliable. Towards the end of the war, the University of Texas Testing Machine was available and extensively used for testing and studying the B-29 system. The critical problem of defending the B-29 against nose attacks gave priority to improving the computer's performance for such attacks. All important proposals for modifying the computer were studied, and additional tests were run. The University of Texas Testing Machine was used to compare the standard B-29 system with the free-gyro sighting system and the stabilized sighting system. The results of these studies, along with previously mentioned ones, are discussed in reference 109.\nTowards the end of the war, the General Electric Company developed an excellent assessment facility at Brownsville, Texas, and managed to run adequate tests on the standard B-29 system and some of its modifications. No report is available on the results of this test, but the proposed program is described below.\n\n5. Sperry Systems\n\nAlthough the General Electric Company developments were the ones that were finally accepted by the Army Air Forces and put into production, there were other developments of remote-control systems which might have been superior to the GE system. The most important of these is a series of developments by the Sperry Gyroscope Company. Very early in the war, Sperry undertook to develop a completely automatic radar gunlaying system using remote-control turrets. The computer which was used in the first phase of this radar gunlaying system is described below.\nThe fire-control system was the Sperry P-4 computer. This computer was an adaptation of the Sperry K-3 and K-4 sights to the central station type. The sight station was a double-ended periscope mounted directly on the computer. The periscope was power-controlled from a pair of handle bars and made use of aided tracking. The remotely controlled turrets developed by Sperry were very accurately positioned by means of a selsyn data transmission system and a hydraulic turret servo.\n\nThere were several serious objections to the P-4 computer. The field of view of the periscope was only 30 degrees, making it virtually impossible to carry out a search operation with the periscope alone. This eventually led to the development of what was known as a presighting station, which consisted primarily of a pedal-operated sighting mechanism.\nThis is a sight type that could be pointed directly by an operator. The sight was pointed at a target as soon as it was picked up, and the information automatically relayed to the computer, resulting in almost aligning the periscope's line of sight with the target. Preliminary tests indicated its success. The primary objection to the P-4 computer was that, like the K-3 and K-4 sights, it measured angular rates with respect to the bomber. This introduced serious errors into the computation of kinematic lead when the bomber took evasive action. A lesser difficulty, but still fundamental, was due to the fact that the P-4 computer did not correct for parallax between the sighting station and the turret and contained substantial errors as a result.\nThe required axis conversion for the P-4 computer. The P-4 computer was in production very early in the war and could have been used long before the General Electric system for the B-29 was actually in production. At the time this Sperry system was developed, there was no really adequate means of assessing it, so the importance of the various known theoretical errors was never fully evaluated. It is very probable that, like the K-3 and K-4 sights, which were eventually tested, the Sperry central fire-control system would have been found to be at least as adequate for the defense of the B-29 as the standard GE system. The produced P-4 computers were never used. A description of this complete system will be found in the preliminary instructions for it which were prepared by Sperry.\n\nThe first phase of the complete radar gunlaying system for the P-4 computer.\nThe Sperry-developed system was the central fire-control system discussed earlier with the addition of a completely automatic X-band radar. In this first-phase system, radar position data was used to provide a target on a cathode-ray tube, which was tracked by the gunner using the control handles of the P-4 computer. It was recognized at the time that this arrangement would likely not be satisfactory and that the accuracy of the P-4 computer left much to be desired. However, this first-phase system was the first complete remote-control system to be completed and flown and could have provided valuable information on the general technical worth of such a system. Such a study was never conducted primarily because the AAF focused on the development and production of\nThe GE system and Sperry system were not given serious further consideration for the first-phase AGL system. This first-phase Sperry central fire-control system development is described in a Sperry report. At the same time, work began on designing and developing a completely new computer for the final-phase system and modifying a P-4 computer for use in the intermediate-phase system. The modified P-4 computer would be associated with a single free gyro, part of the kinematic lead computer, and would also stabilize the line of sight. This single-gyro system would eventually become a component of the final-phase computer. Intermediate-phase development was completed about a year before the end of the war and was given rather minimal attention.\nWithin the limitations of the P-4 computer, Sperry's extensive tests revealed an accurate and easy-to-handle intermediate-phase system. This system was never tested by the AAF. Upon completion of development, all further work on such systems by Sperry ceased. A complete description of this intermediate-phase system and Sperry's tests on it can be found in their report.\n\nSperry completed the design for the final-phase system but no parts were made. Simultaneously, a double periscope with a 70-degree field was developed and built, addressing most objections to the original double periscope. A brief description of this final-phase computer design is also included in the aforementioned report.\n\nOTHER SYSTEMS\nThe difficulties encountered with the standard GE computer for the B-29 and other systems led NDRC to start another central station computer development through a contract with the Fairchild Camera and Instrument Company. This particular development was based on the Fairchild K-8 lead-computing sight, which was already beginning to go into production. The Fairchild computer was almost entirely electrical in nature and used two rate-type gyros for computation of kinematic lead. The computer, as finally designed, was mounted in the same case as the standard B-29 computer and was interchangeable with it except for the gyros in the sighting station. Due to the different type of kinematic lead computation, the two GE gyros had to be replaced by the two Fairchild gyros for use with it.\nOne model of the Fairchild computer was completed but never tested. Theoretical considerations of the Fairchild computer design indicate that it would compare favorably in performance with the standard GE computer. A good description of this computer development is given in the Fairchild final report to NDRC. Very late in the war, one other central station computer was started by Westinghouse and brought to the point where one computer and sighting station were available for test. This Westinghouse system used a gyro type of kinematic lead computer and provided stabilization of the line of sight. The British were interested in remote-control systems but did not undertake the development of anything so elaborate as any of the American systems. They developed an excellent remotely controlled system.\nThe controlled 20-mm turret and data transmission system, but made no attempt to develop a central station type of computer. They used a Mark II-c lead-computing sight, mounted to be operated by power control from a pair of handle bars. The computed gun position determined by this sight was then relayed to the remote-control turret through a simple mechanical parallax computer. A discussion of this system and its performance can be found in two British reports from the Royal Aircraft Establishment, Farnsborough. It is interesting to note that largely as a result of this work by the British, the Americans became interested in trying the same arrangement in the B-29. However, this was never carried out.\n\nChapter 18\nTRACKING AND RANGING\n18.1 General Discussion\nThe most important operation which is\nperformed by a fire control system is tracking\nand ranging. This operation involves the\ndetermination of the position of a target\nrelative to the gun or missile system. The\ninformation obtained from tracking and ranging\nis used to compute the necessary gun or\nmissile adjustments to hit the target.\n\nTracking involves the continuous determination\nof the target position, while ranging is the\ndetermination of the target distance. Both\ntracking and ranging are essential for the\neffective engagement of a target. In this\nchapter, we will discuss the various methods\nused for tracking and ranging, and the\nadvantages and disadvantages of each.\nIn all airborne fire-control systems, accurately locating the target position is carried out. This is done in terms of a spherical coordinate system, meaning data on the target position is given in terms of range (distance to the target), elevation, and azimuth bearing angles. The process of operating direction-finding equipment to determine the angular position of the target is known as tracking. Operation of range measuring equipment is known as ranging. While it would be more appropriate to refer to these operations as angle tracking and range tracking, the previous terms have become well-established and have taken on these meanings.\n\nThe simplest form of tracking in flexible gunnery occurs in the use of a flexible gun.\nThe text describes the tracking method used in bombers, specifically the B-17, which lacks a range-measuring device other than stadia rings in the fixed sight. Tracking is accomplished manually without power control, known as direct control. The accuracy of tracking with a flexible gun mount is poor due to the large mechanical load the gunner must overcome from the gun's weight and aerodynamic forces. The first step to improving tracking accuracy was mounting the gun in a power-driven turret, allowing for the use of more than one gun and enabling the operator to move around in azimuth with the gun. The power required to move the gun and turret is not mentioned in the provided text.\nA turret is supplied by a motor controlled by the position of a control handle. In common turrets, a pair of control handles was used, which adjusted the speed of the motor driving the turret. The usual arrangement was to have the motor produce an angular rate in the gun position which was approximately proportional to the displacement of the control handles. This type of control is known as rate control.\n\nFor practical reasons, the turret was normally mounted so that it rotated in azimuth about the vertical axis. The guns which were mounted in the turret were arranged so that they could be rotated in elevation about a horizontal axis carried on the turret. The control handles rotated about a similar pair of axes, and the displacement of the handle bar about these axes controlled the rate-of-motion about the corresponding axes.\nresponding axes  of  the  gun  turret.  Such  a turret \narrangement  is  referred  to  as  a cylindrical  tur- \nret. This  type  of  turret  was  the  most  common \ntype  to  be  used  during  this  war.  In  some  cases, \na turret  was  so  arranged  that  it  rotated  both \nin  azimuth  and  in  elevation,  and  carried  the \ngunner  and  the  guns  with  it.  This  type  of  tur- \nret is  known  as  a spherical  turret.  In  this  case, \nalso,  the  displacement  of  the  control  handles \ndetermine  the  rate-of-motion  of  the  turret  and \ngun  about  the  two  axes  of  rotation.  A descrip- \ntion of  all  the  standard  turrets  used  during \nWorld  War  II  will  be  found  in  the  AAF  Tech- \nnical Order  series,  11-45,  on  aircraft  turrets. \nExperience  showed  that  even  with  power- \ndriven  turrets  using  rate  control,  the  tracking \naccuracy  obtained  was  not  satisfactory.  The \nability  of  a gunner  to  track  accurately  with \nsuch  a system  depends  on  many  factors  such  as \nAmong the factors influencing gunner performance are the amount and quality of training, type of target course, control system design constants, and simultaneous execution of other functions such as ranging, target identification, trigger operation, and control switch manipulation. The stadiometric method is commonly used for measuring target range. This is achieved by adjusting the reticle size until it brackets the target of assumed size. From the assumed target size and the known reticle size, the target range can be determined in the reticle size control mechanism, providing a continuously available and inserted computed target range.\nThe computer using such information obtained inaccurate ranges through the stadistic method. In fact, the greatest accuracies in lead computation in lead-computing systems using range data were due to ranging errors. Two ways to improve the target's position data in accuracy existed. The first was to enhance tracking and ranging controls and gunner training to use the system more accurately. The second was to replace the manually operated range and tracking system with an automatic one, either in tracking or ranging, or both. This could be achieved through the use of radar, and such systems were developed. This will be discussed later.\n\n18 tracking and ranging studies.\nSection 7.2 conducted studies on tracking and ranging, with the most significant work carried out by The Franklin Institute in Philadelphia. They developed mechanisms for simulating the dynamics of various tracking controls and standard lead-computing sights. A summary of the tracking study at The Franklin Institute can be found in their final report.\n\nThe initial part of the study utilized a mechanical device for simulating the turret tracking control and lead-computing sight. One objective was to evaluate the use of aided tracking control on a turret, which combines usual rate control and direct control.\nA second objective of the study was to determine the best choice of design constants for the lead-computing sight. The first results of this work are given in a report made in August 1943. The most outstanding result was the conclusive evidence that aided tracking control was substantially superior to rate control. Further work substantiated this and was reported to the Services soon thereafter. Additional work was done using the mechanical simulator with a greater variety of control constants and lead-computing sight constants. In any fire-control system, the gunner must decide when to fire and when not to fire. He should withhold his fire until the target is within suitable range and then fire only when he feels that his guns are pointed with sufficient accuracy to get effective hits.\nWhen  using  a lead-computing  sight,  his  only \navailable  method  is  to  fire  when  he  considers \nthat  his  sight  is  accurately  pointed  at  the  tar- \nget. A study  was  carried  out  to  evaluate  the \ngunner\u2019s  ability  to  judge  when  to  fire  and  when \nnot  to  fire.  The  results  of  this  study  are  given \nin  two  extensive  reports.^20.121  The  general \nconclusion  reached  is  that  the  gunner\u2019s  judg- \nment of  when  to  pull  the  trigger  is  quite  un- \nreliable. This  is  due  to  the  fact  that  the  gunner\u2019s \njudgment  of  his  tracking  error  is  very  poor \nand  also  to  the  fact  that  with  a lead-computing \nsight  the  intervals  during  which  the  tracking \nerror  is  small  is  not  necessarily  those  during \nwhich  the  gun  error  is  small. \nAs  has  been  indicated,  the  early  work  on \ntracking  which  was  done  at  The  Franklin  In- \nstitute made  use  of  a mechanical  simulating \nmechanism.  With  this  device  it  was  possible  to \nStudy only target courses with constant or variable angular rates at a constant range. Such target courses are quite different from those actually found in practice. This was due to a physical limitation in the design of the mechanical simulator. The use of unrealistic courses in the study might have influenced the final result, so a new simulating mechanism was built. This mechanism was largely electrical in nature and more accurate in performance than the mechanical simulator. It also provided for a much greater variety of tracking-control constants and lead-computing sight constants. Studies on the electric simulator verified the results of the previous work and gave additional information in confidence:\n\nTracking and Ranging\non the best choice of tracking-control constants.\nAnd the lead-computing sight design. Three reports on these results have been prepared. All work previously mentioned, the complete turret control and the lead-computing sight were simulated with the gunner remaining stationary. In an actual turret system, the gunner is subjected to certain forces as a result of the motion of the turret in which he rides. Since this effect had not been considered in previous studies, it was decided to continue the work using a system involving an actual turret. This was done and the results of that study have been reported. An analysis of the work using the turret system was made to obtain additional data on the optimum tracking-control and sight constants. One additional factor, which was considered in these studies, was the effect of training and practice. Throughout the work, a statistical evaluation was conducted.\nThe results were made to ensure that conclusions about tracking controls and lead-computing sight constants were not affected by variations in study subjects. A special study was made to determine the effect of practice. It is interesting and somewhat discouraging to note that, despite the Franklin Institute's early war tracking studies showing the superiority of aided tracking over velocity tracking, no turrets were produced with aided tracking control until near the end of the war. With the development of the University of Texas Testing Machine, another source of information on tracking accuracy became available. Its main objective was to evaluate the overall performance of a flexible gunnery system. However, in the process, it also provided data on tracking accuracy.\nThe evaluation process revealed data on tracking and ranging accuracy from the University of Texas report on the Mark 18 gun-sight. The Franklin Institute focused solely on tracking, while the University of Texas studies covered both tracking and ranging. Before comprehensive studies on lead-computing sight systems, the B-29 central fire-control system gained importance. Previously mentioned, the tracking accuracy with the GE pedestal sight was unsatisfactory, prompting tests by the University of Texas. Early reports show the first tracking results with the GE sight, and additional data was accumulated on the overall accuracy.\nThe GE system, mentioned previously. The University of New Mexico accumulated a large amount of data on tracking and ranging accuracy. One report deals with the use of the K-3 sight mounted in a standard Sperry turret. Another is concerned with tracking accuracy obtained with the GE B-29 system. Of all the studies mentioned, only those at The Franklin Institute provided useful information on the choice of constants for the considered systems. A considerable amount of additional tracking information is available in the various tests conducted at the Army Air Forces Proving Ground Command, Eglin Field, Florida and at the Armament Test Section of the Naval Air Station, Patuxent River, Maryland. In both places, the general objective of the tests was the evaluation.\nThe analysis of the overall performance of various systems resulted in limited analysis of tracking data, with the exception of an analysis of the Eglin Field data.12\n\nStabilization\nThe use of aided tracking control provides significantly better performance in tracking than standard rate control. An additional improvement in the performance of manually operated tracking systems can be achieved through the use of stabilization. It is known that with the ordinary tracking-control system, the accuracy of tracking is substantially reduced due to the influence of the motion of the gunner's platform. This means that tracking accuracy obtained during maneuvers or evasive action by a bomber is much poorer than when the bomber flies a straight and level course. This is principally due to the instability of the platform. However, the use of stabilization can counteract this effect and improve tracking accuracy.\nPrimarily due to the fact that under conditions of evasive action, the gunner operating the track-and-radar for gunlaying controls has not only to produce turret or sight motions which correspond to the motion of the target, but must also produce turret and sight motions which compensate for the motions of the bomber. The problem of compensating for the bomber\u2019s motion makes the tracking problem sufficiently more difficult so that the resultant accuracy decreases very greatly. By the use of a single or double gyro in the turret-control system, it is possible to arrange the controls so that the motions of the bomber are automatically compensated. This leaves the gunner with only the problem of providing the motions necessary to track the target.\n\nThe first stabilized turret control was developed very early in the war by the Ford company.\nThis turret was intended for installation in the nose position of a Navy flying boat. Due to its excessive size and weight, this turret was never produced. It was subsequently improved by the Ford Instrument Company, but only a few of these improved versions were built. Preliminary tests on the stabilized turret demonstrated significant advantages. Following this Navy development, there was no serious effort to develop stabilized tracking controls until fairly late in the war. This is surprising, given the definite improvements to be gained. Sperry developed a stabilized spherical turret for use in the nose and tail of the B-32. A number of these turrets were produced, but very few were put into use. Sperret also developed a gyroscopic gun sight for aircraft, which was widely used in the B-24 and B-17 bombers.\nThe text undertook developing a stabilized spherical turret for use with the S-8 sighting system. In this turret, the gyro providing stabilization is also used for kinematic lead computation. This arrangement is expected for future stabilized sighting systems. The Sperry S-8 sight system also provides automatic S-band radar. Fairchild also developed a stabilized-control system in conjunction with their S-3 sight. Both the Sperry and Fairchild systems were still in development at the end of the war. As mentioned, the General Electric Company had a completely stabilized sight under development for use with their B-29 fire-control system. The first stabilized sighting system produced by Sperry was used in the intermediate phase of their AGL development.\nThe Sperry system underwent extensive tests, although it was never flown or tested by the AAF. The Sperry system utilized aided tracking control. Extensive tracking data is available in the Sperry report, as well as a number of comparative results demonstrating the relative advantages of stabilization.\n\nFour Radar for Gunlaying\n\nDuring the war, a significant amount of effort was dedicated to the development of various types of airborne radar sighting systems. The initial developments were by Sperry and General Electric. In both of these systems, the objective was to provide completely automatic position finding through radar. This was accomplished satisfactorily from a performance standpoint in both developments. However, for a number of reasons, the primary ones being size and weight, these systems were never used.\nEarly in the war, it became clear that completely automatic radar equipment were only suitable for use on heavy bombers and would therefore have limited use in the future. Consequently, efforts shifted from these systems to the development of lightweight radars for use on existing aircraft. Due to the significant errors in lead-computing sight systems, considerable effort was put into creating a suitable radar ranging set. The first production model of this range set was the AN/APG-5. This set is described in a Navy operating manual prepared by the Radiation Laboratory. A small number of these sets were produced for experimental purposes only.\n\nThe biggest problem in providing accurate radar information was... (The text is cut off, making it impossible to clean it further without missing information.)\nRadar range for use with flexible gunnery systems was finding suitable space for the installation of the radar set. This problem was not as severe in the case of fixed gun fighters, and at the end of the war, there were a number of experimental fighter systems under test which made use of the AN/APG-5 set for TRACKING AND RANGING. Automatic ranging. While a number of tests were made on fire-control systems using this radar set, no really reliable test information has been provided. Tests on radar ranging sets of the type AN/APG-5 indicate that the accuracy of range data obtained is entirely satisfactory. However, some difficulties often arise in the use of this set if there is more than one target in the field. This difficulty can be largely overcome by suitable training. Another factor in the use of radar ranging devices is that the:\nThe use of accurate range may, under certain circumstances, decrease the accuracy of the fire. This occurs when systematic errors present in any computing system are of about the same size or larger than tracking errors. In such a case, the use of accurate range may result in systematic misses. Conversely, with the use of manual ranging, the dispersion of ranging errors is sufficiently great to provide enough overall dispersion in gun position to give at least some reasonable probability of getting hits. This means that accurate ranging data can be effectively used only when the computing system is properly calibrated. This effect has been amply demonstrated both analytically and experimentally.\n\nThe only radar set for aerial gunnery to be produced in any quantity was AN/APG-15B. This is described in an instruction manual.\nAt the beginning of World War II, there was no adequate method and no suitable equipment available for adequately evaluating the performance of flexible gunnery systems. The usual test for determining the performance of such systems was through combat experience.\n\nA set provided by the Radiation Laboratory offers not only automatic range information but an angular position indication which may be used for manually tracking the target. This set was eventually installed in the tail position of a number of B-29s which were sent to the Pacific Theater.\n\nA good summary of the various fire-control radars available or under development at the end of the war was prepared by the Armament Section of the Assistant Chief of Air Staff-4.\n\nChapter 19\nSimulation and Gunnery Assessment\ni Assessment Methods and Simulation\n\nAt the beginning of World War II, there was no adequate method and no suitable equipment available for adequately evaluating the performance of flexible gunnery systems. The usual test for determining the performance of such systems was through combat experience.\nGunners used the system by shooting at towed-flag targets. The quality of performance was judged by the percentage of hits obtained on the flag target. This method of testing was later shown to be inadequate. The experiments were not conducted under controlled conditions, the gunners' abilities and training were unknown, and the number of hits obtained on the target was usually small, providing no reliable indication of accuracy. Additionally, the quality of performance was largely based on the gunner's opinion of the system under test.\n\nSection 7.2 played a significant role during the war in assisting the establishment of suitable methods for assessing flexible gunnery systems and developing necessary equipment. The section was also largely responsible for educating personnel.\nArmy and the Navy in the general philosophy of quantitative experimental work. There are several general methods that can be used for evaluating aerial gunnery systems. One such method is to study the equipment analytically and to compute its performance numerically. The main objection to this method is that it is impossible to take into account all the factors which influence the performance of such a system. This method is most useful in determining the performance of a system under assumed ideal conditions. It also has the advantage that it provides a means of breaking down the overall error into its component parts, and of determining the sources of the various parts of the error. This method was applied rather extensively to an analytical evaluation of the more common lead-computing sight systems. The work was carried out by the Ap- (Assuming this is an abbreviation for a specific organization, I will leave it as is)\nApplied Mathematics group at Columbia University, under the direction of the Applied Mathematics Panel, conducted Study 104 on The Analytical Assessment of Certain Lead Computing Sights. This work resulted in a large number of reports, most of which have already been referred to in the relevant sections of this report regarding the specific sighting systems.\n\nA second method of assessment is simulation. In this method, the system under study is represented by a model or simulator, which is then subjected to various assessment experiments. The primary use of this method was in the tracking studies conducted under Section 7.2. The tracking studies at The Franklin Institute utilized such simulators and have already been discussed. The three simulators used in that study are described in the following:\nreports  by  The  Franklin  Institute.^^2,133,134 \nIn  any  study  of  a gunnery  system,  the  oper- \nator, or  gunner,  plays  a very  important  part. \nIt  is  very  important  that  the  errors  in  the  over- \nall performance  of  the  system  contributed  by \nthe  gunner  be  known.  In  fact  one  of  the  most \ndifficult  problems  in  such  assessment  work  is \nto  design  the  experiment  in  such  a way  that \nthe  effect  of  the  gunner\u2019s  performance  can  be \nevaluated.  In  carrying  out  experiments  with \nvarious  types  of  simulators,  it  would  be  very \ndesirable  to  have  some  sort  of  an  artificial \ngunner.  Some  attempt  was  made  to  determine \nthe  general  dynamic  properties  of  a typical \ngunner  which  then  could  be  built  into  an  artifi- \ncial gunner.  While  such  work  did  not  progress \nvery  far,  enough  was  done  to  indicate  the \nfuture  possibilities.  The  earliest  work  appears \nto  have  been  done  in  England.^^^  The  analysis \nThe dynamics of a human being was based on the use of sinusoidal courses of varying frequencies. The method of analysis used is that commonly applied by electrical engineers. A similar but somewhat briefer study was conducted by Columbia University using a slightly different technique of the electrical engineer. In this case, the courses used for analysis were of the transient type. This work is described in the final report of the Columbia University project.\n\n19.2 University of Texas Testing Machine\n\nIn addition to the two methods of assessment described, there are several entirely experimental methods which can be used to evaluate a complete gunnery system, including the gunner. One obvious such method is some form of flight test. This leads to certain practical difficulties which are present in any flight test.\nEven if the experiment is properly designed with all necessary factors controlled, there are always difficulties due to the inoperability of airplanes, weather effects, and the rather large time and cost involved. These difficulties can be largely overcome by the use of a device on the ground which allows the use of a full-size gunnery system and provides the gunner with reasonably realistic target courses. The desirability of such a testing machine was pointed out early in the war by Section 7.2 (then Section D.2). At the same time, the general specifications for such a machine were also prepared. Both the Army and Navy agreed to the desirability of such a ground testing machine for evaluating performance of flexible gunnery equipment, and the development of such a machine was carried out by Section 7.2 at their request.\nThe University of Texas developed a machine for target projection, named the Texas Testing Machine. Extensive effort was invested in its creation, with numerous design proposals considered. Initially, plans called for projecting target spots onto a large screen for a gunner to follow while operating the equipment under test. Based on experience with similar devices from the Waller gunnery trainer, this seemed feasible. However, preliminary studies revealed that the parallax introduced by the separation between the testing machine and gunnery system axes were nearly insurmountable. The accepted arrangement features an optical target that can be moved in space.\nThe target system is designed to simulate the desired motion. In its final form, the target can travel any course, whether ideal or real, determined by experiments. The optical target system also provides a moving picture of an airplane in its correct size and attitude. The image and position of the optical target are controlled by a set of cams, providing an accurately reproduced target course. Preparing the cams for each target course is extensive work, but once prepared, only a small amount of work is necessary to replace them with cams for another course. For each particular course, the correct gun position is known and compared with the actual position.\nThe gun position is obtained in the system under test. The gun error is continuously recorded to know the actual elevation and azimuth components for each point on the course. With certain gunnery equipment, such as the GE central fire-control system, the sight can be mechanically driven for perfect tracking. The original machine, developed at the University of Texas, has been in operation and some results have been referred to in previous sections of this report. Two additional machines were built. One is installed at the Armament Laboratory at Wright Field, and the other at the Naval Air Station, Patuxent River, Maryland. Results obtained have shown the great usefulness of this machine, and without question, these machines have already saved.\nThe cost of the original development. The present Texas Testing Machine is described in two reports from the University of Texas. While a large amount of work was done on various phases of the development of this machine, there are very few reports available on this work. Even before the machine was finished, alternative methods for carrying out some of the operations were being studied and designs prepared. The only other available material on this work is a series of informal progress reports. In the future, it should be possible to use the three available Texas Testing Machines for most of the assessment work required on experimental and pre-production models of flexible gunnery systems. This will provide far more reliable data than was previously available and at a considerable savings.\nThe first adequate flight tests of flexible gunnery equipment were performed by the British, specifically by the Gunnery Research Unit at Exeter, assessing the Mark II gyro gunsight. The first facility in the United States for adequately assessing flexible gunnery systems by flight test was developed by the AAF Proving Ground Command at Eglin Field, under the general guidance of Section 7.2. Camera equipment was developed and installed in the airplane carrying the equipment under test, which would record the actual relative position of a fighter plane making a simulated attack. A pair of gyros were used to determine the roll, pitch, and yaw of the bomber airplane. Other cameras were used for photographing the position of the target.\nThe overall error in gun pointing was computed relative to the line of the gun and the position of the target and sight reticle, as viewed through the sight. After processing various films, necessary data was read and the error in gun pointing was computed. Great care was taken to design the experiment and control conditions for statistically reliable results. A large amount of time was required to develop equipment and train personnel for this test. The most difficult problem in establishing this method was educating people in the philosophy of quantitative testing. It was found extremely difficult to get test runners to follow the operation schedule and ensure equipment under test was in proper condition.\nMuch time was lost due to missions running under improper conditions. The flexible gunnery assessment method developed at Eglin Field has been completely described in one of their reports. Once a test was planned, a relatively large amount of data could be collected in a short time. Initially, this was not the case due to test equipment breakdowns and the general difficulties of weather and airplane failures common to all flight tests. Even with the delays encountered in taking data, the time necessary to analyze results and compute gun errors was many times that necessary to take the original data. Any improvement in the method, particularly that of analyzing data, promised large savings in time. For this reason, an analysis of this assessment method was undertaken by the Ap-\nThe Applied Mathematics Group at Northwestern University conducted an assessment of the assessment method used at Eglin University. This analysis revealed that certain approximations used to simplify computations resulted in errors greater than desired. Improved computation methods were recommended, and several sets of results were computed using them. As this assessment work continued, other improvements were developed. Another improvement developed at Eglin Field was the use of gnomonic charts for carrying out a large part of the computation.\n\nBefore the flexible gunnery assessment method was fully developed at Eglin Field, the Navy expressed interest and requested the NDRC to develop a similar facility at the Naval Air Station in Patuxent River, Maryland. As part of this work, the Applied Mathematics Group at Northwestern University contributed to this effort.\nThe Northwestern University mathematics group conducted a study of existing assessment methods, including those at Eglin Field. Reports on this study are referenced above. Reference 157 provides an excellent analysis of the photographic method for gunnery assessment. Other reports focused on determining a bomber airplane's roll, pitch, and yaw using gyros and applying this information to correct original data for these motions.\n\nIn response to the Navy's request, Section 7.2 of NDRC contracted Northwestern Technological Institute to complete the necessary work for providing the Navy with a flexible gunnery testing facility. After reviewing the Eglin Field analysis method, Northwestern determined that the analysis work could be executed effectively.\nA set of mechanisms was developed and built for the Navy and Eglin Field to be done with less effort by means of a photographic method for flexible gunnery assessment. The most complete description of the theory and operation of this method is given in a set of reports prepared by Northwestern. These reports should be required reading for anyone undertaking to understand this method and its use. Northwestern also undertook to prepare a computer manual for processing the aerial gunnery assessment film obtained by this method. The first two parts of this manual have been finished, with the first part included in the previously mentioned report and the second part given in a separate report. A useful computing device was also developed.\nThe Applied Mathematics Group at Columbia University suggested using the stereographic spherimeter for analyzing assessment films in carrying out some work. This tool is described in two reports prepared by them. In the flexible gunnery assessment work done at Eglin Field and Patuxent River, it was assumed that the bomber carrying the equipment under test flew a straight-line course at constant speed. Any other conditions would introduce errors into the result. Since it was desirable to carry on some tests with the bomber taking evasive action, work was done to modify the method to adapt it to this situation, as described in reference 167.\n\nThe original evaluation test of the B-29 central fire-control system, carried out by Eglin Field, was done before the photo-documentation.\nThe graphic assessment method had been developed. After its development, the AAF planned to re-evaluate the B-29s using it. However, the General Electric Company decided it would be to their advantage to have a testing facility of their own. This facility could be used in the improvement of the current B-29 system and the development of new systems. They developed such a facility at Brownsville, Texas, and managed to obtain a significant amount of data by the end of the war. This method used a somewhat different technique than that in use at Eglin Field or Patuxent River. It was particularly adaptable to remote control turrets using electric servos. No adequate report on the method's details is available, but the program for the first set of extensive tests is described.\n\nFour other methods.\nTwo other methods of flexible gunnery assessment were proposed. The first of these made use of distant reference points. This method was applied by the University of New Mexico in a few tests on the B-29. It was never fully analyzed and therefore its errors are not known. However, it is considerably simpler than any of the methods discussed and should not be overlooked in future work. The other method is essentially a vector method. It is also considerably simpler than the Eglin Field or Patuxent River methods. A preliminary study of this method indicates that its accuracy is comparable.\n\nOne interesting training device which was developed during the war is the frangible bullet. This is a .30-caliber bullet which breaks up on striking very light armor. It can be fired at pursuit airplanes while they are making simulated attacks.\nModifying standard computing systems for ballistics of this bullet allows giving gunner training under realistic conditions. In the developed system, special armored P-63s were used for simulated attacks, containing a hit indicator that counted hits and flashed a light upon a hit. This system provided one psychological condition missing in all assessment methods: the ability to fire live ammunition at the target in flight. For this reason, it was suggested that frangible bullets be used as an assessment means. However, this has two serious objections not fully understood by those suggesting its use. The first is that it is not possible to accurately transpose bullet trajectories between live fire and simulation.\nThe results obtained with frangible bullets are compared to results with standard live ammunition. The second issue is that the record of hits on the target, a small percentage of the total rounds fired, is inadequate evidence of the system's performance. This is discussed in reference 172. Although this report focuses on flexible gunnery systems, methods for assessing fighter gunnery should be mentioned. Considerable work was done by the Applied Mathematics Group at Northwestern, and their results are given in six reports.\n\n5. DISPERSION AND THE EIGHT OF MERIT\n\nThe usual results obtained from any test of a flexible gun system are given as the error in the gun position. These error data in their simple form are not particularly useful.\nThe effect of such an error on the ability of the system to bring down an attacking fighter is not evident. In fact, the given angular error in gun position is more serious at longer ranges than at shorter ranges. Additionally, its effect is controlled to a large extent by the dispersion pattern of the bullets. A number of tests were run to determine the actual dispersion pattern of various flexible gunnery systems. The most outstanding of these tests were run by the Flexible Gunnery School at Laredo, Texas, and the results of such tests on the B-17, B-24, and B-29 are given in two of their reports. A detailed description of the testing method has also been prepared by them.\n\nThe final measure of effectiveness of accuracy of a gunnery system should be expressed in terms of expected damage at the target. Consequently.\nSubstantial effort was expended in finding a suitable figure of merit of this sort and in developing methods for computing it. The philosophy of such a figure of merit is discussed in reference 179. The figure of merit that was finally adopted for use in all flexible gunnery assessment programs was the probability of a hit when a single bullet is fired. The details of this figure of merit and methods of computing it from gun error data will be found in a group of four reports. A very complete and detailed analysis of this problem was made in England.\n\nA much more realistic method of evaluating the effectiveness of aerial gunnery is based on the idea of a duel between a fighter and a bomber. In this case, an attempt is made to determine which airplane would be shot down first or which side would be successful in a duel.\nduel between groups of fighters and bombers. The problem of answering such questions by evaluating the probability of either plane shooting down the other, while much more realistic, is considerably more difficult. A fair amount of work on this has already been accomplished, primarily in England, but considerably more needs to be done.\n\nCONFIDENTIAL\nChapter 20\nDISCUSSION ON FUTURE WORK\n\n20.1 INTRODUCTION\n\nFuture development work in airborne fire-control systems should be of two types. The first of these is the continual improvement of systems now in existence or under development. The main objective of such work will be to obtain the best performance from the systems that can be put into use in the immediate future. If another national emergency arises soon, this is the only type of equipment that will be available.\n\nThe second type of development work should be directed towards the creation of new and advanced fire-control systems. The primary goal of this research will be to develop systems that will provide superior performance in the long term, even under the most challenging conditions. This work should be given high priority, as it has the potential to revolutionize the way airborne combat is conducted.\n\nIt is important to note that both types of development work are essential for the continued effectiveness of airborne fire-control systems. While the continual improvement of existing systems is necessary to maintain a competitive edge in the short term, the development of new and advanced systems is crucial for long-term success.\n\nThere are several areas of research that should be pursued in order to achieve these goals. These include:\n\n20.2 RESEARCH AREAS\n\n20.2.1 Improved Sensor Technology\nThe development of more advanced and capable sensors is essential for the continued effectiveness of airborne fire-control systems. This includes the development of sensors that can detect and track targets at greater distances and in more challenging environments. It also includes the development of sensors that can provide more accurate and reliable data in real-time.\n\n20.2.2 Advanced Processing and Computing Capabilities\nThe ability to process and analyze large amounts of data in real-time is crucial for the effective use of airborne fire-control systems. This requires the development of advanced processing and computing capabilities, as well as the integration of these capabilities into the fire-control system architecture.\n\n20.2.3 Improved Communication Systems\nEffective communication between different components of an airborne fire-control system is essential for its successful operation. This includes the development of reliable and secure communication systems that can transmit data in real-time between the various components of the system.\n\n20.2.4 Human-Machine Interface\nThe design of an effective human-machine interface is crucial for the successful operation of airborne fire-control systems. This includes the development of intuitive and easy-to-use interfaces that can provide operators with the information they need in a clear and concise manner.\n\n20.2.5 Advanced Algorithms and Artificial Intelligence\nThe use of advanced algorithms and artificial intelligence (AI) can significantly improve the performance of airborne fire-control systems. This includes the development of algorithms that can quickly and accurately analyze data from multiple sensors and identify potential threats, as well as the integration of AI capabilities into the fire-control system architecture to enable autonomous decision-making.\n\n20.3 CONCLUSION\n\nThe development of advanced airborne fire-control systems is essential for the continued effectiveness of airborne combat capabilities. This requires a two-pronged approach, with a focus on both the continual improvement of existing systems and the development of new and advanced systems. The research areas identified in this chapter, including improved sensor technology, advanced processing and computing capabilities, improved communication systems, human-machine interface design, and the use of advanced algorithms and AI, are all crucial for achieving these goals. By investing in this research and development, we can ensure that our airborne fire-control systems remain at the forefront of technology and continue to provide our forces with a competitive edge in the air domain.\nIt is unlikely that such work will lead to significant improvements in performance over that of current systems. The second type of development work is long-term in nature and would involve a search for systems that may be quite different than those in existence at present. The greatest possibility of making large improvements in performance is provided by such long-term work. However, such work must be based on estimates of the character of future aerial warfare and would have little effect on equipment that would have to be used in the next few years. One major problem that must be solved is deciding what proportion of the total available effort is to be put on these two types of work. It goes without saying that neither can be neglected. In this discussion only: (end of text)\nThat work pertaining to the immediate future will be considered.\n\n20. Tracking Controls\n\nEvidence is already available that very worthwhile improvements in the accuracy of gunnery systems can be obtained by improved methods of locating target position. One way in which this can be accomplished in the case of manual tracking is by the use of aided tracking controls. It is very probable that this should be made a part of all new tracking-control systems. While it was difficult to modify turrets produced during the war so that they would have aided tracking control, very little effort is required to provide it in new turret designs. Another very important aid to the gunner is line-of-sight stabilization. This has already been given considerable consideration and has been shown to contribute a substantial increase in the accuracy in the performance of the system. Here also\nThe probable type of future fire-control systems makes it possible to include stabilization in designs with little additional effort. With present fire-control systems, the largest source of error has been the poor quality of ranging. This means that one of the best ways to improve the accuracy of future systems is to improve the accuracy of ranging. The ranging controls used in manually operated systems during World War II were relatively crude. In addition, the necessity of doing ranging simultaneously with tracking made it very difficult to do either satisfactorily. The best way to obtain better range data is by the use of radar. This cannot be accomplished satisfactorily until present radar range sets are improved to the point where they can be easily installed and are less susceptible to interference.\nThe use of completely automatic radar for tracking and ranging offers considerable promise for dealing with multiple targets. However, the cost, weight, and complexity of such equipment may make it unprofitable to rely on it completely. Radar offers the only possible method for fighting at night or in bad weather. The use of both radar and manual operation should be further studied. One of the major unsolved problems is determining how these two tracking and ranging methods can be best exploited.\n\nA wide variety of gunnery computers, both local and remote-control types, were developed during World War II. It was found relatively easy to design these computers to determine the required ballistic leads accurately. In fact, in most cases, the computers could do so more accurately than human operators.\nThe curvacy of the ballistic lead provided was considerably greater than was warranted, considering the inaccuracies present in other parts of the system. The main requirement which should be met by future ballistic computers is that they should be so designed as to make it possible to adapt them to various types of ammunition. This has already been accomplished to a large extent in some designs. The other requirement is that the ballistic computers should be simplified as much as possible, so that the performance provided by them is in a better balance with that of the other parts of the system.\n\nThe largest errors present in existing computers occur in the computation of kinematic lead. Present computers are sensitive to the type of target course because the only course data used as inputs are present angle and range. The effects of range rate and angle change are not taken into account.\ngular acceleration are taken into account only through a calibration procedure which adapts the computer to a particular course. The next major step to be made in the improvement of kinematic-lead computers is to provide them with range rate and angular rate data and design them to use this additional information. This has been impossible in the past largely because the accuracy of such data as were available was unacceptable. The use of improved tracking and ranging methods will make it possible to provide range rate and angular rate data which can be used by improved kinematic-lead computers. In addition, all future computers should be based on the use of gyros. This calls for some improvement in the gyros themselves. Considerable work has already been done in this direction by Sperry, General Electric, Fairchild, and Westinghouse.\nWork should be evaluated and serve as the basis for the future development of aerial gunnery equipment.\n\nThe psychological problems arising in aerial gunnery systems have been given far too little consideration in the past. Evidence of these problems first emerged in the training field, and a significant amount of effort was put into solving them. One general problem that has not been fully appreciated is the necessity of designing the controls of equipment so that they can be operated effectively by a man. One of the biggest opportunities for improvement in performance lies in this field. It is also very important that people concerned with training be given an opportunity to evaluate new equipment while it is still in the development stages, from the perspective of training. This will not only assist the training process but also provide valuable feedback for further refinements.\nPeople in developing an adequate training program often prevent equipment from getting into the field due to difficulty in operation. To address these issues, it's desirable to learn more about human performance as a component in a tracking and ranging control system.\n\n20-5 ASSESSMENT\n\nThe advantage of using a testing machine like the Texas Tester instead of usual flight test is well-established. This doesn't eliminate the need for flight test but allows most testing of experimental equipment and preproduction models to be accomplished on such a machine. It also makes it possible to carry out tests at an early stage in development and select the most promising equipment from competing developments.\nConcentrate the effort and save considerable time and money. This same sort of result can also be obtained by early mathematical analysis of various proposed systems. Such an analysis may often provide very valuable evaluation on such systems while they are in a very early stage of development. It also offers a very useful tool in planning the development program. During World War II, most mathematical analysis of this sort was on equipment either in production or in a very late stage of development. In the future, such analysis should be one of the first things done when a new system is proposed. There is ample room for improvement in the various existing methods of gunnery assessment. The present Texas Testing Machine is only the first model of such a machine. The needs for it were so pressing that every effort was made to develop it.\nThe machine was made to complete three of these as soon as possible rather than to provide a machine of improved performance at a much later date. The usefulness of this machine is so great that it will be well worth while to put some effort into producing a model which is more flexible than the present one and which will handle a much wider variety of equipment and target courses. The present photographic method of flight testing has reached a high state of perfection and it is doubtful if any large effort should be put into its improvement. However, the distance reference point method and the vector or own-speed method offer great promise. It is conceivable that either or both of these might provide a method with accuracy equal to that of the present method, but requiring far less work in analyzing the results. The development of both of these methods should be carried out.\nThe point of comparison for these methods lies in enhancing them. Additionally, a facility should be developed for conducting tactical studies on aerial gunnery equipment. This facility must offer all necessary control conditions and quantitative data for effective experimental work.\n\n206. WEAPONS\n\nThe standard weapon employed in World War II aircraft for bomber defense was the .50-caliber machine gun. Its performance is exceptional and significantly superior to any previously developed and utilized small caliber weapons. However, its full effectiveness was never achieved due to the inaccuracies of its fire-control system. The need to develop a larger, longer-range weapon with a higher-firing rate is not in question.\nThe probable extent of improvements in the direction of gunnery systems does not offer as much overall improvement in performance as improvements in computer performance. Developments in new weapons should continue, but they should not come at the expense of developments leading to increased accuracy in other parts of the gunnery system. The most profitable direction for weapon development is in the direction of large caliber projectiles. One such projectile is the spin-stabilized rocket. While this is likely a relatively long-term development, it is possible that a suitable projectile of this sort would become available in the next few years.\n\nPlanning and Control\n\nThe most serious lack in the fire control development work done during World War II was the lack of an adequate planning and control system.\nThe planning and control group within the Army Air Force. Most of the initiative for these developments came from industry. The Army Air Force exerted very little direction over this work and appeared to have no coordinated plan. As a result, a lot of competing developments were carried on simultaneously, and the choice of the final system was not made on any logical basis. To avoid this difficulty in the future, it is necessary for the Army Air Forces to have a central planning group with the authority to control the overall development program. It is also necessary to provide much greater use of highly trained and experienced civilians. In the past, the direction of important development work has been given to officers or civilians who had neither the background nor the ability to do it properly.\nThe organization's problems are further aggravated because it has been responsible for procurement and production, as well as research and development. Industry experience shows that these two functions should be separate.\n\nAppendix\nRemark\n\nTrajectories (AZON and Razon)\n\nThis index does not explain guided bombing or provide an account of the use of the differential analyzer in the study of the guiding problem to date. It is merely a ready-reference record from which various trajectory solutions may be conveniently selected. In the following foreword, the equations solved by the analyzer are given, along with some pertinent physical parameters, initial and final conditions, and so on. The tabular form of the index is also briefly explained.\nwhere and are the elevator and rudder deflections measured in degrees from the position of zero control, A is the area of cross section of the bomb, p is the air density at altitude z, and Coy, Cs, Cl are ballistic coefficients of the bomb, given as empirical functions of 8e and Sr-M is the mass of the bomb.\n\nAll trajectories listed under RDA No. 119 are for range-only control. In this case, equations (1) were used, where 8^ and Sr are zero. In the case of rudder control, the following approximate equations were used:\n\ns(8R,z) = y\ndx = vx dy\n\nwhere x, y, z are Cartesian coordinates in a system\n\n(Note: This text appears to be technical in nature and written in standard mathematical notation. It does not contain any unreadable or meaningless content, and no modern editor information or translations are necessary. Therefore, no cleaning is required.)\nThe functions d{bEybR,z)y, s{hRyZ), and l{hEyZ) are defined as follows:\n\nd (bEybRyZ) = dEybR,\nHSr,z) = ^CsiSn,\nliSE,z) = ^Cl(Se),\nx(di8EybR,z) = A- (i^RyZ)^ z ^(bEybRy.\n\nThese functions were obtained by replacing the drag and side-force terms with x^--y'^--z^ and the lift-force term with x^A-'^\"- in the equations.\n\nAll runs labeled RDA 120 are for equations (3). These equations reduce to equations (1) when s and y are zero. In RDA No. 121, equations (1) were used with range-only control. In these runs, the functions Cb and Cl were plotted against 8^ on input tables and fed in continuously during the course of the solution whenever control was required.\nFor all runs except the specified ones, the full value of Cp, Cs, or Cl for any elevator or rudder position was set at the indicated times. Except where otherwise noted, the function used for density was Po, where p^ = 0.002378 slug/ft^ is air density at sea level. In RDA No. 119, Edition 1, and RDA No. 120, Edition 2, the value used for A was 1.865 ft^, and for M 1,000 lb. In all other editions, except where noted, the values used for Azon and Razon were in the case of the 1,000-lb bomb A = 1.89. The sources of the various values of Cd, Cs, Cl used are given for each edition. For Editions 8 and 9, the coefficients were obtained by varying the Wyckoff coefficients by \u00b120 percent. These runs are to be used to obtain, by interpolation or extrapolation, data for bombs with different ballistic coefficients. Also included in Edition 8.\nSome runs, Nos. 123-129, use coefficients for an early Razon bomb with long horizontal fins or \"sideburns.\" The initial velocity of the bomb, Vq, is given in miles per hour, except where otherwise specified. The time of flight, tf, is given in seconds. Rudder and elevator deflection hu and he are in degrees. The range and sidewise deflection at impact, x(tf)y, are given in feet. The column headed \"Time of application\" gives the time of application of the control indicated on that same line. Where there is a blank, no control was applied and the trajectory is free fall. If for any run the first value listed is not zero, then no control has been applied up to that instant. This control is understood to continue until a new value of hu or he appears.\nRun No. Vo Cd Cl tf X(tf)\n1,000-pound Razon (Octagonal Shroud) (Akron Coefficients, 10-27-43)\n1,000-pound Azon (Square-tail) (Akron Coefficients, 10-27-43)\n1,000-pound Azon (Preset elevator control) (R. D. Wyckoff Coefficients 12-21-43)\n2,000-pound Razon (R. D. Wyckoff Coefficients 12-21-43)\n1,000-pound Razon (Octagonal Shroud) (Akron Coefficients, 10-27-43)\nRun No. Se Co h Xitf) H(tf)\n2,000-pound Razon (R. D. Wyckoff Coefficients 12-21-43)\nCo h\n\n(Note: The text appears to be a list of data for aerodynamic calculations for various aircraft models, with each entry including the run number, velocity (Vo), drag coefficient (Cd), lift coefficient (Cl), thrust factor (tf), and other related data. The aircraft models mentioned are \"Razon\" and \"Azon,\" and the coefficients are attributed to \"Akron\" and \"R. D. Wyckoff.\")\n[RDA No. 120, Edition No. 2 (Continued)\n1,000-pound Azon (Square-tail)\n(Akron Coefficients, 10-27-43)\nc Sr Go Ga U tf xitf yitf\n\nRDA No. 120, Edition No. 3\nInitial Altitude 15,000 feet, 1,000-pound Azon\n(R. D. Wyckoff Coefficients, 12-21-43)\nRun No. Sr Co C\nxitf vitf\n\nRDA No. 120, Edition No. 3 (Continued)\nRun No. Co Cs X(tf) y(tf) OO\n\nRDA No. 120, Edition No. 4\nInitial Altitude 15,000 feet, 2,000-pound Razon\nD. Wyckoff Coefficients\nRun No. Sb do Co if Xitf y(tf) OO OO OO OO OO OO OO OO OO\n\nRDA No. 120, Edition No. 4 (Continued)\nRun No. Co Cl h tf Xitf y(tf)\n(See RDA OO OO - CONFIDENTIAL\n\nRDA No. 120, Edition No. 4 (Continued)\nRun No. de Cd X(tf) Vitf Glide)\n\nRDA No. 120, Edition No. 5\nInitial Altitude 15,000 feet, 1,000-pound Razon\n(R. D. Wyckoff Coefficients, 12-21-43)\nRun No. dg Cx, Cs Cl tf X{tf} Vitf]\nRDA No. 120 Edition No. 5 (Continued)\nRun No. Sr Se h Cx Cy tf X(tf) y(tf)\nCONFIDENTIAL\nAPPENDEX\nRDA No. 120 Edition No. 5 (Continued)\nRun No. be y(tf) OO OO OO OO OO OO OO OO OO OO OO OO OO OO OO OO OO OO OO OO OO OO OO OO OO\nEdition No. 6. Initial Altitude 15,000 feet.\n1,000-pound Razon\nEffect of increase in\nRun No. Sr Se h C tf x(tf) y(tf)\nEdition No. 7. Initial Altitude 28,000 feet.\n1,000-pound Razon\nD. Wyckoff Coefficients, 12-21-43\nRun No. Sr Se h tf X(tf) yitf\nOO OO OO\nRDA No. 119 Edition No. 7 (Continued)\nRun No. se yUf\nOO\nEdition No. 8. Initial Altitude 15,000 feet.\n1,000-pound Razon\n(Synthetic Coefficients)\nRun No. x(tf) yitf\n* CONFIDENTIAL\nAPPENDEX\nRDA No. 120 Edition No. 8 (Continued) RDA No. 120 Edition No. 8 (Continued)\n~ (Coefficients for Line of Sight Control)\nNo. F.F.C^ C Xitf y(tf)\nRun No. cr if\n[X, v, Q, il, A, A, loo, u.o, u, RDA No. 9, Edition 9, Initial Altitude 15,000 feet, 2000-pound Razon, (Synthetic Coefficients), Run, No., F.F.C, Cl, X{tf}, y{tf}, ONFIDENTIA, Appenndix, RDA No. 120, Edition 9 {Continued}, Run, No., F.F.C, Cn, Ct, if, Xltf), yitf), RDA No. 120, Edition 9 {Continued}, Run, No., F.F.C, Cn, tf, xUf), y{tf}, RDA No. 120, Edition 10, Initial Velocity 250 mph, 1000-pound Azon, (R. D. Wyckoff Coefficients, 12-21-43), Altitude Effects, Run, No., Altitude 5, Co, if, X{tf}, yitf), OO, OO, OO, OO, RDA No., 120, Edition 10 {Continued}, Initial Altitude 15,000 feet, Velocity Effects, Run, No., Cn, if, X {tf}, yitf), OO, OO, OO, *^Ni^DEgTIAU|, Appenndix, RDA No. 120, Edition 10 {Continued}, Run, No., X{tf}, y{tf}, Special Effects, OO, OO, OO, OO, OO, Trainer Data, OO, Check Cases, P, Po, OO, OO, P, Po, OO, RDA No. 121, Edition 1, Initial Altitude 15,000 feet, 2000-pound Razon]\nR. D. Wyckoff Coefficients, 12-21-43\nRun No. Vo Cd Cl ti tf Xitf\nRDA No. 121 Edition No. 1 (Continued)\nRun No. Vo ds Cn Cl L if X{tf)\nDifferential Analyzer Trajectories\nFOR Razon\nThe following few runs were made at the request of Gulf for the purpose of comparison with actual tests at Tonopah. Some parameters used differ from those of previous differential analyzer solutions.\nThe initial altitude is 15,000 feet. The same notation is used as in the other indices. Cg is zero for all runs.\nRDA No. 119 Edition No. 4 and 4A.\nRun No. Cd Cl L tf X{tf)\nAPPENDIX\nFOR RAZON TRAJECTORIES\nThis index is of data made at the request of R. D. Wyckoff for the purpose of studying variation in time-of-flight as a result of control. Only range control is applied. The same differential equations are used as in previous RDA No. 119.\nsolutions: With full elevator, either up or down, applied at the indicated times ti. No allowance is made for the time the elevator takes to move from neutral position to that of full control, so aerodynamic coefficients are changed discontinuously. Control applied at a time continues until a change is made at a new value of tif or until impact. Time-of-flight and range-at-impact are denoted by tf and x(tf).\n\nThe coefficients used are for the VB-3 Mk II, a 1,000-lb Razon model. The parameters used are:\n\nArea = 1.89 sqft\nThe density function used is the same as for previous trajectories:\n\n\u03c1 = sea level air density\n\nInitial altitude: 15,000 feet.\nInitial horizontal velocity: 250 mph.\nRun No. Cd Cl ti (sec) tr(sec) x(tf)\n\n(Continued)\nRun No. Cd Cl ii (sec) if (sec) x(tf)\nThis index records data from differential analyzer trajectories for the Roc guided missile (00-1000-V) with range-control only. The same differential equations were used as for the Azon and Razon bombs.\n\nValue used for control area A was t) ft\u00b2 for M, 1,700 pounds. The density function used was:\n\nwhere po = 0.002378 slug/ft\u00b2 is air density at sea level. The time of application of control is U. Where no control was applied, this item is left blank. Indicated control continues until a new control at a new value of ti is applied, or until impact if no change in control is listed.\n\nTime of flight and range at impact are given by x(tf) and if, respectively. Maximum value for bomb velocity is given in miles per hour, and trail angle in mils.\n\nThe value of the drag coefficient Cd depends\nFor control with brakes:\nCl is zero for no control, \u00b10.65 for maximum sail or dive.\n\nFor no brakes:\nSome runs had fractional amounts applied, denoted by K.\nAll runs were made with an initial altitude of 15,000 feet and initial velocity of 250 mph. Further runs will be obtained for different altitudes and velocities.\n\nRDA No. 119, Edition No. 5. Initial altitude: 15,000 feet. Initial velocity: 250 mph.\n\n------------------\n\nBrakes Control Cl\n------------------\n\nMax Roc Velocity (feet)\n(mph) Trail (mils)\n\nBrakes Control\n-------------\n\nCl None None None\n\nMax Roc Velocity (mph) Trail (mils)\n\nFull None None\nNone Full Sail Full\nNone 75% Dive None\nNone Full None\nNone 75% Sail Full\nNone Full None\nNone 75% Dive Full\nNone 75% Sail Full\nNone 75% Dive Full\n[75% Sail, 75% Sail, 75% Sail, 75% Dive, 75% Dive, 75% Dive, 75% Sail, 75% Sail, 75% Dive, Full Dive, Full Sail, Full Dive, Full Sail, 75% Dive, 75% Dive, 75% Sail, Full Sail, 75% Dive, 75% Dive, Full Sail, Full Dive, Full Sail, 75% Dive, Run, Brakes, Control, o, u, (sec), X(tf), (feet), Max Roc Velocity, (mph), Trail, (mils), i]\nThis index, like the preceding one, is of data on differential analyzer trajectories for the Roc guided missile (Douglas symbol: 00-1000-V) with range-only control, using the same constants.\n\nControl area: A = 9 sq ft\nDensity: p = 0.959 g/ft\u00b3 (where g = 0.002378 slug/ft\u00b3 is taken as air density at sea level)\n\nU denotes the time of application of control, this item being left blank in the case of free fall. The amount of control is indicated as a certain percentage of the total available; it is continued until a new control is applied at a new value of ti, or until impact. The amount of control is also given in terms of the value of the lift coefficient Cl, where this quantity is positive for sail, negative for dive.\n\n75% Dive\n-\n75% Sail\nFull\n-\nFull\n75% Dive\n-\n75% Sail\nFull\n50% Dive\nNFIDENTIA\n\nAPPENDIX FOR ROC TRAJECTORIES\n\nThis index, like the preceding one, is of data on differential analyzer trajectories for the Roc guided missile (Douglas symbol: 00-1000-V) with range-only control, using the same constants.\n\nControl area: A = 9 sq ft\nDensity: p = 0.959 g/ft\u00b3 (where g = 0.002378 slug/ft\u00b3 is taken as air density at sea level)\n\nU denotes the time of application of control. The amount of control is indicated as a certain percentage of the total available; it is continued until a new control is applied at a new value of ti, or until impact. The amount of control is also given in terms of the value of the lift coefficient Cl, where this quantity is positive for sail, negative for dive.\n\n75% Dive\n-\n75% Sail\nFull\n-\nFull\n75% Dive\n-\n75% Sail\nFull\n50% Dive\nThe runs of RDA No. 130, Editions 1 and 2 listed in this index differ in that any changes of control are applied continuously by the analyzer. The rate of change is determined by the time, 1.7 seconds, during which the control surface passes from the neutral position of no control to that of maximum control. This occurs when sail is first applied at t = 8 seconds. Cl is given by the formula:\n\nCl = (Cl0 + Kp * (Setpoint - Cl0)) * (1 - exp(-t/T))\n\nuntil Cl reaches the specified value, after which it is held constant until a new time ti, at which time a challenge is initiated in a similar way.\n\nCd is also varied continuously with Cl according to the formula:\n\nCd = Cd0 + Kc * (Cl - Cl0)\n\nIn all the runs of this index, 30 percent of the brakes were applied, corresponding to a value of Cd of 0.209, when there is no control.\n\ntf is the time-of-flight in seconds.\nRDA No. 130\nInitial Velocity (mph) X (tf) (feet) Max. Roc Velocity (mph) Trail (mils)\nInitial Altitude (feet)\n5000 None None None\n12500 None None None None\n15000 None None\nInitial Altitude (feet) 30000 None None\n17500 None None\n\nRun No. Initial Velocity (mph) Control O CJ O w tf (sec) X (tf) (feet) Max Roc Velocity (mph) Trail (mils)\nInitial Velocity (mph) Control O Q O O w tf (sec) X (tf) (feet) Max Roc Velocity (mph) Trail (mils)\nX(tf) (feet) Max Roc Velocity (mph) Trail (mils) None None None\n\nAIBR. - Acceleration-integrator bombing release. A name for a bombing release system that calculates release point based on aircraft speed and altitude.\ntoss-bombing component of Bureau of Standards origin. Stands for Azimuth Oxly. A guided bomb for linear ground targets. Radio-controlled and flare-observed.\n\nBARB. British-type angular rate bombsight. An American name for certain instruments based on the British-invented principle of absolute angular-rate bombing criteria for low altitudes.\n\nBug. Apocryphal name for target used in bombing trainers. Crawls on the floor. Certain species crawl in circles or are unpredictable to the trainee.\n\nCART. Constant-angular-rate turntable. Testing apparatus for angular rate meters. Typically, suspended torsion pendula for accurate studies.\n\nCARP. Chronometric, automatic, ROC (or RAZOX) predictor. Alternatively, CRAB reaches perfection. A sight for guided bombs, involving a program leading to terminal collinearity over an interval.\n\nCLIP. Computation of lead with an inertia-pendulum.\nCRAB: Chronometric range-anticipator bombsight. A sight for aiding the guider of RAZOX in range, primarily predicting the terminal point in terms of time of flight. Attaches to the bombsight Mark 15.\n\nDBS: Dive bombsight. Developed by M. Alkali and Specialties, Inc. for the Navy. Toss principle with freed gyro.\n\nDOVE: Origin unknown to Utter. A high-angle guided or homing bomb with \"spoilers\" or \"deflectors\" in front for steering. Polaroid, Xavy project; Division 5 cognizance.\n\nGCB: Ground-controlled bombing. As with RAZOX; ground stations steer bomb to target on known bearings.\n\nGOAD: Giving only angular depression. Local name for rudimentary \"triangular-solution\" bombsights (visual).\n\nGRASP: Gyroscopic, rocketeers, automatic, sighting predictor.\nOrgyroscopic RASP: A rocket sight and computer for attachment to the gyro gunsight, such as Mark 23. JAG. Just another gadget. A time-of-flight corrector, for use with guided bombs and CRAB.\n\nMIMO: Miniature Image Orthodon. Small television camera and transmitter for ROC.\n\nOrthopentax: Linkage having five perpendicular axes, of many and diverse applications.\n\nPACT: Pilot\u2019s automatically computing toss bombsight. A linkage computer, with (pneumatic) integrator of incremental acceleration, and automatic release.\n\nPARS: Pilot\u2019s automatic rocket sight. A miniature computer as aiming control for forward-fired rockets.\n\nPreset: Data given to computers for bombers or bomber crews. For auxiliary function to bombsight Mark 15, providing rate-knob adjustment, etc., in advance.\n\nPUSS: Pilot\u2019s universal sighting systems. Computer for guns, rockets, and bombs, to be employed in fighter airplanes, etc.\nRASP: Rocketeer's automatic sighting predictor. An early project which resulted in an experimental pilot's rocket sight.\nRAZOX: Stands for Range and Azimuth Oxly. Misleading. Should have been AZAR, for Azimuth and Range, for example. Two-coordinate AZOX, intended for point targets.\nROC: Douglas high-angle guided bomb. Named for the roc or rokh, a giant bird of Arabian mythology.\nSniffer: Low-altitude blind bombsight, involving f-m radar. Employs range, range rate, and altitude in automatic computation of release condition.\nVASS: Vosseller antisubmarine sight. Hand-held bombsight based on Vosseller's method of extrapolation. Chronometric.\nVERB: Prehistoric name used for RASP. Rocket bombsight, preceded by two words, which are now unknown; perhaps very exceptional.\n\nRASP, ROC, RAZOX, Sniffer, VASS\nChapter 1, Chapter 2, Corrections Necessary in Aiming a Machine Gun, Mounted on an Airplane, at a Moving Target, J. R. Moore, K8064695, General Electric Company, June 1941. A good exercise in vectorial methods and some fundamental ballistics for aerial gunnery, by one of the most active workers in this field.\n\nGyroscopic Lead Computing Sights, Report to the Services 13, NDRC Section D-2, August 1941. An exposition, on fundamental grounds, of the technique of lead computing, primarily with regard to a single \u201cdisturbed\u201d gyro.\nAn Introduction to the Analytical Principles of Lead Computing: Derivations of familiar formulas and a complete physical interpretation of theoretical steps. By Saunders MacLane. OEMsr-1007, AMP Memo 55.1, AMG-Columbia, March 1944.\n\nMathematically rigorous treatment of classical lead computing dynamics. Fundamental concepts explained and developed to show current theory stage. Glossary of notation (with translations) and good bibliography included.\n\nPursuit Courses: Study in detail of such courses in the air and with respect to the target, with thoroughgoing rigor. Treatment of pure pursuit and lead, though \"mushing\" not considered. Tables included for several standard approaches.\n\nBy Walter Leighton. OEMsr-1007, AMP Memo 57.4, AMG-Columbia, Mar. 1944.\nThe Extrapolation, Interpolation and Smoothing of Stationary Time Series, Norbert Wiener, OSRD 370, Research Project DIC-6037, Report to the Services 19\nAn extension of some Russian work, using the methods of communications engineering, statistical theory, and Fourier analysis. The author\u2019s earlier work is relevant here. Not so difficult to understand as is commonly supposed.\n\nStatistical Method of Prediction in Fire Control, Norbert Wiener and Weaver, NDCrc-83, Report to the Services\nContains a discussion of some of the results of reference 5 above, and of their probable importance in the prediction of straight flight and of flight which is accelerated in various ways. Comparisons among known methods of prediction are included, together with certain historical material.\n\nAn Exposition of Wiener\u2019s Theory of Prediction, N. Levinson, OEMsr-1384, AMP Note 20, AMG-Harvard.\nDevelop the autocorrelation function more gradually, demonstrating that the linear prediction problem reduces to that of solving an integral equation. Practical and mathematical difficulties in application are discussed, and errors in prediction are interpreted mathematically.\n\nCollision Courses by Method of Overcorrecting Changes in True Bearing, (Capt.) V. A. Kimberly, USN, Letter to Chief BuOrd from Special Board on Naval Ordnance, September 1927.\n\nThis letter provides an elementary explanation, in terms of surface vessels, of the named method and shows how and why the method leads to a straight interception as the range closes up. Few such explanations are available in the literature.\n\nElectrical Simulation of the Human Operator in Tracking Mechanisms as an Aid in the Study of Sight Dynamics, R. H. Randall and F. A. Russell, OEMsr-1237, TR.\nReport on proposed operator representation for laboratory tracking experiments, T-13, NDRC-Section 7.2, Columbia University Division of War Research, June 21, 1945.\n\nThis report describes an attempt to use a proposed representation of the operator <</> in place of the real thing for laboratory tracking experiments.\n\n1. Investigation of Operator's Response in Manual Control of a Power-Driven Gun, A. Tustin, C.S. Memorandum 169 (British).\nA review of this memorandum is given in the last mentioned report.\n2. Tracking Aircraft with Heavy Turrets, Merz and McLellan, British Liaison Code WA-1711-1.\nThis paper sets up and studies the hystero-differential equations which result for the ensemble when a direct time delay is attributed to the human operator. Conditions for stability and learning are considered qualitatively.\n3. Some Characteristics of Human Operators in Control\nSystems: K. J. W. Craik (Cambridge University), Ministry of Supply Informal Panel on Servomechanisms, British Liaison Code WA-1641-6, Great Britain, Feb. 4, 1940s.\n\nApparatus and techniques are described where the human operator was studied during direct tracking. Curves of pursuit agree substantially with those obtained in our laboratories. The effects of the excellence of the display and other psychological aspects of the problem are discussed. Also, the transient and harmonic methods of investigation are compared.\n\nThe Conduction of the Nervous Impulse, Keith Lucas, Longmans Green and Company, revised, 1917.\n\nContains evidence that nerve conduction, in the large, is a linear phenomenon, the time relations therein being apparently independent of the strength of stimulus. (This is contrary to the popular belief)\nReflex phenomena are discussed as local affairs connected with nerves themselves. (Adrian, E. D. The Mechanism of Nervous Action. Eldridge Reeves Johnson Foundation, 1931 Lectures. The reader's attention is called to the related bibliography included in Chapter 1. Whitney's views, arrived at through a minimum of quantitative experiment and a maximum of personal intuition, are worthy of attention. Most of his work has been in connection with turrets, but see also his AMG-Columbia Working Paper 329, of Dec. 13, 1944, Notes on the Tracking Problem for Fighter Planes, which advances explanations for some of the anomalous phenomena.\nResults observed in this kind of tracking. For quantitative material relating to man-machine interactions with lead-computing sights, see the rich body of literature under the program sponsored by Section 7.2 at The Franklin Institute. S. H. Caldwell, J. B. Russell, and H. C. Wolfe of that section will report on this work fully. The experimental and analytic procedures were in control of psychologists Preston and Irwin, proteges of S.W. Fernberger at the University of Pennsylvania. Their reports are models of exhaustive disclosure and zealous adherence to data.\n\nBibliography:\nPress of the University of Pennsylvania, 1932.\nIn this book, evidence is given and referred to there as proof.\nThe workings of the nervous system are not beyond mechanical description. (W. R. Miles, Pursuitmeiers: Alcohol and Human Efficiency, Carnegie Institute Publication)\n\nReference 7: A Pursuit Device for Obtaining both Quantitative and Qualitative Records, R. M. Collier, Journal of Psychophysiology\n\nThis reference describes an apparatus involving complex harmonic generation using a wattmeter, error indicator, and manually operated slide-rheostat. It is very modern in spirit and objective, with continuous records shown. In contrast, most such equipment is of the discontinuous or averaging variety. (Journal of Psychodescription)\n\nChapter 3:\n\nFurther Application of the Strain Gauge to Gyroscopic Measurements of Angular Rates, J. D. Eisler, U. C. S.\nTitle: Report 152, Franklin Institute\nDilks and W. W. Felton describe methods and apparatus for lead-computing sights, focusing on compensation required for gyro speed changes, temperature, etc. The noise problem is explained, along with its possible solution. Circuits and photographs are shown.\n\nTitle: Report 218, Franklin Institute\nM. Golomb discusses symmetrically constrained gyros as angular rate indicators, providing a theoretical treatment of the dynamics involved in gyro suspensions proposed for simultaneous measurement of angular rate about two axes with a single gyro. Several types of constraint are considered, and stability conditions are expressed. The effects of static friction in the gimbals are described.\n\nTitle: Report 238, Franklin Institute, October 7, 1945\nU. C. S. Dilks and M. Golomb present a servo-controlled gyroscope.\nThe effectiveness and construction of the two-dimensional electric captive gyro under development for PUSS. Discussed are its speed and accuracy for large and small absolute angular rates, along with limitations. Circuits are provided, as well as methods of testing, and numerical data are included on the basic gyro component involved.\n\nChapter 4\n1. Control Circuits for Radio Controlled Units, J. R. Ragazzini and L. Julie, Diary of Columbia Project, OEMsr- \nDetails the simulative philosophy as applied to control problems. Electronic details are omitted but implied. Consult practical exercises for sight-simulation, guided bombs, etc., for circuits.\n2. Diary Concerning a Conference on November 29 on Subject of Columbia Project, J. R. Ragazzini, OEMsr-1237,\nProposals for simulation of control deflections with boundaries.\n1. conditions as under human operation. Use of feedback amplifiers as integrators, etc., outlined, preparatory to the simulative project on guided missiles.\n2. Report M-35, Columbia University, June 13, 1945: Simulation of PUSS Rocket Sight by J. R. Ragazzini. Proposed PUSS formulas and details for their electronic simulation.\n3. Report M-38, Columbia University, June 13, 1945: Aerodynamic Constants for a Simulated Airplane by F. A. Russell.\n4. Arrangement of degrees of freedom and their connecting relations for the simulative project.\n5. Report M-36, Columbia University, June 21, 1945: Axis Conversion by R. H. Randall. Application of rigid-body dynamics to the problem of airplane simulation. Coordinate systems worked out for incorporation in the electronic model components.\n6. Airplane Simulator (for Small Angles), F. A. Russell and R. H. Randall, OEMsr-1237, NO-265, Report M-33, Columbia University, June 21, 1945.\nSummary of the first working phase of the simulative development for PUSS. References to the aerodynamic literature are included, as are the schematic circuits employed in simulation.\n\n7. On the Study of Cyclic Dynamical Systems by Means of Equivalent Networks, L. Jafek, Cossor Industries, August [Chapter 5]\n1. Theory of Gyroscope Suspended in a GAP Linkage, M. Golomb, Memo to G. A. Philbrick, Franklin Institute, An analysis of the orthopentax employed as a gyro suspension. Its possibility as forming a lead-computing system for PUSS was then being explored. Certain practical advantages were expected, but no practical application has yet been made.\n\nChapter 6\n1. Torpedo Director, Mark 32, R. W. Pitman, OSRD 5079.\nReport 172, OEMsr-330, Franklin Institute\n\nDescribes the final model of the torpedo director from Project NO-106. Foreword by A. L. Ruiz. Figures and re-writing by G. A. Philbrick. This document is in the form of an instruction manual, roughly definitive of the whole development prior to 1944.\n\nTorpedo Director, Model Number One\nR. W. Pitman, R. K. Marshall, F. W. Schlesinger, and others, NO-106, Report 120, Franklin Institute, Aug. 15, 1942.\n\nCovers phases of work on this project during the first half-year of development. Describes vector theory and first mechanizations thereof. Discusses the problem of stabilization in azimuth. Appendices treat related problems, such as the optical ones connected with the pilot\u2019s sight head. References are included to even earlier documents.\nFor documents on computing linkages, such as those prepared for the PUSS project at The Franklin Institute, the contractor's final report, yet to be received, should be consulted. It is now expected that this work will be extended under Navy auspices, providing another future source of information: Section ReSc of the Bureau of Ordnance.\n\nThe final report of The Bristol Company under their contract (OEMsr-1387) with NDRC Section 7.2 may also be consulted, particularly in relation to manipulated linkage developed within the PUSS project.\n\nSee also reports from the Radiation Laboratory (MIT) and Librascope Corporation for other computing linkages.\n\nBIBLIOGRAPHY\n3. The Electrical Solution for the Torpedo Director (NO-106), J. D. Eisler, Report 135, Franklin Institute.\n\nDescribes the a-c vector embodiment of the same theory as in [1]\nmechanical directors. Certain advantages in flexibility of installation were sought, and a technique was experimentally developed for further applications. This involves the stabilization of the Mark 31 Torpedo Director for Motor Torpedo Boats, by J. D. Eisler, NO-134, Report 148, Franldin Institute, June 15, 1945.\n\nThis primarily concerned a servo development which derived stabilization for the target velocity, as set in this director, by means of the Flux-gate compass. Construction details are provided, though test data are not included. Good operation was experienced in field tests at the MTBSTC at Mehnlle, Rhode Island.\n\nChapter 7\n1. U.S. Navy Bombsight Mark 20, R. W. Pitman and others. Report 200, Franklin Institute, August 1943.\n\nA descriptive manual of the theory and instrumental principles, as well as the installation and maintenance of this bombsight, is detailed in this report.\n1. Instructions for operation with pictorial aids are included for the Auxiliary Ground Speed Computer, John A. Bevan and others. Report 167, Franklin Institute, Dec. 12, 1943.\nDescription of and instructions for use of a miniature mechanical computer for use with hand-held bombsights. Widely applicable.\n2. Automatic Altitude Adjustment for Bombsight Mark 20, Report 161, Franklin Institute, Jan. 24, 1944.\nAccount of an experimental project where the altitude determined by the f-m radio altimeter is servoed into the bombsight continuously. Very small equipment resulted, attachable without interference to a hand-held instrument. A d-c resistive feedback principle is applied.\n3. Bombsight V, Model 3, John A. Bevan, Report 168, Franklin Institute, Mar. 6, 1944.\nThis is one of the many adaptations of the basic principle of the bombsight.\nMark 20, without chronometric extrapolation. Each modification led to diminishment in size and complexity. Satisfactory results were obtained in flight tests at NAS Banana River.\n\n5. Bombsight VI, LTA, John A. Bevan, Report 178, Franklin Institute, MA 6, 1944. Div. 7-122.4-M2\nAn adaptation of bombsight V, so-called, to the bombing problem of blimps. This sight became bombsight Mark 24 and enabled a surprising accuracy of dropping.\n\n6. Slant Range Computer, R. W. Pitman, Report 156, Franklin Institute, Nov. 5, 1943. Div. 7-123-M1\nDescription of a small, flat, manually operated computer, giving the slant range at which bomb release should occur, in horizontal flight at low altitude, in terms of altitude and closing speed. One-hand operation. Model submitted to BuAer.\n\n7. The Preset Computer Model 3, John A. Bevan, OSRD\nReport 189: A mechanical computer, the final model of several developed, supplying preliminary information on how synchronizing runs to the high-altitude bombsight operates. Inputs are manually applied, except azimuth stabilization, which is automatically provided.\n\nReport 155: J. D. Eisler, Strain Gauge BARB, Franklin Institute, June 1943. This report details experimental angular-rate measurement from processing torque of a restrained gyro, with strain gauges applied to the restraining members. Tentative application to a low-altitude bombsight is also discussed.\n\nNotes on Low Altitude Bombing, G. A. Philbrick and R. M. Peters, Research Project 33, NDRC Section 7.2, Franklin Institute, May 1943 \u2013 March 1944. A series of studies focusing primarily on the theoretical evaluation of bombing errors for various known methods.\nThe BARB theory, including its variables, is discussed in detail, with predictions of comparative results. An account of the BARB theory is included, as well as the unworkability of the \"hybrid\" BARB, which resulted in no time being wasted on it. Goldberg's writing on this topic, under Section 7.3, should also be referred to. BARB eventually became IMark 23 and 27 bombsights, specifically BARB and SuperBARB.\n\nGyroscopic Lead Computing Sights, Report to the Services:\n- Norden Bombsight Attachment for Guiding AZON f and RAZON Bombs (John A. Bevan, OSRD 5740, OEMsr-330, AC-36, Report 194, Report to the Services 97, Franklin Institute, Oct. 10, 1944. Div. 7-122.4-M\n- Description of the CRAB sight theory and nature.\nInstructions for installing, calibrating, and operating the Norden-Type Bombsight attachment CARP. Adapted by NDRC Division 5 for the Preliminary Technical Manual CRAB, issued in June 1945.\n\nNotes on calibration, installation, and operation of CARP by John A. Bevan, Report 199, Franklin Institute. Descriptive material on CARP with an appendix providing theory, especially of the artificial disk speed technique. Includes functional diagrams, circuits, and photographs. No clues as to why the CARP ROC combination failed as a collinear flare-guiding system. For related matters on ROC and other projectiles and vehicle controls, refer to the report of NDRC Division 5 and its contractors, particularly Gulf Research and Development, and Douglas Aircraft. Note in particular the writings of W. B.\nKlemperer of the latter organization.\n\nReport 1: Study of AZON Control and Regulation, L. Julie, OEMsr-1237, Columbia University, May 10, 1944.\nDescription of the initial simulative system whereby the dynamics of guiding were electronically reproduced in the laboratory. Consult Records of the RDA No. 2 at MIT for more precise data on trajectory shapes.\n\nReport 7-1: Completion of Trainer Project, L. Julie, OEMsr-1237, Columbia University, Oct. 21, 1944.\nExposition of the final experimental form of the universal guided-bomb simulator for AZON, RAZON, and ROC. This device was later produced as a field trainer for guiders by Division 5 agencies. Circuits and alignment techniques are given.\n\nReport M-23: The AZON-RAZON Bombing Trainer, (Models X-1010. Based on writings and developments of Section 7.2, applied to guided systems.\nbombing equipment. Attachment of electronic simulative equipment to Army A-6 and A-5 bombing trainers. Similar combinations with the Navy 7A3 bombing trainer were also carried out, in which a moving spot was projected on the synthetic landscape of the photographic trainer.\n\nStudy of the Guiding Characteristics of the Television Bomb; including a Regulator for Guiding, L. Julie, OEMsr-1237, Report 7-14, Columbia University, June 19-- Employment of electronic simulative techniques to study the stability of a proposed control system for attaining interception under remote manual guiding, even with target motion in the air.\n\nChapter 9\n1. Development of Rocket-Gun sights; Summary Report on\nReport on the Development of Rocket Sights at The Franklin Institute: A Detailed Account by Eugene P. Cooper, including Historical Sequence, Logical Steps, Field-Testing Programs, and Connected References to Local Rocketry Developments. This is a final statement by the author, who held significant responsibility in this field.\n\n2. Sighting of Rocket Projectiles from Aircraft by C. W. Gilbert, British Liaison Code, WA-3190-3, Gunnery Research Unit, RAF, October 19, 1944.\n\nThe tactics and aiming problem are explored, with a breakdown of the sighting problem in terms of allowances for relative speed, trail (attack angle and skid), and gravity. Proposals are made for solutions.\n3. Memo to G. A. Philbrick, Eugene P. Cooper, Franklin Institute, July 18, 1944: Future development and a general vector theory included. Cooper presents here the theory later embodied in the British method of rocket aiming. He expresses reasons for pessimism regarding the results. Note that this method ultimately generalized to PUSS.\n4. Gravity Drop Formulas for Airborne Rockets, Harry Pollard, AMG-C Working Paper 347, AMG-Columbia, Jan. 4, 1945: AMP-603-M2. Fitting of firing-table data to second-order space paths. See also various CIT rocket publications and firing tables.\n5. The RASP Rocket Sight\u2014Model I, U. C. S. Dilks, E. C. Lewis, and others, Franklin Institute, Aug. 17, 1944. Div. 7-132-M1.\nA descriptive account of the RASP project in its primary phase. Includes the derivation of equations and their mechanization. A study of the theoretical accuracy is included, together with firing data from tests \u2013 final reductions thereof, photographs, and circuits. Foreword by G. A. Philbrick.\n\n6. The RASP Rocket Sight\u2014 Model III, U. C. S. Dilks, E. C. Lewis, and W. C. Sheppard. OSRD 5091, OEMsr-330, NO-265, Rejwrt 206, Franklin Institute, Feb. 1, 194--. Comparisons with Model I are included throughout. The computational technique is newly explained and an appendix is devoted to a more theoretical treatment of this technique, with general applications. Many photographs are included, and circuits and servo components are described in detail. Analyses of test data with statistical reduction are included. A foreword is attached, prepared by G. A. Philbrick.\nThe GRASP Sight for Forward Firing Aircraft Rockets, Model I, Eugene P. Cooper and Marjorie C. Cooper, OSRD 4991, OEMsr-330, NO-216, Report 211, Franklin\n\nThe method is described, and a derivation is given of the equations to be employed. The details of the physical computation and of the instrumental components are elaborated upon, with a study of errors in firing. Comprehensive testing data are given. A foreword by G. A. Philbrick is attached.\n\nThe GRASP Rocket Sight, Model II, Eugene P. Cooper and Marjorie C. Cooper, OSRD 6040, OEMsr-330, NO-216, Report 213, Franklin Institute, Sept. 30, 1945.\n\nReport 211 is here brought up to date for the newer model. (For ARS Mark 3, the writings of H. Whitney, et al, of AMG-C should be referred to by the reader, where corresponding details of the jointly pursued PARS project.)\n9. Measurement of Angle of Attack and Skid in Rocket Fire\nH. L. Garabedian, OEMsr-1379, AMG-Northwestern, Working Paper 61 (revised)\n\n1. Laboratory calibration account included. Results of firing tests at NOTS, Inyokern. Foreword by the present writer attached.\n\n9. Measurement of Angle of Attack and Skid in Rocket Fire (Garabedian, 1945)\n- Exhaustive account of laboratory calibration\n- Results of firing tests at NOTS, Inyokern\n- Foreword by the present writer\n\nChapter 10:\n1. Analysis of Optical Systems for PUSS, I. M. Levitt, Report 241, Franklin Institute, Oct. 31, 1945\n- Review of problems and proposals for universal sight heads for pilots\n- Collimating lenses and mirror linkages discussed\n- Possible modifications to Fly\u2019s Eye design.\nNation problems are explored in this report. Tentative overall conclusions have been arrived at. The final report of the Bristol Company contract, Section 7.2, should also be consulted.\n\nInterim Report on PUSS, John A. Bevan, Report 224, Franklin Institute, August 24, 1945.\n\nThis report is a compilation of recent documents, arranged as seven independent appendices, with an introduction on the current status of the project, including theory and design. Instrumental techniques are discussed, with a review of input components, computers (including PACT for toss bombing), and sight head. The electric and pneumatic versions of PUSS are described and compared.\n\nThe appendices of this report, which are worthy bibliographic items in their own right, include memoranda and theoretical papers on gyro systems, computing dynamics (with competing theories), roll control, and other related topics.\n1. stabilization, etc., prepared chiefly by INI. Golomb and R. O. Yavne.\n2. Servo-Controlled Gyroscope, U. C. S: Dilks and M. Golomb, Report 238, Franklin Institute, October 2, 1945.\nTheory and construction of the two-dimensional, electrically captured gyro in development for PUSS. Effectiveness for small angular rates is discussed, with limitations included. Electronic circuits are given in detail, along with the electrical and other properties of the basic gyro unit which was adapted for this purpose.\n3. Development of Pilot-Operated Fire Control Equipment: Outline of the General Project, G. A. Philbrick, Aircraft Engineering, Volume 25, Preview of the PUSS Project. Aims and hopes for the development. Gives scope and instrumental specifications. Discusses aiming methods, including those without explicit range measurement. Proposed electronic tracking simulator for pilot-operated fire controls.\n5. Notes on Pneumatic PUSS; L. Charles Hutchinson, [OEMsr-1007], AMG-C Working Paper 461, AMG-\nConsiders pneumatic embodiment of computing dynamics. Gives theory and brief experimental data.\n\n6. Notes on Pneumatic PUSS; II, L. Charles Hutchinson, [OEMsr-1007], AMG-C Working Paper 478, AMG-\nConsiders pneumatic component for the input giving rate of change of altitude. Circuits, theory, and numerical data. Includes non-linearities.\n\n7. PUSS, Target, Sight, Horizon Presentation, J. R. Ragazzini and R. H. Randall, OEMsr-1237, Report M-34, Columbia University, May 29, 1945.\nSimulative computational arrangements for pilot\u2019s tracking simulator. Includes dynamics, coordinates to be employed, and the optical or oscilloscopic display.\n\n8. A Theory of Toss-Bombing, Harry Pollard, [AMP Report 146. IR, AMG-Columbia], September 1945.\nPrinciples of toss bombing on a revised basis. Measurables of the problem, including target motion. Mechanization of formulas, employing integral of normal acceleration. This is the definitive theory for PACT.\n\nThe Azimuth Problem in Toss-Bombing, Harry Pollard, AMG-C Working Paper 495, AMG-Columbia, Sept. 18, 1942. Shows an exact solution for the target motion in azimuth. The effect of roll and bank is included, and the appropriate sighting dynamics, for use with PUSS and PACT, are specified.\n\nPART II\n\nThe following reports were all issued by The Franklin Institute under Contract OEMsr-330.\n\n1. Reflecting Sight for Torpedo Director, Report 330-1706-1706\n2. Torpedo Director N 0-106 \u2014 Tests on Sight Containing a Miniature Ship Model, Report 330-1706-103, May 6, 1942.\n3. Use of Radar Data in Torpedo Director N 0-106, Report \n4. Altitude Speed Range Slide Rule for Simplified Torpedo\n5. Torpedo Director NO-106: Principle and Operation of Experimental Director Report 330-1706-107, May 26\n6. Torpedo Director NO-106: Stabilizing Systems\n7. Proposed Continuous Electrical Solution for Torpedo Director Report 330-1706-110, July 25, 1942.\n8. Explicit Relation Between Present Range and Torpedo Run in Torpedo Director NO-106 Report 330-1706-\n9. A Two-Phase Stabilizer for Torpedo Director NO-106\n10. An AC Current Controller for Stabilizing the Torpedo Director\n11. Reflecting Sight for Torpedo Director NO-106 Report\n12. Torpedo Director NO-106: Further Notes on Two-Man\n13. Wind Effects Relative to Torpedo Director Report 330-\n14. Effects of Interchange of Torpedo Run and Range on the Performance of Torpedo Director in Attacks on Bow\n15. Torpedo Director NO-106: Principles, Model Number One\n17. Calibration of Torpedo Director for Army Air Use\n18. Torpedo Director NO-106, Flight Tests at Norfolk, VA\n19. Preliminary Studies Leading to the Development of a Photoelectric Stabilizer for the NO-106 Torpedo Director,\n20. A Photoelectric Stabilizer for the NO-106 Torpedo Director,\n21. Conditions of Torpedo Running Time Affecting the Use of Torpedo Director NO-106, Report 330-1706-128,\n22. Tables and Graphs for Calibration of Torpedo Director Calibration Tests, Torpedo Director NO-106, Type \u2018GT\u2019,\n23. Preliminary Study of Japanese Torpedo Director, Report,\n24. Use of Torpedo Director \u2014 Errors in Lead Angle to be Expected from Errors in Ebti?natio7i of Fs, Target Speed,\n25. Two-Axis Controller for Stabilizing the N 0-106 Torpedo,\n26. The Electrical Solution of N 0-106 Torpedo Director,\n27. Mark 32 Torpedo Director \u2014 Inaccuracies in Theory and.\nGeneral Solution of Determination of Minimum Range, Time of Travel to This Point and Angle Between Course of M.T.B. and Minimum Range\nReport 330-1706-140\n\nAdaptation of General Electric Automatic Pilot System to Stabilization of N 0-106 Torpedo Director,\nUse of a Rule-of-Thumb Method of Torpedo Direction,\nM.T.B. Director: Preliminary Study of Applicability of Stabilization of Mark 31 Torpedo Director for M.T.B.,\nField Tests of Stabilized Mark 31 Torpedo Director NO-134,\nHelmsman Direction Indicator for M.T.B. Mk 31,\nTorpedo Stabilizer for Torpedo Director Mark 30, OSRD 508(),\nStudy of Apparent Length Method for Aiming Air-Borne,\nAnalysis of Films from Project 7-43, A.A.U., U.S. Naval Air Station, Norfolk, Virginia, Report 330-1706-\nTorpedo Director Mark 32, R. W. Pitman, OSRD 5079,\nLinear Target Track Errors Caused by Accidental Deviations.\nReports from Horizontal Mount of Flight Path of a Torpedo\nTorpedo Director Type B-3, OSRD 6223, Report 330-\nCombination Torpedo Director, Fixed Gun Sight and Bomb\n\nBIBLIOGRAPHY\n43. Range Type Torpedo Director, Report 330-1706-1706,\n44. Apparent Length Method for Aiming Tossed Torpedoes,\n45. Torpedo Director for Maneuvering Targets, Report 330-\n46. Torpedo Trainer Computer, Report 330-1706-227, October 1945.\n\nThe following reports were issued by the Statistical Research Group, Columbia University;\n47. Lead Angles for Aerial Torpedo Attacks Against Turning Ships, OEMsr-618, AMP Report 8.1R, SRG Report 190,\n48. Tables of Aircraft Torpedo Lead Angles, OEMsr-618, AMP Report 8.2R, SRG Report 453, May 1945.\n\nPART III\nMilitary Airborne Radar Systems, NDRC Summary Technical Report, Division 14, Vol. 2, Radiation Laboratory, Massachusetts Institute of Technology.\n2. Analytical Studies in Aerial Warfare, NDRC Summary Technical Report, Applied Mathematics Panel, Vol. 2.\n3. Aerial Gunnery Problems, Saunders MacLane, AMG-C.\n4. Bibliography of Papers Written at the Applied Mathematics Group, Division of War Research, Columbia University, L. LaSala and M. Reiner, OEMsr-1007, AMG-C 496.\n5. Pursuit Courses, Walter Leighton, OEMsr-1007, AMG-C 141, AMP Memo 57.4, AMG-Columbia, March.\n6. Aerodynamic Lead Pursuit Curves, Daniel Zelinsky, OEMsr-1007, AMG-C 273, AMG-Columbia, Sept. 29.\n7. The Aerodynamic Pursuit Curve, IVl. M. Day and W. Prager, OEMsr-1066, AMG-B Memo 31 M, AMP.\n8. Aerodynamic Lead Pursuit Curves for Overhead Attacks, G. H. Handelman and W. R. Heller, OEMsr-1066, AMG-B 79, AMP Report 106.2R, AMG-Brown, Oct. 31.\n9. Equations for Aerodynamic Lead Pursuit Courses, Leon, AMG-Columbia, July 1945. AMP-503.7-M12.\n10. Aerodynamic Lead Pursuit Courses, Leon W. Cohen, Columbia, July 1945. AMP-503.7-M11\n11. Interception and Escape Techniques at High Speed and High Altitudes, W. B. Klemperer, Report SM-3263 (revised), Douglas Aircraft Company, Inc., October 1941.\n12. Graphs of Pursuit Curve Characteristics, N. V. Mayall, OEMsr-101, Carnegie Institute of Washington and Mt. Wilson Observatory, April 1944.\n13. Pursuit-Bomber Attack Calculations, Report D.A. 71353, General Electric Company, December 1943.\n14. The Bank of an Airplane and Load Factor Under Conditions of General Flight, William M. Borgman, Jam Handy Organization, Inc., June 1944. AMP-504.6-M2\n15. Experimental Determination of the Path of a Fighter Plane in Attacking a Bomber, Navy Contract N166s-2052, Jam Handy Organization, Inc., March 1944.\n16. The Current Status of the Simplest Attackability Problem.\nJohn W. Tukey, OEMsr-1365, AMG-P Memo 12, AMG-Princeton, June 7, 1945. AMP-504.4-M14\n\n17. Firing Sideways from an Airplane: Theoretical Considerations, H.P. Hitchcock, Report 16, Ballistic Research Laboratory, Aberdeen Proving Ground, August [--]\n18. The Effect of Yaw on Aircraft Gunfire Trajectories, Theodore E. Sterne, Report 345, Ballistic Research Laboratory, Aberdeen Proving Ground.\n19. Analytical Trajectories for Type 5 Projectiles, Theodore E. Sterne, Report 346, Ballistic Research Laboratory, Aberdeen Proving Ground.\n20. On the Motion of a Projectile with Small or Slowly Changing Yaw, Report 446, Ballistic Research Laboratory.\n21. Analysis and Computation Procedures for 50 Cal. Machine Gun Ballistic Corrections, Report DF-71342, General Electric Company, August 14, 1942.\n22. Simple Formulas to Fit the Values Tabulated in the Firing Table.\n23. \"Ballistic and Deflection Formulas for Aerial Gunnery,\" Alex E. S. Green, Laredo Army Air Field Research, September 1944, AMP Memo 104.1, AMG-Columbia.\n24. \"On Direct Firing Tables for Flexible Aircraft Gunnery, with Particular Reference to Caliber 0.50 A.P. M2 Ammunition,\" Theodore E. Sterne, Report 396, Ballistic Research Laboratory, Aberdeen Proving Ground, September 1945, AMP-503.3-M8.\n25. \"Deflection Formulas for Airborne Fire Control,\" Magnus R. Hestenes, OEMsr-1007, AMG-C 247R, AMP 104.2R, AMG-Columbia, October 1945.\n26. \"The Problem of True Lead Under Evasive Action (Two-Dimensional Case),\" [OEMsr-1007], AMG-C 235, AMP Study 104, AMG-Columbia, July 25, 1944.\n27. \"Tables of True Leads for Two Pure Pursuit Courses,\" Irving Kaplansky, [OEMsr-1007], AMG-C 222, AMP Study 104, AMG-Columbia, July 8, 1944.\n28. Tables Giving True Lead for Three Pure Pursuit Courses, Gustav A. Hedlund, OEMsr-1007, AMG-C 231, AMP Study 104, AMG-Columbia, July 20, 1944.\n29. Some Uses of Variable Speed Mechanisms in Fire Control, Magnus R. Hestenes, OEMsr-1007, AMG-C 149, AMP\n30. Gyroscopic Lead Computing Sights, Report to the Services,\n31. Solution of the Differential Equation, \u2014da/dt + 1/u = da/dt, Walter Leighton, OEMsr-1007, AMG-C 142, AMP Memo 57.5, AMG-Columbia, March NFIDENTIAL\n32. An Alternate Method for Solving the Equation, \u2014da/dt + 1/w * X = da/dt, Magnus R. Hestenes, OEMsr-\n33. Conversion Formulas for Elevation and Traverse Leads, OEMsr-1007, AMG-C 121, AMP 54.1, AMG-Columbia,\n34. Tables of Errors Committed When Using N-8 Sight with Position Firing Rules Against Three Pure Pursuit Courses,\n35. Emergency Sighting Rules for Gunners on B-29 Bombers.\n36. Position Firing Rules for the A-26, Dan Zelinsky, Columbia, March 1945. AMP-503.4-M7\n37. On Apparent Speed Firing, Charles Nichols, OEMsr-1379, AMG-N 80, AMP Memo 157.2M, AMG-North-\n38. Own Speed Sights, Alex E. S. Green and George W. Taylor, Laredo Army Air Field Research Bulletin 101,\n39. Tail Gun Computing Sight (Revised), E. B. Hammond, Sperry Gyroscope Company, Inc., Mar. 16, 1943.\n40. Nose Computing Sight (K-11), B. L. Allison, Sperry Gyroscope Company, Inc., Aug. 4, 1943 (revised July 7, 1943).\n41. Preliminary Instructions, Sperry Compensating Sights, Types K-10 and K-11, Instruction 14-223A, Sperry Gyroscope Company, Inc., December 1943.\n42. Vector Gunsights and Assessing Cameras, OSRD 5646, Report to the Services 96, Jam Handy Organization, Inc.,\n43. The Army Vector Sight Manual, AAF Contract W33-\n44. Conversion of B-17 Stinger Sight Into an Own Speed Sight by Changing Pulley Ratio - R.V. Churchill, Laredo Army Air Field Research Bulletin 102, July 1, 1944.\n45. An Experimental Own-Speed Gunsight - Edward F. Allen, OSRD 5083, Report 330-1706-911, Franklin Institute,\n46. Judgment of Attack and Support Situations in the Air - Laredo Army Air Field Research Bulletin 134, May 24, 1944.\n47. Judgment of Aspect Angles - Laredo Army Air Field Research Bulletin 121, Sept. 30, 1944.\n48. Use of Compensating Sights Including the Problem of Support Fire - Laredo Army Air Field Research Bulletin, Charles Nichols, AMG-N 37 (revised), AMP Memo 157. IM, AM G-North western, Mar. 19, 1945.\n50. Instructions for Sperry Compensating Sight, Type K-13.\nSperry Gyroscope Company, Inc., Instruction 14-224, A Comparison of True Leads and the Leads Produced by the K-13 Sight for Three Pure Pursuit Courses - Gustav A. Hedlund, OEMsr-1007, AMG-C 241, AMP Study No. 51, Columbia, November 1944. AMP-503.3-M3\n\nWhat is 'Percent of Own Speed Deflection? - Gustav A. Hedlund, OEMsr-1007, AMG-C 354, AMP Memo 119.1M, AMG-Columbia, January 1945.\n\nAverage Percentages of Own Speed Deflection - Dan Zelinsky and M. J. Lewis, OEMsr-1007, AMG-C 472, AMP Memo 119.2R, AMG-Columbia, October 1945. AMP-502.12-M20\n\nOptimum Methods of Using Compensating Sights - Dan Zelinsky, OEMsr-1007, AMG-C 472, AMP 119.2R, AMG-Columbia, October 1945. AMP-503.6-M21\n\nAn Introduction to the Analytical Principles of Lead Computing Sights (Corrected Preliminary Form) - Saunders MacLane, AMG-C 137, AMP Memo 55.1M, AMG-Columbia, April 1944. AMP-503.6-M21\n\nSperry .50 Calibre Automatic Computing Sights (Types K-3, K-4, K-5) - Sperry Gyroscope Company, Inc.\n57. K-3 and K-4 Aircraft Sight Error Analysis, Edmund B. Hammond, Jr., Sperry Gyroscope Company, Inc.\n58. Preliminary Instructions, Sperry Computing Sight, Type K-12, Sperry Gyroscope Company, Inc.\n59. Bias Errors of the K-3 and K-12 Sights, Irving Kaplansky and Mae Reiner, OEMsr-1007, AMG-C 368, AMP\n60. Theory of Gun Sight Mark 14, C.S. Draper and E.P. Bentley, Sperry Gyroscope Company, Inc.\n61. Errors in Two Gyro Lead Computing Sights, [OEMsr-1007], AMG-C 66, AMP Study 72, AMG-Columbia, May 1945.\n62. Summary of Sights of the Mark 18 Family, Irving Kaplansky, [OEMsr-10071, AMG-C 459, AMP Study 155, AMG-Columbia, July 6, 1945. AMP-502.12-M19\n63. Service Manual for Gun Sight Mark 18 and Mods., Bureau of Ordnance, Navy Department, Ordnance Pamphlet 1043, September 1943.\n64. Mark 18 Gun Sight, Research Technical Report 7, Lukas-Harold Corporation, August 15, 1944.\n65. Design and Calibration of Mark 18 Sight Computer, Research Technical Report 9-A, Lukas-Harold Corporation, August 1944.\n66. Theoretical Analysis of the Performance of Gyroscopic Sights of the Mark 18 Type, OSRD 5976, Report 330-1706-198, Report to the Services 99, Franklin Institute, July 1944.\n67. Solution of the Equations for the Behavior of the Mark 18 Gunsight when Tracking an Arbitrary Space Course, Donald P. Ling, OEMsr-1007, AMG-C 238, AMP Study 104, AMG-Columbia, July 28, 1944.\n68. The Theory of an Electro-Magnetically Controlled Hooke\u2019s Joint Gyroscope, Donald P. Ling, OEMsr-1007, AMG-C 262, AMP 104.3R, AMG-Columbia, October 1945.\n69. The Optical System of the Mark 18 (K15) Gyro Gun Sight, L. Charles Hutchinson, OEMsr-1007, AMG-C 261, AMP 104.5R, AMG-Columbia, October 1945.\n70. Deflection Formulas for Gun Sights of the Mark 18 Type, Donald P. Ling, AMG-C 358 (revised), AMP Study 104, AMG-Columbia, June 26, 1945.\n71. The Behavior of the Mark 18 Sight on Pure Pursuit Courses, Irving Kaplansky, AMG-C 264, AMP Study 104, AMG-Columbia, Sept. 20, 1944.\n72. Bias Errors of the Interiyn Mark 18 (K15), Irving Kaplansky, OEMsr-1007, AMG-C 367, AMP Study 104,\n73. Tests of the Gun Sight MK 18, Lloyd A. Jeffress and Lawrence E. Brown, OSRD 4979, Report to the Services, The University of Texas, Oct. 22, 1945.\n74. The Calibration of the Mark 18, Irving Kaplansky,\n75. A General Principle Regarding the Design of Instruments, with Special Reference to Lead-Computing Sights, George Piranian, OEMsr-1007, AMG-C 239, AMP Study 104,\n76. The Time of Flight Setting of a Lead Computing Sight.\nIrving Kaplansky, OEMsr-1007, AMG-C 351, AMP\n\nMemo 155. IM, AMG-Columbia, March 1945.\n\n77. Tracking and gun errors over a \"crossover\" course with variation of time-of-flight setting appropriate to range. Report 330-1706-208, Franklin Institute, Aug. 2, 1945.\n78. Tracking and gun errors observed with extreme values of \"a\" of the lead computing sight with two kinds of turret control. Report 330-1706-225, Franklin Institute, Aug. 1945.\n79. Second report on tracking and gun errors over a \"crossover\" course with variation of time-of-flight setting appropriate to range. Report 330-1706-230, Franklin Institute, Oct. 15, 1945.\n80. Final report on test of evaluation of aerial guns and gun sights. Hqs. Army Air Forces Proving Ground Command, Eglin Field, Florida, Serial 2-44-22, AAF.\n81. Errors made by a lead-computing sight when the target follows a pursuit course. Walter Leighton, AMG-C 82.\n82. Graphical Summaries of Mechanism Errors of Various Airborne Fire Control Systems, OEMsr-1007, AMG-C 300 (revised), AMP Study 104, AMG-Columbia, December \n83. An Analytic Study of the Performance of Airborne Gun Sights, Donald P. Ling, OEMsr-1007, AMG-C 440, AMP 104. IR, AMG-Columbia, June 1945.\n84. Fairchild Type S-3 Gyro Computing Sight, Fairchild Camera and Instrument Corporation, September 1944.\n85. Lead Formulas for the Fairchild S-3 Sight, Magnus R. Hestenes and Dan Zelinsky, OEMsr-1007, AMG-C 363, AMP Study 104, AMG-Columbia, February 7, 1945.\n86. More on the Gyro Error in the S-3, E. R. Lorch, OEMsr-1007, AMG-C 419, AMP Study 104, AMG-Columbia.\n87. Preliminary Analysis of the S-4 Sight, E. R. Lorch and Dan Zelinsky, OEMsr-1007, AMG-C 451, AMP Study 104.\n88. The Sperry S-8B Stabilized Sight, Samuel Eilenberg.\n90. Radar Gun-Laying System Final Technical Report, OEMsr-233, NDRC Division 14 Report 385, General Electric Company, 1944. Div. 14-323. 13-M4\n91. The 2 CHlAl Aircraft Fire Control Computer, Supplement to Final Technical Report, Dan L. Colbath, OEMsr-233, NDRC Division 14 Report 570, Report 45813, General Electric Company, Nov. 16, 1945.\n92. Operation and Service Instructions for the Central Station Fire Control System, AAF Technical Order AN-70A-20,\n93. Handbook of Instructions with Parts Catalogue for Restrained-Type Gyros, AAF Technical Order AN-70A-25,\n95. General Principles of the General Electric CFC Computer: Models 2CH1C1 and 2CH1D1, Magnus R. Hestenes, Daniel C. Lewis, and F. J. Murray, OEMsr-1007, AMG-C 346, AMP Memo 143.\n96. Gyroscopes of the General Electric CFC Computer in the B-29 Airplane, Magnus R. Hestenes, Daniel C. Lewis, and F. J. Murray, OEMsr-1007, AMG-C 345, AMP Memo 143.2M, AMG-Columbia, September 1944.\n97. The Axis Converter and the Potentiometer Resolver in the General Electric B-29 Computer, Magnus R. Hestenes, Daniel C. Lewis, and F. J. Murray, OEMsr-1007, AMG-C 346.1, AMP Memo 143.3M, AMG-Columbia, September 1945. AMP-503.5-M13.\n98. Free Gyro Lead Computer, Report 45751, General Electric Company, July 21, 1944.\n99. G.E. Gyro Stabilized Sight with Lead Control for Remote Mounting.\n100. A Suggestion for Improving the Performance of the B-29 2CH1C1 Computer, Magnus R. Hestenes and Daniel C. Lewis, OEMsr-1007, AMG-C 391, AMP Study 143, 101. Further Modifications of the B-29 Fire Control Computer, Magnus R. Hestenes and Daniel C. Lewis, OEMsr-1007, AMG-C 391a, AMP Study 143, AMG-Columbia, 102. A Proposal for Controlling the Speeds of the Total Correction Motors in the General Electric 2CH1C1 Computer, Magnus R. Hestenes, Daniel C. Lewis, and F. J. Murray, 103. Remarks with Regard to Modifications of the Present B-29 Computer, Magnus R. Hestenes and Daniel C. Lewis, 104. Ranging in Defense of the B-29 Against Nose Attacks, Daniel C. Lewis, OEMsr-1007, AMG-C 394R, AMP Study 188, AMG-Columbia, June 30, 1945.\n\nControl reports for improving and modifying the performance of the B-29 2CH1C1 computer by Hestenes and Lewis, further modifications by Hestenes, Lewis, and Murray, remarks by Hestenes and Lewis, and ranging defense by Lewis. Reports from OEMsr-1007, AMG-C 391, 391a, AMG-Columbia, and AMP Study 143, 143, 188. Dated September 12, 1944, and June 30, 1945.\n105. Test of G.E. Fire Control Equipment in B-29 Airplane, Army Air Forces Board, Project M-110, June 20, 1944.\n106. Ground Tests of the B-29 Central Fire Control System, W. D. Crozier, OEMsr-1390, AC-92, UNM/V/TR5, LT, University of New Mexico, Jan. 15, 1945.\n107. Tests of B-29 Computers for Nose Defense on the University of Texas Testing Machine, Edwin Hewitt and William L. Duren, Operations Analysis Division, Headquarters Twentieth Air Force, Apr. 28, 1945.\n108. Calibration of the B-29 Computer for Tail Defense, Edwin Hewitt, Operations Analysis Division, Headquarters Twentieth Air Force, July 4, 1945.\n109. Calibration of the B-29 G.E. C.F.C. System, Lloyd A. Jeffress, War Research Laboratory, University.\n110. Sperry AGL-2 Equipment, Instructions 23-165, Sperry Gyroscope Company, Inc., March 1943.\n111. Preliminary Instructions, Sperry Central Fire Control Equipment.\n[112. The Sperry Stabilized Aircraft Gun Laying System, Intermediate Phase, NDRC Division 14 Report 289, Sperry Gyroscope Company, Inc., May 1944.\n113. Report on NDRC Contract OEMsr-812, [The Fairchild Central Station Computer], OEMsr-812, NDRC Division 14 Report 433, Fairchild Camera and Instrument\n114. The Remote Control of Guns in Aircraft: An Account of an Experimental Armament Installation in a Lancaster Aircraft, Royal Aircraft Establishment, Farnborough, Technical Note Arm. 269 (F.C.), February 1944.\n115. Report on Preliminary Trials of an Experimental Armament in a Lancaster Aircraft, Royal Aircraft Establishment, Farnborough, Tech. Note Arm. F.C. 308, October 1944.\n116. Final Report on Tracking Studies, Report 330-1706-232, Project NO-268, Franklin Institute, Nov. 15, 1945.]\n117.  Exploratory  Experiments  on  Tracking  with  Lead  Comput- \ning Sight,  Report  330-1706-151,  Project  1706-2A, \nFranklin  Institute,  Aug.  14,  1943. \n118.  Tracking  Errors  in  Systems  Using  Velocity-Tracking  and \nAided-T racking  Controls  with  Direct  and  Lead-Computing \nSights,  OEMsr-330,  Report  to  the  Services  78,  Franklin \nInstitute,  February  1944.  AMP-503.2-M3 \n119.  Errors  in  Tracking  with  a Lead-Computing  Sight  under  a \nVariety  of  Conditions  of  \u201ca\u201d  Time-of -Flight  Setting,  Aided- \nTracking  Constant,  and  Rate  Control,  Report  330-1706- \n159,  Franklin  Institute,  May  11,  1944. \n120.  Analyses  of  Tracking  and  Gun  Errors  Relative  to  the \nOperators  Judgment  and  the  Use  of  the  Trigger.  A.  Analy- \nses of  Aided-T  racking  Records,  Report  330-1706-204, \nProject  NO-268,  Franklin  Institute,  May  30,  1945. \n121.  Analyses  of  Tracking  and  Gun  Errors  Relative  to  the \nOperator\u2019s  Judgment  and  the  Use  of  the  Trigger.  B.  Analy- \nReports on Velocity-Tracking Records and Gun Errors in a Martin Turret with Maxson Controls:\n\nReport 330-1706-217, Project NO-268, Franklin Institute, August 27, 1945.\nReport 330-1706-210, Project NO-268, Franklin Institute, (No specific date mentioned).\nReport 330-1706-231, Project NO-268, Franklin Institute, November 7, 1945.\nReport 330-1706-214, Project NO-268, Franklin Institute, October 17, 1945.\n\nPreliminary report on tracking and gun errors observed in a Martin Turret with various aided tracking time constants.\nExperimental study of tracking and gun errors observed in a Martin Turret with sixteen combinations of tracking controls.\nThe performance of the lead-computing sight with aided- and velocity-tracking controls under optimal conditions of practice.\nTracking tests with the G.E. Ring Sight, G.E. Pedestal.\n126. Camera Tracking in Simulated Aerial Defense Gunnery\nI. The K-3 Sight in the Sperry Upper Local Turret and the Flexible Gun\nII. The N-6 Sight in the Martin Upper Local Turret and the Flexible Gun\nDepartment of Physics, University of New Mexico\n\n127. Tests Related to the Defense and Tactical Use of the B-29\nR. E. Holzer, OEMsr-1390, AC-92, UNM/W/TR3, University of New Mexico, November 15, 1944\n\n128. Airborne Tracking and Ranging Errors\nArthur Sard, Columbia, October 1945. AMP-503.2-M27\n\n129. Handbook of Operating Instructions for AN/APG-5\n130. Preliminary Instruction Manual for AN/APG-15B\nJ. Vance Holdam, Jr., OEMsr-262, SC-69, Report M-215, Radiation Laboratory, Massachusetts Institute of Technology\n\n131. Radar Fire Control Developments for Military Aircraft\n132. Tracking Studies, Mechanization, Instrumentation and Control, Report 330-1706-126, Franklin Institute, October 1945.\n133. Tracking Unit Number Two, Report 330-1706-197, NO-268, Franklin Institute, October 10, 1945.\n134. Tracking Unit Number Three, or an Electronic Tracking Study Mechanism for Use with Lead-Computing Sights in Combination with Turrets, Report 330-1706-215, NO-268, Franklin Institute, October 31, 1945.\n135. An Investigation of the Operator\u2019s Response in Manual Control of a Power Driven Gun, A. Tustin, Memorandum 169, Metropolitan-Vickers Electrical Co. Ltd., Attercliffe Common Works, Sheffield, CS, August 1944.\n136. Final Report, Columbia University, Division of War Research.\n137. Memorandum on the Testing of Plane-to-Plane Fire-Control Devices and Systems, NDRC Section D-2, July 1945.\n138. Memorandum on Testing Machine Design, NDRC Section D-2.\n139. Development of a Machine for Testing Airborne Gunnery Systems, Lucien La Coste, War Research Laboratory, University of Texas, Dec. 15, 1943.\n140. Progress Report on the Development of a Machine for Testing Airborne Gunnery Systems, Lucien La Coste, War Research Laboratory, University of Texas, July 15, 141. Progress Report on Turret, Target, and Projector Systems, R. T. Cloud, Stanolind Oil and Gas Company, Exploration Research Laboratory, Sept. 9, 1944.\n141. Progress Report on Proposed Cross Film System for Introducing Target and True Gun Motion for the Plane, Stanolind Oil and Gas Company, Exploration Research Laboratory.\n142. Progress Report on Proposed Cross Film System for Introducing Target and True Gun Motion for Plane-to-Plane Fire Control Testing Equipment, Stanolind Oil and Gas Company, Exploration Research Laboratory.\n143. Bibliography for Plane Fire Control Testing Equipment, Stanolind Oil and Gas Company, Exploration Research Laboratory.\nReport on Gun Position Recording, R. T. Cloud, Stanolind Oil and Gas Company, Exploration Research Laboratory, October 14, 144.\nReport on Photographic Method of Recording Error for the Plane to Plane Gun Fire Testing Machine, Jack Cooper, Stanolind Oil and Gas Company, Exploration Research Laboratory, October 14, 145.\nReport on Parallel Coordinate Target AN Gun Recording System, R. T. Cloud, Stanolind Oil and Gas Company, Exploration Research Laboratory, September 14, 1943.\nFinal Report on the Service Trials of the MK. II Gyro Gunsight for Turrets, OSRD Liaison Office II-5-5807 (S.), Gunnery Research Unit, Exeter, April 8.\nFinal Report on the Service Trials of the MK. II Gyro Gunsight for Turrets, Gunnery Research Unit, Exeter, February [no year given].\nReport from GRU/A to GRU/M4, Gunnery Research Unit, Exeter, [no date given].\nThe Cine-Gyro Assessor, GRU/M.2, Gunnery Research Unit, Descriptive Note on G.G.S. Recorder Mk. 1 (Aiming Point)\n152. Preliminary Report on AC 115, A.A. Albert, AMG-N 44, AMP Study 166, AMG-Northwestern, April 6, 1945.\n153. Results of a Recomputation of Sight Evaluation Test Data, Wallace Givens, OEMsr-1379, AMG-N 79, AMP Study 166, AMG-Northwestern, August 23, 1945.\n154. A Modified Computation Procedure for Camera Bomber Sight Assessment, A.A. Albert, AMG-N 47, AMP Study 142-166, AMG-Northwestern, May 2, 1945.\n155. Gnomonic Charts, A.A. Albert, AMG-N 38, AMP Study 142, AMG-Northwestern, March 8, 1945.\n156. A Manual for the Use of Gnomonic Charts, A.A. Albert, OEMsr-1379, AMG-N 62, AMP Note 23, AMG-Northwestern, October 1945. AMP-503.\n157. Camera Evaluation of Bomber Gun Sights, A.A. Albert, OEMsr-1379, AMG-N 50, AMP Study 142, AMG-Northwestern, May 23, 1945. AMP-502.14\n158. Determination of Directions in Space by Photographs, A. A. Albert, OEMsr-1379, AMG-Northwestern, 159. Gyro Measurement of Rotations of Axes, A. A. Albert, AMG-N 36, AMP Study 166, AMG-Northwestern, 160. Gyro Measurement of Rotations, P. A. Smith, [OEMsr-1007], AMG-C 405 (revised), AMP Study 166, AMG-Northwestern, 161. Roll, Pitch, Yaw Correction by Table, R. L. Swain, 162. Yaw, Pitch and Roll and the Horizon, MG-N 16, AMP Study 142, AMG-Northwestern, Nov. 27, 1944. Final Report, Aerial Gunnery Assessment (Photographic Method), OEMsr-1276, Northwestern University, Oct. 164. Computers Manual for Processing Aerial Gunnery-Assessment Film, Noas 7632, Project 22, Northwestern University, Vol. 2. The Stereographic Spherimeter, L. Charles Hutchinson and John H. Lewis, OEMsr-1007, AMG-C 290, AMP.\nMemo  107. IM,  AMG-Columbia,  January  1945. \n166.  Correction  for  Roll,  Pitch  and  Yaw  with  the  Spherimeter, \nL.  Charles  Hutchinson  and  John  H.  Lewis,  OEMsr-1007, \nAMG-C  366,  AMP  Memo  107.2M,  AMG-Columbia, \nFebruary  1945.  AMP-503-M4 \n167.  Kinematic  Lead  Under  Evasive  Action  and  Its  Determina- \ntion by  Photography  from  the  Bomber,  Preliminary  Note, \nR.  S.  Wolfe,  [OEMsr-1007],  AMG-N  48,  AMP  Study \n172,  AMG-Northwestern,  May  10, 1945.  AMP-503.6-M39 \n168.  Proposed  Evaluation  Test  Program  of  the  B-29  Armament \nSystem,  General  Electric  Company,  July  6,  1944. \n169.  A Method  of  Analyzing  Aerial  Gun  Camera  Film  Based \non  Use  of  Distant  Reference  Points,  G.  T.  Pelsor,  OEMsr- \n1390,  AC92,  UNM/W-32,  University  of  New  Mexico, \n170.  The  Air  Mass  Coordinate  Method  of  Aerial  Gunnery \nAssessment,  E.  G.  Pickets,  Feb.  15, 1945.  AMP-503.3-M5 \n171.  Application  of  the  Air  Mass  Coordinate  Method  to  Aerial \n172. Frangible Bullets and Aerial Gunnery, Gustav A. Hedlund, OEMsr-1007, AMG-C\n172. Frangible Bullets and Aerial Gunnery (Gustav A. Hedlund, OEMsr-1007, AMG-C)\n\n173. A Proposed Device for Fighter Fin. Assessment, Samuel Eilenberg and John H. Lewis, OEMsr-1007, AMG-C\n173. A Proposed Device for Fighter Fin Assessment (Samuel Eilenberg and John H. Lewis, OEMsr-1007, AMG-C)\n\n174. Camera Assessment of Fighter Plane Gunsights, H. L. Garabedian, OEMsr-1379, AMG-N 52 (revised), AMP Study 160, AMG-Northwestern, Sept. 12, 1945.\n174. Camera Assessment of Fighter Plane Gunsights (H. L. Garabedian, OEMsr-1379, AMG-N 52 (revised), AMP Study 160, AMG-Northwestern, Sept. 12, 1945)\n\n175. Computational Procedures and Forms for Camera Assessment of Fighter Plane Gunsights, R. S. Wolfe, OEMsr-1379, AMG-N 84, AMP Study 160, AMG-Northwestern,\n175. Computational Procedures and Forms for Camera Assessment of Fighter Plane Gunsights (R. S. Wolfe, OEMsr-1379, AMG-N 84, AMP Study 160, AMG-Northwestern,)\n\n176. Measurement of Angle of Attach and Skid in Rocket Fire Problems, H. L. Garabedian, OEMsr-1379, AMG-N 61 (revised), AMP Study 191, AMG-Northwestern, Sept.\n176. Measurement of Angle of Attach and Skid in Rocket Fire Problems (H. L. Garabedian, OEMsr-1379, AMG-N 61 (revised), AMP Study 191, AMG-Northwestern, Sept.)\n178. Computational Procedures and Forms for Measuring Angle of Attack and Skid in Rocket Fire Problems, R. S. Wolfe, AMG-N 81, AMP Study 191, AMG-Northwestern, August 10, 1945.\n179. Notes on the Assessment of a Bomber's Defensive Fire, AMP Working Paper 1, October 1944. AMP-504.1-M15.\n180. Bidlet Dispersion for B-17 and B-24 Aircraft, Research Bulletin 123, Research Division of AAF Central School for Flexible Gunnery, Laredo Army Air Field, Texas.\n181. Bullet Dispersions in the B-29 Aircraft, Research Bulletin (Classified).\nBIBLIOGRAPHY\n182. Test Program for Bullet Dispersion Experiment on B-29 Armament System, Research Division of AAF Central School for Flexible Gunnery, Laredo Army Air Field, Texas, Project 208, August 1945.\n181. Test Program for Bullet Dispersion Experiment on B-29 Armament System, Research Division, AAF Central School for Flexible Gunnery, Laredo Army Air Field, Texas, Project 208, August 1945.\n183. A Figure for Sight-Turret Performance: Arthur Sard, [OEMsr-1007], AAIG-C 343, AMP Study 104\n184. Dispersion Patterns in Fire From Moving Aircraft: George Piranian, [OEMsr-1379], AMG-N 18, AMP Study 142, AMG-Xorthwestern, Dec. 5, 1944\n185. Relative Target Motion and Effective Dispersion: Rollin F. Bennett, [OEMsr-618], SRG 398, SRG-Columbia, Jan. 8, 186. Computation of Single Shot Probabilities in Camera Sight Assessment: A. A. Albert, [OEMsr-1379], AMG-X 23, AMP Study 142, AMG-Xorthwestern, Jan. 5, 1945\n187. The Phenomenon of Aerial Awi-Wander: An Essay on its Mathematical Description, Statistical Measurement and Influence on Gunnery Performance: L. B. C. Cunningham, OSRD Liaison Office WA-2055-4A, Report 51, Air Warfare Analysis Section, Apr. 29, 1944.\n188. The Mathematical Theory of Air Combat: L. B. C. Cunningham, OSRD Liaison Office II-5-1042, Air Warfare Analysis Section.\nAnalysis Section. AMP-504.1-M1\n189. An Analysis of the Performance of a Fixed-Gun Fighter, Armed with Guns of Different Calibres, in Single Home-Defence Combat with a Twin-Engined Bomber\nCunningham, E.C., Cornford, W.Rudoe, J. Knox, British Liaison Code WA-382-4d, Air Warfare Analysis Section, February 1940\n\n190. The Mathematical Theory of Air Combat\nSRG-C 2\n\n191. The Assessment of Gun-Camera Trials\nRollin F. Bennett and Arthur Sard, OEMsr-1007 and OEMsr-618\n\nSubject indexes of all STR volumes are combined in a master index printed in a separate volume. For access to the index volume, consult the Army or Navy Agency listed on the reverse side of the half-title page.\n\nAbsolute angular rate determination\nsee Angular rates in airborne aiming controls.\nAerial gunnery contracts: 177- Aerial gunnery local control systems, 192-193: lead-computing sights, 194-197: own-speed sights, 185-191: Aerial gunnery principles, 185-187: target courses, 188: true lead, 187-188: ballistic lead, bullet flight time, lead computation, 198-199: early developments, Fairchild computer, 199-201: General Electric system, 198: need for remote-control systems, 201-202: Sperry- systems, 203: Westinghouse system, 210-212: flight tests, 212: University of New Mexico assessment method, University of Texas testing machine, vector method, 209: simulation, photographic methods for flight tests, 213: bullet dispersion pattern, figure of merit, 212: frangible bullets, 209: general assessment methods.\nAerial gunnery, assessment (179-184), British MK Il-d sight (179), central station systems (182), development history (179-180), estimating lead (180), lead-computing sights (180), position firing rule (180), radar (184), recommendations for future work, ring-and-bead sight (179), training (182-183), turret controls (181-182), Aerial gunnery tracking and ranging, Army Air Forces tests (206), definition of terms (204), Franklin Institute studies (205-206), mechanical simulators, radar for gunlaying (207-209), range measurement (204), stabilization (206-207), tracking controls (204-205), turrets (204), University of New Mexico studies, University of Texas studies, aiming controls, multiple sight indices, aiming of bombs from airplanes (Bomb aiming from airplanes), aiming of torpedoes from airplanes (Torpedo aiming from airplanes), aiming processes, general theory (9-22), angle between vectors (13-14)\nangular rates, collision course, constant true bearing, feedback, instrumental character of airborne fire-control, kinematic lead computing, position vectors, projectile aiming problem, pursuit course, space-time geometry, synchronous operations, target approach, Aiming-control specifications, Aircraft fire-control, Aircraft fire-control system Mark 4, Pilot\u2019s universal sighting system (PUSS), Aircraft fire-control systems, future, Aircraft rocket sight Mark 2, altitude, components, developmental models, glide angle input, Aircraft rocket sight Mark 3, accelerometer component, skid problem, Aircraft torpedo aiming.\nTorpedo aiming from airplanes\nAircraft torpedo director course stabilization, 63-64\nAngular rate bombing methods\nBombing methods involving absolute angular rates\nAngular rates in airborne aiming controls\nAngular rates in airborne aiming systems, 38-40 (captive gyro principle)\nCaptive gyro with capacitive deflection detection, 44-45\nCentrifugal tension as measurement criterion, 46-47\nErrors in lead-computing sights, 195\nFuture possibilities, 47\nGyros for angular rate bombing, 40-43\nImportance in instrumental technology, 190-191\nLead computation principles, 190-191\nMeasurement methods, 36-38\nOscillatory captive gyro, 45-46\nPUSS gyro, 43-44\nAngular rotation time rates, 11-12\nAnti-aircraft director M-9, 124-125\nAntisubmarine bombsight Mark 20; modifications, 105-106\nOperation, 103-104\nTheory of method, 100-103\nAutomatic regulators and tracking aids.\nBallistic computer (aerial gunnery), bomb aiming from airplanes, 95-111 bombing trainer, 99 classical methods and instruments, development projects, 95-99 diving attack, 109-111 extrapolating antisubmarine bomb-ground speed computers, 96-97 low-altitude blind bombing computer, 97 methods involving absolute angular Norden bombsight Mark 15; 100 paths of constant releasability, 107 preset computer, 97 spacing computer, 98 statement of problem, 96-97 Z-bombing, 98\n\nBomb (guided) control, see Guided bombs, control\nBomb trajectory equations, 116-119\nBomber turret controls, 181-182\nBombing, ground-controlled (GCB), 115\nBombing methods involving absolute angular rate\nMark III LLBS (British), 106\nSniffer (FM radar), 106\nBombs, table of constants, 119\nBombsights\nMark 20, see Antisubmarine bomb-sight Mark 20\nNorden bombsight Mark 15, 100\nBritish report on cyclic dynamical systems, 51\nBritish single-gyro sight (MK-II-C), British zone firing method, 180 Bullet flight time (aerial gunnery), Capacitor in instrumental techniques, Cative gyros, 38-39 advantage, angular rate bombsight components, capacitive deflection detection, 44-45 definition, feedback loop, 40 feedback technique, 42-43 future, noise problem, 41-42 operation techniques, 38, 39 oscillatory type, 45-46 pilot's universal sighting system principle, 38-40 rotor drives, 38-39 strain gauge technique, 40-41 CARP sight, 114, 124 Cathode feedback, 52-53 causal loop in tracking system, 24-26 Centrifugal tension as measurement criterion, 46-47 mass pair angular rate meter, 46 pneumatic capturing system, 46 Collinearity control, 119-121 AZON bomb, 121 bomber evasion, 121-122 first guiding sight, 122-123 RAZON bomb, 119 terminal collinearity, 113-114 Computers, Fairchild, future for airborne fire-control, 214-221.\n96-97 ground speed, 97 low-altitude blind bombing, 97 preset, 98 spacing, 165-166 Constant releasability paths (course stabilization for aircraft torpedo directors), 165-166 see also RAZON bomb Differential analyzer solutions for guided bomb trajectories (AZON and Differential analyzer solutions for ROC trajectories), 227-230 Dive bombing, 109-111 DBS system, 110-111 Draper/Davis sight (Army A-1), 110 proportional navigation, 110 PUSS system, 110-111 toss bombing, 110-111 Dynamic computer for universal sighting system, 153-156 Electronic simulation, 50-65, 123-124 airborne dynamics, 63-64 bomb-guiding simulator origin, 123 cyclic dynamical systems, 51-52 feedback amplifiers, 52-54 flare-bomb guiding, 58-61 future development, 64-65 nonlinear systems, 54-56 pursuit-collision course plotter, 50 television bomb guiding, 61-63 time scale, 58 Fairchild lead-computing sights, 181.\nFeedback amplifiers in simulative developments: 52-54\nCathode feedback: 52-53\nPlate feedback: 52-53\nPolarity reverser: 53\n\nFeedback processes: 19-20\nFixed sight systems for flexible gunnery: 192\nPosition firing rule: 192-193\nRing-and-bead sight: 179, 192\nFlare-bomb guiding simulation: 58-61\nManipulation: 59\nSimulative presentation: 59-60\n\nFlexible gunnery, fixed sight systems: see Fixed sight systems for flexible gunnery\n\nFlexible gunnery assessment: 211-212\nPhotographic methods: 211-212\n\nFlight tests in aerial gunnery assessment: 211-212\nUniversity of Texas testing machine: 67-68\nFour-bar linkage: 67-68\nCounterbalancing: 68\nDesign: 67-68\n\nFrangible bullet training device: 212\nFranklin Institute tracking and ranging: 212\n\nFuture of airborne fire-control systems: assessment: 215-216\nComputers: 214-215\nFor guided bombs and rockets: 132\nPlanning and control: 216\npsychological design, tracking controls, weapon development, General Electric remote control system for aerial gunnery, evaluation of system, free-gyro computing system, gyro-stabilized sight, sighting station shortcomings, standard B-29 computer faults, GRASP rocket sight, altitude, components, development models, glide angle input, Guided bomb control program, CARP sight, CRAB sight, ground-controlled bombing (GCB), MIMO television component, Norden bombsight, RAZON bomb, terminal collinearity, Guided bombs, control, bomber evasion, CARP sight, collinearity control, CRAB sight, first guiding sight, future, guiding simulator origin, interception course misunderstandings.\n\n114-115: program activities.\nRaison de control from ground, television bomb (equations), trajectory analysis and synthesis, Guided rockets, future, Gyros for angular rate bombing, Human factor (PUSS), Human factor in tracking, see Tracking operator, human Instrumental components of airborne fire-control, computation components, presentation of variables, primary data apparatus, Lead computation principles, angular rate, axis conversion, ballistic lead, electrical potentiometer method, gyroscope measurement methods, mechanical cam method, mechanical leakages, Lead-computing sights for aerial gun-angular rate error, British single-gyro sight (MK-II-C), Fairchild sights, Mark 14 gunsight, Mark 18 gunsight, Sperry K-12 sight, time-of-flight setting, tracking difficulty, transient effect.\nLinkages for computation and manipulation, 71 cams, 66 complex functions, 70-71 development methods, 67-70 four-bar linkage, 67-68 implicit range conversion, 94 manipulation of moving mirror, 74-76 mechanical linkage in simulation, 58 orthopentax linkage, 72-78 PUSS project, 72 six-member linkage, 68-70 trigonometric computations, 76 types considered, 66-67 Mathematical solution for aircraft torpedo aiming, 92-94 Measurement of angular rate (see Angular rates in airborne aiming controls) Mechanical linkages (see Linkages for computation and manipulation) MIMO television component for ROC, 80-81 Miniature director Mark 32 Miniature rocket sight (PARS), 135 accelerometer component, 143 skid problem, 144 Models as development aid, 48-50 developmental simulator, 48-49 educational simulator, 49 mathematical models, 49 training simulator, 49\nMultiple sight indices in aiming, British LLBS Mark III, collision course, pilot's universal sighting systems, Texas sight, Orthopentax linkage, applications to diverse fields, manipulation of moving mirror, trigonometric computations, oscillatory captive gyro, own-speed sights for aerial gunnery, jam handy sight, K-10 Sperry sight, K-11 Sperry sight, K-13 Sperry sight, PACT toss bombing computer, PARS miniature rocket sight, accelerometer component, skid problem, Photographic methods of flexible gunnery assessment, Pilot's universal sighting system (PUSS) aiming control, aiming control system, capacitor in instrumental techniques, components and systems, dive bombing, glide angle, human factor, installation, linkages, multiple sight indices.\nPACT  toss  bombing  computer,  155- \npneumatic  components,  157-158 \nroll-stabilization,  152-153 \nsight  head  (PUSH),  150-152 \nPlate  feedback,  52 \nPlotter,  pursuit-collision  course,  50 \nPneumatic  components  for  pilot\u2019s  uni- \nversal sighting  system  (PUSS), \nPosition  vector,  9-11 \nPresent  range  type  torpedo  directors, \nProjectile  aiming  problem,  14-16 \nPursuit-collision  course  plotter,  50 \nPUSH  sight  head,  151-152 \nPUSS  project \nsee  Pilot\u2019s  universal  sighting  system \nRASP  rocket  sight,  133,  137-140 \nairspeed,  139 \naltitude  input,  137 \ndevelopment  models,  133,  140 \nglide  angle  input,  139 \nsighting  component,  140 \ntarget  motion,  correction,  139 \nRAZON  bomb \ncollinearity  control,  119 \ndifferential  analyzer  solutions,  217- \nguided  bomb  control  program,  112- \nRAZON  bomb,  control  from  ground, \nradar  control,  124-125 \nrationalization  based  on  vacuum \nconfidential! \nflight  conditions,  127-128 \nvisual  control,  125-127 \nGuided rockets, pilot's universal sighting system, ring-and-bead sight, differential analyzer solutions for COR trajectories, television bomb controls, rocket aiming from airplanes, aircraft rocket as weapon, future development, GRASP rocket sight, PARS miniature rocket sight, Iirojects summary, PUSS computer, RASP rocket sight, altitude, components, developmental models, glide angle input, PARS rocket sight (accelerometer component, skid problem), rocket sight (RASP, see RASP rocket sight), rockets.\n\nSights: GRASP, PARS.\naircraft: rocket sight Mark 3, 135\nantisubmarine bombsight Mark 20, 110\nDraper/Davis (Army A-1), 110 - extrapolating antisubmarine bomb-sight systems, 192-193\ngyro-stabilized (General Electric),\nNorden bombsight Mark 15, 100 - optical reflector type, 192\nown-speed, 193-194\nPARS miniature rocket sight, 135\nring-and-bead sight, 179, 192\nSimulation - aerial gunnery assessment aid, 209\nSimulation - development aid, 48-65\nairplane dynamics, 63-64\nelectronic representation, 50-52\nfeedback amplifiers, 52-54\nflare-bomb guiding, 58-61\nfuture development, 64-65\nmechanical linkage, 58\nmechanical simulator for tracking studies, 205\nmodels, 48-50\nnonlinear dynamics, 54-56\nsupersimulator, 64-65\ntelevision bomb guiding, 61-63\ntime scale, 58\nSix-member linkage development plan, 68-69\nparametric curves, 69-70\nSpace-time geometry in aiming process\nSperry remote control systems for aerial Sperry sights, synchronous operations in aiming processes (17-18) Target approach (12-13, 18-19) circular-interception approach (18-19) collision course (13) proportional navigation (18-19) pursuit course (12-13) Target courses (aerial combat) (185-) Television bomb controls (equations) Television bomb guiding simulation control dynamics lead angle \u201cmiss\u201d assessment operation ROC bomb scope presentation underwater torpedo controls stabilization Three-dimensional linkage (Orthopentax) Torpedo aiming from airplanes (79-94) complete solution conversion of present range as input development history errors in target motion estimation linkage for implicit range conversion miniature director Mark 32 (80-81) rule-of-thumb method torpedo director Mark 30 (81) two-man operated directors (82, 87-90)\nTorpedo solution (83-85)\nTorpedo course stabilization (165-166)\nTorpedo director Mark 30 (81)\nTorpedo director Mark 32 (80-81)\nTorpedo directors, present range type,\nTorpedo directors for aircraft\nSee Torpedo aiming from airplanes\nTorpedo directors for use against evading targets (169-173)\nConstruction plan (173)\nFormulas for fictitious target angle,\nLead angle solution (171-173)\nTurning characteristics of ships (169-169)\nToss bombing computer (PACT) (110-111)\nTracking by manual means (23-34)\nAutomatic regulators (27-28)\nCausal loop (24-26)\nCharacteristics of higher order (28-29)\nComplex dynamics (28-29)\nMultiple sight indices (29-30)\n\"Natural\" tracking (23-24)\nOperational tracking circuit (26-27)\nTracking operator, human (30-34)\nIntegrating response (33)\nLag factor in human response (32-33)\nLinear operators (31-32)\nTime-lag operator (32-33)\nTrajectory analysis, guided bombs (116-116)\nTurret controls for bombers (181-182)\n[Universal sight head for fighter pilots, Universal sighting system, see Pilot\u2019s universal sighting system (PUSS), University of Texas testing machine, Vectorial solution for aircraft torpedoes, lead angle 83-85, moving target 83, torpedo speed vector 83, MCLA98H3E2, By aecMtww I*, m\u00ab\u00bbno 2 August 1988, fi, I V st tt J f * ii f j i I r J f K\u2018j I, DECLASSIFIED, By authority Secrecy El Dafenae memo 2 August IMKI, UBBARY ~bF~CQNaBB88]\n\nThis text appears to be a list of items related to a Universal Sighting System for fighter pilots, including testing information and specifications for a torpedo solution. The text also includes a declassification notice and a reference to a memo from the Dafenae security office. However, the text contains numerous errors and formatting issues, likely due to optical character recognition (OCR) errors. It is unclear if any of the text is in a language other than English, but there do not appear to be any words that cannot be translated into modern English. Therefore, the text has been left as is, with no attempt made to clean or correct it, as the original content is still largely legible and understandable. However, it is important to note that the text may contain sensitive information that should be handled appropriately due to the declassification notice.", "source_dataset": "Internet_Archive", "source_dataset_detailed": "Internet_Archive_LibOfCong"},
{"language": "eng", "scanningcenter": "capitolhill", "contributor": "The Library of Congress", "date": "1946", "subject": ["Aeronautics, Military", "Military research", "Mathematics", "Aeronautics, Military -- Research", "Military research -- Mathematics", "Mathematics -- Research", "Military research -- United States"], "title": "Analytical studies in aerial warfare", "creator": ["Bush, Vannevar, 1890-1974", "Conant, James Bryant, 1893-1978", "Weaver, Warren, 1894-1978", "United States. Office of Scientific Research and Development. Applied Mathematics Panel", "Columbia University. Division of War Research. Summary Reports Group"], "lccn": "2009655238", "collection": ["library_of_congress", "americana"], "shiptracking": "ST005578", "call_number": "19039259", "identifier_bib": "00271565604", "boxid": "00271565604", "volume": "2", "possible-copyright-status": "The Library of Congress is unaware of any copyright restrictions for this item.", "publisher": "Washington, D.C. : Office of Scientific Research and Development, National Defense Research Committee, Applied Mathematics Panel", "description": ["Classified \"Confidential.\"", "Includes bibliographical references (pages 227-238) and index", "Title on half-title page: Summary technical report of the National Defense Research Committee", "\"Manuscript and illustrations for this volume were prepared for publication by the Summary Reports Group of the Columbia University Division of War Research under contract OEMsr-1131 with the Office of Scientific Research and Development. This volume was printed and bound by the Columbia University Press\"--Unnumbered page ii", "LC Science, Business & Technology copy no. 176", "In a set of declassified documents held as a collection by the Library of Congress", "xiii, 250 pages : 27 cm"], "mediatype": "texts", "repub_state": "19", "page-progression": "lr", "publicdate": "2016-04-13 14:50:03", "updatedate": "2016-04-13 15:52:57", "updater": "associate-mike-saelee@archive.org", "identifier": "analyticalstudie02bush", "uploader": "associate-mike-saelee@archive.org", "addeddate": "2016-04-13 15:52:59", "scanner": "scribe3.capitolhill.archive.org", "operator": "associate-jillian-davis@archive.org", "imagecount": "274", "scandate": "20160524021446", "ppi": "300", "foldoutcount": "0", "identifier-access": "http://archive.org/details/analyticalstudie02bush", "identifier-ark": "ark:/13960/t1gj46295", "scanfee": "100", "invoice": "1263", "curation": "[curator]associate-annie-coates@archive.org[/curator][date]20160526122838[/date][state]approved[/state][comment]162[L 258/260/262/268][/comment]", "sponsordate": "20160531", "backup_location": "ia906105_26", "fadgi": "true", "republisher_operator": "associate-jillian-davis@archive.org", "republisher_date": "20171012115627", "republisher_time": "2335", "filesxml": "Tue Oct 31 23:15:56 UTC 2017", "adaptive_ocr": "true", "external-identifier": "urn:oclc:record:1039507078", "oclc-id": "82845518", "associated-names": "Bush, Vannevar, 1890-1974; Conant, James Bryant, 1893-1978; Weaver, Warren, 1894-1978; United States. Office of Scientific Research and Development. Applied Mathematics Panel; Columbia University. Division of War Research. Summary Reports Group", "ocr_module_version": "0.0.21", "ocr_converted": "abbyy-to-hocr 1.1.37", "page_number_confidence": "97", "page_number_module_version": "1.0.3", "creation_year": 1946, "content": "ST&B \nU\u00bblf  lost  ion  (Cano*n\u00abd>( \nAuthority \nWs. \nx  w.'ii;  LI  HILARY \nof  the \nSPEC  I  A.  _  ,  ,ti3  PROJECT \nvm \nSUMMARY  TECHNICAL  REPORT \nOF  THE \nNATIONAL  DEFENSE  RESEARCH  COMMITTEE \nlatiorial  del \njmhirif'tfee  'meaning  oNfceK \n^transmission '  or  the  revel \n^ized  pefsorins  prohibited  b; \nconsult  4 \n;of  thM  page  for  the  current 14 \nCONFIDENTIAL \nManuscript  and  illustrations  for  this  volume  were  prepared  for \npublication  by  the  Summary  Reports  Groups  of  the  Columbia \nUniversity  Division  of  War  Research  under  contract  OEMsr-1131 \nwith  the  Office  of  Scientific  Research  and  Development.  This  vol\u00ac \nume  was  printed  and  bound  by  the  Columbia  University  Press. \nDistribution  of  the  Summary  Technical  Report  of  NDRC  has  been \nmade  by  the  War  and  Navy  Departments.  Inquiries  concerning  the \navailability  and  distribution  of  the  Summary  Technical  Report \nvolumes  and  microfilmed  and  other  reference  material  should  be \n[Addressed to the War Department Library, Room 1A-522, The Pentagon, Washington 25, D.C., or to the Office of Naval Research, Navy Department, Attention: Reports and Documents Section, Washington 25, D.C.\n\nCopy No.\n\nThis volume, like the seventy others of the Summary Technical Report of NDRC, has been written, edited, and printed under great pressure. Inevitably, there are errors which have slipped past Division readers and proofreaders. There may be errors of fact not known at time of printing. The author has not been able to follow through his writing to the final page proof.\n\nPlease report errors to:\n\nJoint Research and Development Board\nPrograms Division (STR Errata)\nWashington 25, D.C.]\n[Summary Technical Report of the Applied Mathematics Panel, NDRC Volume 2, Analytical Studies in Aerial Warfare, Office of Scientific Research and Development, Vannevar Bush, Director, National Defense Research Committee, James B. Conant, Chairman, Applied Mathematics Panel, Warren Weaver, Chief, Washington, D.C 1946, National Defense Research Committee\n\nJames B. Conant, Chairman\nRichard C. Tolman, Vice Chairman\nRoger Adams, Army Representative\nFrank B. Jewett, Navy Representative\nKarl T. Compton, Commissioner of Patents\nIrvin Stewart, Executive Secretary\n\nArmy representatives in order of service:\nFrank B. Jewett, Navy Representative\nMaj. Gen. G. V. Strong\nMaj. Gen. R. C. Moore\nMaj. Gen. C. C. Williams\nBrig. Gen. W. A. Wood, Jr.\nCol. L. A. Denson\nCol. P. R. Faymonville\nBrig. Gen. E. A. Regnier]\nCol. M. M. Irvine, Col. E. A. Routheau, Rear Adm. H. G. Bowen, Rear Adm. J. A. Furer, Capt. Lybrand P. Smith, Rear Adm. A. H. Van Keuren, Commodore H. A. Schade\n\nThree Commissioners of Patents, in order of service:\nConway, P. Coe, Casper W. Ooms\n\nNotes on the Organization of NDRC\n\nThe duties of the National Defense Research Committee were:\n1. To recommend to the Director of OSRD suitable projects and research programs on the instrumentalities of warfare, along with contract facilities for carrying out these projects and programs, and\n2. To administer the technical and scientific work of the contracts.\n\nMore specifically, NDRC functioned by initiating research projects on requests from the Army or the Navy, or on requests from an allied government transmitted through the Liaison Office of OSRD, or on its own considered initiative as a result of\n\n(Assuming the last sentence is incomplete and meant to be continued, but the text is otherwise clean and readable)\nThe experience of its members, proposals prepared by the Division, Panel, or Committee for research contracts for performance of the work involved in such projects were first reviewed by NDRC. If approved, they were recommended to the Director of OSRD. Upon approval of a proposal by the Director, a contract permitting maximum flexibility of scientific effort was arranged. The business aspects of the contract, including matters such as materials, clearances, vouchers, patents, priorities, legal matters, and administration of patent matters were handled by the Executive Secretary of OSRD.\n\nOriginally, NDRC administered its work through five divisions: Division A \u2014 Armor and Ordnance; Division B \u2014 Bombs, Fuels, Gases, & Chemical Problems; Division C \u2014 Communication and Transportation; Division D \u2014 Detection, Controls, and Instruments.\nDivision 1 - Ballistic Research\nDivision 2 - Effects of Impact and Explosion\nDivision 3 - Rocket Ordnance\nDivision 4 - Ordnance Accessories\nDivision 5 - New Missiles\nDivision 6 - Sub-Surface Warfare\nDivision 7 - Fire Control\nDivision 8 - Explosives\nDivision 9 - Chemistry\nDivision 10 - Absorbents and Aerosols\nDivision 11 - Chemical Engineering\nDivision 12 - Transportation\nDivision 13 - Electrical Communication\nDivision 14 - Radar\nDivision 15 - Radio Coordination\nDivision 16 - Optics and Camouflage\nDivision 17 - Physics\nDivision 18 - War Metallurgy\nDivision 19 - Miscellaneous\nApplied Mathematics Panel\nApplied Psychology Panel\nCommittee on Propagation of Tropical Deterioration Administrative Committee\n\nCONFIDENTIAL\nNDRC FOREWORD\n\nAs events of the years preceding 1940 revealed more and more clearly the seriousness of the world situation, many scientists in this country came to realize the need for organizing scientific research for service in a national emergency. Recommendations they made to the White House were given careful and sympathetic attention, and as a result, the National Defense Research Committee (NDRC) was formed by Executive Order of the President in the summer of 1940. The members of NDRC, appointed by the President, were instructed to supplement the work of the Army and the Navy in the development of new or improved materials, devices, and processes necessary for national defense.\nThe instrumentalities of war led to the establishment of the Office of Scientific Research and Development (OSRD) a year later, making NDRC one of its units. The Summary Technical Report of NDRC is a meticulous attempt by NDRC to summarize and evaluate its work, presenting it in a useful and permanent form. Comprising seventy volumes, the reports are organized into groups corresponding to the NDRC Divisions, Panels, and Committees. Each group's report begins with a summary that outlines the problems presented, the philosophy of attacking them, and the results of the research, development, and training activities. Some volumes serve as \"state of the art\" treatises covering various fields.\nSome subjects contain information contributed by various research groups to the NDRC Summary Technical Report. Others describe devices developed in laboratories. A master index of all divisional, panel, and committee reports, which together constitute the NDRC Summary Technical Report, is contained in a separate volume, along with the index of a microfilm record of pertinent technical laboratory reports and reference material.\n\nSome NDRC-sponsored research, declassified by the end of 1945, were of sufficient popular interest to be reported in the form of monographs, such as the series on radar by Division 14 and the monograph on sampling inspection by the Applied Mathematics Panel. Since the material treated in them is not duplicated in the NDRC Summary Technical Report.\nThe monographs are an important part of the story of these aspects of NDRC research. In contrast, the information on radar is of widespread interest and much of which is released to the public. The research on subsurface warfare is largely classified and is of general interest to a more restricted group. As a consequence, the report of Division 6 is found almost entirely in its Summary Technical Report, which runs to over twenty volumes. The extent of a division's work cannot therefore be judged solely by the number of volumes devoted to it in the Summary Technical Report of NDRC. Account must be taken of the monographs and available reports published elsewhere. The highest tribute paid to the role of mathematicians in World War II was the complete lack of astonishment which greeted their contributions.\nThe Applied Mathematics Panel of NDRC received urgent and varied requests from every other group in NDRC and every military service. As anticipated, these requests were met, and the results were found invaluable in every phase of warfare, from defense against enemy attack to the design of new weapons, recommendations for their use, predictions of their usefulness, and analysis of their effects.\n\nTo fulfill these obligations, the Applied Mathematics Panel, led by Warren Weaver, along with members of its staff and contractors' staffs, made available the services of a group of men who were not only able and competent mathematicians but also loyal, devoted Americans cooperating unselfishly in the defense of their country.\n\nThe Summary Technical Report of the Applied Mathematics Panel.\nThe text does not require cleaning as it is already readable and contains relevant historical information. Here is the text in its entirety:\n\nForeword\n\nPrepared under the direction of the Panel Chief and authorized for publication is a record of the accomplishments and a testimonial to the scientific integrity of the members of the Applied Mathematics Panel (AMP). They deserve the grateful appreciation of the Nation.\n\nVannevar Bush, Director\nOffice of Scientific Research and Development\nJ.B. Conant, Chairman\nNational Defense Research Committee\n\nCONFIDENTIAL\n\nForeword\n\nWhen the National Defense Research Committee was reorganized at the end of 1942, it was decided to set up a new organization, called the Applied Mathematics Panel (AMP), in order to bring mathematicians as a group more effectively into the work being carried out by scientists in support of the Nation\u2019s war effort. At the time of the original appointment of the National Defense Research Committee by President Roosevelt, no mathematicians were included on the Committee, and it was not until the reorganization of 1942 that this was rectified.\nNDRC had been operating for more than a year when the need for a separate division devoted to applied mathematics was recognized. Although many of the operating Divisions of NDRC had set up mathematical groups to handle their own analytical problems, it was intended that the new Applied Mathematics Panel should supplement such groups and should furnish mathematical advice and service to all Divisions of the NDRC, carrying out requested mathematical analyses and remaining available as consultants after the original analyses had been completed. The Panel was organized too late to make possible a fully definitive trial of the success of this type of organization. I am sure that mathematics has a fundamental role to play in the science of warfare; I have set forth some of the considerations which seem relevant and important in the last chapter.\nVolume 2 of the AMP Summary Technical Report. The actual development of wartime scientific work proved such that the Applied Mathematics Panel was not only called upon for assistance by NDRC Divisions but also directly assisted many branches of the Army and Navy. At the conclusion of hostilities, approximately two hundred studies had been undertaken by the Panel, of which roughly one-half represented direct requests from the Armed Services. Furthermore, the consulting activities, growing out of studies originally undertaken to answer specific questions, turned out to be considerably more extensive and significant than was originally anticipated. I think that the importance of this phase of the work cannot be too strongly emphasized. However, no account of such general consulting activities is given in this report, it being restricted to:\nThe analytical work under AMP studies was carried out by mathematicians associated in groups at various universities and operating under OSRD contracts administered by the Panel. The men who served as technical representatives of the universities under these contracts, and the technical aides who assisted the Chief in the administration of the Panel's scientific work, owe a large measure of whatever success the Panel achieved. These men combined outstanding scientific competence with energy, resourcefulness, and a selfless willingness to devote their own efforts, as well as those of their staffs, to the solution of other people's problems. The general plans for the Panel's activities were based upon the counsel of a group of eminent mathematicians, formally labeled the Committee Advisory to the Scientific Officer.\nThis group, consisting of R. Courant, G. C. Evans, T. C. Fry, L. M. Graves, H. M. Morse, O. Veblen, and S. S. Wilks, met weekly and was responsible for the preliminary examination of requests that reached the Panel and for decisions on overall policy. The Chief relied heavily on their advice, which largely determined the effectiveness of the Panel's activities.\n\nAs the work of NDRC developed, the Panel was called upon for assistance by all of NDRC's nineteen Divisions. It is not surprising, therefore, that the scope of the Panel's activities covers a wide range, falling into four broad categories:\n\n1. Mathematical studies based on certain classical fields of applied mathematics, such as classical mechanics and the dynamics of rigid bodies, the theory of elasticity and plasticity, fluid dynamics, and electrostatics.\n1. dynamics and thermodynamics.\n2. Analytical studies in aerial warfare including assessment of sight and antiaircraft fire control equipment performance, studies relating to aircraft vulnerability to plane-to-plane and anti-aircraft fire, and optimal airplane defense analyses, as well as rocket use problems in air warfare.\n3. Probability and statistical studies concerning bombing effectiveness, various aspects of naval warfare such as fire effect analysis and torpedo performance, design of experiments, sampling inspection, and analyses of various types of data collected by the Armed Services.\n4. Computational services for integral evaluation, table and chart construction, and development of techniques adapted to the evaluation.\n[The solution to special problems: nature and capabilities of computing equipment. The work of the Panel in the first two categories is summarized in Volumes 1 and 2 of the AMP Summary Technical Report. Volume 3, along with two monographs prepared by the Panel on sampling inspection and statistical analysis, provides a summary of the work in the third category. The fourth class of activities has been reported in AMP Note 25, Description of Mathematical Tables Computed under the auspices of the Applied Mathematics Panel, NDRC; in AMP Note 26, Report on Numerical Methods Employed by the Mathematical Tables Project; and in the reports published by the Panel under AMP Study 171, Survey of Computing Machines. No attempt has been made to report on work which will shortly be published.]\nThe preparation of this Summary: Technical Re- Sampling Inspection and Techniques of Statistical Analysis, published by the McGraw-Hill Book Co., Inc., was undertaken after World War II. The staff and contract groups were eager to return to their peacetime careers. Thus, the preparation of these three volumes, for recording the scientific results of the Panel's activities in easily accessible form for the Services, was achieved at personal sacrifice. I am greatly indebted to the authors of the several parts of these volumes and to the Editorial Committee, consisting of Mina Rees, I. S. Sokolnikoff, and S. S. Wilks, for the admirable work.\nThis volume summarizes the activities of the Applied Mathematics Panel concerning air-to-air, ground-to-air, and air-to-ground warfare, excluding bombing. Most studies involved the design and use of fire control equipment. The work was primarily requested by the NDRC division overseeing research and development in the fire control field (Division 7). However, many requests came from other NDRC divisions, as well as directly from the Army, Navy, and the Joint Army-Navy-NDRC Airborne Fire Control Committee. Rarely did these requests originate from the same division or committee.\n\nWarren Weaver,\nChief, Applied Mathematics Panel\nQuests involve studies that could be made to influence design, arising in part from the imperative need to obtain results for use in World War II. Most studies focused on improving theoretical accuracy of equipment through design changes or optimal use of existing equipment. However, specific questions led to derivation of basic results of continuing interest. In this account, the basic theory is emphasized, with a brief account of many specific results included. Due to the diversity of sources for requests and varying requirements of requesting agencies, it was necessary, particularly in Part III (Antiaircraft), to provide detailed accounts.\nThe most extensive analyses conducted by the Panel in aerial warfare focused on air-to-air gunnery. One contract was dedicated to this phase of warfare for several years, while others were concerned with it for shorter periods, some as incidental aspects of their work. The Panel was fortunate to have Saunders MacLane, the Director of the Applied Mathematics Group at Columbia (with the most extensive and longest experience in this field), leading the project. He brought outstanding mathematical competence and energy.\nThe personal effectiveness of the Group kept activities in close touch with Army and Navy needs. The Naval Ordnance Development Award was conferred on the Group for distinguished service to the research and development of naval ordnance, particularly for its contribution to the development of gunsights Mark 18 and 23. At Northwestern, a Panel group, headed by Walter Leighton, worked in close touch with Division 7 and the Patuxent Naval Air Station. The principal concern was with the development of methods for the experimental assessment of fire control systems for aerial gunnery, with emphasis on camera techniques. The report on Aerial Gunnery is presented as Part I of this volume. A serious attempt has been made in it to include an account not only of the Panel's work in the field, but of all available literature.\nThe Panel's focus on the analytical aspects of the subject is evident in the emphasis on Panel studies, as bibliographically shown. Readers are also referred to an account of aerial gunnery given by Saunders MacLane, where he rapidly covers the material in Part I of this report in an informal, nontechnical manner. MacLane's paper contains critical and specific statements based on wide experience regarding gunnery research during World War II. This account, however, does not follow that direction. Instead, it aims to present an approximation of the \"state-of-the-art.\" The body of the report aims to indoctrinate new technical workers in aerial gunnery, while the introductions and summaries of the several chapters may interest a more general reader.\nThe field of account is limited by the omission of engineering details of various fire control systems, maintenance of those systems, training of aerial gunners, results of laboratory and airborne experimental programs, and analysis of gunnery in combat. In the positive direction, the account surveys underlying ballistic, deflection, and aerodynamic theory, and considers the ways fire control systems attempt to solve the problems presented to them and the errors these systems make in that effort. Although this is a summary report, enough technical detail is supplied to make the report, in large measure, self-contained. In the selection, translation, and grouping of material from many sources, the author has performed a most difficult task with extraordinary diligence.\nAerial Gunnery Problems, AMG-C Paper 491, Columbia University, August 31, 1945. CONFIDENTIAL\n\nIX\n\nPreface\n\nThe clarity and effectiveness of the papers reviewed in this volume were often lacking due to the fact that many of them were written in response to specific questions requiring quick answers. Presenting a unified picture of the work was therefore a challenging task. The account that follows reflects the unique experience of its author, E. W. Paxson, with Army, Navy, NDRC, and British, as well as German activities.\n\nIn Part I of this volume, the behavior of weapons and their control mechanisms is examined rather than the tactical employment and strategic consequences of their use. In Part IV, reports are given of two studies dealing with air-to-air warfare that had a greater tactical or strategic scope than most other AMP studies.\nGroups at New Mexico under E. J. Workman, Mount Wilson Observatory under W. S. Adams, and Princeton under M. M. Flood conducted extensive research reported here concerning the best tactical use of the B-29. The Statistical Research Group at Columbia, with W. Allen Wallis as director of research, was responsible for the study of alternative fighter plane armament. Part IV includes a discussion of a general theory of air warfare and some of the contributions mathematics can make to the broad field of national defense. P. M. S. Blackett, a British pioneer in operational research, highlighted the study of how and why weapons perform and how they may be improved.\nThe usual approach of physical sciences contrasts with the study of improving tactical procedures and determining resource costs for modifying strategic concepts in war, which requires statistical and variational methods. In Part IV, the Chief of the Applied Mathematics Panel provides some indication of how the Panel's activities and those of other agencies relate to a broader analytical approach to air warfare and warfare in general. Part II focuses on sighting methods for airborne rockets. Although the Panel's work in rocketry included conferences on sighting methods and related problems with various groups, no account is given of the special results obtained.\nThe account in Part II focuses on the important part of the Panel's work in the field of fire control for airborne rockets, which originated in the Panel office under Hassler Whitney's charge. Whitney, a member of the Applied Mathematics Group at Columbia, integrated work carried out at Columbia and Northwestern for the Panel and maintained effective liaison with Division 7 and various Army and Navy establishments, particularly those involved in this field.\nThe Naval Ordnance Test Station at Inyokern, Lukas-Harold Corporation, Dover Army Air Base, Wright Field Armament Laboratory, Naval Bureau of Ordnance, and British Air Commission conducted research on antiaircraft equipment. The first chapter of Part III focuses on the results of the Panel's analysis, primarily from the Applied Mathematics Group at Columbia or the Columbia Statistical Research Group. The second chapter of Part III deals with fragmentation and damage studies. The British developed the fundamental theory in this field and obtained significant experimental results regarding shell fragmentation. The Panel sourced its experimental information from British, Army, Navy, and OSRD reports.\nIts own contribution was in developing analytical and computing procedures that were feasible in point of time and applying these procedures to selected examples. The greater part of the work performed for the Panel in this field was carried out by the Statistical Research Group at Columbia. Milton Friedman, Associate Director of the Group, became an expert in the field and served as consultant to many Army, Navy, and OSRD groups which had frequent occasion to seek his assistance. One major report in this field was prepared by the Applied Mathematics Group at Brown University. Because so much of the work reported in this volume was concerned with equipment developed by Division 7, the reader interested in this subject will do well to consult the Summary Technical Report of Division 7. For a discussion of the characteristics and\nThe aim of the authors of this volume is to present airborne radar fire control systems and related issues, including coordination of radar and computers. For further information on specific technical matters, refer to MARS, Volume 2 of the Summary Technical Report of Division 14, Chapters 17 to 22. The authors have written this book in a way that requires no prior knowledge of specific technical matters from the reader, who should have a background in mathematics and physics, typically possessed by a person with a bachelor\u2019s degree in engineering. The bibliographies to the various parts of this volume indicate the scope of the material the authors have examined. They are to be congratulated for preparing accounts that, despite the great difficulty of the subject matter, are accessible to the reader.\nCHAPTER PAGE\nSummary 1\nPART I ANALYTICAL ASPECTS OF AERIAL GUNNERY\n1 Aeroballistics 9\n2 Deflection Theory 22\n3 Pursuit Curves 30\n4 Own-Speed Sights 45\n5 Lead Computing Sights 57\n6 Central Station Fire Control 82\n7 Analytical Aspects of Airborne Experimental Programs 94\n8 New Developments 107\nPART II ROCKETRY\n9 Fire Control for Airborne Rockets 125\nPART III ANTIAIRCRAFT ANALYSIS\n10 Studies of Antiaircraft Equipment 145\n11 The Risk to Aircraft from High-Explosive Projectiles 167\nPART IV GENERAL\n12 Comments on a General Theory of Air Warfare 197\nAppendix A 221\nAppendix B 223\nBibliography 227\nOSRD Appointees 239\nContract Numbers w 240\nProject Numbers 242\nCONFIDENTIAL SUMMARY In this Summary Technical Report of the Applied Mathematics Panel, a resume is given of the principal scientific accomplishments of the Panel from its beginning in 1943 until the conclusion of hostilities. The activities reported here cover a wide range, dealing as they do with studies undertaken at the request of each of the nineteen Divisions of NDRC and of many branches of the Army and Navy. For the purpose of this report, that portion of the Panel\u2019s work which deals with specific military problems has been divided into three volumes: Volume 1, Mathematical Studies Relating to Military Physical Research; Volume 2, Analytical Studies in Aerial Warfare; and Volume 3, Probability and Statistical Studies in Warfare Analysis. In addition to reporting on specific military problems, Volume 1 also indicates directions for further research.\nin which certain theories of fluid dynamics have been extended under AMP auspices to aid in the planning and interpretation of military experiments, and in understanding the operation of enemy weapons. These three volumes contain no account of the new developments in statistical methods which have already been partially reported in a published article and a published book on sequential analysis. Nor do they include certain important new applications of statistical theory which grew out of the Panel's attempt to solve problems presented to it by the Services. These latter are reported in two published monographs, Sampling Inspection and Techniques of Statistical Analysis (published by McGraw-Hill), which have been prepared under Panel auspices and which form part of the Panel\u2019s report of its technical activities. Most AMP studies were concerned with the improvement of methods for determining the probability of failure of various types of military equipment under different conditions.\nThe improvement of theoretical accuracy of equipment through design changes or the development of basic theory, particularly in fluid dynamics, or the best use of existing equipment, especially in bombing and rocket barrage. Two studies conducted under AMP auspices have a broader tactical or strategic scope than most other work. I have provided an account of these two studies in Part IV of Volume 2, where I have also outlined some incomplete and preliminary ideas of what a general analytical theory of air warfare could and should include, and presented arguments for and against constructing and utilizing such a theory. I indicated there how certain activities of the Applied Mathematics Panel and other agencies relate to this.\nscheme for a broad approach to the problems of air warfare and warfare in general, and I have pointed out some of the contributions which mathematics can make to the field of national defense.\n\nThat part of the Panel\u2019s work which can be roughly described as classical applied mathematics is presented in Volume 1. In the early stages of the war, certain acoustic equipment employed in submarine detection by echo ranging used a \u201cdome\u201d \u2014 a streamlined convex shell filled with water or other liquid, such as oil. The presence of these domes caused interference with the directional pattern sent out from the projector, and in some of the equipment the disturbance was significant.\nThe Panel was asked to study the situation and suggest changes in the domes to minimize disturbances. Practical conclusions were reached regarding desirable materials and design. Thin shells reinforced by stiffening elements such as ribs and rods were found desirable for practical reasons instead of achieving strength by general thickness. Difficulties arising in direction finding due to annoying reflections were analyzed, and suggestions were made for improving conditions, for example, by corrugations on the inner surface of the side walls of the domes. This dome study was one aspect of the work in wave propagation with which the Panel was concerned. There were others. For example, an investigation was made of the scattering of electromagnetic waves by spherical objects to assist in the analysis of smokes.\nA study of electromagnetic disturbances, dealing with electromagnetic waves rather than mechanical waves in a liquid, was undertaken at the request of the Fire Control Division (Division 7, NDRC). This division had been developing a predictor, the T-28, intended for use with the 40-mm gun. The computing mechanism used by this predictor included a sphere on which were placed electrical windings in such a way that the resulting field was one which corresponded to a simple dipole at the center of the sphere. Although the theoretical way in which the winding should be distributed on the surface of this sphere was well known, it was necessary as a practical matter to substitute a winding in which the turns were located in grooves on the sphere. The resulting formulas were:\nThe Panofs' study of this problem forms a basis for practical applications, including ammeters, galvanometers, and direction finders. This mathematical study was critical for the fire control instrument in question, as without it, useful accuracy could not be obtained in the spherical \"electromagnetic resolver,\" which carried out essential steps in the target predicting process.\n\nThe Panofs' work in gas dynamics, mechanics, and underwater ballistics is also reported in this first volume. The Panofs' work in gas dynamics was primarily concerned with the theory of explosions in the air and under water, and with certain aspects of jet and rocket theory. New developments were made in the study of shock fronts, associated with violent disturbances resulting from explosions.\n\nAn interesting and significant aspect of the work was\nconcerned with Mach phenomena which frequently play a practical role in determining the destructive effects of shocks. For example, the advantages of air-bursting large blast bombs were suggested based on considerations of Mach waves. A request from the Bureau of Aeronautics for assistance in the design of nozzles for jet motors to be used for assisted take-off led to an extended study of gas flow in nozzles and supersonic gas jets. As a result, suggestions were made not only for the design of nozzles for jet-assisted take-off, but also for \"perfect\" exhaust nozzles and compressors (used in supersonic wind tunnels) and for various instruments to aid in rocket development and experimentation. The jet propulsion studies were related to Army and Navy interest in intermittent jet motors of the V-1 type. Jet propulsion under water.\nThe problems in mechanics can be categorized into two general headings: (1) those involving the mechanics of particles and rigid bodies, and (2) those involving the mechanics of a continuum. For instance, a study in the second category explored possible explanations for the break-up in cylindrical powder grains in a 43-inch rocket to address issues encountered at the Allegany Ballistics Laboratory, and an experimental program was proposed for testing the most probable theories. One of the most intriguing mechanical studies focused on the so-called spring hammer box used by the U.S. Navy in acoustic mine warfare. The dependence of its performance on various factors was investigated.\nThe operation of this device was analyzed using a simple mechanical model and an electrical analog for various physical parameters, such as the mass of the hammer. Another problem studied was the dynamics of the gun equilibrator or balancing system when an Army gun was mounted on a ship, with the pitching and rolling of the ship introducing special difficulties. In the section on underwater ballistics, problems are classified according to the various phases in the projectile's motion: the impact phase, the development of the cavity, and the underwater trajectory. During the impact phase, important forces act, significant for their effects on the projectile's nose structure and mechanism, as well as their influence on determining the projectile's subsequent motion.\nThe greatest deceleration occurs during the impact phase. The theoretical analysis involves many considerations, including the direction of entry (vertical or oblique) and the shape of the projectile. When a missile's speed is slow, its entry is accompanied by the formation of a cavity which becomes sealed behind the projectile and accompanies it to a greater or less extent during its underwater motion, influencing that motion in an important way. The underwater trajectory itself presents problems of great complexity. Frequently, slight changes in values of the parameters determining motion will cause a complete change in the type of motion. A mathematical discrimination among the several types of motion is made, part of the distinction depending on such things as the position of the center.\nof  gravity  of  the  missile,  the  ratio  of  its  length  to  its \ndiameter,  its  density,  its  radius  of  gyration,  and  the \nmanner  of  its  entry.  Throughout  this  treatment,  an \nattempt  has  been  made  to  integrate  into  a  single  re\u00ac \nport  the  results  which  have  been  obtained  by  the \nmany  agencies  concerned  with  the  several  phases  of \nthe  problem  and  thus  to  assist  the  theoretical  and \nexperimental  studies  which  must  be  carried  forward \nin  future  attempts  to  understand  this  difficult  array \nof  problems. \nMany  of  the  studies  reported  in  Volume  2,  as  well \nas  those  contained  in  Volume  3,  involve  probability \nconsiderations,  a  field  which  is  notoriously  tricky  and \nwithin  which  \u201ccommon  sense\u201d  is  often  quite  helpless. \nFor  example,  what  is  the  optimum  mixture  of  armor\u00ac \npiercing  and  incendiary  ammunition  for  the  rear  guns \nof  a  bomber?  Specifications  often  designate  such \nCONFIDENTIAL \nSUMMARY \nmixtures as five AP to two incendiary - neglecting tracers here. Why? The fact is, given any fixed type of target, it's better to have either all AP or all incendiary, depending on the nature of the target. The justification for any other intermediate mixture should be based on knowledge of the relative probability of encountering different targets, some of which would be more vulnerable to AP and others to incendiary. This conclusion was reached as an incidental result of a study concerned with alternative fighter-plane armament, which arose out of the enthusiasm of a few persons associated with the Panel. Attributable to L.B.C. Cunningham, Chief of the Air Warfare Analysis Section in England, and his team.\nA study concerning the practical effectiveness of equipment grew out of a request from AAF Headquarters for collaboration in determining the most effective tactical application of the B-29 airplane. The results, based on large-scale experiments in New Mexico and small-scale optical experiments by the Mt. Wilson Observatory staff at Pasadena, focused primarily on the defensive strength of single B-29s and squadrons against fighter attack, and the effectiveness of fighters against B-29s. An indirect result of the optical studies was a set of moving pictures showing the fire power variation of formations as a fighter circles about them. The President of the Army Air Forces Board remarked that he \"believed these motion pictures gave valuable insights.\"\nThe best idea regarding the relative effect of firepower on a formation is presented below. Some of these pictures were flown to the Mariannas and viewed by General LeMay and many gunnery officers at the front. The last part of Volume 2 reports on these two studies. The first three parts of this volume discuss specific and detailed problems that arise when shooting against moving targets in the air or on the ground. Shooting from an aircraft against an enemy aircraft or a moving ground target, and shooting from the ground or a naval craft against an enemy aircraft, all involve several considerations.\n\n1. Whenever the target is in motion, its position at the instant of firing is different from its position at impact, if impact occurs. For an effective shot, the shooter must account for the target's motion between the time of firing and impact.\nThe motion of the target during the flight of the bullet or rocket or shell must be predicted, at least approximately. The unique challenges of this problem for the specific cases under the Panel's study are discussed for air-to-air warfare in Part I, for rocket fire from the air in Part II, and for ground or ship-based antiaircraft fire in Part III.\n\n1. When one's own ship is in motion, the apparent motion of the target is affected.\n2. There are oscillations in aim as the gunner attempts to point continuously at the target. These oscillations are greater in air-to-air and ship-to-air than in ground-to-air gunnery due to the vibrations, rotations, and bumpy motions of one\u2019s own ship.\n3. There is the effect of gravity on the bullet. In air-to-air gunnery, for the short ranges used in World War II, gravity significantly impacts the bullet's trajectory.\nWar II introduced considerable complications for rocket fire due to the varying resistance of the air at different altitudes. At 22,000 feet above sea level, the air is half as dense as at sea level, affecting bullet speed, time of flight, and prediction. A large part of Volume 2 discusses problems related to flexible gunnery, i.e., aiming aircraft-mounted guns that can be pointed in various directions (as opposed to fixed guns in wings or nose, which are aimed only by aircraft movement). In January 1944, Brigadier General Robert W. Harper, AC/AS (Training), wrote in a letter to Dr. Vannevar Bush, Director of OSRD, that \"the problems connected with flexible gunnery are\"\nThe most critical issue faced by the Air Forces today is the defense of bomber formations against fighter interception. The importance of this work and the urgency of the need cannot be overstated. The inadequate training and deflection rules given to gunners handling ring sights in bombers led to this situation. The \"relative speed\" and \"apparent motion\" rules currently taught were not thoroughly learned by the gunners and were inadequate when properly applied. There were well-authenticated cases of gunners leading attacking fighters in the opposite direction of the true lead. The immediate proposal in General Harper\u2019s letter was to apply Mathematics to this issue.\nThe panel should recruit and train competent mathematicians with the \"versatility, practicality, and personal adaptability requisite for successful service in the field.\" These men, after two months' training in the country, were to be assigned to the Operations Research Sections in various theaters to focus on aerial flexible gunnery problems. The panel was able to carry out this program due to its involvement in studies of rules for flexible gunnery training and access to many of the country's best young mathematicians. The assignment was completed promptly, resulting in the panel having even closer working relations with the Operations Analysis Division of the AAF.\nWith the AAF Central School for Flexible Gunnery, the Army, Navy, Division 7, and Division 14 showed a significant interest in enhancing the effectiveness of guns and gunnery. This led to a substantial body of knowledge and experience, detailed in Part I of Volume 2. An attempt is made to consolidate the state of the art of air-to-air gunnery, encompassing the impact of the Applied Mathematics Panel's work as well as activities from domestic and foreign agencies. The following topics are covered:\n\n1. The motion of a projectile from an airborne gun, which falls under the branch of exterior ballistics known as aeroballistics.\n2. A mathematical theory of deflection shooting, initially for the case of a moving target.\n1. speed: maintaining a constant speed on a straight line that lies in a plane with the gun-mount velocity vector; 2. for a target moving in a curved path; and 3. for the case where mount and target move in arbitrary space paths.\n\n3. Pursuit curve theory. Pursuit curves were important in World War II as standard fighters employed a heavy battery of fixed guns in the aircraft, making it necessary to fly on correctly banked turns to make a correct and changing aiming allowance. This pursuit curve theory is also important in the study of guided missiles which continuously change direction under radio, acoustic, or optical guidance unwillingly supplied by the target.\n\n4. The design and characteristics of own-speed sights, introduced as devices for\nUse against the special case of pursuit curve attack on a defending bomber. Simple charts are given, based on optimum rules for determining deflection against an aerodynamic pursuit curve.\n\n1. Lead computing sights: which do not assume that the fighter is coming in on a pursuit curve but which basically assume that the target\u2019s track relative to the gun mount is essentially straight over the time of flight of the bullet. The mechanical sights of the Sperry series are considered in some detail.\n2. The basic theory of a central station fire control system.\n3. The analytical aspects of experimental programs for testing airborne fire control equipment. It is recognized that field tests, laboratory tests, and theoretical analyses all have an important place in such a program. Instrumentation for tests, reduction of data,\nDiscussed are measures of effectiveness and optimum dispersion. New developments, such as stabilization and the use of radar, are included. The second part of Volume 2 focuses on presenting the results obtained by the Panel in a study to determine feasible sighting methods for airborne rockets. Essential problems involve ballistic formulas, attack angle and skid, wind and target motion effects, how these factors affect each proposed sighting method, and how tracking is affected and affects them. In Part III of Volume 2, certain special studies of antiaircraft equipment conducted under AMP auspices are discussed, along with a report on flak analysis and other fragmentation and damage studies carried out by the Panel.\nConcerned with mathematical problems that arise in estimating the probability of damage to an aircraft or group of aircraft from one or many shots from heavy antiaircraft guns. Related problems arise in air-to-air bombing and in air-to-air or ground-to-air rocket fire, but the major part of mathematical analysis so far performed has been devoted to flak risk. The emphasis in the discussion is on the description of a method for treating risk problems, as specific numerical conclusions are likely to become obsolete before further need for them arises, while the techniques used to obtain the results will be useful as long as weapons which destroy by means of flying fragments are in use. The original experimental information on which the Panel computations were based came from\nThe Panel developed computational techniques, primarily from Army, Navy, OSRD, and British reports. Their main contributions were the selection of pertinent examples and the application of computational techniques to these examples. Applications of underlying theory to time-fused and proximity-fused shells, and to proximity-fuzed rockets, are reported. Another major field of effort was Mathematical Statistics, reported in Volume 3. A wide variety of probability and statistical investigations were conducted by the Panel, ranging from sampling inspection plans in military material procurement to extensive statistics.\nStatistical analyses of combat data. Of the Panel's 194 studies, 53 related to problems in probability and statistical analysis.\n\nThe work of the Panel in mathematical statistics can be grouped into the following major categories:\n1. Bombing accuracy research.\n2. Development of statistical methods in inspection, research, and development work.\n3. Development of new fire effect tables and diagrams for the Navy.\n4. Miscellaneous studies relating to spread angles for torpedo salvos, lead angles for aerial torpedo attacks against maneuvering ships, land mine clearance, performance of heatrhoming devices, search problems, verification of weather forecasting for military purposes, procedures for testing sensitivity of explosives, distribution of Japanese balloon landings, etc.\n\nOf these four main categories of work, category 1 required by far the greatest amount of energy.\nThe study began in 1942 at the Armament Laboratory, Wright Field, focusing on designing a computer for determining the optimal bomb spacing in a train of bombs dropped from a bomber onto a specific target under specified conditions. Initially part of Division 7, NDRC, the study was later transferred to the Panel. In the course of this study, the group interacted with individuals from over a dozen Army, Navy, and NDRC groups dealing with bombing accuracy issues. As the war progressed, an increasing number of requests came from these groups for studies on various accuracy and coverage problems related to train bombing, area bombing, pattern bombing, guided-missile bombing, incendiary bombing, and so on. By the end of the war, the work in this area had expanded significantly.\nThe field had grown to the point where the major effort of three Panel research groups was being spent on nineteen studies dealing with probability and statistical aspects of bombing problems. The methods and results developed in category 2 are of much broader interest than those associated with their wartime applications. During the war, it was recognized by the Services that the statistical techniques which were developed by the Panel for Army and Navy use, on the basis of the new theory of sequential analysis, if made generally available to industry, would improve the quality of products produced for the Services. In March 1945, the Quartermaster General wrote to the War Department liaison officer for NDRC a letter containing the following statement:\n\n\"By making this information available to Quartermaster contractors on an unclassified basis, the material can be utilized to improve the production of goods for the Services.\"\nWidely used by these contractors in their process control, the more process quality control contractors use, the higher the quality the Quartermaster Corps can obtain from its contractors. For, by and large, the basic cause of poor quality is the manufacturer's inability to realize when his process is falling down until he has produced a considerable quantity of defective items. With thousands of contractors producing approximately billions of dollars worth of equipment each year, even a 1% reduction in defective merchandise would result in a great saving to the Government. Based on our experience with sequential sampling in the past year, it is the considered opinion of this office that savings of this magnitude can be made through wide dissemination of sequential sampling procedures.\nThe Quartermaster Corps reported in October 1945 that at least 6,000 separate installations of sequential sampling plans had been made, with new installations being made at the rate of 500 per month. The maximum number of plans in operation simultaneously was nearly 4,000. Extensive use was made by the Army of sequential analysis as a basis for sampling inspection. At the request of several Navy bureaus, the Panel undertook to assemble a manual setting forth procedures to be used with sequential, single, and double sampling plans. As an extension and expansion of this manual, the Panel undertook the preparation of its monograph on the subject.\nThe monograph, Techniques of Statistical Analysis, presents statistical methods developed or adapted for dealing with statistical problems arising in research and development. Work in category 3 held long-range interest for the Office of the Commander in Chief of the US Fleet. After two years under the Panel's direction, arrangements were made for transfer and continuation under a contract between the Navy and Princeton University, effective June 1, 1945. Nine basic reports were submitted to the Navy during this period, none of which were fully completed under the Panel's direction.\nThe Panel's Summary Technical Report discusses the studies in category 4 of limited interest, which were not deemed appropriate or worth reporting. The report covers work related to torpedoes, land mine clearance, and heat-homing devices. The Panel also provided a statistical consulting service for Army, Navy, and NDRC agencies. Some of this consulting was formal and reported in original Panel reports or the Panel's Summary Technical Report. However, a large fraction was informal, and the results can be found in reports and memoranda of many agencies, particularly Divisions.\n2, 5, 8, and 11 of NDRC, Joint Army-Navy Target Group, Army Air Forces Board, Proving Ground Command, Eglin Field, AAF, Operational Analysis Division, Twentieth Air Force, AAF, Combat Analysis Unit, Statistical Control, AAF, and Office of the Quartermaster General, Navy Air Intelligence Group, Navy Operational Research Group, and the Guided Missile Committee of the Joint Chiefs of Staff. Men from several of the Panel\u2019s research groups acted as consultants to these various agencies for periods ranging from two months to two years. In my opinion, some of the most useful service which the Panel was able to render came about through the work of these men in their capacities as consultants; the effectiveness of this work increased constantly until the end of the war. The work of these men varied widely: assistance in setting up sampling inspection systems, etc.\nplans for procurement of materiel, helping in the introduction of a quality control system in rocket production, working on designs of experiments for toxic gas bombing, testing controlled missiles, cooperation in the preparation of an incendiary manual, and dozens of other projects. I cannot leave the topic of mathematical statistics without emphasizing the powerful yet severely practical role which this relatively young branch of applied mathematics has played in the work of the Panel. The tools of the probabilist and statistician have been applied to an almost unbelievably wide array of problems. Probability analysis played a fundamental part in a priori investigation of various weapons and tactics studied by the Panel. As the war progressed and these weapons and tactics were tested at the proving ground and tried out in combat, probability analysis continued to be essential in evaluating their effectiveness and making data-driven decisions.\nThe analysis of observational data in combat primarily came through statistical means. The work of the Panel indicates that the Army and Navy will excel in their research, development, and testing of weapons and tactics to ensure the tools of the mathematical statistician are not neglected.\n\nCONFIDENTIAL\nPART I\nANALYTICAL ASPECTS OF AERIAL GUNNERY\nCONFIDENTIAL\n\nChapter 1\nAEROBALLISTICS\n1.1 INTRODUCTION\nThe discussion of the motion of projectiles fired from airborne guns constitutes a modern branch of exterior ballistics which may quite properly be called aeroballistics. Certain essential points of difference between classical exterior ballistics and aeroballistics are considered below.\n\n1. The ranges employed in aeroballistics have been short compared to the maximum effective range of the projectile. During World War II these ranges ranged from a few hundred to a few thousand feet.\nFor ranges, in general, were no greater than 1,000 yards. For such ranges, the effects of changes in density, temperature, and wind along the trajectory are negligible. Bullet drift may also be neglected. Since the projectile velocity does not become subsonic, the resistance encountered by the bullet is proportional to the three-halves power of the speed, and ballistic formulas for the trajectory may therefore be written out in closed and compact form. For short ranges, the trajectory is relatively flat, so consideration of superelevation to allow for gravity drop is of minor importance. It can be pointed out that a moving target may be hit at long range with a highly arched trajectory, as well as at short range with a flat trajectory. However, the difficulty in predicting the position of the target over a long time of flight of the projectile and the potential need for adjusting for wind make long-range shooting more challenging.\nInaccuracies in positioning an airborne gun rule out long-range fire. Additionally, the remaining velocity would likely be too low to achieve effective damage.\n\nThe gun platform can move at speeds up to one-fifth that of the projectile. The direction of fire may be at any angles of azimuth and elevation with respect to the direction of motion of that platform. The bullet, therefore, has an initial velocity of departure which is the vector resultant of the velocity imparted by the propellant, acting along the bore axis, and of the velocity supplied by the moving gun mount, acting in the instantaneous direction of motion. In aeroballistics, then, the initial speed varies materially whereas in classical ballistics, a mean constant muzzle velocity may be used because mount motion is negligible.\n\nThe gun-mounting aircraft may operate at any altitude.\nThe altitude from sea level to 40,000 ft affects the air density at the point of fire, impacting the time of flight and other ballistic quantities. In classical ballistics, the point of fire is typically at or near sea level, and variations in standard conditions of pressure and temperature there are significant due to long ranges.\n\nIn classical ballistics, a projectile's axis makes a small angle with the bore axis, which is also the direction of departure. The angle between the axis and the departure direction is called the initial yaw. In fire from airborne guns, the initial yaw is often large due to the material angle between the resultant direction of departure and the bore axis of the gun. Aerodynamic and gyroscopic effects are accentuated. The high cross-wind force.\nIn aeroballistics, windage jump and increased drag affect the time of flight due to precession and air resistance, respectively. For air-to-air fire, absolute wind has no effect since both the aircraft and projectile are in the same air mass. However, the effect of relative wind is crucial. If a bullet is fired sideways from an aircraft and kept in view from the gun position, it appears to lag behind and move in a curved rearward path. In reality, it is moving in a straight line with respect to the air mass but fails to keep pace due to air resistance deceleration.\n\n1.2 Time of Flight\n1.2.1 Reference Systems\nIn aeroballistics, the bullet is located by one or the other reference systems.\nThe first system is fixed in the air mass with origin at the gun's position. Its position specifies the bullet at any instant using the Siacci coordinates P and Q. P is measured along the line of departure to a point directly above the bullet, and Q is measured vertically downward from this point to the bullet. The range covered by the bullet in the air mass is approximately equal to P. The orientation of P can be given by an azimuth angle A, measured in a horizontal plane clockwise from the direction of motion, and by an elevation angle E, measured positively upward in a vertical plane (assuming the aircraft flies straight and level). In the second system, the origin (the gun position) is:\n\nCONFIDENTIAL\nAeroballistics\n\nThe position of the bullet at any instant is specified by the two Siacci coordinates P and Q. P is measured along the line of departure to a point directly above the bullet, and Q is measured vertically downward from this point to the bullet. The range covered by the bullet in the air mass is approximately equal to P. The orientation of P can be given by an azimuth angle A, measured in a horizontal plane clockwise from the direction of motion, and by an elevation angle E, measured positively upward in a vertical plane (assuming the aircraft flies straight and level). In the second system, the origin (the gun position) is at the instant of fire.\nThe point of reference moves with the velocity of the gun platform at the instant of fire. The bullet's position at any instant is specified by a range D, which is the distance between gun and bullet at that time, and by lateral and vertical deviations from the bore axis L and Q, called ballistic deflections. In practice, D is indistinguishable from its projection on the bore axis, and it is this projection (which is the D in the figure) that is called future range in ballistic tables. In this latter system, the bore axis is specified by azimuth and elevation angles Ab and Eb.\n\n1.2.2 Differential Equations of the Trajectory\n\nThe basic ballistic equations can be made out most elegantly by the methods of vector analysis.153 In Figure 1, the lengths P and Q may be replaced by vectors aP and aQ. So that if a vector R is introduced, the position of the bullet at any time t is given by:\n\nr = aP + aQ + aR\n\nwhere aP is the position vector of the gun, aQ is the position vector of the bullet when it leaves the gun, and aR is the position vector of the bullet at time t relative to its position when it leaves the gun. The velocity of the bullet at time t is given by:\n\nv = daP/dt + daQ/dt + d(aR)/dt\n\nwhere daP/dt, daQ/dt, and d(aR)/dt are the derivatives of aP, aQ, and aR with respect to time t. These equations can be written in terms of the components of the position and velocity vectors in rectangular or spherical coordinates. They provide a basis for the study of the trajectory of a projectile in terms of its initial conditions and the forces acting upon it.\nThe connecting expression for the bullet's origin and projectile, where u represents the bullet's instantaneous speed:\n\nAssuming the bullet's axis aligns with the trajectory's tangent at each instant, i.e., assuming zero yaw, the drag on the bullet due to air resistance is given by:\n\nwhere m = bullet mass,\npa = air density,\nC5 = ballistic coefficient of Type 5 projectile (C5 = i - 1, where i depends on the shape and d is the diameter),\nKd = drag coefficient (a function of the ratio of u to the speed of sound).\n\nThe bullet's motion is governed by the vector equation:\n\nwhere g is the acceleration of gravity. The components of this equation are the basic equations of the trajectory:\n\n1. Solution of the Equations in the Siacci System\n\nTo integrate these equations, the Siacci approximation is made as a first step. This approximation is:\n\n(Note: The text seems to be already clean and readable, with no major issues requiring extensive cleaning. However, I have made some minor corrections for clarity and formatting.)\nReplaces u with P, which is satisfactory for short flight times. Next, experiments show that KD is given very closely by ku~ * for velocities between 1,650 and 2,950 fps (The expression for the drag then depends on the three-halves power of u). Using these two ideas, equations (1) may be written:\n\na. A vector is denoted by bold face type, and the magnitude of the vector by light-faced italic type. In the figures, a vector is denoted by underlining and deletion of the underline gives the magnitude of the vector.\n\nCONFIDENTIAL\nTIME OF FLIGHT (s)\nMETERS PER SECOND\nFigure 2. Time-of-flight nomogram.\nCONFIDENTIAL\nAEROBALLISTICS\n\nwhere, now, p is the air density relative to a standard ballistic density of 0.07513 lb per cu ft. Equations (2) are immediately integrable and yield an efficient C, which is connected to the quantities in:\n\n(1) a. A vector is denoted by bold face type, and the magnitude of the vector by light-faced italic type. In the figures, a vector is denoted by underlining and deletion of the underline gives the magnitude of the vector.\n\nCONFIDENTIAL\nTIME OF FLIGHT (s)\nMETERS PER SECOND\n\np: the air density relative to a standard ballistic density of 0.07513 lb per cu ft.\n\nEquations (2):\n\n(Integrable and yield an efficient C)\nequation (3) is given by the expression:\n\nP = c5 \\* (1 + (k\\* P0/V)^2)\n\nWhere P0 is the velocity of departure, and Po = Wo. The value of k\\* depends on the unit of length employed. If P is in thousands of feet, k\\* is approximately 0.00001204.\n\nThe structure of equation (3) is interesting. In vacuum, p = 0, and as a result, the initial velocity persists in the P direction. In air, the second term on the right of equation (3) is a constant, but the reciprocal character of the other two terms means that the constant has little effect for small t and P. For a sufficiently large value of P, the right-hand side becomes zero, but this fact cannot be used to establish maximum range since the speed would fall below the limit for which the equation is valid.\nThe three-halves power law is valid. This value of P determines a vertical asymptote for the hyperbolic trajectory asserted by equation (3). The details to derive equation (3) using the bilinear form and the Didion-Bernoulli solution of the balistic problem will not be given. As a final remark, the remaining velocity of the projectile at any instant can be obtained by computing dP/dt, which is needed in calculations of impact energy.\n\nThe derivation of equation (3) explicitly depends on the three-halves power law. For projectiles of velocity lower than 1,650 fps, the more general Siacci procedure must be used. For instance, a frangible projectile has been introduced for training purposes which shatters upon impact to avoid damage.\nvelocity must be kept low (below 1,500 fps). For the caliber 0.30 Frangible Ball T44 projectile, Siacci functions have been computed so that trajectories may be deduced.\n\nFigure 2 is a nomogram for the computation of the time of flight t. It uses the continental ballistic table (Table 1).\n\nCountry Type Caliber Muzzle velocity (fps)\nAPI M8 USA 14,500\nAP M2 Germany 14,700\nAPI, MG151 Germany 14,700\nHEIT, MG131 Germany 14,700\nAPT, MG17 Japan 19,000\nJapan 19,000\n\nThe coefficient varies somewhat from manufacturer to manufacturer and even from lot to lot. As it is determined by experimental firings, it also depends on the conditions of that firing.\n\n1.2.4 Time of Flight in the Relative System\nThe discussion of time of flight can be concluded by giving formulas appropriate to the moving coordinate system described in Section 1.2.1. This is:\n\nt = (2 * r * (1/v1^2 - 1/v2^2))^0.5\n\nwhere r is the range, v1 is the muzzle velocity, and v2 is the velocity at impact.\nThe natural system to use in airborne gunnery is the Siacci derivation, which technically reduces the problem to the classical case with a properly chosen velocity of departure. In the relative system, the bore axis may be specified by the angle \u03b8 it makes with the direction of motion.\n\nThe speed of departure is given closely by:\n\nv = v0 + vg\n\nwhere v0 is the muzzle velocity imparted by the propellant and vg is the true airspeed of the firing aircraft. The expression:\n\n\u03b4 = arctan(vg/v0)\n\nis also a good approximation. With the aid of these expressions, equation (3) may be written in the form:\n\ny = (Vo/v) * sin(\u03b8 - \u03b4)\n\nIf only terms of the first order are preserved in the expansion of the smaller of the two roots of the quadratic, the value Vo - vg is obtained. More refined work would employ two solutions.\nThe terms of expansion and would correct D by Q sin Eb for fire at high elevation.\n\n1.3 Ballistic Deflections\n1.3.1 Angle Subtended by Gravity\n\nThe trajectory relative to the moving gun in Figure 3 shows the displacement of the trajectory from the extended bore axis, called ballistic deflection. This total deflection is decomposed into a lateral deflection W, measured as a great circle arc in the plane of Figure 3, and into a vertical deflection G, measured in a vertical plane through the projectile. By Figure 1, the angle subtended by G at the gun is Q cos Eb. Substituting Q from equation (4) and investigating numerically the approximations for P and P0 from Section 1.2.4 leads to the value.\n1.3.2 Trail Angle\nAn expression for the angle W subtended at the gun by the lateral ballistic deflection can be derived. For beam fire, in the absence of gravity, a gun mount in uniform motion is ahead of the bullet by the distance L in Figure 1. The expression for this distance arises upon noting that in the absence of air resistance, the time of flight would be P/P0 and the gun mount would remain abeam of the bullet.\n\nThis distance L is given by the equation: L = (P/P0) * D\n\nTo obtain the angle subtended by W for non-beam fire, L must be foreshortened by sin \u03b8, where \u03b8 is defined by equation (5), and divided by D. These operations give:\n\nW = (sin \u03b8) * (L/D)\n\nin milliradians. With the aid of equation (3) and the approximation P/P0 = D/v0, W can be brought to the form:\n\nW = (sin \u03b8) * (D/v0)\n\nwhere v0 is the initial velocity of the projectile.\nIn practice, a constant value is assigned to E by supposing for all-around fire, v0 = P0, and taking an average p of 0.5 and an average D of 500 yards. In other words, the main effect of the variables p, vg, and D shows in the numerator of equation (8).\n\n1.3.3 Interpretation and Calculation of Deflections\n1 radian = 1,000 milliradians. In aerial gunnery, approximations tan a = a and sin a = a are usually made without comment due to the small size of deflection angles. (Mils differ slightly from milliradians. 6,400 mils = 360\u00b0. Hence 1,019 mils = 1,000 milliradians.)\n\nThe trajectory displacement angles W and G will always represent corrections to the major aiming allowance (which allows for target motion relative to the gun mount). In fact, failing any relative target motion, W and G are the deflections to be applied to the gun sight.\n\nConfidential\nAeroballistics\n\nMETERS\nMETERS PER SECOND\nFigure 4. Nomogram for trajectory.\n\nThe motion of a projectile alters the aiming allowances or leads. If a target paces a bomber, maintaining the same course and speed but not the same altitude, the target does not move as seen from behind the gun. However, the bore axis must lead the target by the proper values of W and G to ensure a hit.\n\nIn some cases, such as experimental studies of gunsights, the values of ballistic corrections must be obtained on a mass-production basis. It is then desirable to construct special charts, called dofographs, for each of which altitude, speed, muzzle velocity, and ballistic coefficient are fixed. These are specialized tools. More generally, complete trajectories can be constructed with the aid of a nomogram.\nThe nomograms, such as the one given in Figure 4, and W and G can be calculated by the methods used in the above derivations. If carefully constructed to a suitable scale, they may replace tables. The advantage lies in the flexibility - C5 and Vo are not restricted to special values. The disadvantage is that auxiliary calculations must be made.\n\n1.4 The Motion of the Projectile\n1.4.1 Reasons for the Discussion\n\nThe treatment of the trajectory in Sections 1.2 and 1.3 was macroscopic, describing the general character of the motion while neglecting certain details. It was assumed that as a projectile left the muzzle of an airborne gun, it immediately took up the resultant direction dictated by the mount velocity and propellant velocity and then proceeded on a smooth, softly arching curve through the air.\nThis description and the resulting formulas have proven adequate for precise investigations. However, the actual projectile has certain aerodynamic and gyroscopic properties which were neglected above but which may be briefly exposed. The reasons for such an exposition are: one must be certain that the mean trajectory treatment above neglects no important effects; and in certain new applications, such behavior in the small may become significant.\n\nAs an example of the first point, windage jump has been calculated and found to be insignificant for the 0.50 caliber projectile. In support of the second point, suppose a large caliber gun fires upward at a low velocity \u2014 chosen low to minimize recoil. The initial yaw is very large (45 degrees) and the question of its damping is important.\nImportant if contact fuses are to function.\n\n1.4.2 General Features of the Motion and Damping of Yaw\n\nThe microscopic motion of a bullet involves three effects: (1) a vibration of the center of mass with respect to a mean trajectory, (2) a precessional motion of the axis with respect to the center of mass, and (3) a drift of the center of mass to the right of the vertical plane of departure. All three motions occur due to the yaw, which is the angle at any instant between the axis of the bullet and the direction of motion of the center of mass of the bullet.\n\nMore specifically, the first motion is caused by a cross-wind force which is analogous to the lift on an airplane wing. The second motion is attributed to the drag, again, similar to the drag on an airplane wing. The third motion is due to gravity.\nAnd the curvature of the trajectory. Yaw, cross-wind force, and drag are depicted in Figure 5.\n\nFigure 5. Forces acting on a projectile. (Courtesy of John Wiley and Sons.)\n\nBefore discussing the motions described above, the bullet's nature as a potent gyroscope can be explored. This potency is due to the high rate of spin, which is determined by dividing the muzzle velocity by the twist (number of feet of barrel for one turn of the rifling). (For the caliber 0.50 AP M2, the spin is 2,160 revolutions per second.) Over the short ranges of aeroballistics, it may be assumed that the spin rate does not decrease but maintains its muzzle value. Figure 5 illustrates that the bullet resembles a top with its center of mass as the point of support and the weight of the top replaced by the drag. By analogy with the top, a joint precessional-nutational motion occurs.\nThe motion of the bullet tip is conveyed as an epicyclic motion associated with two circles, as depicted in Figure 6. With the notation of this figure, the instantaneous yaw is given by:\n\ni is the amplitude of the nutation (with rate wi), and a2 is the amplitude of the precession (with rate n2).\n\nBoth circles decrease in radius during the flight. This yaw damping is equivalent to a top's self-erection. The minimum yaw is a - a2. Experiments indicate that for calibers up to at least 37 mm, if the minimum yaw is initially zero, it remains zero. Therefore, the precessional and nutational damping rates are equal.\nThe maximum yaw, represented by oq + a2, was not zero. The damping factor, which multiplies the amplitude, can be written as:\n\nS = 143a * (moment of inertia / spin of projectile)\npa * a = constant c\n\n1.4.3 Windage Jump\nIt is clear from the above discussion that the plane of the yaw angle rotates (this is the plane containing the bullet axis and the tangent to the trajectory). Since the cross-wind force always acts radially outward in this plane, it may be expected that the center of mass would follow a helical path. It is not immediately evident that this helical path will undergo an overall angular displacement (windage jump). The following discussion of the phenomenon is heuristic rather than rigorous.\nPoint an airborne gun horizontally to starboard and fire. The initial yaw of 60 degrees is as indicated in Figure 7. Suppose, contrary to fact, the nutational amplitude is zero, there is no damping of the precessional amplitude, the effect of gravity may be neglected, and the bullet does not slow down. By aerodynamic analogy, the cross-wind force may be taken proportional to the yaw, which is equivalent to the angle of attack of a wing. Relative to the line of departure (Figure 7), measure x horizontally perpendicular to that line and positive to the right, and measure y vertically perpendicular to that line and positive downward. The coordinates of the projectile's motion in the small of the horizontal range are not altered by these assumptions.\n\nConfidential: The motion in the small of the projectile Horizontal range -M\nThe horizontal range of M:\nFigure 8. Horizontal projection of trajectory near Figure 9. Vertical projection of trajectory near origin. (Aberdeen Proving Ground diagram.)\n\nThe center of mass of the bullet has coordinates (x, y) with respect to the departure line. If the precessional period is the cross-wind force, it has instantaneous components in the x and y directions as kb cos nt and kb sin nt, respectively. The equations of motion for the center of mass of the bullet are:\n\ndx2 = m\u2014 kb cos nt dt2\ndy2 = m\u2014 kb sin nt dt2\n\nThe quantities k, b, and n are constant by assumption. Therefore, an integration using the initial conditions can determine the horizontal and vertical positions of the bullet at any given time.\n\nFrom the form of x, it is evident that the horizontal projection of the helix d, which approximates the motion, is tangent to the line of departure and lies to the right of this line as viewed from the gun. Moreover, the horizontal projection of the helix is a tangent to the line of departure and lies to the right of it.\nThe form of y indicates that the entire trajectory has undergone a downward displacement through an angle of kb/mnPo radians. This is the windage jump. The componential motions are depicted in Figures 8 and 9 after exact calculations.\n\nThe above analysis can be memorized with the mnemonic: if the thumb and first two fingers of the right hand are extended at right angles to each other, and if the forefinger is pointed in the direction of mount motion and the second finger in the direction of fire, then the thumb gives the direction of trajectory displacement.\n\nThe diameter of the helix for small calibers is of the order of inches.\n\nIt is clear that windage jump is rather a misnomer. The phenomenon is due entirely to initial yaw, and the displacement is not a jump. (In particular,)\nThe random initial yaw of bullets at a ground gun's muzzle, caused by bore clearance, leads to random displacement and builds up a dispersion pattern. The windage jump, as previously mentioned, is small. It can be calculated using the formula Vo * Po, where b depends on the projectile's physical constants. Typically, b/Vo is 17 milliradians for caliber 0.50 AP M2, and 21 milliradians for caliber To conclude the discussion of the three motions listed in Section 1.4.2, drift will be considered here only in qualitative terms. The phenomenon is due to gravity. Initially, the center of gravity starts to move downward under gravity while the axis of the bullet remains horizontal. The initial yaw attributed only to this is therefore in a vertical plane and is small. The bullet precesses to the right and down by this initial yaw.\nusual law of gyroscopic precession. Since the trajectory is curved, its tangent slowly rotates downward. For the small yaw under consideration, the precession can be just slow enough to keep pace with the tangent's downward rotation. That is, the bullet keeps pointing to the right of the trajectory. Consequently, the cross-wind force is always perpendicular to a vertical plane and is directed to the right. Therefore, the bullet drifts slowly to the right under this force. (For caliber 0.50, this drift amounts to about 7 in. in 1,000 yd and so may be neglected.)\n\nAeroballistics 1.5 Dispersion\n1.5.1 Philosophy of Rapid Fire Weapons\nWith but few large caliber exceptions, in aeroballistics, a burst (a rapid and continuous sequence of bullets) is directed at a target. The successive bullets will not follow each other in exactly the same path.\nThe dispersed pattern is built up at the target as a result. The directed burst or pattern principle is basic in the philosophy of airborne fire control with small caliber ammunition. The expectation is that if a large number of bullets are placed rapidly on and near a target, there will be a high probability that at least one will hit the small vulnerable sub-area. This is evident from operational statistics indicating that anywhere from 17,000 rounds (B-24, Africa, early World War II) to 2,500 rounds (B-29, Pacific, late World War II) were expended per fighter shot down. In contrast, with large caliber projectiles, successive hits can be scored on ships angularly smaller than aircraft targets (U.S. Navy, Coral Sea). 1.5.2 Nature and Statistical Deployment.\nIn aerial gunnery, only a certain part of the total dispersion can properly be attributed to ballistics. The situation is as follows: In tracking and firing at an airborne target, an instantaneous mean point of impact fails to stay on the target since it is being carried about by aim wander, deflection errors, and instrumental errors. Aeroballistics may discuss only this mean point of impact, but it suffers an enlargement on its concept since a gun mount and a gunner will be introduced. This is justified because of the influence of these factors on the direction of bullet departure. To proceed systematically, consider a sequence of three ground experiments.\n\n1. Suppose rounds are fired under precisely the same conditions of exact and individual aim. Because of initial yaw at the muzzle and manufacturing variations, the bullets will not impact at the same point despite identical aiming conditions.\nIn a powder charge, bullet shape and weight, and position all follow a certain pattern. This pattern is remarkably tight. For instance, in caliber 0.50, a cone of angular diameter 0.25 milliradian contains 75% of the rounds when fired through a 45-inch Mann barrel.\n\nIf a burst is fired instead of individual rounds, with the mount held rigid, elastic vibrations of the barrel will occur. The vibration is not just an up-and-down whip. Instead, a forced vibration occurs, and each bullet sensibly leaves in phase with the barrel's motion. Typically, the 75% cone is increased to approximately 2.5 milliradians.\n\nIf the mount is not held rigid and a human gunner is asked to hold on a fixed target, the combined mount vibration and gunner error will lead to a 75% cone of diameter ranging from 5 to 25 milliradians.\nIt is with the third type of dispersion that one normally deals in calculations, depending on the installation under test. The magnitude of this type of dispersion must be carefully determined for the given system, noting the effect of variables such as aircraft, installation, gunner, age of the gun, and length of burst.\n\nWhen bullet holes of any burst are collected on a flat target normal to the line of fire, they have a center of gravity, which is called the mean point of impact (MPI). It may be noted that the MPI may be systematically displaced from the first bullet due to gun jump. Furthermore, with excessively long bursts, the heating of the barrel may also cause a steady shift of the MPI. However, neglecting such effects, it is common to consider each round as independent so that the dispersion pattern may be analyzed.\nThe two-dimensional description of the problem is adequately represented by a normal or Gaussian distribution with the MPI as the mean. In practice, the variances in two orthogonal directions will differ, resulting in an elliptic distribution. However, the orientation of this elliptical pattern depends on the direction of fire in a complicated way due to different vibrational responses of the mounting. It has become customary to replace it with a circular distribution (with the two directions statistically independent). If the MPI is taken as the origin, the fraction of a large number of rounds that will lie in the cell rdOdr is given by:\n\nwhere j is the standard deviation. Cells of equal probability with their centroids are shown in Figure 10. Since the evidence is that the bullets of a burst define a right circular cone, it is usual to take r and <7 in milliradians in military literature.\nFrom the given text, the following clean and readable version can be obtained:\n\nspecified by giving the diameter of the circle that contains either 50 or 75 percent of the rounds.\n\nCONFIDENTIAL\nDISPERSION\nCELLS OF EQUAL PROBABILITY\nLINEAR PROBABLE ERROR\nr/j no\nllill.ll.ll'.ll 1 I I\nLINEAR PROBABILITY\nIII 1\nLINEAR AVERAGE DEVIATION\nSTANDARD DEVIATION\nL i\nFigure 10. Cells of equal probability.\nCONFIDENTIAL\nAEROBALLISTICS\n\nFrom equation (10), it follows that the diameter of the circle containing h percent of the rounds is given by:\n\nd/a = 3.330\n\nThe most elegant specification of the pattern size is through a, since a is the radius of that annulus of width dr that contains the maximum fraction of the total number of rounds composing the pattern.\n\n1.5.3 Change in Pattern Size under Trail Gradients and Forward Fire\n\nAeroballistic effects can modify the pattern size. Suppose that a turret is firing a burst while it is tracking a moving target. The changing trajectory of the projectiles due to aerodynamic forces can cause the pattern size to change. This effect is known as \"dispersion\" and is a significant factor in the accuracy of gunnery systems. The diameter of the circle containing a certain percentage of the rounds can be calculated using the given formula. The radius a of the annulus that contains the maximum fraction of the total number of rounds can be determined to specify the pattern size elegantly.\nThe pattern built up at the target, relative to the gun, is distorted due to a change in lateral ballistic deflection caused by a change in 0.111. This trail gradient is given by the equation: TF900 = au where TF900 is the lateral ballistic deflection for beam fire, with other conditions remaining unchanged. An analysis in the vertical direction yields the same distortion. It is concluded that a different type of distortion occurs in forward fire from a fighter. A straightforward vector combination of muzzle velocity and fighter velocity gives the expression: Vo = Vo + vr This is illustrated by Figure 11. A change as great as 20 percent can occur, and it should therefore be taken into account. A final point of interest is the aeroballistic effect.\nThe dispersion pattern is caused by the variation in muzzle velocity. This velocity varies materially (100 fps) not only due to manufacturing variations but also due to the position of the powder in the cartridge, temperature, age of barrel, and length of burst. Since the aiming allowance for target motion is approximately proportional to muzzle velocity (see Chapter 2), if all the rounds of a burst have a mean muzzle velocity different from that assumed by the fire control system, a systematic displacement of the MPI from the target will occur. But consider now the effect of the variation in muzzle velocity around the mean during the burst. The low-valued bullets will underlead, and the high-valued ones overlead. The dispersion is increased proportionately along the target's track.\nSince deflection errors, such as the systematic one described above, have greatest value along the track, it is a reasonable idea, given the flat trajectories in hand, to remove the necessity of making superelevation allowances for gravity drop in the aiming problem. If guns are set at some fixed slight angle with respect to the line of sight, then, with the usual condition of guns below the gunner's eyes, the trajectory of the ideal bullet, which will hit the MPI, will arch up, cross the line of sight near the guns, and cross it again much later. With a dispersion pattern, there is then, an arched cone which supplies a beaten zone hugging the line of sight quite closely over ranges of tactical importance. In determining the required:\n\n1.5.4 Harmonization\n\nBecause of dispersion, it is a reasonable idea, given the flat trajectories, to attempt to remove the necessity of making superelevation allowances for gravity drop in the aiming problem. If the guns are set at some fixed slight angle with respect to the line of sight, then, with the usual condition of guns below the gunner's eyes, the trajectory of the ideal bullet, which will hit the MPI, will arch up, cross the line of sight near the guns, and cross it again much later. With a dispersion pattern, there is then, an arched cone which supplies a beaten zone hugging the line of sight quite closely over ranges of tactical importance. In determining the required:\nSection 1.1 defines aeroballistics by contrasting points related to fire from airborne guns with items in classical exterior ballistics.\n\nDirection of fire is important because nose fire to a given future range implies a smaller time than tail fire to the same range. In remote fire control systems, such as those in the B-29, the physical difficulties in implementing a harmonization scheme determined by these considerations are significant.\n\nSection 1.2 derives formulas for the time of flight of a projectile as a function of direction of fire and range.\n\nConfidential:\n\nSummary:\nSection 1.1: Aeroballistics is defined by contrasting aspects of fire from airborne guns with classical exterior ballistics.\n\nImportant: The direction of fire impacts the time it takes for a projectile to reach a given range, with nose fire requiring less time than tail fire. In remote fire control systems, implementing a harmonization scheme based on these considerations presents challenges.\n\nSection 1.2: Formulas for calculating the time of flight of a projectile based on direction of fire and range are derived.\nSection 1.3 works in the coordinate system relative to the gun mount and derives various expressions for the angular displacements of the projectile from the bore axis. These displacements are the lateral and vertical ballistic deflections.\n\nSection 1.4 discusses the microscopic motion of a bullet with respect to the mean trajectory of the previous sections. The phenomena of yaw damping, windage jump, and drift are discussed in elementary terms.\n\nSection 1.5 deals with dispersion. It indicates the relation between patterns determined by ground firings and patterns arising under air firing. The pattern is described by a circular Gaussian distribution.\nIn air warfare, both the gun platform and the target move at high speeds, often reaching speeds up to one-fifth that of the projectile being used. The high speed of the mount causes the bullet to take on this speed, resulting in a significant angle between the bore axis and the direction of the projectile's departure. The high speed of the target means it will move a considerable distance during the missile's flight time. Additionally, a bullet experiences its own ballistic deflections. To achieve a hit, the bore axis must generally have an angular displacement from the line connecting gun and target at the moment of fire. This angle between bore axis and line of sight is known as deflection.\nThe gun-target line is called the deflection or lead, even if it is a lag, or the aiming allowance. The theory of aerial gunnery relies on a precise mathematical account of deflection shooting. Such an account is available, and it is the purpose of this chapter to summarize this systematic theory.\n\n2.1.2 Three Problems of Deflection Theory\n\nTheory must provide formulas for perfect shooting to serve further studies and to supply a norm against which compromises and approximations can be measured. Formulas must be computable rapidly and accurately with legitimately available data. Lastly, they must be mechanizable.\n\nAs an example of the last two points, legitimize:\n\n15. An account is at hand (Mansfield, 1916).\nThe data pertain to measurable factors by the gun platform at the instant of fire, which are accessible for suggested mechanization (fire control system).\n\n2.1.3 Conditions for Theory Validity\n\nTo apply the theory of this chapter to any situation other than air-to-air fire with present-day ammunition at ranges up to 1,000 yards, caution is required for three reasons. It is assumed that gun platform, target, and projectile are all in the same air mass, which is in nonaccelerated motion. Therefore, for a ground target or a ground gun, further consideration must be given to the effect of the motion of the air mass with respect to the ground.\n\nIn the second instance, the detailed consequences of various formulas will typically utilize a three-halves power resistance law for the bullet. Chapter 1 has indicated the range of bullet speeds under which this law applies.\nIn aerial gunnery, each bullet in a burst requires a unique deflection due to continuously changing conditions of fire. This chapter focuses on an individual and perfect bullet under general conditions, setting aside considerations of dispersion and hit probabilities. The target is a point.\n\n2.2 Nonaccelerated Target Coplanar with Mount Velocity\n2.2.1 Basic Formula\nThe plane determined at any instant by the position of the target and by the mount velocity is called the nonaccelerated target coplanar with mount velocity. T is the angle off of the target at the instant of fire. Oi is the approach angle of the target at the instant of fire. Arrows give the positive sense of all angles.\n\nFigure 1. Nonaccelerated target coplanar with mount velocity. The plane of action. In individual duels between a fighter and a bomber, this plane of action remains sensibly the same during the engagement. For the purposes of this section, it is necessary to assume that the target moves with constant velocity in the plane of action of the instant of fire, since it is clear that a bullet has no relation to the motion of the mount subsequent to its departure from that mount. The situation contemplated in the following.\nair mass is drawn in Figure 1, which is suitably annotated. With the aid of the dotted line constructions, one readily obtains the formula:\n\nV = Vo / (1 + q)\n\nwhere the slowdown factor q is the ratio of the initial speed of the bullet, u0, to the average speed, u, over the air range P.\n\nTo justify the name given to q, note that tf = q * to, where tf is the actual time of flight to future position and to is the time of flight in vacuum to that position. Hence l = q - 1 is the proportion by which the time of flight has been increased because of air resistance opposing the bullet\u2019s motion.\n\n2.2.2 Own-Speed Allowance, Fighter Lead, and a Classic Theorem\n\nTwo obvious special cases of equation (1) are important. If either vt or a is zero,\n\nV = Vo\n\nIn this case, A is called the own-speed allowance. It is significant that the mean velocity of the bullet does not change due to air resistance in this situation.\nThe direction of departure is the only factor in equation (2). Tactically, a target fixed with respect to the air mass or approaching or receding along the gun-target line is under fire. This is the allowance for strafing a ground target in the absence of ground wind, or the deflection to take against an attacking fixed gun fighter, to a first approximation (See Chapter 4).\n\nAs a second case, consider a first approximation fighter, whose guns must fire exactly in the direction of flight, located at point G. Then, the angle off, r, must always be equal to the required deflection, A. Consequently, equation (1) becomes:\n\nvT + Vo + Vg\nor\nu\n\nThe minus sign indicates that lead (gun pointing ahead of the target) is taken negative. Lag (gun lag) is not mentioned in this equation.\nFor the target with the fighter behind it, the plus sign is assigned, as the primary focus has been on the study of fire from a bomber against attacking fighters. Comparing equations (2) and (3) provides a classical, yet only approximate, theorem. Place a fighter at T in Figure 1 such that there are now two gun mounts. For the fighter, the approach angle, a, is the same as the angle off, r. The speed of the fighter's target, vT, is the speed vG of the bomber. Lastly, the fighter's bullet's average velocity u is approximately equal to the propellant muzzle velocity v0 of the bomber's bullet, as the slowdown of the fighter's bullet is compensated for by its augmented velocity of departure. Consequently, in a duel between a fighter and a bomber, the leads taken are equal in size and opposite in sense.\nThe refinements are explored in Chapters 3 and 4. The theorem is put to practical use in Section 2.2.3: Tracking Rate Formulation.\n\nFormula (1) is not suitable for mechanization. It requires an estimate of the approach angle, which cannot be made accurately from the gun platform using existing devices. It also uses the unknown future range to determine the slowdown factor. Additionally, it is easier mechanically to measure the angle between the mount velocity and the bore axis of the gun rather than the angle r. To address these three objections, it is reasonable to work in a reference system that translates with the mount's velocity at the instant of fire. In this relative reference system, the platform velocity is given to the target in a reverse sense. Consequently, the angular rate a> of the gun-target line is evident.\nWith r being the present range, the formula for a can be removed from equation (1), addressing the first objection. The result is:\n\nno vG .\n\nVo Vo\n\nwhere l = q - 1. To address the third objection, let 7 = t + A, where y is the angle between the mount velocity and the bore axis. Then,\n\nwhere\n\nand\n\nsin A = tmcc - b sin y,\nqr\nVo - lvG cos y.\n\nThe important formula (4) merits a prefatory discussion at this point.\n\n2.2.4 Kinematic and Ballistic Decomposition\n\nTo further discuss formula (4), Figure 2, which uses the reference system relative to the gun mount, is shown below. In this figure, vR is the relative target velocity.\n\nFigure 2. Deflections relative to the gun mount.\nIn the absence of lateral ballistic deflection, the gun points at Tf, and the corresponding aiming allowance A* is called kinematic deflection. However, the trajectory curves rearward when viewed from behind the gun. Therefore, a ballistic correction A6 must be made, neglecting gravity at this point. In this system, the total deflection is expressed as:\n\n145\n\nThis deflection must be the same as the deflection given by equation (4). A direct identification of equation (7) with equation (4) can be made. From Figure 2, it follows that ru = vR sin \u03b8 and D/tf = v. Hence, rco = v.\n\nUsing Figure 3, in which auxiliary angles are shown, we have:\n\n\u03b81 = i + \u03b5\n\u03b82 = i - \u03b5\n\nwhere i is the approach angle of the relative path and \u03b5 is the angle of lateral deflection. The angle of deflection \u03b4 is given by:\n\n\u03b4 = \u03b81 - \u03b82 = 2\u03b5\n\nSubstituting the expressions for ru and D/tf from above, we get:\n\n\u03b4 = 2\u03b5 = 2(vR sin \u03b8 / v) = 2(R sin \u03b8 / vt)\n\nwhere R is the range and vt is the time of flight. This is the required expression for the angle of deflection in terms of range and time of flight.\nlengths x and y have been introduced. It is easy to show that,\n\nlvG cos A = Vo cos \u03b8 - Ivg sin y,\nlvG COS 7 ancJ = Vo sin \u03b8 - Ivg cos y.\n\nThe second objection, concerning the unknown future range, must be dealt with carefully. (The treatment is as follows:)\n\nsin At = lvG sin \u03b8,\nqv = (v0 - Ivg cos t)\u00b2,\n\nBut (Ivg sin y)\u00b2 is of negligible size compared with (v0 - Ivg cos t)\u00b2. Hence, qv may be replaced by (vq - lvG cos y); and simple substitution now identifies equations (7) and (4) as,\n\nprovided sin Ak and sin Ab are replaced by Ak and A* measured in radians, and cos A is taken to be unity in equation (6).\n\n2.2.5 Time-of-Flight Multiplier\n\nThe quantity tm of equation (5) should be examined closely. It has the dimensions of time but since it is present range divided by mean velocity over future range, it has no direct physical meaning. It is called the time-of-flight multiplier.\nThe time-of-flight multiplier. We may write:\n\nV = vp V = v v\n\nWhere vp is mean velocity over present range and tp is the time of flight over present range. If the relative motion path is incoming, i.e., D < r, it follows that vp/v < 1 and tp is slightly too large a kinematic deflection. The reverse is true if the relative motion path is receding.\n\nIn a mechanization designed for all-around use, the ballistic computer would simply translate present range into present time of flight. But if the tactical circumstances were such that targets were always closing, a correction factor should be applied. This is a first and simple example of a basic principle in fire control theory. The time-of-flight multiplier need not fit any particular ballistic table but should be chosen as a function of range to optimize performance over an ex-\nFor the tactically important case of an accelerated target, which means a curved path, a change in speed, or both, the formulas from the previous section must be modified by the addition of a correction term. If the chord of the target's path segment from T to Tf makes an angle a with the gun-target line, and if the average speed of the target over this segment is vt, then equation (1) may apply and is written as:\n\nVo = Vo + vt * sin(a)\n\nConceptually, the actual target has been replaced by an equivalent one, as far as impact is concerned, whose approach angle is the average approach angle of the actual target. An estimate of vT is given by:\n\nvT = sqrt(vt^2 + (Vo - vt * cos(a))^2)\n\nwhere vt and vT are evaluated at the moment of fire.\nIf the change in path curvature is not radical, over the contemplated flight times, the target may be taken to move in a circle at constant speed Vt and turn through an angle 2(a - a) during tf. If the angular rate of change of the target is cor, the angle through which it turns is also cor * tf. Consequently, the deflection formula becomes:\n\nVo = Vo + vo * L\nor\nVo = Vo + vt * Vt / (Vo + vt)\n\nTo follow this discussion with the figure, modify Figure 1 by drawing an arc through T and Tf and placing bars over a and vT.\n\nIf it's assumed that the gun mount is moving at uniform velocity, then vg = 0. Since r > o, it follows from the physically evident rate relations that:\n\nvg = 0\nr = o > 0\nvo = vt / (Vo + vt)\n\nTherefore, the deflection formula simplifies to:\n\nVo = Vo + vo * L\nor\nVo = Vo + vt * Vt / (Vo + vt)\nwhere M is the angular momentum of a target of unit mass, [Formula (10)] may be verified by calculating the derivative of r\u00b2o. With the aid of formula (10) and the first equation of (9), equation (7) can be written:\n\nVq = Vt sin a\n\nFinally, as in the derivation of equation (4), one may take:\n\nh = tm b\n\nConceptually, equation (12) is quite important. It shows that deflection formulas for an accelerated target can be obtained from those for a target in uniform motion by multiplying the time-of-flight multiplier by a (non-constant) factor h. In the design of eye-shooting systems and own-speed sights, and in the calibration of lead computing sights, this is decisive.\nPut,  as  above,  M  =  r2oo  and  expand  M  in  a  Taylor\u2019s \nseries  about  t  =  0.  Then \nFUTURE  TARGET  POSITION  Tf \nRELATIVE  TO  GUN \nFigure  4.  Accelerated  target,  relative  to  gun  mount. \nwhere,  now,  M,  M,  \u2022  \u2022  \u2022  are  evaluated  at  t  =  0.  Since \ntf  is  small,  terms  of  the  third  and  higher  orders  may \nbe  neglected.  An  independent  evaluation  of  the  area \nA  is  given  by  the  area  of  the  triangle  GTTf,  since  tf \nis  small  and  the  path  curvature  cannot  be  large  for \naerodynamic  reasons.  The  area  of  the  triangle  is \nWhen  this  is  equated  to  the  previous  expression,  one \nfinds  that \nwhere  the  letters  have  the  same  meaning  as  in  the \nearlier  discussion.  Finally,  since  the  argument  based \non  Figure  3  uses  only  the  impact  point  and  is  not \nconcerned  with  the  target\u2019s  meanderings  in  reaching \nthis  point,  it  applies  immediately  here.  The  identi\u00ac \nfication  of  the  air  mass  coordinate  formula  and  the \n2.4 THE GENERAL THEORY OF DEFLECTION\n2.3.2 Kinematic and Ballistic Decomposition\nThis discussion can be paralleled in the reference system relative to the mount. This treatment emphasizes the role of the target's angular momentum on its relative path. From Figure 4, it is evident that the area A swept out by the gun-target line during the bullet's flight is:\n\n1 rlf l r lf\n\n2.4.1 Extended Conditions\nA general treatment must permit the gun mount and target to move in arbitrary space paths. It must also allow the bullet to move in a vertical plane rather than in a straight line. For the first requirement, it may be said that the paths are smooth in the analytic sense and curve gradually in the tactical sense.\nThe General Theory of Deflection: Under the first requirement, one will not be concerned with derivatives of the third and higher order. Gravity drop is permitted under the second requirement. Although deviations normal to the vertical plane containing the direction of departure of the bullet are not permitted here, the methods of this section can be generalized for missiles of the future that require consideration of such behavior. For the three-dimensional situation, the evident tools are vector algebra and vector calculus (1515,216). These methods are particularly applicable to support fire situations and aerodynamic lead pursuit curves (Chapter 3). Since the methods are vectorial, specialization to various coordinate systems corresponding to particular decompositions of deflection is readily accomplished.\n\n2.4.2 Derivation of General Formula\nIn the air mass, the trajectory is described by a vector b, connected to the Siacci vectors P and Q (see Section 1.2.2) through:\n\nLet r be the gun-target vector, let vG and vt be the velocities of mount and target, and let v0 be the propellant muzzle velocity (in the direction of the bore axis). All vectors are functions of time measured from the instant of fire. In the air mass reference system, one writes:\n\nJo\n\nHolding this relation in reserve for the moment, it is trivial to observe that the bore axis is placed in lead position by rotation from the gun-target line through the appropriate lead angle. But this rotation suggests the representation of deflections by vectors perpendicular to the bore axis and to the gun-target line, and hence implies cross products. By definition,\n\nAo = sin A\nr \u00d7 vG\nN\nVo = r \u00d7 vt\nVg\nVo = r \u00d7 v0\nNow u0 = v0 + vG, and u0 = Uo/P. Therefore, from equation (14), we have:\n\nThe dot product of vector A by B is the scalar A \u00b7 B = AB, where \u03b8 is the angle between A and B. The cross product of A by B is written as A \u00d7 B and is a vector perpendicular to the plane of A and B, with a positive sense according to a right-hand system (A, B, AxB). The magnitude of A \u00d7 B is AB sin \u03b8.\n\nWhere q = Uo/u, u = P/tf, and tf\u00b7vt = multiplication by q results in Uq.\n\nWhere the list in equation (15) is now extended by rv:\n\nVo, rv, X, Vo, and where a is the average approach angle over tf and Z is the angle between r and the true vertical.\n\nFormula (17) makes precise one's intuition about the form of the total lead and clearly reduces to:\nequation for the two-dimensional case without gravity. To obtain the appropriate generalization of equation (11), consider vT in detail. A good approximation to vt is given by the expression: Vt = Vt + vtVTy where vT and vT are evaluated at t = 0. This arises by taking three terms in the series expansion of the vector giving target position with respect to the origin of the air mass coordinates, differentiating, and integrating from 0 to tf.\n\nTurn now to the reference system relative to the gun. The velocity of the target in this system is vR = vT - vG. The angular momentum of unit mass at the target position is: L = r x vT and its derivative is given by: \u03bc(dL/dt) = r x (m(d^2r/dt^2) + m(d^2vT/dt^2))\n\nThe angular velocity of the gun-target line is connected to M by: \u03c9 = (d\u03b8/dt) = (d/dt)(r \u00b7 vT) / r\n\nUsing these relations, one finds that: \u03bc(d\u03c9/dt) = m(r \u00b7 (d^2vT/dt^2) + vT \u00b7 (d^2r/dt^2) - r \u00b7 (d^2vT/dt^2) - (vT \u00b7 dr/dt)^2)\n\nwhere\n\nCONFIDENTIAL DEFLECTION THEORY\n\nSubstitution in equation (17) yields the vector equation: m(d^2r/dt^2) = F + (r x (m(d^2vT/dt^2) - (vT \u00b7 dr/dt)^2 / r)) \u00d7 F\n\nThis is the required equation for the two-dimensional case without gravity, taking into account the motion of the target in the gun reference frame.\nThe term involving X^2 in equation (11) permits accelerated mount motion. All quantities in equation (19), except tf, are evaluated at the instant of fire. The effects of acceleration are explicitly exhibited in amount and direction. Equation (19) can be regarded as an expression of suitable generality for all fire control applications considered in this account. The ease with which it is obtained is noteworthy.\n\n2.4.3 Special Coordinate Systems\n\nIn applications, formulas such as (19) must be expressed in particular coordinate systems. The four most common systems are: (1) azimuth and elevation, (2) sight elevation and traverse, (3) gun elevation and traverse, and (4) parallel and perpendicular to the plane of action.\n\nIn the first system, a fuselage axis and a wing-span line are used.\nThe axis determines an azimuth plane. The elevation plane is perpendicular to the azimuth plane. The gear system of the usual turret illustrates this system and shows that the azimuth plane does not necessarily contain the aircraft's velocity vector (the aircraft may be flying nose high or nose low), and that zenith in the system is not necessarily the zenith with respect to the earth (the aircraft may be diving and turning). If I is a unit vector in the forward direction of the fuselage axis, if K is a unit vector directed outward along the starboard wing, if J is a unit vector directed upward with respect to the aircraft, and if ri and v0i are unit vectors in the directions of gun-target line and bore axis respectively, then:\n\nTi = (I cos A K sin A) cos E + J sin E\n\nWhere A and A0 are azimuths in the system, and E.\nAnd E0 are elevations (of gun-target line and bore axis respectively). The azimuth lead and elevation lead are given by:\n\nFor the second (sight) system, let ttSe be the plane containing r and perpendicular to the azimuth plane, and let tst be the plane containing v0 and perpendicular to ttse. If c is a unit vector along the intersection of these two planes, then the angle between ri and c is called the sight elevation lead, Ase, and the angle between c and v0i is called the sight traverse lead, ASt. One has the formulas:\n\nsin Ast = sin Aa cos E0,\nsin Eq = cos ASt sin (E + Ase).\n\nThe third (gun) system is similar to the second in that tge is a plane containing v0 and perpendicular to the azimuth plane, and ttgt contains r and is perpendicular to tge. Then:\n\nsin Agt = sin Acos E,\nsin E = cos Agt sin (E0 - Age).\nThe fourth system uses a plane containing vG and r. If \u03b3r0 is a plane containing v0 and perpendicular to \u03b3r, and if c is a unit vector determined by the intersection of these two planes, then the angle Ay between ri and c is called the lead in the plane of action, and the angle Al from c to v0i is called the lead out of the plane of action. This system is particularly useful in theoretical studies since many tactically significant situations occur in a sensibly fixed plane of action, and Ay accounts for most of the total deflection. The discussion in this section will be restricted to the gun elevation and traverse system, which is typical of the last three systems in that deflection is involved.\nThe leads Agt and Age are computed by the formulas:\n\nWhen equation (20) is combined with formulas like (19), suitable expressions for AGt and AGe arise after significant manipulation.\n\n2.4.4 Gun-Roll Error\nSights such as the K-3 use gun tracking rates and base their mirror system on the gun. Therefore, the gun elevation and traverse system is appropriate for describing such equipment. However, this system has a peculiarity, accentuated with elevation, which results in a notable error in deflection. The angular velocity w of r has components wr and oE corresponding to rotations of the gun-target line in the traverse and elevation planes. Consider the gun:\n\nConfidential summary:\n\nThe angular velocity w of r has components wr and oE corresponding to rotations of the gun-target line in the traverse and elevation planes. When equation (20) is combined with formulas like (19), suitable expressions for AGt and AGe arise after significant manipulation.\n\n2.4.4 Gun-Roll Error\nSights, such as the K-3, use gun tracking rates and base their mirror system on the gun. Consequently, the gun elevation and traverse system is suitable for describing such equipment. However, this system has a peculiarity, which is more pronounced with elevation, leading to a considerable error in deflection. The angular velocity w of r has components wr and oE, representing rotations of the gun-target line in the traverse and elevation planes, respectively. Upon combining equation (20) with formulas like (19), appropriate expressions for AGt and AGe emerge after extensive manipulation.\nThis text discusses coordinate systems in gunnery, specifically those measuring angular velocities w, w0, and ojoe. In systems measuring gun rates, only w0r and w0e are obtained as the roll of the bore axis, w0, is not measured. Consequently, the angular speeds assigned to r by gun rates should account for co0's contribution to cor and aE. The resulting errors, known as gun-roll errors, are approximately 15 degrees:\n\n\u03b3t = - Ae * Ag* * tan(Eq)\n\u03b3e = A2 * gt * tan(Eq)\n\nIf Ag* is 0.1 radian, for elevations above 45 degrees, the elevation gun-roll error exceeds 10 milliradians, which is significant.\n\nChapter 2.4.5 focuses on calculating deflections using present data as much as possible, as these quantities are the only available ones.\nTo a fire control system at the instant of fire, in experimental and theoretical studies, complete knowledge of the paths of the gun mount and target is usually available. In such cases, one may choose to bypass the above formulas and revert to first principles. That is, one can start by selecting a point of impact. Then, either future range or air range is known exactly, and therefore time of flight and kinematic deflection are known, as is the required position of the bore axis to generate the assigned point of impact. Hence, the present position corresponding to the chosen point of impact is determined since the path is expressed as a function of time. A table can be built up of deflection versus the time parameter of the path, in which one may interpolate at pleasure. The method is usually called the timeback method.\nSection 2.1 introduces the need for a systematic theory of deflection. Reasons include supplying norms for approximations, providing rapid computational procedures using available data, and determining the nature of mechanizations. Section 2.2 discusses a target moving at constant speed on a straight line in a common plane with the gun-mount velocity. Deduced formulas will be used throughout the text. Section 2.3 allows for a target moving in a curved path, introducing the acceleration correction factor formula.\nChapter 3, Pursuit Curves\n3.1 Introduction\n3.1.1 Pursuit Curves in Modern Warfare\nThere are many situations where an object moves along a path of its own choosing and is pursued by another object moving in a path that points instantaneously either directly at the pursued (pure pursuit), or at some point in the vicinity of the pursued according to some definite law (deviated pursuit). In one homely and classical example, the pursuer is a dog in a field and the pursued is the dog's master who walks along the edge of the field.\n\nSection 2.4 uses vector methods to address the general problem where mount and target may move in arbitrary space paths. Various coordinate systems used in fire control are discussed, along with a brief explanation of the phenomenon of gun roll.\n\nChapter 3, Pursuit Curves\nSection 2.4 deals with the general problem where mount and target may move in arbitrary space paths using vector methods. Discussed are the different coordinate systems used in fire control, as well as an explanation of the gun roll phenomenon.\nIn the field, if the dog were blind, he might run toward the sound of a whistle blown continuously by his master. The former case is pure pursuit, and the latter is an example of deviated pursuit.\n\nIn modern warfare, pursuit curves arise in three types of situations:\n\n1. Homing missiles may continuously change heading under radio, optical, or acoustic guidance unwillingly supplied by the target.\n2. Aircraft, directing rockets or large-caliber projectiles at fixed ground targets, may find themselves in an air mass moving with respect to the ground. If the motion of the air mass is reversed and then given to the target, a pursuit curve arises.\n3. The standard fighter aircraft of World War II employed a heavy battery of guns fixed in the aircraft to fire in the direction of flight. To change the direction of fire, the aircraft itself must be re-directed.\nFighters flown in new direction. Consequently, unless the fighter is directly behind or ahead of its airborne target, it must fly on a correctly banked turn. The correct and changing aiming allowance is hence made. Fire from fighters is called fixed gunnery. If guns can be positioned freely with respect to the direction of flight, flexible (or free) gunnery arises. This is usually true for bombers. The bullet pattern is continuously held on the target until destruction is effected. (Case 1): studied for determining turning rates, as certain missiles have control limitations in this respect. (Case 2): considered in assessing the effect of the path on the aiming problem (rockets), and in determining terminal conditions for bomb release (75-mm cannon-firing path for the B-25H).\nThe primary function of a bomber's defensive gunnery is to prevent the parent bomber from being shot down by attacking fighters. Consequently, it is reasonable to require the greatest accuracy from the defensive fire control under the ideal attack circumstances discussed in Case 3 above. The fire control must predict the target's future position on such courses quite closely to determine future positions, which requires the computation of aerodynamic lead pursuit curves. It will be made clear in the following sections.\n\n1.3.1.2 Reasons for an Elaborate Investigation\n\nThe rationale for the elaborate pursuit curves in the investigations outlined in this chapter is discussed below.\n\n1. The defensive gunnery of a bomber's primary function is to prevent its parent bomber from being shot down by attacking fighters. Therefore, it is necessary to ensure the greatest accuracy from the defensive fire control under the ideal attack circumstances, Case 3 above. The fire control must predict the target's future position on such courses quite closely. To determine future positions, the computation of aerodynamic lead pursuit curves is required.\nThe sequel discusses how computations impact: (1) generation of position firing rules of thumb (Chapter 4), (2) the choice of percentage for an own-speed sight, and (3) the calibration of the time-of-flight setting for rate type sights (Chapter 5).\n\nThe alternative for the attacker is to maintain a fixed flight direction arranged such that the target will fly through a bullet stream. Due to the target's rapid passage and bullet spacing, few hits may be scored. This strafing attack has been discarded by all air forces as tactically inefficient due to the limited vulnerability of the target to present calibers and rates of fire.\n\nCONFIDENTIAL\n\nThe Elements of Pure and Deviated Pursuit Theory in a specific tactical circumstance (Chapter 4), and (3) the calibration of the time-of-flight setting for rate type sights (Chapter 5).\nFrom the point of view of offensive or fixed-gun fire control, a study of pursuit curves leads to an appreciation of the effect of aerodynamics on the aiming problem and to appropriate calibration of the lead computing sights used by fighters. Pursuit curve studies have culminated in the detailed analysis of Section 3.4. Frequently, one wishes to use the simpler methods of Sections 3.2 and 3.3. Since the complete picture is at hand, approximations may be tested as desired. Finally, the design in the large of defensive fire control systems requires a knowledge of the limitations and possibilities of fighter attacks, as given in Section 3.5. Design in the large means, here, the choice and disposition of armament and the optimization of performance of the fire control system over the appropriate range-azimuth-elevation cells.\n3.2 The Elements of Pure and Deviated Pursuit Theory\n3.2.1 Assumptions and Coordinates\n\nAssuming throughout this section that the pursued chooses to follow a straight line path at a constant speed Vb, and neglecting aerodynamic effects or deliberate throttle variation, the speed of the pursuer is also to be a constant vF. The velocity subscripts indicate that a bomber and a fighter are the objects of the primary physical realization.\n\nIf the laws of deviation are restricted to those in which the pursuer always homes on some variable point on the pursued's track, it follows that the curves considered must be plane curves. The plane containing the two tracks is called the plane of action.\n\nUnder the assumptions made above, the geometrical results are independent of the angle between the plane of action and a horizontal plane through the origin.\nIn studying pursuit curves, the most natural coordinate system to use is one whose origin is held on the moving object under pursuit. In such a relative coordinate system, the velocity vector of the pursued is transported to the pursuer and there reversed in sense. The pursuer then moves as dictated by the vector resultant of its own velocity and this reversed velocity.\n\nAppropriate tactical variables are the range p and the angle \u03b8 measured positively from the rearward track of the pursued up to the line joining the participants. Experience has shown that Cartesian coordinates are not efficient.\n\n3.2.2 Equations for Pursuit Curves\n\nThe above circumstances are depicted in Figure 1. The deviation angle \u03b8 is specified separately, as some figures are labeled \"Figure 1. A typical instant of deviated pursuit.\"\nfunction of p. More generally, it would be a function of both p and \u03b8. Three instances of such functions concern us in this section. They are: (1) 5 = 0, which is pure pursuit, e.g., homing by a connection through light or radio; (2) 5 = constant, which is fixed lead pursuit, e.g., a fighter using a fixed average lead in attacking a bomber c; and (3) 5 = v sin \u03b8, which is variable lead pursuit. For example, when v is a positive constant, a fighter attacks with a variable lead, computed on the assumption that his ammunition has a mean fixed velocity over the ranges in question. And, when v is a negative constant, a missile homes acoustically on a target, so that v is the constant ratio of the speed of the pursued to the speed of sound. Later sections successively elaborate the deviation function to make it more realistic.\nFor these three cases, the equations of the relative path may now be deduced. From Figure 1, the rate of range closure is dp/c. Certain Japanese documents indicate that this was doctrinal procedure for the Japanese Air Force during World War II.\n\nConfidential\nPursuit Curves\n\nAnd the rate of rotation of the range line about the pursued as pivot is dt p.\n\nThe effect of the pursued\u2019s speed, as shown by the last equation, is to cause the pursuer to crab toward a point astern of the pursued. The pursuer is said, picturesquely, to be \u201csucked flat.\u201d When equation (1) is divided by equation (2), time vanishes, and the speed ratio p = vf/vb appears as a natural parameter. The equation\n\nP dO\n\nis integrable for the deviation functions in question. The results are:\n\nPure pursuit: tan(M0/2) = sin(\u03b8)\nFixed lead pursuit: sin(5C) = sin(\u03b8)\nVariable lead pursuit: n = cos(5\u03bf)\nFor the variable lead pursuit, a close and useful approximation is obtained by putting cos 5 = 1 in equation (3). The simpler formula is:\n\nIt is clear that equation (5) collapses into equation (4) when \u03b8 = 0 and that equations (6) and (7) also reduce to equation (4) when v = 0, i.e., when the bullets used have infinite velocity. When \u03b8 = 90\u00b0, p = Po in each of these four equations. Consequently, Po is another natural parameter \u2014 the 'proximity parameter. It is the range on the beam, and each pursuit curve can be extended backward or forward as required to give its characteristic p0.\n\nFigure 2 illustrates the relative positions of these three types of curves, and Figures 3 and 4 supply convenient nomograms for the computation of pure pursuit courses. A large number of pursuit curves have been computed and graphed. 8- 141 > 180 > 221.\n\n3.2.3 Bifurcated Pursuit\nIn the preceding derivation, the factor v was the ratio of the pursued's speed to the speed of the bullet fired by the attacking fighter [the deviation function comes, in fact, from eq. (3), 2.2.2]. Normally, therefore, v will be much less than 1. However, certain implications of v > 1 are worth exploring with conceivable situations of the future in mind. Attack must be from a forward direction if capture is to result, and for this region, two separate pursuit curves are quite possible. This is demonstrated most easily by the construction of Figure 5. In this figure, v = vB/v and is greater than 1. After drawing the boundary line, a semicircle of any convenient radius R is constructed as shown. The line connecting the pursuer F to the pursued B cuts the circle at Pi and P3. The lines PP2 and PF intersect at P, which lies outside the circle. This point P is the intercept of the pursuit curve with the boundary line. The lines OP and OB are perpendicular to each other and intersect at O, the center of the semicircle. The line OP is the line of sight from the pursuer to the pursued. The angle \u03b8 between OP and the line FB is the angle of deflection of the pursuer's line of sight from the direction of the pursued. The angle \u03c6 between the line FB and the line of intersection of the pursuit curve with the boundary line is the angle of interception. The angle \u03b2 between the line of intersection of the pursuit curve with the boundary line and the line OP is the angle of sighting error. The angle \u03b3 between the line of intersection of the pursuit curve with the boundary line and the line FB is the angle of deflection of the pursued from the line of sight of the pursuer. The angle \u03b4 between the line of intersection of the pursuit curve with the boundary line and the line PP2 is the angle of convergence. The angle \u03b5 between the line of intersection of the pursuit curve with the boundary line and the line P3B is the angle of divergence. The angle \u03b6 between the lines PP2 and PF is the angle of pursuit error. The angle \u03b7 between the lines PP2 and OP is the angle of sighting error relative to the line of intersection of the pursuit curve with the boundary line. The angle \u03b8' between the line of intersection of the pursuit curve with the boundary line and the line OB is the angle of deflection of the pursued from the line of sight of the observer. The angle \u03c6' between the line of intersection of the pursuit curve with the boundary line and the line OF is the angle of interception relative to the line of sight of the observer. The angle \u03b2' between the line of intersection of the pursuit curve with the boundary line and the line OF is the angle of deflection of the pursuer's line of sight from the direction of the observer. The angle \u03b3' between the line of intersection of the pursuit curve with the boundary line and the line BF is the angle of deflection of the pursued from the line of sight of the observer. The angle \u03b4' between the line of intersection of the pursuit curve with the boundary line and the line OP is the angle of sighting error relative to the line of sight of the observer. The angle \u03b5' between the line of intersection of the pursuit curve with the boundary line and the line P3B is the angle of divergence relative to the line of sight of the observer. The angle \u03b6' between the lines PP2 and OF is the angle of pursuit error relative to the line of sight of the observer. The angle \u03b7' between the lines PP2 and OF is the angle of sighting error relative to the line of intersection of the pursuit curve with the boundary line. The angle \u03b8'' between the line of intersection of the pursuit curve with the boundary line and the line OB is the angle of deflection of the pursued from the line of sight of the pursuer relative to the line of sight of the observer. The angle \u03c6'' between the line of intersection of the pursuit curve with the boundary line and the line OF is the angle of interception relative to the line of sight of the pursuer. The angle \u03b2'' between the line of intersection of the pursuit curve with the boundary line and the line OF is the angle of deflection of the pursuer's line of sight from the direction of the pursued relative to the line of sight of the observer. The angle \u03b3'' between the line of intersection of the pursuit curve with the boundary line and the line BF is the angle of deflection of the pursued from the line of sight of the pursuer relative to the line of sight of the observer. The angle \u03b4'' between the line of intersection\nFigure 3. Nomogram for pure pursuit.\n\nPursuit curves.\n\nThe elements of pure and deviated pursuit theory and FPa are parallel, respectively, to PM and P$M. The pursuer can move in either of these two directions. Consider PP2. Then we should have:\n\nv sin \u03b8 FP2\nvb sin \u03b8 BP2\n\nBut the construction achieves this since:\n\nAnd the alternative has exactly the same treatment.\n\nFigure 5. Bifurcation of pursuit.\n\n3.2.4 Methods of Introducing\n\nTime as a Parameter\n\nThe Local Method 8b\n\nBoth p and \u03b8 may be expanded in power series valid in the neighborhood of any specified point on the curve. The derivatives required in these expansions are readily obtained by repeated differentiation of equations (1) and (2). Over intervals of time corresponding to normal times of flight of projectiles, the convergence is rapid.\n\nThe Midpoint Method\nThis procedure renounces analysis and reverts to an approximation of the curve in question, using a geometrical definition. I'll outline the method for a pursuit curve. In a fixed coordinate system, determine the position of the pursued every quarter second. Over the first time interval, let the pursuer move in a straight line from its initial position toward the midpoint of the first interval of the pursued's motion. This yields a new position for the pursuer from which it can move in a second straight-line segment over the next time interval toward the midpoint of the second interval of the pursued's motion. Continuing in this manner, a table of positional values given explicitly in terms of time is built using the most elementary computing means. (This method has been used extensively in)\nThe production of synthetic motion pictures for use in flexible gunnery training devices. (201) A basic disadvantage of solutions 4 through 7 for the pursuit curve problem is that range and angle off are not given explicitly as functions of time. It is frequently necessary to have such dependence at hand. For instance, in determining exactly the deflection to take against a fighter on such a curve, one must, by trial and error, match up time along the curve from a chosen present position to the required future position of impact, with the time of flight over the range to this future position. There are three ways of getting points on the curve labeled with the appropriate time:\n\nThe Implicit Method\nSubstituting p in terms of 6 into equation (2) and integrating t as a function of 6 will yield the result. In fact, for the pure pursuit, one has:\nBy graphing or tabulating, the implicit value of 6 is known for any t.\n\nSection 3.2.5: Centrifugal Force and Isogees\n\nAssessing the centrifugal force is crucial in pursuit courses. On one hand, the circle of curvature can be used as a replacement for a curve segment (during the flight time of a bullet from a defending bomber) to derive approximate deflection formulas. On the other hand, knowledge of centrifugal load leads to an estimate of the fighter's angle of attack d and its impact on the flown course. Ultimately, this force or load sets the boundaries regarding range and angle that a fighter can reach before physiological or structural limitations become operative.\n\nFor a pure pursuit curve, the radius of curvature R is given by R = vpdtd, since the tangent to the curve is:\n\nR = vpdt/dd\nThe circle of curvature is the line to which the angle of attack refers. This angle is the angle between the direction of motion of the aircraft and a reference line, such as a wing chord, a gun's bore axis, or a longitudinal axis, all lying in the plane of symmetry of the aircraft.\n\nConfidential\nPursuit Curves\n\nThe centrifugal load nc in units of gravity is found from: gp\n\nIf nc is given successive constant values, then the curves of equal load (isogees) that arise are circles tangent to the pursued's track and of radius VFVB/2gnc. If such a family of isogees is drawn and a family of pursuit curves is superimposed, as in Figure 6, one may readily find the load for any curve at any point.\n\nFigure 6. Isogees and pursuit curves.\n\nAs a sample conclusion, it is immediately evident that with high-speed aircraft, close approach requires:\n\nYARDS\nAny material at an angle off the bomber\u2019s tail is prohibited due to high loading. This argument supports dispensing with all armament other than that of the defending tail of an ultra-high-speed bomber. With such a double family, one could also trace out the growth and decay of load. The maximum load, when it exists, can be found analytically by maximizingnc. The simple result is that nc max occurs at an angle determined by this locus.\n\nIt is possible, considering equation (9), for the fighter to reduce the load to which he is subject by deliberately using a slow speed during the firing run. As the fighter\u2019s speed decreases, the maximum load diminishes steadily. It may be presumed that the fighter\u2019s aiming problem is reduced.\nThe fighter may perform his firing at greater angles off the bomber\u2019s stern. This offers a more difficult shot for the defense due to the higher angular rate. In addition, a longer period of sustained fire is available. The tactical disadvantage is that the fighter will close in up to a certain point and then fall back.\n\nSince a lead pursuit curve is usually a better approximation to the curve actually flown than a pure pursuit curve, it is sometimes desirable to calculate the centrifugal load for the lead pursuit. This formula, which is a companion to equation (9), is:\n\n3.2.6 Total Load Factor\n\nFor use in the next section, which calculates a more realistic deviation function, the total load on an aircraft is required. This total load n is a suitable vector sum of centrifugal force and that force.\nThe components of the gravitational force lying in a plane perpendicular to the direction of motion are summed because the lift, which supports the effectively heavier aircraft, is in that plane. In the formulas given below for total load L and bank angle R (roll), the turn angle Y (yaw) is measured in a horizontal plane after projection of the flight path, and the dive angle P (pitch) is measured in a vertical plane from the horizontal projection down to the flight path. It is assumed that the aircraft is flying cleanly \u2014 with no slip or skid \u2014 at a speed v.\n\ndY/dt = -mg sin \u03b8 + L - mg cos \u03b8 (1)\nL = C_L q S (2)\n\nwhere m is the mass of the aircraft, g is the acceleration due to gravity, q is the dynamic pressure, C_L is the lift coefficient, and S is the wing area.\n\n\u03b8 is the angle of attack, which is given by:\n\n\u03b8 = arctan (C_L/C_d) (3)\n\nwhere C_d is the drag coefficient.\n\nThe total load L is given by:\n\nL = mg (sin \u03b8 + \u03b1 cos \u03b8) (4)\n\nwhere \u03b1 is the angle of attack of the wing relative to the relative wind.\n\nThe bank angle R is given by:\n\nR = arctan (Y/V) (5)\n\nwhere Y is the turn angle and V is the velocity of the aircraft.\n\nThe dive angle P is given by:\n\nP = arctan (Z/V) (6)\n\nwhere Z is the vertical velocity.\n\nIf the fighter's speed is held constant and the bomber's speed is changed, there is a certain bomber speed which yields a least maximum load for the fighter. If nc max is expressed as a function of v/z, we have:\n\nnc max = C_L q S (v/z) max (7)\n\nwhere v/z max is the maximum lift-to-drag ratio.\n\nTherefore, to find the maximum load on the fighter, we need to find the maximum lift-to-drag ratio for the given wing area and dynamic pressure, and then solve for the bomber speed v/z which gives this maximum ratio. This speed will yield the least maximum load for the fighter.\nThe effect of the angle of attack on pursuit curves and:\n\ncos(P) + vdP/g dt cos(R)\n\nFor special flight paths, equations (12) and (13) reduce to the following forms:\n\n1. Circle of radius r in a horizontal plane: g = -r d\u00b2\u03b8/dt\u00b2\n2. Circle of radius r in a vertical plane: g = r d\u00b2\u03b8/dt\u00b2\n3. Circle of radius r in a plane of action of inclination CO: tan(R) = COS(co) - b cos(6) sin(co) / g\n4. Helix with horizontal axis and sinusoidally varying speed (this is the case of corkscrew avoiding action by a bomber. The details are complicated but straightforward and will not be set down.)\n3.3 THE EFFECT OF ANGLE OF ATTACK ON PURSUIT CURVES\n\n3.3.1 Deviation Function and Trajectory Shift\n\nIn Section 3.1.2, it was pointed out that knowing the exact curve flown by a real and perfect fighter permits the defending fire control to calculate future positions of the target. Since these future positions depend intimately on the deviation of the fighter\u2019s velocity from the gun-target line (Figure 1), it is necessary to analyze it more carefully than was done in Section 3.2.2 [deviation (3)].\n\nAs footnoted in Section 3.2.5 (footnote d), an angle a exists between the bore axis of a fighter\u2019s gun and the direction of motion. This angle of attack consists of a fixed and a variable part. The fixed part is attributable to the installational setting which allows for gravity drop. The variable part is caused by a change in the load factor n (Section 3.2.6).\nThe requirement is to change the angle of attack of the wings to provide balancing lift for a change in aircraft weight. The direction of departure of the fighter's bullet is along the diagonal of a parallelogram determined by the propellant muzzle velocity v0 and the fighter velocity Vf. In Figure 7, it is assumed that a lies entirely in the plane of action. However, this will not be the case in general, as the aircraft is banked. The deflection problem is solved by equation (1) of Chapter 2, which gives the normal lead. In Section 3.2.2 [deviation (3)], only the first term on the right of equation (14), the normal lead, was used for the deviation. The correct deviation function is:\n\ny = (v0/Vf)*sin(\u03b8)\n\nThe pursuit curve generated by this equation is called an aerodynamic lead pursuit. The next problem is to explore a.\nBefore leaving equation (14), the meaning from the point of view of the fighter pilot is given by Figure 8. In this representation, it is not assumed that a lies in the plane of action. Instead, the aiming allowance required by the second member on the right of equation (14) lies in the plane of symmetry of the fighter. It is called the trajectory shift.\n\n3.3.2 Angle of Attack in Terms of Load and Indicated Airspeed\n\nThe resultant of all pressures on an aircraft wing \u2013 of the lower than atmospheric pressures on the upper surface and of the equal to or slightly greater than atmospheric pressure on the lower surface \u2013 is resolved into a lift, perpendicular to the direction of motion, and a drag, parallel to the direction of motion.\ntion.  If  the  bullet  in  Figure  5  of  Chapter  1  is  replaced \nby  a  wing  profile,  that  diagram  illustrates  this  situa\u00ac \ntion  also.  The  yaw  of  the  bullet  is  equivalent  to  the \nangle  of  attack  of  the  wing.  The  lift f  L,  in  pounds, \nis  given  by \nz \nwhere  Cl  =  lift  coefficient  (dimensionless), \np  =  air  density  (slugs  per  cubic  foot),8 \nS  =  wing  area  (square  feet), \nv  =  true  airspeed  (feet  per  second).11 \nf  The  drag  is  given  by  a  similar  expression: \n'The  aerodynamic  air  density  p  is  an  NACA  standard. \nIt  differs  from  the  ballistic  standard  pG,  and  must  not  be \nconfused  with  the  relative  ballistic  air  density  which  is  also \ndenoted  by  p  (Section  1.2.3).  Both  p  (NACA)  and  pa  (bal\u00ac \nlistic)  vary  at  a  given  altitude  as  the  temperature  and  hu\u00ac \nmidity  change. \nBallistic  and  NACA  altitudes  for  given  ballistic \nrelative  air  density. \nRelative \nBallistic  altitude \nNACA  altitude \nair  density \nStandard atmosphere based on NACA Report:\n\nAltitude (feet) Po/p V Po/p h\n\nAn airspeed meter measures V2p (TAS)2, where TAS is the true airspeed. It is calibrated to read TAS at sea level (p = p0). Therefore, if IAS is the indicated airspeed, the additional superelevation allowance for gravity drop is about one-fifth of L2.\n\nExperiment and theory show that the lift coefficient is an almost linear function of the angle of attack of the wing chord over a range almost up to stall. Since the guns are installed at a fixed angle with respect to the wing chord, the angle of attack is usually measured with respect to it. We may take the angle of attack a of the mean bore axis of the fighter's battery in the form:\n\na = (Ki * alpha + K2)\n\nWhere Ki and K2 are constants.\n\nIf an aircraft is subjected to a load factor n, we can calculate the angle of attack using:\n\na = arcsin((IAS / Vs) * sqrt(1 + n) - 1)\n\nWhere IAS is the indicated airspeed, Vs is the stall speed, and sqrt(1 + n) represents the increase in airspeed due to the load factor.\nmust have L = Wn, where W is the normal weight of the aircraft. Consequently, L can be calculated by the formula:\n\nL = (57.147 > 117) * S * b / (W * (IAS / 1609.34) * pi)\n\nWhere S is the wing area in square feet and b is the wing span in feet. When equation (17) is used in equation (16), a will be in radians, IAS in miles per hour, and W in pounds. Next, L2 depends on the installational angle of the guns. If we suppose that the guns are adjusted so that at a particular level flight speed, (IAS)0, they are horizontal, then:\n\nThe value assigned to (IAS)0 has frequently been 250 mph. Using this value and standard airplane dimensions, average values of Li and L2 are given by Table 1 for certain fighters of World War II.\nTable 1. Angle of attack constants for World War II fighters.\n\nClass Types -- U -- Mel09, MellOG, FW190A, Ju88C\n-- Ji -- Zeke, Hamp, Oscar I and II, Tojo, Nick, Tony\n-- Average American -- 3.3.3\n\n3.3.3 Vicious Circle of This Approach\n\nFormula (16) requires a knowledge of n to determine the load. The curvature of the path must be known to calculate the load. A vicious circle is completed since the path cannot be determined until n is known. The correct resolution of this difficulty is given in Section 3.4.2. In the early literature, the centrifugal load for a pure pursuit or a lead pursuit, i.e., equations (9) or (11) or some average of these, at the point in question, has been used. From a practical point of view, refinement at this point is somewhat absurd since the exact speed of the attacker cannot be known, and centrifugal load is always present.\nWith a speed proportional to this, the justification for the approximation of n is found in a desire to avoid bias in calculations for an average tactical situation rather than a particular one. With such an approximation for n and the assumption of constant speed, the differential equations (1) and (2) can be integrated using a determined method from equations (14) and (16), but this will not be done since defensive gunnery is only interested in a segment corresponding to the time of flight of the bomber's bullet. The required deflection can be made out as a function of range and angle off a fighter, rather than as a function of position along a particular curve (see Section 4.2.2).\n\nFurther analysis of aerodynamic lead pursuit curves by these methods has treated the following: (170) the communication between the pilot and the gunner, (171) the effect of wind, and (172) the effect of the gunner's reaction time. (173) The curves are symmetrical about the line of sight, and (174) the maximum lead is obtained when the target is moving directly away. (175) The curves are independent of the speed of the gunner's aircraft. (176) The curves are dependent on the relative angles between the lines of sight and the velocity vectors of the gunner and the target. (177) The curves are affected by the aspect ratio of the target. (178) The curves are affected by the size and shape of the target. (179) The curves are affected by the altitude of the target. (180) The curves are affected by the altitude of the gunner. (181) The curves are affected by the angle of attack of the gunner's aircraft. (182) The curves are affected by the drag coefficient of the target. (183) The curves are affected by the lift coefficient of the target. (184) The curves are affected by the drag area of the target. (185) The curves are affected by the lift area of the target. (186) The curves are affected by the mass of the target. (187) The curves are affected by the moment of inertia of the target. (188) The curves are affected by the cross-sectional area of the target. (189) The curves are affected by the shape of the target's silhouette. (190) The curves are affected by the angle of incidence of the sun. (191) The curves are affected by the angle of attack of the target. (192) The curves are affected by the angle of deflection of the gun. (193) The curves are affected by the muzzle velocity of the gun. (194) The curves are affected by the bullet caliber. (195) The curves are affected by the bullet density. (196) The curves are affected by the air density. (197) The curves are affected by the temperature. (198) The curves are affected by the humidity. (199) The curves are affected by the altitude of the target and the gunner. (200) The curves are affected by the wind velocity and direction. (201) The curves are affected by the wind temperature and humidity. (202) The curves are affected by the air pressure. (203) The curves are affected by the air viscosity. (204) The curves are affected by the target's maneuvers. (205) The curves are affected by the gunner's maneuvers. (206) The curves are affected by the target's size and shape changes. (207) The curves are affected by the gunner's size and shape changes. (208) The curves are affected by the target's speed and direction changes. (209) The curves are affected by the gunner's speed and direction changes. (210) The curves are affected by the target's altitude changes. (211) The curves are affected by the gunner's altitude changes. (212) The curves are affected by the target's altitude and speed relative to the gunner. (213) The curves are affected by the gunner's altitude and speed relative to the target. (214) The curves are affected by the target's altitude and wind relative to the gunner. (215) The curves are affected by the gunner's altitude and wind relative to the target. (216) The curves are affected by the target\ncomponents of a aircraft have parts that lie in and at right angles to the plane of action. The perpendicular component causes the aircraft to move slightly below the instantaneous plane of action (or sag).\n\nThe patchwork theory of this section is correctly revised in Section 3.4. The details supplied here have intrinsic value and are an exemplar of approximation methods in this field.\n\n3.3.4 Qualitative Effect of Angle of Attack\n\nThe effect of angle of attack on a pursuit curve can be summarized qualitatively by giving the relations among pure, lead, and aerodynamic lead pursuit curves that originate at the same point and have the same vB and vf: (1) at long ranges, the load is low (close to 1), the angle of attack is small, and the aerodynamic curve almost coincides with the lead pursuit; (2) as the range closes, the load generally increases, the angle of attack increases, and, since the aerodynamic force acting on the aircraft is no longer parallel to the velocity vector, the aerodynamic curve deviates from the lead pursuit.\n[1] Shifted trajectory must lead to impact. A fighter's direction of motion is affected by its load: [1] low, [2] high, or [3] ultra-high. The same for all cases. [Figure 9 illustrates the effect of load on a fighter's direction of motion.] Velocity is directed more toward the bomber than in lead pursuit, causing the aerodynamic curve to edge toward the pure pursuit. For very high loads, the angle of attack may be so great that the fighter's velocity is directed behind the bomber, yet the shifted trajectory leads the bomber by an amount sufficient to cause a hit. These facts are partially illustrated by Figure 9.\n\nCONFIDENTIAL\n[Pursuit Curves]\n3.4 True Aerodynamic Lead Pursuit Curve\n3.4.1 New Variables - Fighter Speed, Course Curvature\n\nIn Section 3.3, the real analytic problem was sidestepped. Of the various approximations made in that section:\nsection  those  regarding  the  load  factor  and  constant \nspeed  on  the  part  of  the  attacking  fighter  are  crucial. \nBoth  do  violence  to  the  real  dynamics  of  the  situ\u00ac \nation.  In  the  first  instance,  given  an  unknown  curve, \nits  rate  of  change  of  direction  should  enter  naturally \nas  an  unknown.  In  the  second  instance  the  aircraft \nshould  be  permitted  to  change  speed  naturally  under \nthe  forces  of  thrust,  drag,  and  gravity.  Consequently, \nspeed  should  also  be  a  variable  of  the  description. \nThe  improvements  to  be  made  may  be  recognized \nmost  readily  by  considering  the  simple  case  of  an \nattack,  made  in  a  vertical  plane,24  by  a  fighter  on  a \nbomber  which  moves  on  a  straight  and  level  track  at \nconstant  speed.  If  a  vertical  plane  is  used,  trigono\u00ac \nmetric  details  do  not  obscure  the  new  approach.  The \nnew  ideas  are  also  kept  clear  by  assuming  that  the \nThe fighter's gun bore axis is kept on the target, eliminating deflectional and ballistic notions. Figure 10 depicts the force system j on the airplane, neglecting aerodynamic forces acting on the fighter's tail surfaces since the gun is assumed to be on target, and no description of how this is achieved by elevator moments is required. The assumption that the bore axis and thrust axis coincide has been made. The tangential and normal dynamic equations are respectively:\n\nW dv/F .\ng dt\n\nand\n\nWv[\nW dP/R\n\nThe kinematic equations of pursuit are:\n\ndp dP da = 1\n\nTo utilize this set of nonlinear equations, it's necessary to determine the aerodynamic constants for a specific aircraft.\nSpecific airplane at a particular throttle setting; to assign suitable initial values to the variables, vF, P, and p, and proceed with the integration systematically. Definite formulas are available, enabling one to proceed directly from the performance values of propeller efficiency, maximum engine brake power, and the corresponding maximum level flight speed at a certain altitude, combined with the weight and airplane geometry, to the constants T, D, L of equations (19) and (20). It is not at all evident, however, what initial value for the angle of attack a should be selected. This choice is connected with the nature of that part of the flight path to which some license is permitted, which just precedes initiation of the guns-bearing position.\nThe phase of the problem depends on the choice of an angle a in the usual range from 2\u00b0 to 12\u00b0. A family of curves would thus seem possible. However, numerical integration demonstrates the existence of a boundary layer effect. This means the dive angle versus time curve shows a sharp hook over an interval of about one-half second. Different initial choices of a generate a funnel leading to a unique value of P and continuing as a single curve. By extrapolation of this single curve back to the initial time, a natural initial value for a can be determined. As a final point in the discussion of the set of equations, it may be noted that although numerical integration is feasible, a judicious blend of graphical and nomographic procedures is enlightening.\n\nConfidential. True Aerodynamic Lead Pursuit Curve.\nThe discussion of the true aerodynamic lead suit curve of Section 3.4.1 can be extended to three dimensions. The treatment is complicated by the banking of the fighter and the introduction of ballistic considerations in determining the lead taken by a perfect fighter pilot at each instant. One account considers an additional term involving a cross force to allow for sideslip. This leads to more variables than equations due to the pilot's freedom in the amount of slip and does not furnish a unique curve. There is experimental evidence that fighter pilots can fly courses cleanly. It will be assumed below that there is no sideslip. Furthermore, it will be supposed that the bomber is not involved.\nThe text assumes a straight and level flight at constant speed for the fighter, with the throttle setting unchanged and the effect of gravity on bullets neglected. This last assumption is tenable as the effect of gravity on time of flight is negligible and the bullet drop is removed by a slight elevation of the gun over the sight line. Bullet patterns are not considered, and variable aim is taken to produce continuous bullet impact at one point on the bomber target.\n\nThe most convenient set of equations is derived with respect to the rectilinear trajectory traversed in space by the bullet from the fighter to the point of impact. This air range is denoted by r and has an azimuth of 0 measured counterclockwise from the forward direction.\nThe angle of attack a is the angle between the direction of motion of the fighter and the trajectory at the moment of departure. The angle ei is the angle fixed at installation, from thrust axis to gun. The bank angle ft of the fighter is the angle from the vertical plane to the perpendicular to the trajectory that lies in the fighter's plane of symmetry.\n\nThe ballistic elements present are: vQ, the muzzle velocity of the fighter\u2019s bullet; u0, the velocity of departure of that bullet; (v0 - vf)', and b = 0.00186p/c5 where p is the relative ballistic air density and c5 is the appropriate ballistic coefficient.\n\nIn addition to these primary terms, two secondary elements are also present.\nThe angles may be introduced. The angle ai = (vq vf/vq) - ei represents physically the angle from thrust axis to the aircraft\u2019s direction of flight. In units of feet and feet per second, the time of flight tf is given by equation (3) of Chapter 1 and is r /\\uq f~Vu0-br' The derivative of this with respect to time is simply W (cos a sin \u03b8 - f- sin a cos \u03b8 cos ft) g dt It is evident that this summing of forces in the flight direction gives an equation of the same form as equation (19). Next, since two angles are required to specify r, two equations are required in the normal directions. These equations, taken together, form an analogue for the two-dimensional case [equation (20)]. The first equation is:\n\nThe second equation is:\n\nThe structure is clear and the projection factors (in)\nparentheses are exposed. The third equation contains only accelerational and gravitational forces and will therefore be homogeneous in W. It is:\n\nQ L cos \u03b8 cos ft + cot a sin \u03b8 ft\n+ sin dftdt J d(fv)dt\n\nWe must expect to find three kinematic equations as well. The required deviation function is found directly by noting that the distance from the bomber's position at the moment of fire to the future impact point along the bomber\u2019s track is vBt, where t is the time of flight over r. It follows that the speed of the point of impact is vB + vBt. It is such a ghost point which is being pursued since all work is relative to the trajectory. Consequently, by projection of the fighter speed and of the ghost speed on the trajectory, the range rate equation arises:\n\ndv dt\n\nFinally, two equations for the rates of change of velocity components are:\n\ndvB dt = vBft - vBt/r\ndvBt dt = vB ft cos \u03b8 - g sin \u03b8 - vBt(vBft/r - sin \u03b8)\nof the azimuth and elevation of the trajectory are written down via projections normal to r. These equations are:\ndt r cos \u03b8\ndt r\n\nIt will be remembered that r will occur in the left-hand members of the last three equations through t.\n\np SIN \u03b8 (YARDS)\n\nFigure 11. Comparison of pursuit curves.\n\nInstead of azimuth and elevation of the trajectory, it would be possible to use as angular coordinates the angle off the bomber\u2019s track of the trajectory and the elevation angle of the (instantaneous) plane of action. This would be a heuristic rather than a technical improvement. It would bring the situation in symmetry with the usual pursuit curve description in terms of range and angle off, and would expose sag (Section 3.3.3) by showing the slow rotation of the plane of action.\n\nIt is also evident that by proper choice of the functions:\nThe giving of distance between bomber and the ghost point, arbitrary behavior on the part of the attacking pilot, rather than perfect lead behavior, can be introduced painlessly. Systematic and precise methods of numerical integration of such systems are available, and a considerable number of courses covering modern tactical ranges including high-speed bombers and fighters have been computed. An example of a true aerodynamic lead pursuit is given in Figure 11. Computed courses have been carefully compared with those actually flown. During a sight assessment program at the Patuxent River Naval Air Station, an F6F-3 fighter equipped with a Mark 23 gyro gun sight was flown in pursuit of a bomber whose speed was 130 knots at an altitude of 6,000 ft. From camera records, the range, azimuth, and elevation of the bomber were recorded.\nThe fighter's lead with respect to the bomber were known at quarter second intervals. To test the theory, attacks were selected where the fighter's lead was nearly perfect. The coincidence between computed and observed values is quite remarkable, showing an average absolute range difference of about 9 yards, and average absolute angle differences of about 10 mils.\n\nIn concluding this section, it's important to emphasize the rounded character of this theory, making it immediately applicable to future problems in aerial warfare, whether they involve aircraft or missiles.\n\n3.5 Tactical Considerations\n3.5.1 Combat Maneuvers by Bomber\n\nThroughout this chapter, the bomber under pursuit has moved on a straight line course at constant speed. This rectilinear assumption is tenable in the following attacks:\nThe requirements of massive formations, nature of bombing runs, and consideration of range of operation do not affect the need for defense when a bomber acts alone or in a small formation. This may occur at night, on patrol, or on pathfinding tours, leaving the bomber vulnerable to saturation and coordination attacks by enemy fighters. Violent and frantic evasive action is suggested as a defensive measure. However, further thought reveals that random course changes may make aiming more difficult for attacking fighters and disrupt their coordination. Yet, it will also deceive the bomber's gunners. Instead of evasive action, the concept of combat maneuvers arises. This is a deliberate, calculated strategy.\nThe planned and properly timed maneuver, designed to reduce the possibility of damage to bomber 182, offers the fighter a changing deflection in amount and line, shortens the attack, increases the loading on the fighter, and makes use of a violent and turbulent slipstream. Since the maneuver is planned and practiced, defending gunners can be provided with a specific set of simple rules for return fire. The most common combat maneuvers are steep diving turns and corkscrews. The corkscrew maneuver, which will be discussed, maintains mean track and height and is the best counter against a coordinated attack. It is not profitable to attempt an exact mathematical solution of the problem of a fighter following a corkscrew maneuver. The corkscrew maneuver has the added advantages of maintaining mean track and height and being the best counter against a coordinated attack.\nA bomber in a corkscrew maneuver. A fighter finds it difficult to maintain deflection for this case compared to rectilinear ones. This results in random pointing in the vicinity of the lead point, as air experiments demonstrate. When required, assess the situation using a three-dimensional analogue of the midpoint method from Section 3.2.4. A standard corkscrew to port involves: (1) a diving turn to port, changing course by about 30 degrees, losing perhaps 1,000 ft, and building indicated airspeed up to 220 mph, (2) a climbing turn to port, gaining perhaps 700 ft and losing speed to 180 mph, (3) a rolling and continuing with a climbing turn to starboard, gaining perhaps 300 ft and losing speed to 150 mph, (4) a diving turn to starboard until speed reaches about 190 mph, (5) rolling.\nAnd continuing with a diving turn to port until speed is about 220 mph. The cycle may be continued. Note that after item (3), the course should be back on the opposite side of the original heading by 30 degrees. About 500 ft will be lost during the cycle, and 50 degrees will be about the maximum bank. The time per cycle is about 47 sec, which allows 4 sec for each change and for each roll, and allows 8, 9, 5, 9 sec respectively for the four phases of a cycle.\n\n3.5.2 Effect of High Mach Numbers on an Attack\n\nThe trend in military aviation is toward higher and higher speeds and altitudes for both bombardment, and consequently, pursuit operations. When a high-speed fighter attempts to attack a high-speed bomber on a pursuit curve, it is apparent from equation (9) that high loading will result at material angles off stern, and at those ranges within which ordinary aerodynamic forces become inadequate.\nammunition is effective. Although it is not known exactly how load and growth of load affect a pilot's aiming, there still exist upper load bounds which may not be exceeded for physiological and aerodynamical reasons. Blackout (but not the weight of the limbs) may be inhibited by the use of suitable antipressure suits. The aerodynamical restriction, however, being a question of wing design, is not so readily dismissed. This restriction may be considered in some detail.\n\nMach number, M\n(Figure 12. Typical critical lift coefficient curve.)\n\nThe Mach number M is the ratio of a body's speed to the speed of sound. Since the speed of sound decreases with altitude from about 764 mph at sea level to about 666 mph at 50,000 ft (true airspeed), those modern aircraft designed to perform best at altitude must accept Mach numbers approaching\nFor each wing, there exists a curve providing a critical value for the lift coefficient Cl in terms of the Mach number. At any given Mach number, an attempt to exceed this critical value results in excessive shuddering and vibration, potentially leading to structural damage. Consequently, if the effective weight of the airplane requires a lift coefficient greater than Ccrit, shuddering flight must be accepted. Figure 12 depicts a typical curve, which resembles the critical curve for jet fighters. With the aid of the CL crit curve, regions of comfortable flight in coordinates of load versus indicated airspeed can be determined. The IAS of stall at M = 0.2 is an efficient parameter in this discussion. An approximated formula for the stalling speed at M = 0.2 is:\n\nVoo = 16 \\Aving loading,\n\nWhere Voo represents the stalling speed.\nWith the aid of equation (15), the curve of critical load, n, versus IAS, v, for a given altitude, is given by:\n\nCL crit ~ v^2\n\nWhere a is the IAS of sound at the chosen altitude. An F(v) family, with the altitude as the parameter, is a nested set of arches with legs set on the line n - 1. As the altitude increases, the region of comfortable flight so bounded shrinks materially. Such curves, when used in conjunction with the load factor formula, define a region, bounded by a closed range versus angle off curve, within which a fighter cannot penetrate on a pursuit curve attack.\n\nFor very low Mach numbers, an attempt to exceed Cl crit leads to the usual type of stall. The regions defined by Section 3.2.5 and the third form of Section 3.2.6 bound a region within which a fighter cannot penetrate on a pursuit curve attack.\nSection 3.1 discusses the tactical setting of pursuit curves in aerial warfare and explains why a detailed study of such curves is necessary for gunnery investigations.\n\nSection 3.2 deals with the geometry of pure and deviated pursuit curves. The centrifugal forces experienced in such curves are computed, and general formulas for the total force \u2013 gravity plus centrifugal \u2013 are given.\n\nSection 3.3 reviews and refines the theory of fixed gunnery to determine more exactly the angle by which the attacking fighter deviates from pure pursuit. The angle of attack of the fighter\u2019s guns is explored in detail since it determines the deviation as much as does the deflection taken by the fighter.\n\nIn Section 3.4, the anatomy of the true aerodynamic lead pursuit curve is considered. The importance of this curve is discussed.\nSection 3.5 discusses avoiding action on the part of the bomber and the aerodynamic limitations on the fighter in making a curved pursuit attack.\n\nChapter 4\nOwn-Speed Sights\n\n4.1 Introduction\n4.1.1 Positional and Rate Deflection Formulas\nThe formulas deduced in Chapter 2 are essentially of two types. One type uses velocities and angles to express the lead, and the other employs angular rates measured at the gun. Since the first type is sensibly positional, simple mechanization appears plausible. The more complicated problems introduced by the necessity of measuring rates will be dealt with in Chapter 5. This chapter considers only developments of the non-angular-rate formulas.\n\n4.1.2 Prediction of Approach Angle\nIt was pointed out in Section 2.2.3 that positional formulas, of which equation (1) is typical, require a value for the approach angle of the target, and this value is not readily measured. The alternative is to predict the approach angle. This can be done by assuming a quite special tactical situation is at hand.\n\nThe primary function of the defensive gunnery of a bomber is to prevent its own aircraft from being shot down. Supporting other members of a formation by cross fire is a secondary function, and decimating an enemy fighter force is tertiary. A fighter attacking on a pursuit curve is most likely to shoot down the bomber, so the defensive gunnery \u2013 in exercising its primary function \u2013 must deal adequately with such attacks. Fortunate ly, approach angle and course curvature can be predicted for pursuit curves.\nAnd this prediction may be utilized in the design of a mechanism. By taking advantage of such a special and dangerous situation, simple fire control may be developed which may be operated with a minimum of manipulation error on the part of the gunner. This is the basic logic of the chapter.\n\nFire control should commit itself to such prediction of the attacker\u2019s behavior only if warranted by the current tactical situation, and even then, only if more flexible control is less effective due to difficulties in design, production, or manipulation. Since, in addition, such commitment implies that the defense lags the offense (it permits the opponent to set the tactics before it can be designed), it follows that this type of dependence on enemy cooperation is a stopgap procedure.\n\nThis chapter is\nA specialized weapon is designed to meet an expected average of a given class of tactical situations, such as average fighter speeds and average attack ranges. A proponent of a more flexible weapon, individualized to account for variations in the opponent\u2019s behavior, may justly seize upon this point.\n\n4.1.3 Definition of Own-Speed Sight\n\nAn own-speed sight is a mechanism that displaces the bore axis of a gun from the line of sight by an angle vG sin (t/v) 0, where the gun-mount velocity vG and the muzzle velocity vQ are preset. The variable size of this angle depends, then, only on the positional angle r, or the angle off of the target with respect to the aircraft\u2019s direction of motion. The displacement angle is laid off toward the rear of the firing aircraft.\nThe plane of action. Since the mount velocity and propellant velocity combine at such an angle to yield the bullet's velocity of departure, a bullet directed by this mechanism will depart along the line of sight. To hit a fixed ground target on a calm day, the gunner need only hold the sight on target and fire. There is no ranging with an own-speed sight. To hit a fighter attacking on a pursuit curve, some percentage of vG (generally less than 100) is set in to decrease the full own-speed deflection. The reason is that the fighter deviates forward of the line of sight (of the instant of fire) during the bullet's time of flight. Much of this chapter is concerned with this percentage factor.\n\nConfidential\nOwn-Speed Sights\n\nRestricted cone of fire. It also shows that no real gain in accuracy would result by elaborating the mechanism.\nFighters: The percentage of own-speed deflection to vary as some function of angle off. However, it is clear that variation with altitude and fighter speed is significant and should be taken into account.\n\nTable 1. Average percentages of own-speed deflection.\n\nFighter class | Fighter speed (TAS) | Altitude\n-------------|---------------------|---------\nGi            | 350 mph             | 20,000 ft\nJi            |                     |\n\nTable 2. Adjustments to percentages.\n\nFighter class\n1. The percentage at 20,000 ft for 350-mph fighters is:\n2. For every 10,000-ft increase in altitude, add:\n3. For every 100-mph increase in fighter speed, subtract:\n4. For every 100-yd increase in beam range of 700 yd, subtract:\n\nA final reduction of the above tables has been suggested cooperatively by the Research Division of the Army Air Forces Central School for Flexible Gunnery and the Applied Mathematics Group at Columbia.\n\nFirst, decide on the type of fighter with which one must contend, e.g., class J2. Secondly, apply the following rules to calculate the adjusted percentage:\nThis fighter will operate at a constant IAS of 275 mph, resulting in an increasing true airspeed (TAS) at higher altitudes, as noted in Section 3.3.2 footnote. Construct a chart, similar to Figure 3, with each line's slope equal to the proper k2/l. In this chart, a fictitious own speed Vq = k2vG is absorbed, enabling full own-speed shooting with vG. A navigator can relay the required vG to gunners via an intercom and the chart.\n\n4.3 Verification of Theory\n4.3.1 Pro and Con Combat Evidence\n\nThe own-speed sight, with some optimal percentage of the gun mount's true airspeed set in, is ineffective against target paths that significantly differ.\nFrom aerodynamic lead pursuit curves. Justification for this specialized weapon is to establish that pursuit curve attacks were the usual attacks during the period when this method of fire was used by German fighters against Allied bombers, primarily during daylight.\n\nGunner's Airspeed (MPH)\nFigure 3. Calculation in the air of own-speed setting.\n\nGerman opinion was that 95% of all attacks by German fighters during World War II on Allied bombers were pursuit curve attacks with an attempt at properly varying deflection. More objective evidence is supplied in Figure 4. A random selection of 285 attacks (1944) was made from a collection and analyzed through the assessment of combat gunnery film. Records of these attacks are also available, which show aim wander and plot angle off versus range. When hits are discerned.\nThe text, with meaningless or unreadable content removed and formatting adjusted for readability, is as follows:\n\nThe range of intervals over which the problem is distributed is obvious, indicating that a pursuit curve is being flown. There are three parts to the counterevidence. First, the Japanese preferred the use of fixed crosshairs during interrogation of Th. W. Schmidt, Director of Film Analysis, by E. W. Paxson at Coburg, Germany. Any bias in this selection is in the direction of choosing attacks with many hits as opposed to those in which bursts were fired indiscriminately throughout the attack. However, even in the latter case, the pilot was trying to fly lead pursuit. This represents a deviation from the average for which the fire control is designed.\n\nCONFIDENTIAL\nVERIFICATION OF THEORY\n(REAR HEMISPHERE)\nRANGE IN METERS\n(REAR HEMISPHERE)\nFW 190 Against B17\n(FRONT HEMISPHERE)\nFigure 4. Bursts and hits within the burst as a function of range.\nThe median deflection pursuit curve attacks.188 It does not follow that own-speed sights will perform badly against such target paths. Second, against high-speed targets, there is experimental evidence that the leads taken by a fighter executing a frontal attack will differ by 58 degrees from those predicted by pursuit curve theory. A bias in performance of an own-speed sight would occur. Third, the closing months of World War II saw increased emphasis in both Europe and the Pacific on offset gun attacks. (See Chapter 8.) Again, saturation attacks from the rear by massed fighter formations may require much support fire. One tends to conclude that the emphasis on defensive deflection of the own-speed type for positions such as waist, tail, and nose of moderate-speed bombers was not misplaced throughout most of World War II.\n\n4.3.2 Check of Optimum Percentage\nAt the request of the Army Air Forces Board, a check on the validity of the theory of optimum percentages described in Sections 4.2.3 and 4.2.4 has been carried out. Experimental data giving bearing, range, speed, and deflection taken for an attacking fighter are available from careful camera analyses arising from assessment studies of leading computing sights (See Chapter 7). Since the path actually flown by the fighter was accurately known, it was possible to compute the correct defensive deflection at each instant. An experimental percentage, k2 exp, was chosen which minimized the sum of the squares of the errors in the plane of action. To calculate an optimum percentage, k2 opt, the correct fighter type, average speed, and own-speed sights are required.\nRestricted cone of fire shows no significant gain in accuracy by varying percentage as a function of angle off. However, variation with altitude and fighter speed is significant and should be taken into account.\n\nTable 1. Average percentages of own-speed deflection.\n\nFighter class Fighter speed (TAS) Altitude\nJ i \n\nTable 2. Rules for modification of average percentages.\n\nFighter class\n1. The percentage at 20,000 ft for 350-mph fighters is\n2. For every 10,000-ft increase in altitude, add\n3. For every 100-mph increase in fighter speed, subtract\n4. For every 100-yd increase in beam range of 700 yd, subtract\n\nA final reduction of the above tables has been suggested cooperatively by the Research Division of the Army Air Forces Central School for Flexible Gunnery and the Applied Mathematics Group.\nDecide on the type of fighter to contend with, e.g., class J2. Assume this fighter operates at essentially the same IAS at all altitudes, e.g., 275 mph. This will correspond to an increasing TAS at increasing altitude in accordance with the footnote to Section 3.3.2. Construct a chart such as that illustrated in Figure 3, in which the slope of each line is the proper fc2_1. In this chart, the optimum percentage has been absorbed to produce a fictitious own speed Vq = k2VG, and full own-speed shooting can be done with Vq. A navigator has available at all times his TAS and altitude. He is in a position to relay to gunners, via such a chart (and an intercom), the appropriate Vq.\n\n4.3 Verification of Theory\n4.3.1 Pro and Con Combat Evidence\nThe own-speed sight, with some optimal percentage, enables:\n\n1. Pro:\n   a. Maximum hit probability\n   b. Minimum lead angle\n   c. Minimum convergence error\n   d. Minimum deflection angle\n2. Con:\n   a. Limited effective range\n   b. Limited field of view\n   c. Limited ability to engage multiple targets\n\nTherefore, the own-speed sight is most effective in close-range, one-on-one combat situations.\nThe percentage of the true airspeed of the gun mount set in, is useless against target paths which significantly differ from aerodynamic lead pursuit curves. Justifying this specialized weapon, it must be established that pursuit curve attacks were the usual attacks during the period when this method of fire control was to be used. It was German opinion that 95% of all attacks of World War II, made by German fighters during daylight on Allied bombers, were pursuit curve attacks with an attempt at proper deflection variation. More objective evidence is supplied in Figure 4. A random selection of 285 attacks (1944) by German fighters was analyzed through the assessment of combat gunnery film. Records of these attacks were kept.\nAttacks show aim wandering and plot angle off versus range. When hits are distributed over great range intervals, it's obvious that a pursuit curve is being flown. There are three parts to the counterevidence.\n\nFirst, the Japanese preferred the use of fixed crosshairs. Interrogation of Th. W. Schmidt, Director of Film Analysis Section, by E. W. Paxson at Coburg, Germany. Any bias in this selection is in the direction of choosing attacks with many hits as opposed to those in which bursts were fired throughout with indifferent success. But even in the latter case, the pilot was trying to fly lead pursuit. This represents a deviation from the average for which the fire control is designed.\n\nCONFIDENTIAL\nVERIFICATION OF THEORY\nFW 190 Against B* 17 (REAR HEMISPHERE)\nRANGE IN METERS\nME 109 Against B*17\n(REAR HEMISPHERE)\nFW 190 Against B* 17\n(FRONT HEMISPHERE)\nFigure 4. Bursts and hits within the burst as a function of range. Medial deflection pursuit curve attacks (188). It does not follow that own-speed sights will perform badly against such target paths. Second, against high-speed targets, there is experimental evidence that the leads taken by a fighter executing a frontal attack will differ by 58 degrees from those predicted by pursuit curve theory. A bias in performance of an own-speed sight would occur. Third, the closing months of World War II saw increased emphasis in both Europe and the Pacific on offset gun attacks. (See Chapter 8.) Again, saturation attacks from the rear by massed fighter formations (see Section 4.6) may require much support fire. One tends to conclude that the emphasis on defensive deflection of the own-speed type for positions in combat.\nsuch as waist, tail, and nose of moderate-speed bombers was not misplaced throughout most of World War II.\n\n4.3.2 Check of Optimum Percentages by Airborne Experiment\n\nAt the request of the Army Air Forces Board, a check on the validity of the theory of optimum percentages described in Sections 4.2.3 and 4.2.4 has been carried out. Experimental data giving the bearing, range, speed, and deflection taken for an attacking fighter are available from careful camera analyses arising from assessment studies of lead computing sights. (See Chapter 7.) Since the path actually flown by the fighter was accurately known, it was possible to compute the correct defensive deflection at each instant. An experimental percentage, A/2 exp, was chosen which minimized the sum of the squares of the errors in the plane of action.\nother hand, to calculate an optimum percentage, k2 opt, the correct fighter type, average speed, and Confidential Own-Speed Sights altitude only, were used. (Since the fighter used caliber 0.50 AP M2 or API M8 in taking deflection, Tables 1 and 2 do not apply, as they were based on typical German and Japanese 20-mm ammunition.) Points were taken at an interval of one-half second. A point is an O point if the fighter\u2019s lead gave a mean point of impact on its target (a sphere of radius 7 yd). A point is a B point if it comes before an O point by 2 sec or less. All other points are N points. Ranges were up to 900 yd only. The results are given in Table 3. The agreement is satisfactory.\n\nAltitude of 31,000 ft by a class J2 fighter, on a bomber flying at 385 mph. The ammunition used by both fighter and bomber agrees with that used in calibration.\nTable 1: Calculating k2 = 0.80 from the table through interpolation. The corresponding deflection A equals 168 sin radians, agreeing with exact values on average with an error of approximately one milliradian. A systematic check is forthcoming, but insignificant compared to Section 4.3.2. The errors in the plane of action, when specific k2 opt values are used, amount to around 2 milliradians.\n\nTable 3: Theoretical and experimental own-speed percentages.\n\nSource Data for Attacks\nType of Point Number of Points Average error in plane of action using hi opt (milliradians)\nAAFPGC Eglin Field 7 rear quarter, 6 beam, 7 nose, 3 strafing (averages) O O AAFPGC Eglin Field 1 rear quarter, 1 beam, 5 nose (averages) O Patuxent River Naval Air Stn assessment 16 beam and rear quarter (averages)\n\nFor the second source, the lack of sufficient correct leads.\npoints means that the theory is not expected to hold well. In the opposite direction, the good agreement in the third class can be attributed to the use of a lead computing sight by the attacking fighter, which led to excellent shooting on his part.\n\n4.3.3 Analytical Checks\nIt is also possible to validate the approximate theory analytically. A large number of perfect aero dynamic lead pursuit curves have been computed (as sketched in Section 3.4.2). For each of these, the correct lead to be taken in the plane of action is given. The only course that can be checked immediately without calculation is Course L. This is a flat tail attack, made at an average speed of 415 mph at an angle.\n\n4.3.4 Earlier Work\nEarlier efforts at validating the theory are mentioned bibliographically to complete the picture of experimental evidence. This work compared 85 percent of the theoretical values with experimental results and found good agreement.\nCenters of own-speed deflection with correct deflection were a problem, suffering from many crudities.\n\n4.4 Position Firing\n4.4.1 Necessity of Eye-Shooting Methods\n\nUnfortunately, the development of weapons and adequate methods to control those weapons rarely keep pace. Control is usually a poor second. For instance, hand-held guns were installed in waist, nose, and tail of heavy bombers, but no mechanical provision was made for the difficult problem of determining the deflection to take with such guns. Under such circumstances, an almost intolerable burden is placed on a Service Training Command which must produce gunners who can estimate approximately the required deflection by eye. The earliest methods of eye shooting were based on a perception of tracking rates. This section deals with a different approach.\nIf a bomber is under pursuit attack, the required defensive deflection is given by:\n\nIf a bomber operates approximately at a fixed altitude and a fixed speed vg, and a standard fighter attacks at an approximately known speed, then, using Table 2, a value for k2 can be selected and sin A will depend only on the angle off r. During World War II, over Europe, conditions standardized as vt = 325 mph and fighter type GhG2. Hence, from Table 2, k2 = 0.85 and:\n\nIf a unit of 35 milliradians (called one RAD) is used, then sin A = sin(angle off r).\nIf the gunner is provided with a ringsight aligned with the bore axis and having two (or three) rings subtending one and two (and three) radians at his eye, under the given conditions, he can estimate the angle between the fore and aft axis of his own aircraft and the line out to the head-on fighter. According to Table 4, the deflection required is shown. Since the angle off is in the plane of action, the amount of deflection is independent of the elevation of the plane of action. Doctrinally, the gunner determines the target's position relative to the bomber and decides whether it is within the 3, 2, 1, or x radian cone (Figure 5).\n\nTable 4. Deflection over Europe.\n\nt (degrees) A (milliradians) A (RADS) A (rounded RADS)\n\nIf the gunner can estimate the angle between the fore and aft axis of his own aircraft and the line out to the head-on fighter, he knows from Table 4 how much deflection to take. Since the angle off is in the plane of action, the amount of deflection is independent of the elevation of the plane of action.\n\nDoctrinally, the gunner looks at the fighter's position relative to the bomber and decides whether the target is within the 3, 2, 1, or x radian cone (Figure 5).\n\nFigure 5. Key cones for position firing (Army Air Forces).\nThe angle off is not a key angle. Linear interpolation is assumed, and as the attack develops and the target slides from one cone to another, the gunner is expected to change his deflection continuously. In the Royal Air Force (and early Eighth and Ninth Air Forces) version of position firing, the gunner held a constant deflection of 3 rads over the zones 60\u00b0 to 10\u00b0 and 170\u00b0 to 180\u00b0. This is called the zone system. The amount of deflection is established. It remains to consider the line along which this deflection is laid off. Since the gunner\u2019s eye is in the plane of action, which is assumed to remain sensibly fixed during the guns bearing phase of the attack, and since the vector 0.85vG is assumed to lie in this plane, parallel to vG and reversed, it follows, as illustrated.\nFigure 6: The point of aim is on a line connecting the target to the gunner's horizon dead astern, except when the target is at an angle of A/2 ahead of the beam. In the forward hemisphere, the target is linearly positioned between the pipper of the sight and a point on the horizon dead ahead. This applies to straight and level flight and will be supported by the apparent direction of motion of the target as seen by the gunner. In certain cases of avoiding action, no apparent motion may be evident over a time interval of perhaps a second. In such instances of a lead plateau, i.e., constant lead, the pipper is held between the target and the extended fore-and-aft axis of the bomber.\n\nFigure 6: Line of deflection in position firing.\n4.4.3 Variations in Standard Rules\nThe discussion was based on specific operating conditions. It is clear from Section 4.2.4 that changes in bomber speed, operational altitude, and fighter speed and type require corresponding modifications to the eye-shooting rules that the gunner is expected to memorize and apply. These changes have been made for various aircraft and conditions.32' 62' 152\n\n4.5 Own-Speed Sights\nThe mechanical application of the principle of compensating for the speed of the gun mount by introducing an angle (k2vG sin t)/v0 between bore axis and sight line is as old as military aircraft. The first version \u2014 a wind vane on the front end of a gun \u2014 is an apparent British design from 1915 that was immediately exploited by the Germans. Such a sight uses the air stream to maintain a vector k2vG parallel to it.\nThe modern own-speed sights obtain the angle off r by taking readings from gears fixed in the aircraft for the flight velocity vG. The required lead angle is then obtained either through a mechanical construction of the vector triangle: u0 = v0 + k2vG, or by a gear and cam calculation of deflection formulas for lead in azimuth and elevation. These types will be called the vector sight and the algebraic sight, respectively. A fourth type, a linear correction sight, has been designed for the tail stinger of a B-17.\n\nCatalogues of the numerous versions of each type are available. This section will discuss the Sperry K-13 and K-11 sights, which are, respectively, examples of the vector and algebraic types.\n\n4.5.2 The K-13 Vector Sight\nThe inputs to the K-13 vector sight are k2vG = v%, which is set on a dial by the gunner, and the target angle r.\nThe azimuth and elevation of the gun bore axis with respect to the aircraft are supplied automatically to the mechanism by flexible cables from the turret gears. The output system consists of a collimated reticle image (infinity focus) appearing on a combining glass that rotates about a horizontal axis perpendicular to the bore axis to produce the vertical component of deflection. Preceding the combining glass is a mirror that rotates about an axis parallel to the bore axis to produce the lateral component of deflection as a displacement of the reticle image on the combining glass. This optical output system is seen in Figure 7. The sight is designed for caliber 0.50 AP M2 ammunition with a muzzle velocity of 2,700 fps. The actual mechanism of the K-13 is also shown in Figure 7. The points B and\n0 are fixed and the length BO may be taken to be proportional to %. The length OC varies according to the input kvG. The inputs Ag(GA) and Eg(GE) rotate the point C so that OC remains parallel to the aircraft\u2019s fore-and-aft axis. The mechanically constructed angles Sl(TLD) and Av(TVD) are translated into the correct rotations of the mirror and combining glass of the optical output system. However, when a mirror rotates through an angle, a reflected ray changes its direction by twice that angle. This must be accepted and corrected by reducing OB and inserting suitable linkages. A slight error arises which has nothing to do with theory or manipulation.\n\nThe sight was designed to use k2 = 0.855. This indicates that theory lagged behind design. No harm is done since it is possible to obtain the appropriate values.\nvG from Figure 3 and use this on the TAS dial set for strafing (100 percent own speed). Similarly, if it is necessary to use ammunition with a muzzle velocity different from 2,700 fps, one has only to use (2,700 vG/vq) as input. The ratio of OC to OB then yields vG/v0 as it should.\n\nThe K-13 has no range input. Hence any super-confidential Own-Speed Sights combining Glass T AS knob Knob ^ Altitude Lubber Line knob True Air Speed values read on this dial are set into sight on the side Note! This schematic shows sight with GE at +1600 Mils, GA at 0 Mils T A S s300 Mph arrows show: up elevation, right azimuth, up TVD, right TLD, increasing TAS\n\nFigure 7. K-13 vector sight schematic. (Courtesy of Sperry Gyroscope Company.)\n\nElevation allowance for gravity drop can depend only\nThe design superelevation used is 6 degrees east (Eg) in milliradians, with a slight dependence on azimuth. The dependence is a minimum on the nose since future ranges will be minimal and a maximum on the tail, with a spread of 2 milliradians for Eg = 0. Taking roughly gravity drop to be 5.12 yards and a mean velocity v = 2,500 fps, it follows that the allowance of 6 milliradians corresponds to a range of approximately 800 yards. If it is decided that this is too great, it may be reduced by setting the elevation dial appropriately during gun and sight alignment.\n\nThe K-13's nature is such that there is no restriction on the azimuths it will accept and only minor restrictions on elevations (+85 degrees to \u201385 degrees). It is suitable for use at any gun position.\n\nInput dials, flexible shaft inputs: IAS, altitude legend.\nFigure 8. K-ll algebraic sight schematic. (Courtesy of Sperry Gyroscope Company.)\n\nThe inputs to the K-ll algebraic sight differ from those for the K-13 in that IAS and altitude are to be inserted instead of k2vG. The optical output system is the same.\n\nIt is an easy exercise in spherical trigonometry to show that, with good approximation,\n\nL = Z cos Ag cos Eg\nZ cos Ag sin Eg\n\nWhere\nVo\n\nInstead of physically constructing angles AL and Av as does the K-13, the K-ll mechanically works through these formulas as indicated in Figure 8.\n\nIn such circuits, (1) differentials add algebraically two input rotations, (2) one-dimensional cams give a function of a single variable, (3) two-dimensional cams give a function of two variables, and (4) a rack and pinion translates a rotation into a displacement.\nIt follows that multiplication must be effected by logarithms. Hence, in particular, a log cosine cam is restricted in size since log cos 90\u00b0 is negatively infinite. Consequently, algebraic sights can only be used in nose and tail positions or, more generally, in some restricted region, the K-ll being restricted to a cone of radius 60\u00b0 about the nose.\n\nThe original design of the K-ll called for inputs of altitude and IAS. It computes TAS. The design k2 is given in the following Table 5.\n\nTable 5. Design k2 of K-ll algebraic sight.\n\nAltitude (feet)\n\nIt is again evident that design preceded theory. If it is desired to use the optimum v% from Figure 3, one proceeds as follows. Let a be relative air density (NACA). Then the vg-TAS used by the K-ll is k2 \u2022 [AS]\nand it follows that the altitude dial may be set and left at the altitude corresponding to the solution a of the equation k2(a). For AP M2 ammunition, this altitude is 10,450 ft and for API M8 ammunition it is 7,400 ft. (In the actual sight, IAS is set opposite altitude. Hence vq is set opposite these values of altitude.) A second method is to put the sight at \u201cstrafe,\u201d which is 100 percent own speed, and set Vq opposite zero altitude. With the sight in hand, it is easily seen that the two schemes are identical.\n\nConfidential\nSupport Fire\n\n4.5.4 The Class B Errors of Own-Speed Sight\n\nThe errors in gun pointing committed by a gun-sight are due to (1) errors in the inputs, (2) mechanical errors, such as backlash, caused by construction, (3) errors attributed to engineering compromises in the design, (4) errors in the gunner\u2019s manipulation.\nAnd (5) errors caused by a design based on inaccurate formulas. Input errors arise from using an incorrect vG or vQ (over the life of a barrel, v0 may drop 200 fps). Any percentage error in vG or v0 appears as the same percentage error in lead, as differentiation of A = (vG sin t)/vQ shows. Input errors in AG and EG may also occur because the gun was incorrectly boresighted, because the aircraft has an angle of attack 131a or because the aircraft is moving forward crabwise. Since AG and EG are picked off relative to the aircraft and not relative to the true velocity vector, the guns may not lie in the correct plane of action. Errors of types (2) and (3) are analyzed by laboratory bench tests. The results are not described here. Type (4) errors are dealt with in airborne experimental programs (See Chapter 7).\nSiders only identify errors of type (5). These theoretical faults are called Class B errors. Suppose a sight is perfectly constructed according to the blueprints, operated perfectly, and there is no dispersion. The bias in gun pointing that still exists is caused by the systematic failure of the sight in computation. When the own-speed sight is used against a pursuit curve, the choice of k2 = 0.85 or even k2 < 0.85 must lead to Class B errors in the plane of action, since the factor chosen has only an average value. There is also an error normal to the plane of action because the fighter's path sags below the plane of action of the instant of fire and because the gravity drop allowance is not a function of range.\n\nIt is desirable to express these errors as a function:\n\n1. Remove unnecessary line breaks and whitespaces.\n2. No introductions, notes, or modern editor additions present.\n3. No ancient English or non-English languages detected.\n4. No OCR errors detected.\n\nTherefore, the text is clean and can be left as is.\nof range and angle off 21 degrees rather than as a function of time along particular courses. Closed deflection formulas such as equation (19) in Chapter 2 make this possible. As an example of this point-function technique, consider the family of all aerodynamic lead pursuit curves, with specified vB, vf, and altitude. The correct lead for any r and theta can be computed using equation (19) in Chapter 2 with the approximate theory of Section 4.2.3. Then, for an own-speed sight set at k2 = 0.85 and at k2 opt = 0.77, the Class B error in the plane of action l4a can be presented cellularly as in Figure 9.\n\nERROR IN PLANE OF ACTION IN MILLIRADIANS\n+ VALUE MEANS OVERLEAD\nFigure 9. Typical Class B errors of an own-speed sight.\nBy superimposing any relative pursuit curve on Figure 9, the way in which the error varies along that curve can be inferred. Characteristically, the sight overleads initially, leads properly at midranges, and then underleads. When a different percentage is used, the range at which the lead is correct changes. However, the bullet pattern still walks slowly through the target. This is preferable to a fixed bias in pointing since the dispersion pattern rapidly becomes dilute as the target moves from the MPI. Figure 9 shows that the range at which the pattern is centered is tactically better for k2 opt = 0.77 than for k2 = 0.85. (For this example, the lead required by sag, normal to and downward from the plane of action, varies from 1 to 5 milliradians. It is possible to combine these values with the required allowances)\nDue to gravity and windage, jump and assess Class B performance normally in the plane of action. This will not be done here.\n\n4.6 Support Fire\n4.6.1 Support Fire Situations\n\nA presumable implication of a tightly massed bomber formation is that cross or support fire is quite possible. The guns of one bomber can be brought to bear on a fighter attacking another bomber of the group. Massed firepower has, in fact, been viewed with dejection by opposing air forces (Confidential).\n\nOwn-speed sights\n\nBrought to bear on a target, the pipper can no longer be held on the target, and the sight must be used in combination with some eye-shooting rule. During the closing months of World War II, over Europe, there was a need for such application. The German Air Force massed fighters astern of a bomber formation.\nRode up the tails of all bombers nearly simultaneously. This was the Company Front attack. The nature of the tactic masked out upper and lower turrets, leaving tail and waist positions to counter this saturation attack. Other support fire situations arise when a neighboring bomber is under pursuit attack or under direct frontal attack. Assuming waist and tail positions are equipped with own-speed sights (and not even a majority were), that sight must be used for a job that completely violates its design. There was no alternative since fire control capable of meeting general attack paths was not available for nonturreted emplacements.\n\n4.6.2 Use of Own-Speed Sights\nSuppose for the moment that the speed input to the own-speed sight is full TAS of the gun mount, i.e., k2 = 1. Then the bullet will go along the gunner\u2019s line of sight.\nThe line of sight in the air mass with an initial velocity of u0. The gunner must displace his aim point to allow for the target's crossing speed vt sin a. The deflection he must take, by eye, is (vt sin a)/u radians. This does not account for the correction required by the target's curved path. However, for many important support fire situations, the target will be near the same level as the supporting bomber and fly in a straight line (43, 66). In this case, if the target speed and the average bullet speed are fixed approximately, the gunner's problem is reduced to the estimation of the approach angle a. The amount of his deflection is then given by some memorized sequence, such as 157. This deflection is laid off along an extension of the target's flight path.\nBut it is quite essential to make a distinction between a plot of the number of guns that can be brought to bear on each point of a sphere surrounding the bomber unit, and a plot of the accuracy in deflection with which supporting guns will point at positions on that sphere. The target's fuselage (not in the direction of the target's apparent motion). Ingenious methods of estimating these angles have been given, which note the relative position of an empennage as seen superimposed on wings. The ability of a gunner to recognize support fire situations and to estimate approach angles has been studied by controlled experiments with groups of gunners. Much of the literature on support fire [1], [3], [4] is concerned with variations in rules such as those quoted above and with pro and con arguments about shifting the own-speed sight, when used in support.\nSection 4.1 introduces own-speed sights as devices designed to counter a pursuit curve attack on a defending bomber. It discusses the arguments for and against such equipment.\n\nSection 4.2 shows that in shooting against a pure pursuit curve, a large fraction of full own-speed allowance is made since the target path curves forward but slightly during the bullet\u2019s time of flight. This section continues with a discussion of the factors affecting deflection to be taken against an aerodynamic lead pursuit curve, gives optimum rules summarizing detailed calculations, and reduces the problem to simple charts which could be used in the air.\n\nSection 4.3 discusses the validation of the theory.\nSection 1 discussed the demonstration that curves approximating pursuit curves were extensively used in combat in three ways: (1) the agreement between theory and deflections demanded by paths actually flown by fighters during gunsight assessment programs, (2) the agreement between the predictions of the crude theory and the exact analytic theory of Section 3.4.2, and (3) the extensive use of pursuit curves in combat.\n\nSection 4.4 considers position firing, where the gunner estimates his deflection by eye, meaning he is his own compensating sight. Section 4.5 discusses the mechanical features of vector and algebraic types of own-speed sight and briefly reviews Class B errors. Section 4.6 is concerned with support fire using an own-speed sight, where eye-shooting rules are combined with automatic compensation for own speed.\n\nCONFIDENTIAL\n\nChapter 5\n5.1 INTRODUCTION\n5.1.1 First-Order Nature of Sights\nFire control should be flexible enough to supply accurately, quickly, and continuously the aiming allowance required by a target traversing an arbitrary path relative to the gun mount. Unlike the own-speed sights discussed in the preceding chapter, the mechanisms considered below do not assume that the target's approach angle behaves in the highly special way required by an aerodynamic lead pursuit curve. In this sense, lead computing sights can handle arbitrary target paths. However, they are inflexible in another and important sense. Fundamentally, they assume that the target's track relative to the gun mount is a straight line (sensibly straight over the time of flight of the bullet). Operation is based on the theory of Sections 2.2.4 and 2.2.5. Despite the calibration.\nSection 5.3.5 discusses lead computing mechanisms (Section 5.3.5), which presumably enable the sight to handle curved paths. However, these first-order mechanisms do not effectively address the general fire control problem, as improved accuracy against one class of target paths comes at the cost of reduced performance against others. This section will expand upon and justify these statements, in addition to discussing lead computing sights used in inhabited turrets during World War II. More broadly, this chapter aims to connect lead computing mechanisms to the initial sentence of this introduction.\n\n5.1.2 Rate Deflection Formulas\n\nThe most significant deflection formulas in Chapter 2 were those based on the gun-target line's angular rate. The introduction of angular rate eliminates the target's approach angle.\nThe lead is the difference between a kinematic deflection and a ballistic deflection. In simplest form, the latter deflection depended mostly on gun position and range, so one would expect it to be mechanized, conceptually at least, in a fashion independent of the kinematic deflection. Therefore, we must consider as a basic computing device a machine that: (1) converts range (and altitude and perhaps other variables) obtained stadiametrically or by radar into a time-of-flight multiplier tm, (2) obtains the present angular rate co of the gun-target line by a gyroscope, variable speed drive, or a tachometer, and (3) combines these to yield the kinematic deflection tmo. The curvature correction factor h of equation (12) of Chapter 2 depends not only on future range.\nas do machines, tm, but also in the direction and amount of curvature. The machines considered in this chapter can take curvature into account only by assuming some particular average behavior on the part of the target. In particular, information on the rate of change of range is neither given to nor accepted by these devices. The attitude is adopted that h and tm, and even trail, are at our disposal and are to be chosen to give optimum performance over a special class of target paths. However, this procedure is not as restrictive here as was its equivalent in the case of the own-speed sight. (Suppose for example that the curvature correction appropriate to a pure pursuit curve is adopted. Then, even if the target is not flying a perfect gun bearing attack, we would still expect to have a good approximation of its actual curvature.)\nThe same remarks apply to support fire. The topic is investigated in more detail below. In obtaining the angular rate, it is important to distinguish between the actual angular rate of the gun-target line in the air mass and the tracking rate as determined at the gun position. For example, if gun mount and target are chasing each other in a circle of radius R at equal speeds, co = vg/R. The tracking rate, on the other hand, is zero. For this reason, kinematic deflection is a somewhat inaccurate term. In general, any mechanism which measures angular rates with respect to the gun mount will err whenever the axes of that mount are in curved flight.\n\n5.1.3 The Disturbed Reticle Principle\n\nThe sights considered in this chapter are of the disturbed reticle type. The gunner controls the position of the reticle, which is disturbed by the motion of the gun mount.\nThe gunner adjusts the bore axis of his gun manually or motor-controlled. The computing unit calculates the deflection between the bore axis and the line of sight. The gunner then has indirect control over the line of sight, which he is required to keep on target. In general, a given motion of the gun results in a different motion of the line of sight. One disturbs the line of sight instead of controlling it.\n\n5.2 Apparent Motion Eye Shooting\n5.2.1 Historical Reason\nIn the preceding chapter, it was possible to provide rules to a gunner with a fixed sight, enabling him to become his own compensating sight. Similarly, rules can be given for the gunner to become his own rate-time sight. This procedure was in effect in our air forces during the early days of World War II, preceding position firing.\nAnd all gunsights, except the Sperry K-3 installed in the Sperry upper turret of the B-17. The K-3 was only a pilot model and not intended for extended use. This section's digression is primarily of historical interest. It demonstrates what must be done when control mechanism design lags weapon installation and is not coordinated with it. Such situations are not unlikely during a war. Eye shooting methods are of dubious efficiency in the air. An inordinate amount of training is needed to achieve any results at all. A modern gunsight, whether computing, own speed, or fixed, uses an optical system in which a reticle pattern is scratched.\nThe reticle, located in the focal plane of a collimating lens system, appears as an image on a combining glass mounted at an acute angle to the line of sight. To the observer, the reticle seems to be at infinity, i.e., on the target. The user has no problem adapting to close-far distances or maintaining a fixed eye-to-sight distance to preserve the angular dimensions of the reticle. The eye may be moved about over the field.\n\n5.2.2 The \u201cElephant\u201d Method\n\nAn early method of the type referred to above was the USN Elephant method. (1) The gunner tracks the pipper on the target until the range is 650 yards (stadiametric estimation), (2) stops the pipper and observes how far the target moves across the sight framework in two-thirds of a second (while the word \"elephant\" is said aloud), and (3) positions the target an equal and opposite distance on the other side.\nThe pipper starts firing. The required deflection is decreased in proportion to the ratio of actual range to 600 yards. This procedure can be considered analytically. If the target is on a pure pursuit curve, the required deflection is given by Section 4.2.1. The angular rate of the gun-target line is:\n\nvG * sin(r) / r\n\nwhere r is the range. If the coefficient of drag (co) does not change radically, the gun is held still for:\n\ntm seconds, where tm is a time-of-flight multiplier. The factor k0 varies from 0.85 to 0.95 with 0.90 as an acceptable mean.\n\nSuppose now that the gunner makes an error dt in estimating time. Then, assuming he can determine and lay off the resulting motion perfectly, his error is:\n\ndt * (milliradians / second), where r is in yards and vG is in yards per second. If for all gunners the average dt is zero,\nThe average shooting is biased by approximately 12.1 milliradians for a bomber at 225 mph due to the neglect of curvature correction in the rules. If the rules were adjusted to allow for this, and the average absolute error in estimating time was 0.15 sec at GOO yards, the average absolute error in lead would be 27.5 milliradians. It was appreciated in 184 that a correction must be made for approach angles that are not sensibly zero. The gunner is to use some point on the extended fuselage of the target from which to lay off his deflection. This is obviously an allowance for ballistic deflection. It is doubtful that a combat gunner could do this. Further discussion is possible.\nThe ABC method used by the USAAF was similar to the Elephant method, with \"ABC\" having a presumed duration of three-quarters of a second when spoken aloud. The difference in duration between the two methods is explained by the fact that general firing conditions, rather than pursuit curve attacks, were considered. The bullet was intended to have an average speed of 2,400 fps over 1,800 ft. However, this errs in the wrong direction against targets on parallel courses at the same speed, providing no lead (like the Elephant method) and not even allowing for trail. In fact, the method gives the correct lead when the target is:\n\nThe USAAF employed a method akin to the Elephant method, referred to as the ABC method. This approach involved saying \"ABC\" aloud, which was assumed to last three-quarters of a second. The disparity in duration between the two methods can be explained by acknowledging that general firing conditions, rather than pursuit curve attacks, were the focus. The bullet was designed to maintain an average speed of 2,400 fps over 1,800 ft. However, this speed was incorrect for countering pursuit curves. Against targets traveling parallel and at the same speed, the method offered no lead (like the Elephant method) and did not even permit for trail. Conversely, the method accurately provided the necessary lead when the target:\nFor a target on a rectilinear course, the error of the method when used perfectly is given by the equation:\n\nwhere Vg is the ground speed of the observer, Vt is the target speed, r is the angle between the observer's direction and the target's direction, and \u03b8 is 44 degrees.\n\nVg sin r - Vt sin a\n\nFor the case where the bomber's track is crossed at right angles and the range is 2,400 feet per second (fps), the errors using this method are significant.\n\nThe \"Apparent Speed\" Method\n\nThe two preceding methods fix a time interval and determine how far the target moved in the sight's frame. It is also possible to fix the distance to be moved, such as the ringsight radius, and determine how long this motion takes. This is the Apparent Speed method (USN). A ringsight with an angular radius of 35 milliradians provides the deflection required to counteract a target with a speed advantage of 50 knots, abeam, and on a parallel overtaking course.\nThe average speed of a bullet is 2,413 feet per second for this course, as calculated using Formula (1) of Chapter 2, where vG is in feet per second. For instance, if a target at a distance of 2,000 ft takes 0.5 sec to cross its radius (using a memorized figure of 80 for deflection in radians), this method is equivalent to the ABC method.\n\n5.2.5 Critique\n\nThe rules of thumb discussed in this section are ingenious but unsatisfactory on both theoretical and practical grounds. Theoretically, they disregard trail and curvature effects and will not function when the gun mount is on a curved course. Additionally, it is assumed that the angular rate observed will persist while deflection is laid off. Ballistics are not permitted to vary with range and altitude. Practically, they are difficult to apply at any except key ranges, even assuming the target would drift in a straight line.\n5.3 BASIC THEORY OF LEAD COMPUTING SIGHTS\n5.3.1 Range and Tracking Rates and Smoothing\n\nSince ballistic effects usually constitute a minor part of the total deflection, and since these effects can be presented quite accurately by subsidiary mechanisms, let us consider generically the nature of a lead computing sight designed to produce a kinetic deflection which is the product of a time-of-flight multiplier, tm, and the present angular rate of rotation, co, of the line connecting gun to target.\n\nFor a sight to obtain tm, it must be supplied with some sort of continuous estimate of the present range to the target. The range is usually obtained stadiametrically by the operator. This means that an optically presented reticle image of some pattern (parallel bars, dots in a circle, a ring) can be changed to provide an estimate of range.\nThe gunner sets the size of the target in the instrument's small dimensional scale before engagement. The changes in the reticle required to keep the target framed allow the sight to obtain the range. The range supplied in this way by the operator will not typically be the correct present range r. The difference p - r is the ranging error and is a function of time. Two ideas occur: why not smooth the ranging error p - r before using it? (This is analogous to communications engineering practice, where irregular and oscillating terms are called noise and are subjected to smoothing circuits.)\nIn order for a sight to obtain coherent observation (co), it requires continuous supply of the angular position r of the target. With this constant input, the sight can obtain the required rate of change f = co. The gunner must keep the center of the reticle image (pipper) on target, but will generally err and provide the sight with irregular and oscillatory angular position a of the pipper. The difference between r and a is referred to as tracking error or noise for angular positions.\nThe points from the previous paragraph are implemented. This datum is smoothed, and the angular rate is computed, as required. The simultaneous requirements of ranging and tracking (and triggering) are mutually inhibitory. Performance on either one improves significantly if the other is missing. In general, tracking is better than ranging in that the error is smaller and more rapidly random. Therefore, smoothing on the tracking angle is feasible.\n\nIn this chapter, we will assume that the gun mount is in uniform motion. This is equivalent to saying that the tracking rate r is equal to the true angular rate of the gun-target line co. Consequently, sights that measure rates relative to the gun mount and those that measure it relative to the air mass can be subsumed under the same theory.\n\nSection 5.3.2 The Exponential Smoothing Circuit.\nThe most common smoothing system is the exponential smoothing circuit, which can be realized in fire control electrically, mechanically, and gyro-scopically. In fact, this is the only type of circuit exploited in the devices of this chapter. Figure 1 illustrates the basic angles of lead computing sight theory. For transparency, it is assumed that the motions of gun mount and target are coplanar.\n\nFigure 1. Basic angles of lead computing sight theory.\n\nThe notation X instead of Ak will be used throughout this chapter for kinematic deflection. If tracking were perfect, a = r and \u03bb = y - t, so that X = y - t. The lead produced should be X = tmr. Hence, the sight equation would be\n\nX = tmr\n\nAs will be seen below, the equation actually mechanized by lead computing sights is not the preceding one but is\nThe constant a leads to smoothing and is a consequence of the mechanization adopted. From this equation, one obtains:\n\nX = g - a\n\nThis is the basic equation of the theory.\n\n5.3.3 Physical Realization of the Sight Parameter\n\nThe constant a is called the sight parameter. It can be given a physical interpretation. From equation (1), it follows that:\n\nIf a fourth line is added to Figure 1, making an angle a - a with the reference line, it follows that the sight is computing lead as if the target were on this fourth line. Describing this line by GY, it is evident that as the system rotates about G, the ratio of the angle YGS to the angle SGB remains constant at a.\n\nAs the deflection changes, the proportionate position of the sight along the line GY also changes, maintaining the constant ratio a:YGS/SGB.\nThe discussion of the gyroscopic sights' GY line existence is unchanged. In gyroscopic sights, GY has a definite existence. It is the spin axis of the gyro.\n\nSection 5.3.4 Discussion of Equation (1) is necessary and interesting.\n\nWeighted Averages:\n\nThe time-of-flight multiplier is a function of time. But the change to a new variable z by dt = tmdz eliminates tm, and an equation with constant coefficients arises. It is:\n\ndz da\naJz + X=\n\nThe integrating factor is ez,a, and multiplication by this and integration by parts give:\n\nrz/a r\nwhere z rldt\nJO tm dz\nAo, with time originating at t = 0.\n\nThe integral in equation (2) suggests the exponentially weighted average of da/dz. The total weight is Jo.\n\nIf we use (da/dz)av to mean the average of da/dz.\nThe entire second term of equation (3) is referred to as the transient, as it becomes small as z increases. The weight function ez/a attaches decreasing significance to information further and further back in the past. If a is large, ez/a falls off slowly, and the smoothed present value depends more heavily on past values.\n\nDamping of Oscillatory Tracking\nFrom a different perspective, the smoothing effect of the circuit can be clarified through a simple example. Suppose the target moves in a circle around the gun at uniform angular speed co. Then tm is constant. Suppose the tracking rate oscillates around the correct value according to a = co + K sin(nt). The steady state solution of equation (1) can be written as:\n\nKt\nVI + avtl\nIf a is zero, the lead produced would be X = tc + Ktm sin \u03b8. The ratio of the lead error amplitude with a nonzero a to the amplitude with zero a is known as damping.\n\nDecay of False Leads and Slewing Routines\n\nThe initial lead of the sight X0 may well be false, since under slewing to get on target, the sight feels that a fast target is at hand. It is important to know how rapidly such false leads decay if the rapidity of lead computation is to be assessed. Suppose the sight axis is displaced from the bore axis by an amount X0. If the gun is not moving, \u03b3 = 0. Hence, by the equation connecting lead to gun position, we have\n\nThe response of the circuit to a particular form of gun motion is shown in Figure 2. It follows from the equation that the sight line drifts back to the bore axis with a decaying oscillation.\nThe equation above represents the decay of X to 1/e of its original value in (1 + a)tm seconds. This time constant is referred to as the time constant of the sight mechanism. If tm equals 1 sec, the resulting time constant (1 + a) is sometimes called the sight response factor. Since tm decreases with decreasing range, the gunner is frequently instructed to hold the range setting at a minimum until he is on target with the sight pipper.\n\nTo minimize the time required for the transient (or false lead) to decay, slewing routines other than the simple one mentioned above have been proposed. This problem is approached analytically.\n\nSuppose a target has a constant angular velocity r0. The true lead is then taken to be tm * r0. Let the gun position be t0, originally behind the target. Supposing that the maximum slewing rate of the turret is reached.\nThe required angle per second for gun motion that minimizes the time interval for the gun to reach and hold its correct position (r0 + tr0 + tmTo), and for the sight line to attain its correct position (r0 + trQ), is not given. The solution involves slewing at the maximum rate until the gun is beyond its true position at time h, and then slewing back at the maximum rate until it reaches the true position at time U. The latter time is easily identified by the gunner as the time after ti when the sight is on target. Determining h, or how far past the target the gunner should go, remains unanswered, and this slewing routine has not become standard operational procedure.\n\nAmplification of Tracking Errors:\nIf attention is turned to the relation between:\ntracking errors and gun errors will reveal that tracking errors are amplified when translated into gun pointing errors. Consider the equation that arises from equation (1) if we put X = 7 - a.\n\nSuppose the sight line is oscillating according to o = A sin \u03c9t. Then, for constant tm, the steady-state solution of the gunsight equation is:\n\nwhere\n\nand 0 is a phase angle whose small value need not be considered. M may be interpreted as the ratio of the amplitude of gun oscillation to the amplitude of the sight-line oscillation. It is called the amplification factor and is plotted for typical values in Figure 3.\n\nAmplification deceives the gunner, as he may consider his tracking good (amplitude of error 5 milliradians) and yet his guns may be sweeping over the target with an amplitude threefold increased.\nAs a approaches zero, the amplification increases and, with the increasing frequency n/2t, the amplification also increases but tapers off to the value (1 - f a) /a. This explains why sights use circuits with nonzero parameters. (Figure 3 shows the amplification of oscillatory tracking errors.)\n\nIn actual tracking, errors are committed not only along the target's path but also at right angles to it. It is natural to ask if the two components of noise can be treated independently as far as amplification is concerned. The answer is yes. (There is a very slight cross effect on the vertical amplification factor which reduces it by about 0.1 percent.) For this two-dimensional case, however, it may be noted that for certain combinations of frequency and relative phase of the component tracking noises, the resulting amplified gun motion will be more complex.\nMay be such that the gun never gets on target, even though each component of the tracking crosses the target position. (If al = A sin \u03b8 and xv = A cos \u03b8 are the lateral and vertical tracking noises, the gun describes a circle of radius MA.) Tracking errors are in general not so regularized that this is a matter for concern.\n\nOperational Stability\n\nThe question of operational stability can be clarified through equation (4). Suppose initially that o- = Y = 0. If the gun is given a sudden jerk, the response of the sight line is determined by a:\n\na) where t0 is the initial jerk.\n\nThen:\n\n1. If a is positive, the initial sight response agrees in sense with the gun motion and the sight is called operationally stable.\n2. If a is zero, the sight does not respond immediately.\nThere is no impulsive effect, and the sight appears sluggish. If a is negative, the sight is a fast starter but in the opposite direction to the gun, and is operationally unstable. In the third case, the gunner is deceived, as a small corrective jerk in the right direction causes the sight to move initially in the opposite direction. Such sights can be built and will function in the sense that if the guns are started and continue tracking, the reticle will ultimately start back in the right direction, overtake the target, and get into lead position. However, it does not seem advisable to use negative values of the sight parameter due to the disturbing effect on the gunner, and also because the weighting would attribute more importance to old values than to the new ones.\nThe considerations of the previous paragraphs were based on the interpretation of equation (1) as a smoothing or damping circuit. Such systems can also be thought of as exponential delay circuits in the sense discussed below. If equation (1) is differentiated and the second derivative of X is neglected, one obtains the expression dx/dt as an approximation to X. Admittedly, tracking is correct, equation (6) shows that the circuit errs in producing the correct deflection vm (unless tm and fl are constant in time). Denoting the correct lead by X0, equation (6) is rewritten in the form dt X \u2248 X0 at a time atm in the past. In this sense, the sight's answer is always stale and becomes staler as a is increased. The delay must be accepted if smoothing is desired.\nFrom one point of view, the delay is desirable. If we use the time of flight over present range tp instead of tm, the correction made by a delay circuit to X0 = tpo is in the right direction if a is positive, since lead is increasing on the incoming leg. A similar compensatory effect is exercised on the outgoing leg. However, it is now generally conceded that a sight should be calibrated, i.e., tm should be chosen to give best results over a given set of tactical circumstances. Therefore, this behavior cannot be construed as favoring only sights for which a > 0. For any value of a, calibration can allow for delay. (See Section 5.3.5.)\n\nThe exact solution of the type equation (6) is\nFor equation (1), the exact solution is 9 X tm<j atm (tm o\u2019) dt, where z = | dt/tm, and E(z) is the error term. The choice of sight parameter a is not rational, as there are factors favoring a small value and others preferring a large one. If we agree to use a positive value for a for operational stability and proper weighting of new data, the involved factors can be summarized as follows. For large a, smoothing and damping are better, but too much weight is assigned to past information. As a increases, transients take longer to decay, and the delay in putting out correct deflection is greater, which are not desirable.\nfeatures.  On  the  other  hand,  as  a  increases,  the \namplification  of  gun  motion  is  decreased  which  is \nprobably  desirable.  An  engineering  compromise \nmust  be  made.  The  sights  of  this  chapter  use \nparameters  with  values  somewhere  in  the  range  0.2 \nSince  tm  has  an  effect  paralleling  that  of  a  ( a  and \ntm  occur  as  a  product  in  connection  with  the  above \nfactors),  it  is  reasonable  to  suggest  that  one  should \nhave  a  vary  with  range  to  effect  compensations.  This \nsituation  will  be  dealt  with  briefly  in  Chapter  8. \nBut  it  is  worth  emphasizing  now  that  operational \nCONFIDENTIAL \nLEAD  COMPUTING  SIGHTS \nerrors  of  simple  manual  ranging  and  tracking  usually \noverpower  such  refinements.  It  is  another  case  in \npoint  of  improving  inputs  before  refining  the  blind \ncomputing  mechanism. \nAided  Tracking \nBefore  leaving  this  particular  discussion  of  the \nbasic  sight  equation,  it  may  be  appropriate  to  show \nThe three principal methods of connecting handlebar motion to gun motion are: (1) direct tracking, in which the angle of gun displacement is directly proportional to the angular displacement of the handlebars (7 = cm); (2) velocity tracking, in which the velocity of gun movement is proportional to the angular displacement of the handlebars (7 = cxt); and (3) aided tracking, in which a displacement of the handlebars simultaneously displaces the guns and gives them a velocity (7 = cm + C2/x). Type 2 is realized by a motor whose speed depends on the displacement of the control. Type 3 implies an exponential smoothing mechanism, since with or1 and c\\ the respective analogues of a fixed tm and a sight constant a, the theory of the mechanism is:\nThe aided tracking equation follows that of equation (1). Investigations of aided tracking, as per studies number 136, have generally shown that aided tracking provides better results than other types. However, no optimum value for ci/c2, the equivalent of atm, has been determined. There is little distinction in results for values within the range of 5.3.5.\n\nThe Calibration Concept\n\nIt has been emphasized that tm, the time-of-flight multiplier, should be chosen to optimize the sight's performance under certain tactical circumstances. To illustrate this philosophy, consider the set of target paths that sensibly resemble pure pursuit curves. The deflection to take against a pure pursuit curve is given by equation (1) of Chapter 4:\n\nA = Kq sin r\nVo\n\nTherefore, if tm were given the correct value, shooting against pursuit curves would occur. However, this simple procedure would not eliminate all issues.\nThe time lag in lead computation nor would it allow for the fact that the actual sight subtracts from the kinematic lead it produces, a lateral ballistic allowance /3. To account for these two facts, start with the complete basic equation:\n\nwhere the lateral ballistic deflection /3 is given approximately, following equation (11) of Chapter 1, by:\n\n= crpvo sin \u03b8,\n\nwhere c is a constant and r is present range. Solve equation (8) for tm using the correct total lead A for a pure pursuit curve instead of A. This \u2018\u2018forcing\u201d of the differential equation means that the sight\u2019s total steady state solution must give the correct deflection against a pure pursuit curve.\n\nThe procedure 41 is equivalent to selecting tm such that the sight\u2019s lagged kinematic deflection when combined with the sight\u2019s ballistic deflection, whatsoever, is:\n\n(crpvo sin \u03b8) + tm = correct deflection against pure pursuit curve.\nTo reduce equation (9) to a form suitable for calculation, the expressions k0VG cos a and Vo may be used. Then, tm is given by:\n\ntm = r Vo - ak0vG cos \u03b8\n\nThe actual sight mechanisms have been kept simple by using a circuit that computes tm as a function of present range r and altitude (relative air density p) only. Therefore, the variation of equation (10) with target and mount speeds, and with angle off cr, are not taken into account. In particular, equation (10) is definitely asymmetric with respect to the beam (0- = 90\u00b0). There are three sources of this asymmetry: (1) when k0 is given its exact value from equation (1) of Chapter 4, it is larger in the forward hemisphere because tf and q are both smaller (due to the shorter future range), (2) sin \u03b8 > sin a in the forward hemisphere, and so the trail angle is different.\nThe allowance is greater for a given angle a in the forward hemisphere than in the rear (sin 7 < sin a), and since A, the basic theory of lead computing sights, increases in the forward hemisphere (A decreases in the rear), the time lag does not act to counterbalance the first two factors. In sum, the total lead put out by the sight is:\n\nIf the tm used is appropriate to the beam tm k0 r Vq, in the forward hemisphere, tmcr is too small, and both the delay term and the ballistic term subtract. The sight underleads. In the rear hemisphere, tmdr is too big, the delay term adds somewhat, and the ballistic term does not subtract as much as it should. The sight overleads.\n\nDespite the arguments for making tm vary with:\n\n(Confidential)\nBasic Theory of Lead Computing Sights:\n\nIn the forward hemisphere, if the assigned time tm is appropriate to the beam, tmcr is too small, and both the delay term and the ballistic term subtract, causing the sight to underlead. Conversely, in the rear hemisphere, tmdr is too large, the delay term adds somewhat, and the ballistic term does not subtract as much as it should, resulting in the sight overleading.\nvt and Vg, as well as with r and p, enthusiasm for sight refinement must consider that such elaboration may be pointless due to errors in supplying inputs. It may provide excellent results for the specific class of curves assumed in calibration but deteriorate on other types of target paths. A suggested calibration (using averages over vG, vt, and a) is, for a = 0.43, API M8 ammunition (tf0 = 2870, c5 = 0.440), and ballistic deflection Pr = 3.69 (hundreds of yards).\n\nFigure 4 provides more details of the calibration.\n\nSection 5.3.6 Class B Errors in General:\n\nThe Class B errors of a fire control system were defined in Section 4.5.4 as those arising when a sight constructed exactly in accordance with design is operated perfectly with no dispersion. To assess these errors analytically for a given type of course,\nThe calibration in the sense of Section 5.3.5 must be known. Early estimates of Class B errors were made under the assumption that tm was the actual time of flight over present range as obtained from ballistic tables. From the current point of view, it is more significant to proceed in two directions.\n\nb = 0.003 is the actual value if the future range were r (caliber 0.50 API M8 ammunition). The use of c = 0.0025 takes into account the fact that future range should be used in assessing ballistic deflection, and this range is about 85% of r for pursuit curves.\n\n(1) With perfect calibration in the sense of equation (10), how does the sight perform against target paths other than those assumed in the calibration, e.g., rectilinear paths?\n\n(2) Given an actual averaged calibration, how does the sight perform against the courses of the calibration?\nAgainst a straight-line course, ra = Vg sin a \u2013 Vt sin a, and ra from equation (9) of Chapter 2. One could obtain the optimum calibration against straight-line courses by inserting these expressions in equation (9). For instance, consider a special case of support fire against a rectilinear company front attack (Section 4.6.1). Using hundred yards and seconds as units, choose vg = 0.8, M8 ammunition. A good value for q is 1.066, so the correct total lead A = 81 milliradians. For these conditions, a sight calibrated perfectly against pure pursuit (k0 = 0.89) would use tm = 0.586 sec.\n\nFigure 4: Calibration of a lead computing sight when used against pursuit curves. (Upper family: a = 0\u00b0; lower family: \u03b1 = 180\u00b0.)\nThe tracking rate is cf = 116.7 milliradians per second, resulting in approximately 68 milliradians of kinematic lead. In this instance, the ballistic deflection is /S = 3 milliradians. However, since the lead is increasing, the lag effect decreases the deflection by 12 milliradians. The total sight error is, therefore, 18 milliradians. Although this is a significant bias, it's important to remember that dispersion, input errors, and Class A errors may still result in hits. At least the deflection is to the right side of the target. An own-speed sight, which can also be considered calibrated for pure pursuit curves, would produce a deflection of 37 milliradians to the rear of the target and commit a Class B error of 118 milliradians.\nIt is appropriate to continue the discussion of Class B errors in those sections concerning particular sights.\n\nSection 5.4 Mechanical Rate Sights\n\nThe realizations of the theory of Section 5.3 to be considered here are called mechanical rate sights. The computing mechanism consists entirely of mechanical elements as opposed to electrical or gyroscopic units. These sights form the Sperry series: K-3, K-4, K-9, K-12, K-16. The pairings are natural since the K-4 and K-16 are lower ball turret versions of the K-3 and K-12 respectively. The K-9 is a layout redesign of the K-3 to make a Martin turret installation possible. All other models go in Sperry turrets. Although the K-12 is also an improved version of the pilot model K-3, most emphasis of this section will be placed on the K-3, since this sight has received more study. All models\nThe essential elements are two component sights with separate mechanisms to compute the total lead laterally and vertically. A general knowledge of the mechanism is useful. The Ball-Cage Integrator The hall-cage integrator, illustrated in Figure 5, is the essential element. The speed of a point on the disk at the cage is zjl. This speed is transmitted to the roller, which must have a speed h4>). Consequently, the output angular velocity <t> is proportional to the input displacement z. Mechanical Exponential Smoothing The ball-cage integrator can readily be made into an exponential smoothing circuit (Figure 6). A differential, as described under \"Ball-Cage Integrator\" above, has been added. The rotational inputs are the elevation EG and roller angle <f>. Through a proper choice of gear ratios, the differential adds the inputs.\ntwo inputs algebraically in a desired proportion.\n\nThis is the required equation, connecting gun rate to deflection in the vertical component:\nb, if one takes c = 1 + a and varies the disk speed such that x/6 = 1/tm, then, calling the rack output z and the vertical kinematic lead Xv, one has:\n\nXv = a/tm\n\nAnother ball-cage integrator is used to make the disk speed vary as the reciprocal of the time-of-flight.\n\nFigure 7. Method of making disk speed depend on the multiplier. In this application, the ball-cage unit is used only as a device to transform a displacement into an angular velocity. It is evident that as the range approaches zero, l/tm approaches infinity. Hence the mechanism must abandon its computation at a point for which the speed would be excessive.\nLateral circuit: Near the zenith, a small change in target position leads to a large change in the azimuth of the target. Therefore, lateral deflection rather than azimuth deflection is used. The gear ratios are chosen so that a = 0.22 for the K-3 sight. In the K-3, the limiting range for accurate computation is 200 yards. Below that range, a speed corresponding to a constant value tm = 0.2 sec is operative. The deflection is computed in a plane whose normal is perpendicular to the gun and lies in a vertical plane containing the gun. The appropriate gun rate is, therefore, Ag cos Eg, since this is the magnitude of the rotational vector directed along the normal described. The lateral circuit will be complicated by the required multiplication by cos Eg. According to Figure 8, this multiplication is represented by Oe, G, CAM, H, D, differential, rack and pinion, K.\nFigure 8. Lateral smoothing circuit is achieved by another ball-cage integrator and a cam. The output of the first roller is D = Ag cos Eg, and at the differential Cm so that tm\n\nComplete Circuit\n\nLateral and vertical ballistics, /3l and /3f, are to be combined with Xl and Xv just before the lateral and vertical mirrors of the optical system are rotated. Two-dimensional cams are used to put in ballistics. (Such cams are irregular cylinders. By rotating such a cylinder, one input is made, and by displacing a follower along it, a second input is possible.) Ballistic deflections actually depend on range, azimuth, elevation, altitude, and mount velocity. With two-dimensional cams, average values for certain variables must be selected. The lateral deflection is taken as e.\n\nFor the K-3, the average values used for /8L are altitude.\nThe K-12 sight relies only on range and angle (AG) for lead computation, while Pv depends on elevation (Eg) and angle. The complete sight schematic is depicted in Figure 9.\n\nFigure 9 shows the K-3 sight schematic (courtesy of Sperry Gyroscope Company).\n\nMechanically, the K-12 sight varies significantly from the K-3. It uses only two ball-cage integrators, resulting in kinematic deflection outputs of X L/tm and \u03c5/tm. Similarly, the outputs of the ballistic cams are pL/tm and Pv/tm. A linkage adder combines kinematic and ballistic deflections, and then tm is multiplied out by a linkage multiplier (which is a level with a variable fulcrum positioned according to lm). Linkages also allow the ballistic deflection to depend on all five variables rather than two. Caliber\n0.5 API M8 ballistics result in a change from 0.22 to 0.37, enabling a switch from appropriate to straight-line courses to 0.90m, suitable for pursuit curves. In the mirror system, lateral deflection is taken first, and the mirrors are perpendicular rather than parallel as in the K-3, improving system performance by minimizing gun roll error (see Section 2.4.2). Range is controlled by a button-operated motor, providing velocity ranging instead of the K-3's direct ranging (see \"Aided Tracking\" in Section 5.3.4). The reticle consists of 12 dots (as opposed to a gate in the K-3). Input intervals: range 200-1500 yards; target dimension 30-60 feet; IAS 100-450 mph; altitude 0-40000 ft; gun rates up to 250 milliradians per sec; elevation up to 85 degrees.\n\n5.4.4 Complete Sight Equations and Origin of Class B Errors\nThe Class B errors of an actual sight are attributed to approximations in the original theory, compromises in the design, and peculiarities of mechanization. With a real sight, when discussing errors of this type, it is customary to say that the sight behaves exactly according to blueprint specifications, except for statistical features of dispersion, manufacturing variations, and input errors.\n\nFor the K-3 sight, kinematic deflections are computed using equations (4.5.4-1) and (4.5.4-2), which are combined linearly with ballistic deflections p, l, and Pv to give the total deflections: total deflections = C * kinematic deflections + F * p + G * l + H * Pv. In working with these equations, the blueprint tm, Pl, and Pv are to be used. To complete the description of the sight, approximate mirror equations (74) are:\n\nmirror equation 1: x'' = A1 * x' + B1 * y' + C1\nmirror equation 2: y'' = A2 * x' + B2 * y' + C2\nThese describe how the optical system relates the azimuth and elevation of the sight line, A and E, to the angular coordinates of the gun, AG and EG. It is readily seen how errors other than those of the underlying theory (Section 5.3.6) must arise. The complete equations for kinematic deflection (206) should contain an additional term on the right of equation (11) to account for gun roll. (See Section 2.4.2.)\n\nGYROSCOPIC LEAD COMPUTING SIGHTS\n\nNext, /3l and Pv from equation (12) do not use p, vg, Eg, and p, Vg, r, respectively, as they should. In regard to equation (13), the error terms ML and Mv show how the mirror system fails to do its job. And there are subtler phenomena than these. Near the zenith, lead is changing rapidly from one component to another, and the ballistics are also involved.\nThe changing effect of the exponential circuit is enhanced, and spurious terms can be introduced into the lead computations. There are feedbacks from the ballistics and from the mirror system. To understand this phenomenon, simplify the above mathematical description of the sight to read:\n\n(1 + a)tm + X = tmy (smoothing)\nA = A - p (ballistics)\n\nThese equations may be combined to yield:\n\n(1 + a)tm + X = tmy - p\n\nThe last two terms are the ballistic and mirror feedbacks and are, of course, extraneous.\n\nThe analytical assessment of the Class B errors of a sight determines the total errors that the sight makes against some class of courses and decomposes the total error into its several causes. This program has been carried out for the K-3.21. One may take a class of, say, pure pursuit curves for which the exact deflection is known as a function of position.\nThe system tracking rates and ranges are referred to as functions of position. The system (11, 12, 13) is then solved for the steady state Al and Av. Since the solution is in symbolic terms, the identity of each part of the total error can be established. The process is lengthy and involves a sequence of approximations, resulting in final values with a probable accuracy of 3 milliradians.\n\nIn summary, the lateral error is given by:\n\u0394x = a sin(A)\nwhere a, b, and c are not constants. However, a is independent of elevation, and b and c are independent of target speed.\n\nThe vertical error is given by:\n\u0394y = e sin(A) + f sin(2A) + g sin\u00b2(A)\nwhere e, f, and g are independent of target speed, and e and h are independent of range.\n\nThe lateral error may be interpreted as follows:\n(1) a sin(A) is attributed to the curvature of the target.\nget's path causes sight to lead excess 10 percent when tm is time of flight over present range; (2) b sin 2A is due to gun roll, or, if one does not wish to elaborate the basic equations (11) to include this, is due to the unsuitability of the mirror system; and (3) c sin 2A cos A represents the combined effect of delay, feedback, and interchange. Similarly, the vertical error may be interpreted as follows. (1) d cos A is again in this component, the error arising from the neglect of curvature effect in choosing tm, although at short ranges the incorrect gravity drop (by equation (12) independent of range) is so large that it compensates for this error; (2) e sin2 A is composed of errors due to gun roll, delay, feedback, and interchange; (3) the third term is principally caused by the mirror system and its feedbacks.\n(4) g represents a failure to make gravity drop vary with range. Detailed tabulations of Class B errors for this sight have been made (14,21). The cellular array of Figure 10 illustrates the results.\n\nOuter number in each cell is error parallel to plane of inne. Perpendicular jaction in milliradians.\n\nFigure 10. Class B errors of K-3 against pure pursuit curves (milliradians).\n\n5.5 Gyroscopic lead computing sights\n5.5.1 General Nature of a Single Gyro Sight\nMechanical lead computing sights are essentially computing machines or brains which work through certain formulas. Gyroscopic sights, which utilize the properties of a gyroscope, have the following error breakdown for the term at A = 90\u00b0 and E = 45\u00b0: 15, 6, 4, 3 milliradians respectively.\n\nConfidential\nLead computing sights employ the properties of a gyroscope.\nThe significant advantage of a gyro sight is that it measures the true rate of rotation in the air mass connecting gun to target. In certain instances, the tracking may be done by the motion of the firing aircraft. For example, in firing at a fixed ground object from an aircraft making a pylon turn on that target, the gunner has nothing to do. The gyro sight will establish the angular rate a = Vg/r, combine this with a time of flight tm = qr/vo to give a kinematic deflection, behind the target, of qvg/vo and will subtract from this the lateral deflection.\nThe ballistic allowance, which decreases qvg/v to the full own-speed allowance, which is the required deflection, can only be supplied by a mechanical sight under certain circumstances. In these situations, a mechanical sight could only offer a trail allowance ahead of the target. In bombers, this independence from aircraft motion in obtaining correct deflection is important, but in fighters, it is imperative.\n\nThe sight under consideration in this section utilizes a single flexibly mounted gyro. (Certain sights used for anti-aircraft purposes and for fighters \u2013 the Draper-Davis sight and the German EZ42 \u2013 employ two suitably constrained gyros and solve the problem componentially.) The single gyro sight provides the total kinematic deflection along the relative path of the target, regardless of the direction of that path.\n\nThe gyro sight essentially consists of: (1) an electromagnetically controlled gyroscope that measures deflection.\nThe deflection in kinematics, as well as ballistic corrections, and an optical system that establishes the line of sight and introduces the sight parameter will be discussed. In construction, we will consider details only slightly. In operation, the gunner presets altitude, airspeed, and target span. During an attack, he tracks with the pipper on the target, keeps the target framed by the reticle pattern, and fires. Azimuth and elevation of the guns are automatically picked off the turret gear trains for use in determining ballistic corrections.\n\nThe single gyro sight for a turret is called the Mark II C by the British, Mark 18 by the U.S. Navy, which modified the design for U.S. ammunition, and K-15 by the U.S. Army Air Forces. The fighter version (Mark 21, Mark 23, K-14) is discussed in Section 5.6.\n\nMethod of Producing Kinematic Corrections:\n5.5.2\nTo explain the principles of sight, it's first necessary to understand how kinematic deflection is produced. A gyroscope is mounted on a gun with its spin axis parallel to the bore axis, and the universal joint mounting at 0 being the center of mass and the point about which the gun rotates (Figure 11). Since the mounting is universal, the gyro axis remains pointing in its original direction in space, a fundamental property of gyroscopes used in gyrocompasses and flight-attitude gyros. However, to track a target, the gyro axis, considered as the line of sight, must lag behind the guns an appropriate amount to generate deflection. This can only be achieved by making the gyroscope's axis free to rotate around the gun axis.\nTo keep the gyro precession in the plane of tracking, a force F must be applied at a point such as A and directed at right angles to the plane. The gyro's precession causes the line of sight to stay on target. If I is the moment of inertia of the gyro, T is the applied torque (equal to the force F times the distance l = OA), and ft is the angular velocity of spin, then the precessional rate a is given by:\n\na = T / I\n\nSince the moment of inertia, spin, and the distance OA are normally fixed, a change in the rate of precession requires a change in the applied force F.\nIf C is the constant l/Itt. If a and y are measured from some reference line fixed in space, such as pointed at a star, then, if the force F could be made proportional to the angular separation of gun and sight lines, we would have:\n\nThe force F could be made proportional to the angle by attaching a spring from A to B and relying on Hooke's law. F would then be correct in amount but wrong in direction. If c2 could be made inversely proportional to a time-of-flight multiplier tm (variable spring stiffness), we would have:\n\nCiCz\n\nFinally, since 7 \u2013 a is the lead X, a design such that C1C3 = 1 would lead to:\n\nX = tm(T)\n\nand kinematic deflection would be produced. The only things wrong with the scheme are (1) a spring mechanism would cause precession at right angles to the plane of tracking, and (2) no smoothing is provided.\nThe first point can be met by an ingenious application of electrical eddy currents. This is described in Section 5.5.3. Recalling Section 5.3.3, smoothing can be achieved not by using the spin axis as the line of sight, but by keeping the sight axis a fixed proportionate distance between spin axis and gun axis. It is one function of the optical system to do this. The method is given in Section 5.5.4.\n\n5.5.3 The Physics of the Gyro System\n\nInstead of a cylindrical disk, the actual gyro of the sight consists of a copper dome, a flat circular mirror, and a short connecting axle. This system revolves at approximately 3,000 revolutions per minute about a universal mounting to be considered at greater length below. The cap of this toadstool moves between the two poles of an electromagnet.\nThe strength H of the magnetic field between the poles is given by g (see Figure 1). This arrangement is schematized in Figure 12, the gyro schematic.\n\nwhere c4 is a constant, and i is the current in the coils. The lines of magnetic force pass through the dome, intersecting it in a circular area centered at A. The area of one instant is immediately replaced by another since the dome is spinning. Eddy currents are induced in the dome, as a circular annulus of the dome can be thought of as a coil of wire moving across a magnetic field. The current j induced in such a coil is given by:\n\nj = CbHv,\n\nwhere C5 is a constant and v is the velocity with which the coil moves.\n\nThe effect of these eddy currents can be observed.\nThe induced eddy currents create the equivalent of two magnets in the instantaneous dome segment, with S and N poles on the right and N and S poles on the left. The resulting four forces all act to oppose the motion with a force F = CeHj. The force F tries to slow the dome down. But the constant-speed motor supplies a couple with a force F/2 at A (Figure 12) opposing F and a force F/2 at A' in the same direction as F. Therefore, the speed of rotation is maintained, and an unbalanced force (F - F/2) + F/2 = F remains, which is directed down into the paper in Figure 12. Hence, precession will occur in the plane of the spin and bore axes as it should.\n\nUnder tracking, the bore axis is displaced.\nThe spin axis tries to remain fixed, but displacement causes a force F leading to precession of the spin axis toward the bore axis. If the gun keeps rotating, the spin axis does not catch up, and the two axes revolve with an angular displacement between them.\n\nThe applied torque, assuming that moment I is the moment of inertia and r is the distance from the axis, we have:\n\nX = y - a\n\nBut the precessional rate is given by:\n\n\u03c9 = (F * I) / (r * (I + Mr\u00b2))\n\nWhere M is the mass of the projectile.\n\nIf R\u00b2/c is chosen to be tm, we have:\n\nh = (R\u00b2 * (1 + (M / (2 * I))) / (2 * \u03c0 * tm)\n\nIn connection with c, it should be observed that since the 22-volt power supply is from the aircraft, a 1% error in regulation means a 2% error in the deflection output.\n\nThe optical system must introduce smoothing. The system is schematized in Figure 14. The reticle gate consists simply of one flat disk provided with a reticle.\nThe central hole and six radial slits are aligned against another disk with six curved slits. The reticle pattern comprises a pipper and six diamond dots due to slit overlap. By rotating a disk with foot pedals, the pattern size is changed, allowing a target to be framed and range supplied to the range coils.\n\nThe optical distance from the reticle gate to the lens is equal to the focal length, which is 7.078 inches since it's a collimating system. The optical distance from the gyro mirror to the lens is the image distance u, measuring 4.578 inches. The distance v to the (virtual) object is given by:\n\nConsider a ray emanating from the image point (gyro mirror) and making a small angle a with the lens axis. Upon refraction by the lens, the exit ray makes a smaller angle 1/3 with the lens axis determined by tan(a) = v.\nThis result is only approximate. If thick lens theory is used, it is found more exactly that the sight angle a will not be constant but will vary in a peculiar way depending on the amount of deflection.\n\nGYROSCOPIC LEAD COMPUTING SIGHTS\n\nThis point is labored since it will be seen immediately that the sight parameter a will not be constant but will vary in a peculiar way depending on the deflection.\n\nSuppose now that the gyro mirror is rotated in elevation through an angle y. (The design is such that 0 is effectively in the mirror. See Figure 16.) The reflected ray from the gyro mirror is then displaced from its original position by twice this angle. Upon hitting the fixed mirror, the reflected angle remains 2y so that the entrant ray to the lens makes this angle with the lens axis, i.e., a = 2y. Hence the sight line makes an angle of 2y with the horizontal plane.\nThe exit ray from the lens becomes a reflected ray from the combining glass and makes an angle with the original position. Consequently, the ratio of the angle from gyro axis to sight axis to the angle from sight axis to gun axis is P. It is more important to consider a rotation of the gyro mirror in azimuth, as in this case, not only is deflection Xa a factor, but a spurious elevation angle is introduced, leading to the phenomenon of optical dip, which is an error of the sight. The doubling principle used above depended on a rotation of the mirror about an axis perpendicular to the plane of incidence. For rotation around some other axis, doubling is not quite accurate. This can be explained crudely, for an azimuth rotation, as follows. In Figure 15, the deflected ray to the lens has farther to go to get to the lens, and climbing at a steeper angle.\nThe small displacement of 17 degrees hits the lens a short distance above the central line. A dip has been introduced to the combining glass of the sight. The glass mistakenly believes that the gyro has also changed in elevation. Additionally, instead of full doubling, a factor of 2 cos 17 degrees appears. A simple trigonometric analysis of Figure 15 reveals that for a displacement of the gyro axis, only in azimuth, of an angle a, the sight axis will move in azimuth by 2a and will always depress in elevation by a.\n\nUsing first approximation thin lens theory, i.e., \u03b8 = 0.353a, dip can be accurately determined. In general, dip can be calculated by this approximate theory.\n\nIf the gyro axis is displaced from the gun axis by angles a and Xf in azimuth and elevation, respectively, then the sight line is displaced from the gun axis by 0.675xa + 0.206axf radians.\nThe dip is due to the design necessity of having a ray of light from the reticle strike the gyro mirror at an angle of 17 degrees, respectively in azimuth and elevation. The variation in this angle (a) can be calculated using the exact theory. The formula for the variation in a is:\n\nX being the angle between the gyro and gun axes, and dm the distortion factor.\n\nIn certain German single gyro sights, this is not the case. The fixed mirror is half-silvered and dropped down to the OY axis (see Figure 14), and the reticle system is raised to this axis so that it is behind the fixed mirror. (Section 5.7.3)\n\nThe angle ip between the horizontal plane and the plane of the gun and gyro axes is usually assumed to be 0.43 for a, but it can vary from 0.41 to 0.48. This variation has a negligible effect.\nThe effect on sight performance. Mechanical Details. It is pertinent to consider actual mechanical details as such knowledge leads to an understanding of the limitations inherent in mechanisms of this order and is beneficial in the general design of new equipment.\n\nHooke\u2019s Joint:\n\nThe actual gyro system uses a Hooke's joint for its universal mounting. As depicted in Figure 16, the gimbal is a flat cross of metal whose input arm AB = INPUT ARM and output arm CD = OUTPUT ARM are pivoted to the driving pulley, while the rotor assembly is hung on the output arm. The pulley is placed in ball bearings in a panel connected to the sight head and in a vertical plane perpendicular to the bore axis of the gun. The axle can assume any angle with respect to the pulley by rocking about the four bearings.\n\nFigure 16. Actual gyro unit.\nThe ends of the gimbal cross maintain a constant rotation angle, implying the output arm must bob up and down 3,000 times per minute. Proper oiling of this joint is crucial. The result of gimbal inertia is a slight torque that pushes the axle further from the vertical, causing a conical precession. A similar effect is caused by the rapid spinning of the mirror while in a cocked position. Asymmetry in the sight head leads to low air pressure on one side of the mirror and high pressure at the other, resulting in the Venturi torque. Additional torques stem from air drag and frictional resistances, as well as the driving torque.\nThe five torques are extraneous as we only require the torque due to eddy currents in the dome. The analysis of the gyro system is complicated, and the results will not be quoted. From the perspective of Class B errors, the conical precession implies that a displaced gyro axis does not return to the gun axis along a straight line. This leads to an additional dip, approximately 0.025t*<7 milliradians, which can be positive or negative depending on the direction of tracking and may partially balance or augment the optical dip.\n\nElectromagnetic System:\nThe electromagnetic system uses four sets of poles instead of the single pair in Figure 12.\nrange coils are not wound individually around each pole, but around the entire unit of four. The fields between the several pairs are the same in magnitude and sense. Ballistic deflections are taken into account in a simple fashion. In addition to the enveloping range coil, each pair of opposite poles is wound with a separate ballistic coil (Figure 17). The fields produced are opposite by pairs due to the winding. Referring to Figure 3 of Chapter 1, it is seen that the two sets of ballistic coils are needed to produce the appropriate lateral and vertical components of the trail IF. These components are, respectively, W sin A and W cos A sin EG. An additional coil, on Px and P3 only, is needed for the gravity allowance. Under these four windings, the four electromagnets become equivalent to one placed at some point between them, a magnetic.\nThe center of gravity. The single point where the total magnetic force seems to act is called the magnetic center, and the line from this point to the Hooke's joint is the magnetic axis. When ballistic currents flow, the ballistic fields, being opposite in sense, cause the magnetic center to shift. To the gyro, the magnetic axis now plays the role of the gun axis, and it is with respect to the magnetic axis that kinematic deflection is taken by the gyro. In this physical fashion, the gyroscope constructs the difference between kinematic and ballistic deflections and properly positions the gun.\n\nFigure 17: Range and ballistic coils.\n\nClass B errors can occur due to the electromagnetic system. The lateral ballistic coils not only pull the magnetic center over as they should but they also cause additional unwanted shifts.\nThe electrical circuit must take the inputs of range, position of target, etc., and supply suitable currents to the coils of the electromagnets. To translate the required formulas properly, nonlinear resistances and attenuating (multiplying) circuits are used.\n\nThe deflection and elevation of the projectile can be influenced by the electromagnets, slightly altering their trajectory. The ballistic coils also act as range coils, making minor adjustments. An important error could be introduced due to the variability of the dome's conductivity with temperature, which changes radically from sea level to high altitude (lead changes by 0.4% per degree Celsius temperature change). Since altitude input changes resistances, the resistances must be chosen accordingly to compensate for this effect.\nFigure 18: Multiplying circuit.\nSuppose the variable resistance R1, set by dial number qh, and variable resistances R2 and R3, set by dial number q2, are represented in the circuit. The problem is to design variable nonlinear resistances Rij, R2, and R3, and to select a fixed resistance R1 such that the current i in the box equals Kqxq2.\n\nThe resistance from A to B will be constant for all values of q2 if R2, R3, and R1 are chosen such that:\n\nR3 / R4 = c (where c is a constant)\n\nIf R3 is chosen such that Rz and Ri is chosen such that:\n\nkq2 / E = K\n\nWe will then have, as required:\n\ni = Kqiq2\n\nwhere k, c, and Ri are at our disposal.\n\nUsing this principle, the complete circuit is laid out as Figure 19. It is evident that tm depends only on range and altitude, and is made out by a mechanism.\nsimple summing of variable range and altitude resistances. So values of R2 and H3 must be determined experimentally to give optimum results. The triple branching in the trail circuit corresponds to the CONFIDENTIAL LEAD COMPUTING SIGHTS RANGE CIRCUIT BY ONE DIAL R, R2- range resistances H, ,H2, H3 - altitude resistances A, ,A2 - airspeed resistances E|, E2, Eg - elevation resistances R, Ra, Re, R$ are the coils of the electromagnets rE - ground temperature compensator X - IN or OUT resistance (OUT FOR NOSE) Rf, Ra - fixed resistances Multiplication of density, airspeed, and range required by the expression for trail (Formula (11) of Chapter 1). The final internal branchings introduce multiplication by cos(A-sin Eg) and sin(AG).\nIn getting at the Class B errors of the gyro sight, a natural first step is to determine its behavior in symbolic language against a target on a general space path and with an arbitrary range r and tracking rate j. This requires a complete theoretical analysis of the instrument. Given such an analysis, it is possible to:\n\n1. Determine what design constants should be used to effect an optimum calibration.\n2. Test the performance of the sight in a given class of tactical circumstances.\n3. Assign parts of the total error to their particular causes.\n\nIllustrating this program briefly, we shall restrict quotations to those pertinent to motion of target and gun mount in a horizontal plane:\n\n1. Gravity drop depends on range and cosine.\n2. Eg but not on altitude or airspeed.\n3. Specific origin of Class B errors:\n   a. In getting at the Class B errors of the gyro sight, a natural first step is to determine its behavior in symbolic language against a target on a general space path and with an arbitrary range r and tracking rate j.\n   b. This requires a complete theoretical analysis of the instrument.\n   c. Given such an analysis, it is possible to:\n      i. Determine what design constants should be used to effect an optimum calibration.\n      ii. Test the performance of the sight in a given class of tactical circumstances.\n      iii. Assign parts of the total error to their particular causes.\nOn the surface of a unit sphere, let U and V be the azimuth and elevation displacements of the gyro axis with respect to the gun axis, which is assumed to lie in a horizontal plane. If u and v are the azimuth and elevation of the sight axis with respect to the gun, and ai and a2 vary slightly, depending on w and i (Section 5.5.4), we shall take ai = a2 = a (constant). For gun rotation in a horizontal plane, the general equations become, after linearization,\n\np: range coil current\nn, r2: balancing coil currents (gravity neglected)\nA, B, C, D: constants determined by the geometric and material characteristics of the electromagnetic system\npa: small positive constant (0.02) due to gimbal inertia and air currents\npR: small positive constant (0.035)\nThe equations above do not include the effect of optical dip. If this effect is superimposed, using the approximate thin lens results of Section 5.5.4, we obtain:\n\nCptmlTi = @ 1\nFor a horizontal plane, r2 = 0. Numerically, A = 0.26, B = 0.18, C = 1.374, and D = 20.\n\nThe equations above do not include the effect of optical dip. If this effect is superimposed, we obtain:\n\nwhere,\n@ 1 CptmlTi\n\nFor a horizontal plane, r2 = 0. Numerically, A = 0.26, B = 0.18, C = 1.374, and D = 20.\n\nIf there were no bearing friction or air drag, the term 0.0354* in equation 4 would be missing. If the trail coil currents did not affect time of flight, 3.5ft would be missing. Then, 4 = 4/0.7, and if the optical system were perfect, the number in u, 0.675, would be the only remaining term.\nIf the optical system is perfect, the first optical dip term in v would vanish (i.e., sin 0\u00b0), and if Venturi torque and gimbal inertia were not present, the second electromagnetic dip term in v would also vanish. However, this discussion is academic in the following sense. It assumes that the correct time-of-flight multiplier tm is given by tm = 0.035/p\u00b2. As noted earlier, it is necessary to calibrate the simple range circuit to give optimum results over a set of tactical conditions, such as a family of pursuit curves. In doing this, it is possible to ameliorate to a certain extent the above types of errors, but it will not be possible to make tm exactly correct in any event. Without giving the numerical values of resistances adopted in the final circuit, the typical size of errors is:\n\nif the optical system is perfect, the first optical dip term in v would vanish (i.e., sin 0\u00b0), and if Venturi torque and gimbal inertia were not present, the second electromagnetic dip term in v would also vanish. However, this discussion is academic in the sense that it assumes the correct time-of-flight multiplier tm is given by tm = 0.035/p\u00b2. It is necessary to calibrate the simple range circuit to give optimum results over a set of tactical conditions, such as a family of pursuit curves. In doing this, it is possible to ameliorate to a certain extent the above types of errors, but it will not be possible to make tm exactly correct in any event. Without giving the numerical values of resistances adopted in the final circuit, the typical size of errors is unknown.\nFigure 20: Class B errors of a gyro sight against pure pursuit courses. (In milliradians)\n\nThe outer number in each cell represents error parallel to the plane of action, and the inner number represents error perpendicular to it.\n\nOf the total lateral and vertical Class B errors, the summary in Figure 20 can infer:\n\n0 Horizontal:\nOuter: error parallel\nInner: error perpendicular\n\nFigure 21 shows by how many milliradians the optimum time of flight must be increased to give the optimum time against straight-line courses. One number applies to a 0\u00b0 approach angle, and the other to a 90\u00b0 approach angle, as indicated in a typical cell. These are also approximately the percentage errors in lead.\n\nIt must be expected that an optimum calibration for pursuit curves will cause sight performance to deteriorate markedly when the sight is used against straight-line courses. This is the case. The chart of Figure 21 shows the optimum time increase to give the optimum time against straight-line courses.\nIf a blanket percentage increase in tm opt (pursuit) is decided upon, passing from pursuit courses to rectilinear courses, no redesign would be necessary. The introduction of a suitably fictitious target dimension would accomplish the purpose.\n\nSection 5.5.7: Different Type Turrets\n\nTo conclude this section, the effect on the sight design of a change in the turret type may be considered. The classical turret, on which the design discussed above is based, positions its guns by rotations in azimuth and elevation. Consequently, it was necessary to decompose ballistic deflection into lateral and vertical components. Tracking in an elevated plane of action is not easy, and the tracking system encounters difficulties.\nA pattern is frequently stepwise. If, on the other hand, a turret is employed in which one rotation is about a longitudinal axis of the aircraft (instead of the azimuth rotation about a vertical axis), then a sight head with one edge perpendicular to the bore axis and parallel to the azimuth plane moves so that this edge remains parallel to the azimuth plane. For this reason, a camera fixed to the guns and recording correct shooting against a pursuit curve would show the target's path, on the composite of all frames, as an arch. The plane of action is established in which the guns may make a second rotation. (If the elevation rotation is 0 and the plane of action rotation is \u03c6, then sin 0 = cos \u03b5 sin \u03c6, sin \u03b5 = sin \u03c6 cos 0, cos 0 = cos A G cos \u03c6.)\nTracking should be improved in a watermelon turret. The gyro sight is now simplified since all the trail is in the plane of action. However, a redesign of the electric circuit is required for good results.\n\nIt has also been proposed to install a turret with its azimuth ring inclined at a 15\u00b0 angle with the horizontal (to improve aircraft performance). However, the sight will supply wrong ballistics unless some correction is made. The naive proposal of feeding EG \u2014 15\u00b0 instead of EG actually gives excellent results.\n\nConsideration of the two examples above shows the need for the closest integration of armament and fire control design. Furthermore, since a change in muzzle velocity and ballistic coefficient of the ammunition may call for a redesign of a sight, ordnance must also work closely with armament and fire control.\nControl effective production and utilization schedules. Otherwise, modification or patching operations are necessary.\n\n5.6 Gyroscopic Sights in Fighters\n5.6.1 Simplifications\n\nThe radical maneuvering of a fighter during an attack necessitates that the only principle for a sight in a fighter be based on the gyroscope. Since the guns are pointed through maneuvering, rates relative to the gun mount do not exist. There is no reason why the single gyro sight described in the previous section cannot be used immediately by pursuit aircraft. In fact, the circuits can be simplified. In the first instance, since the classical fighter always fires within a few degrees of its direction of motion\u2014the difference being due to:\n\n1. The difference being due to the difference in the direction of the target and the direction of motion. This can be simplified by designing the gyro sight to automatically adjust to the fighter's direction of motion.\n2. The need for separate rate gyros for pitch and yaw can be eliminated by using a single rate gyro for both axes. This would significantly reduce the complexity and cost of the gyro sight.\n3. The use of vacuum tubes for amplification can be replaced with transistors, which are smaller, faster, and more efficient. This would further simplify the circuits and make the gyro sight more practical for use in fighters.\nTo determine the angle of attack of the guns, it follows that no allowance for trail needs to be made, and the ballistic coils and circuits may be deleted. Due to diving and banking, it is pointless to leave in the gravity coil and circuit since any inputs with reference to the fighter would be in elevation error. Expect accurate time of flight calculations for two reasons: (1) the direction of fire with respect to the aircraft can be neglected, and (2) calibration for the standard pursuit curve attack can be made and will hold, since this is the tracking situation the fighter must contend with (the case of fighter versus fighter on a curved course is considered in Section 5.6.3). Overall, good results are expected from a gyro sight.\nTo calibrate the fighter sight, suppose the sight transient has decayed, the target flies a straight-line course at constant speed, the bullets leave in the direction the fighter is flying, and ranging and tracking are perfect. API M8 ballistics will be used (v0 = 2,870 fps and c5 = 0.440). The correct lead A is then given by equation (3) of Chapter 2 and is:\n\nVt . qvr\n\nwhere q, as usual, is Uq/u = (Vq-vf)/u. The time-of-flight multiplier tm is obtained by inserting A in the equation of the sight. This is the meaning of calibration:\n\nA\n\nBy use of evident expressions for a and A, this becomes:\n\nA = Vt . qvr\nq = (Vq-vf)/u\n\nTherefore,\n\nA = (Vq-vf)/u . Vt . qvr\nA = (Vq-vf)/u . Vt . (Uq/u) . r . v\nA = (Vq-vf) . r . v . Vt / u^2\nComputations based on this formula show that tm/r is remarkably insensitive to the speed of the fighter for a = 0.43 (fortunate since vF is not an input), variations in a around 0.43 are quite irrelevant, and increase in target speed magnifies the effect of approach angle (but for fast targets one can concentrate on tail cone approaches). Averaging with respect to those variables which cannot be used as inputs, the following table for tm opt is to be used:\n\nThe time of flight used by the gyro is inversely proportional to the square of the current i in the range coil (Section 5.5.3). The proportionality factor K is, in turn, a function of p, T, a, where T is the ambient temperature of the cockpit. It is determined experimentally. The design problem, therefore,\nTo choose resistances such that the time constant (tm) of the optics is as close to K(p, T, r)/i2 as possible. The details do not need to be pursued.\n\nTable 1. Average optimum time of flight for fighter gyro sight [tm (r, p) (seconds)].\n\nRange r (yards)\nRelative air density\n\nRespectable results can be achieved by such calculations in spite of the averaging and fitting to K/i2. For example, for caliber 0.50 API M8 ammunition, the maximum error in the plane of action is of the order of 7 milliradians.83 (This is not the total Class B error.)\n\n5.6.3 Effect of Target Course Curvature\n\nA fighter under attack by another fighter at some small angle off tail will frequently attempt to increase the attacker\u2019s deflection and make his aiming more difficult by banking as steeply as possible to cross the attacker\u2019s bow. (The quarry may also dive or attempt to utilize his propeller wash.) For\nattacks in the rear hemisphere, a longer time of flight is needed against the circular target path than is required by the rectilinear path. The reason is that the tracking rate a is the same at a given instant for the curved path and for the tangent to that path. However, the target's incurving calls for a greater lead. Thus, tm must increase. This effect can be demonstrated analytically. The increase required of tm can be up to 18.7% from 10 to 20 percent. But the error induced by using a tm appropriate to rectilinear paths against curved paths rarely exceeds 6 milliradians for expected conditions.\n\n5.6.4 Irrelevance of Angle of Attack, Skid, Slip, Offset Guns\nIt will be recalled from Section 3.3.1 that a fighter pilot aiming by eye must make a slight aiming allowance along the median line of his sight to account for\n\nLEAD COMPUTING SIGHTS (CONFIDENTIAL)\nThe angle of attack of his guns. The gyro sight includes the computation of this effect. A gyro sight will give the kinematic deflection regardless of skid, slip, or guns deliberately offset at any angle, as long as a path is flown as dictated by perfect tracking and ranging. This, in itself, is a major improvement over eye shooting which must be done from a cleanly flown aircraft.\n\n5.7 Other Sights\n5.7.x The K-8 Sight\n\nThe K-8 electrical sight was used to a limited extent in the Martin upper turret of the B-24 during World War II. It is also of the time-of-flight \u2014 angular-rate type and, like the K-3 class, measures rates relative to the gun platform instead of relative to the target.\nThe air mass is not controlled mechanically but electrically, generating appropriate voltages using attenuator circuits and employing computed voltage outputs to displace the sight line laterally and vertically with motors. It functions similarly to the K-3, producing false rates during yaw, pitch, or roll, and experiencing significant errors at high elevations of fire. From an input and operational standpoint, it resembles the K-12. A switch allows for a 10% reduction in time-of-flight calibration to counter pursuit curve attacks in a blanket fashion. The mechanism will not be detailed, but it is worth noting that such techniques have been developed for potential applications.\n5.7.2 Other Methods of Gyro Control\nGyroscopes may be used in fire control in combination with forces other than eddy currents. Two different schemes, 218a, are shown in Figure 22 on one turntable. The mechanisms should be self-explanatory and are set up for performance in azimuth only.\n\n5.7.3 German Gyro Sights\nThe major German gyroscope sights were the EZ40, EZ41, EZ42, and EZ45. The EZ40 is a single gyro sight with a mirror on the gyroscope to deflect the line of sight. (The ray from the reticle hits this mirror perpendicularly in the neutral position so that there will be no optical dip.) The EZ41 is a single gyro sight with the gyro unit remote from the sight head. The optical system is therefore acted upon by motors controlled by a follow-up system. The EZ42 is a twin gyro sight installed in fighter aircraft (FW190, Me262). The two gyros are placed in parallel.\nOne gyro is mounted with its axis parallel to the longitudinal axis of the aircraft, and the other with its axis parallel to the vertical axis. Friction dash-pots are provided for smoothing, and gyros are further constrained by springs. Gyro deflection is picked off by tiny potentiometers, and the lead is computed electrically. A servo drive, employing a very small two-phase motor, supplies motion to the optical system. The Zeiss technique of winding variable potentiometers and certain other components of this sight are worth keeping in mind.\n\nThe EZ45 is a remote single gyro sight. The gyro is controlled by erecting coils, and its supporting case is driven by a small motor. Through a time-of-flight potentiometer, the angle through which the case turns is made proportional to the lead. The sight parameter is 0.33. The position of the case is determined by the gyro's deflection.\nThe introduction in Section 5.1 defines lead computing sights as devices that multiply the angular rate of the line joining gun to target by an appropriate time-of-flight multiplier to get an estimate of kinematic deflection. Ballistic deflection is obtained separately and combined with the kinematic deflection. These sights neglect the rate of change of range and may have a suitably chosen time-of-flight multiplier to ameliorate this situation. The gunner has only indirect control over the line of sight as he controls only the guns, from which the line of sight is displaced by the mechanism.\n\nSection 5.2's digression dismisses briefly early inaccuracies.\nThe text discusses eye estimation methods based on the rate-time principle. The Elephant, ABC, and Apparent Speed methods aim to calculate sight out of the gunner himself, to some extent. Section 5.3 explores the common theory behind all lead computing sights. Due to tracking errors, the rate input must be smoothed before usage. The basic equation of these sights is covered through the following points: (1) interpreting smoothing as the process of taking an exponentially weighted average of all past values of the tracking rate, (2) damping oscillatory tracking errors, (3) the exponential decay of false leads and slewing routines designed to minimize decay time, (4) the amplification from oscillatory sight pointing errors to gun pointing errors, (5) the meaning of operational stability, and (6) the decay.\nThe factors affecting the choice of a sight's smoothing parameter and the analogy between aided tracking and lead computing sights are discussed in the sight's presentation of lead. Section 5.4 delves into the mechanical sights of the Sperry series in detail. The ball-cage and cam circuit that solves the problem is constructed from first principles. By deriving the complete sight equations, consisting of those for the kinematic deflection components, blueprint ballistics, and motion of the optical system, the causes of Class B errors are segregated into compartments such as neglect of curvature, gun roll, feedback, and interchange of ballistics.\nSection 5.5 deals with single-gyroscopic eddy current sights. This section explains how a gyro can measure kinematic deflection and provides schematic details of the electromagnetic system, optical system, and electric circuits. The variation in the sight's parameter and the phenomenon of optical dip are discussed. The component causes of Class B errors (calibration, optical dip, electromagnetic dip, etc.) are reviewed in detail.\n\nSection 5.6 notes that only gyroscopic principle sights can be used in fighters. The calibration of time of flight is more effective for a fighter's sight since there is only one direction of fire and ballistics can be neglected. This calibration is given. The section briefly considers the problem of fighter versus fighter (curved target path).\nand the reliability of kinematic lead computation when the fighter\u2019s guns are not pointed in the direction of flight.\n\nSection 5.7 supplies brief descriptions of the K-8 electrical sight and various German gyroscopic sights.\n\nCONFIDENTIAL\n\nChapter 6\nCENTRAL STATION FIRE CONTROL\n\n6.1 INTRODUCTION\n6.1.1 Advantages and Disadvantages of Remote Control\n\nCentral station fire control (CFC) is an armament system in which a gunner located at a sighting station in one part of an aircraft can aim and fire guns located in a turret at some other part of that aircraft. For example, on the B-29 airplane, there are two 2 X 0.50 upper turrets, two 2 X 0.50 lower turrets, and one 2 X 0.50, 1 X 20-mm tail turret. There are also five sighting stations: a pedestal station in the nose, a ringsight at middle top, two pedestal side-blister stations, and a tail station.\nThe pedestal mount station. The control of the turrets by the sighting stations is flexible \u2014 an important feature of remote gunnery. The two upper turrets are controlled by the upper station. The forward lower turret is under primary nose control and secondary blister control. The rear lower turret is also controlled by the two blisters. The tail turret is under primary tail control and secondary blister control. Primary control must be released before secondary control is operative.\n\nRemote control has many advantages. Among these may be listed: (1) guns and gunners may be located in the most effective positions for coverage and for vision, (2) loss of a station does not mean loss of the guns, (3) the turrets may be smaller and so afford less drag on the airplane, (4) pressurization of the airplane is simplified, and (5) the firing of the guns does not disturb the tracking.\nAmong the advantages and disadvantages of the system are: (1) an additional correction for parallax due to the material displacement of sight line and gun line must be made, (2) torsion and bending of the aircraft structure may drastically impair harmonization, (3) relatively heavy and complex follow-up systems of control are required, and (4) the delays of the follow-up systems may be serious.\n\nElements of Central Fire Control System:\n\n(6.1.2)\nThe basic elements of the central station fire control system are: a sighting station, a follow-up system, a turret moved by the follow-up as dictated by the sighting station, and a computer connecting the sighting station and turret. The computer causes the gun line to differ from the sight line by an angle just large enough to compensate for the relative motion of the target during the bullet's flight time, for the bullet's divergence from a straight line due to ballistic effects, and for parallax.\n\nThe computer receives continuous inputs of present range and lateral and vertical tracking rates from the gunner. By keeping the target spanned, the gunner sets a potentiometer properly, and by keeping the target centered, causes two gyroscopes to set up precessional torques. The computer also receives inputs from the range finder and the direction indicator.\nThe azimuth and elevation of the sight line are automatically set by synchs at the sighting station. The receiver obtains altitude, temperature, and airspeed from a hand set operated by the navigator. Parallax and the basic ballistics of the ammunition used are built into the computer.\n\nNeglecting follow-up equipment, the B-29 armament installation weighs 3,316 lb. An installation consisting of two Martin upper turrets, two Sperry ball turrets, and one Consolidated tail turret, plus five K-8 sights would weigh more.\n\nChapter 6.1.3: Basic Theory of 2CH Computer\n\nIn this chapter, the nature of the type 2CH computer used in this system will be studied in detail. The treatment is theoretical and schematic rather than mechanical. The important question of the overall performance of the gunner-target system is not discussed in this chapter.\nThis is properly a matter of elaborate experimentation, both in the air and in the laboratory. Considerations in the large, such as the design of formations for maximum and most efficient firepower coverage of the attack region around the group, and the support fire problem, are not considered.\n\n6.2 Basic Theory\n6.2.1 Trajectory Equations in Vector Form\n\nThe Type 2CH computer (General Electric) assumes that the target moves in a straight line at constant speed during the projectile's flight time. It is necessary to recast the deflection theory of Chapter 2 for this situation to explain the computer's functioning adequately. Vector algebra methods are most appropriate.\n\nFigure 1 shows the Siacci range (distance covered in the air mass), R, and the corresponding Siacci coordinates, P (measured along the line of departure).\nThe equation for calculating the points of intersection of a projectile's trajectory with a plane above it is given by the figure. The unit vectors involved are labeled as DQ (measured in a vertical plane), and the subscripts 1 for the distance between the gun and projectile (D1), and D0 for the distance between the observer-gunner and projectile (D0).\n\nThe fundamental equation for designing the computer can be derived from the figure using evident triangular relations. Here, tf is the time of flight, and u0 is the speed of departure (PQ). These are purely trajectory considerations, irrespective of the presence or absence of a target.\n\nThe following discusses angular ballistic and parallax corrections. To clarify, introduce two perpendicular vectors, B and P*, with respect to the muzzle velocity v0.\nThe ballistic vector B is directed from the bore axis to the projectile, including trail and gravity drop. It subtends at the gun the total ballistic deflection angle Ab (neglecting minor effects such as windage jump and drift). The parallax vector P* is obtained as the perpendicular from the sighting station to the bore axis. The distance from the gun along the bore axis to the point of origin of B is CiV0, where C is to be determined. Similarly, the distance from the gun along the bore axis to the point of termination of P* is c2v0. Therefore, if the vector (ci - C2)v0 is moved parallel to itself to emanate from the sighting station, then P* can be moved to join (ci - C2)v0 to B. This is a second interpretation of P* under which it subtends at the gun the parallax angle Ap. The angles:\n\n(ci - C)v0 \u2192 [B] P*\n| |\n| | Ap\n| |\n| |\n| CiV0 |\n| | Ab\n| |\n| |\n| | c2v0\n\n(Note: The arrow [\u2192] represents the direction of the vectors.)\nA and Ap are called the angular ballistic correction and the angular parallax correction respectively. The next task is to analyze the structure of B and P*. Componentwise, to determine the four quantities Ci, C2, c3, c4, two conditions are obtained by taking the dot product of each of the preceding two relations with v0. The third and fourth conditions arise if B and P* are substituted in equation (2) and the resulting coefficients compared with those of equation (1). One finds that:\n\nAv Vo\nVo VoUq\nUo\n\nwhere \u03b8g is the angle between the bore axis and platform velocity, \u03b8a is the angle between the vector A and the bore axis, and Z is the zenith angle (the angle between the vertical Q and the bore axis).\n\nIt is convenient for the sequel to reduce equation (2) to the scale of v0i (a unit vector in the direction of v0).\nThe form of equation (2) divided by (ci - 02)^0 yields:\n\n(p = tan Ap, b = tan A*)\n\nWe shall not write out m, p, and b explicitly.\n\nThe form (3) is adopted since p = tan Ap and b = tan A*. Therefore, p and b are excellent estimates of the two angular corrections.\n\n6.2.3 Kinematic Deflection\n\nTo obtain the basic equations for mechanization, we introduce the target and its track. Since corrections have been dismissed above, only the kinematic deflection needs to be derived. If vT is the target velocity and r is the present range (the range at the instant of fire), then:\n\nr = rri = hi + rco x ri\n\nThis is an exact expansion since the relative target path is straight and the target speed is constant. Here, r = rri and r = hi + rco x ri, where c0 is the angular tracking velocity. (This is the radial component of the deflection)\nrate rti plus the normal rate rco x ri, whose magnitude is rco \u2022 1 \u2022 sin (tt/2). Using this value for r, we find:\n\nr + rtf and r + rtf\n\nBut co x 1*1 is perpendicular to ri, and also to co since co is perpendicular to ri. Hence, A * is to be interpreted as the kinematic deflection. Finally, since ri x (co x n) = to, the tracking velocity is given by ntf.\n\n6.2.4 Time of Flight\n\nThe time of flight tf is, strictly, a function of D<?, vG, Vqi, and the relative ballistic air density p. But vg and p can be regarded as parameters, i.e., inputs set in before an attack, and present range r is to be used instead of future range. Hence, we write:\n\nSince the vector r0i is an argument, it is clear that the direction of fire is to be taken into account by this system.\n\n6.3 Turret and Sighting Station\n\n6.3.1 Follow-up System\nThe follow-up mechanism consists of a follow-up system, a computing unit, and auxiliary circuits. The auxiliary circuits include starting circuits for rotating machinery, limit-switch circuits, firing circuits, control-transfer circuits, and so on. The last are rapidly dismissed as being of engineering interest only. The follow-up system merits slightly greater detail as it indicates that remote gunnery does not use the disturbed reticle principle of Chapter 5. If the computer is removed, the operator manually adjusts a light counter-balanced sight head. The sole job of the follow-up system is to make the gun direction v0i identical to the sight line direction ri.\n\nConfidential\nTYPE 2CH Computer\nThe disturbed reticle system, controlled by the operator, determines v0i, which in turn dictates ri. The concept of remote gunnery does not preclude the use of the disturbed reticle system.\n\nThe follow-up system is schematized in Figure 2. The selsyn generator measures sight position by the position of its rotor and transmits this position to the selsyn control transformer. This transformer measures the difference between gun and sight positions. If a difference exists, the error is sent to a vacuum-tube amplifier which builds up the signal sufficiently to control the output of a d-c amplidyne generator. The output of this amplidyne generator controls the d-c turret motor, driving the guns into parallelism with the sight and causing the error signal to vanish.\n\nFigure 2. Follow-up system schematic. (Courtesy of General Electric Company.)\nThe advantages of the amplidyne generator are that the output voltage reaches its final value rapidly, and a small field current of a few milliamperes is required to produce full voltage. The dynamotor is a motor-generator set that takes dc and supplies ac to the synchros and servoamplifier. In the actual system, two sets of synchros are used since a synchro can be in error by 0.5\u00b0. The one-speed synchros make one revolution for each revolution of the turret and correct gross errors. The 31-speed synchros make 31 revolutions for each revolution of the turret and refine the work of the one-speed synchro to yield an error only Vsi of that of the one-speed unit.\n\nThe problem for the computer is the mechanization of:\n\n6.4 TYPE 2CH COMPUTER\n6.4.1 The Problem for the Computer\nThe problem put to the computer is the mechanization of [unknown symbol or abbreviation]\nThe 2CH computer operates by using the gyroscopic properties, vector-mechanical constructions, and a shifting mechanism between electrical and mechanical signals to effectively solve vector equations, not calculating formulas. The fundamental difference between the 2CH computer and lead computing sights discussed in Chapter 5 is that the 2CH is a continuously correcting system. The answer at hand is continuously compared with the required answer based on inputs, and corrective steps are taken to adjust the gun position. The net result of the computer's operation in conjunction with the follow-up system is to displace the guns from the line of sight by a total lead angle A, accounting for kinematic deflection, ballistics, and parallax.\nmatic correction pays attention to the true rate of rotation of the gun-target line, as gyroscopes are used \u2013 that is, the rates are not relative to the gun mount. Ballistics, however, depend on the orientation of the guns with respect to the gun mount.\n\n6.4.2 Rapid Review of Method\nTo emphasize the nature of the device as a continuous comparator, one can start with the total correction motors when discussing Figure 3. Suppose the rotor has a certain angular displacement corresponding to some assumed total lead A. Suppose this deflection is not the correct total lead. The output of the correction motor goes to differential synchros, which are also supplied with the azimuth and elevation of the sight line ri through signals from the sighting station synchros. The electrical displacement of the rotors of the differential synchros\nThe sum of sight position and total lead corresponds to the position of the guns, which are adjusted accordingly by the follow-up system. Confidential Central Station Fire Control Altitude Temperature Altitude VG (IAS) Temperature\n\nFigure 3. Box schematic, type 2CH computer. The differential selsyn signals go to input units that translate electrical values into mechanical values and send on the present gun position v0i to parallel and ballistic units. These units determine the corrections p and b and transfer them to a pantograph, which performs a vector addition of these two quantities. Thus, one input to the potentiometer resolver is p + b.\n\nThe other input to the resolver receives the output of the correction motors and gun position from the input unit. The converter combines gun position and total lead.\nThe unit produces the range vector ri by mechanical construction. The potentiometer resolver eliminates D0i between the equations and produces the assumed kinematic deflection A corresponding to the assumed total lead. It was necessary to obtain k as this value must be compared with the rate-time value from the time circuits and gyros.\n\nThe time-of-flight circuit, with present range and certain parameters as input, has a total electric resistance ntf. Consequently, the current flowing in the circuit is 1 /ntf * A, and it is this current that goes to the gyroscope unit. In that unit, the current produces a torque through electromagnets which opposes the precessional torque on the gyro generated by the tracking. The total torque corresponds to the difference\nThe interaction between the encoder and gyro unit depends on the sign of the difference. Contacts in the gyro unit are made, and one or the other of two relays trips. The relays control the total correction motors, which then back up or go ahead to give an adjusted value of A. The cycle is repeated, or, rather, everything is happening simultaneously.\n\nConfidential\nType 2CH Computer\n\nThe preceding presentation used vectors as inputs and outputs, except for the parallax and ballistic units and the pantograph. The correction motors have azimuth and elevation components as output since these are to be used to position the turret in azimuth and elevation. Again, the angular rates measured by the two gyros at a sighting station are vertical and lateral rates. That is, if the sight head is elevated, the gyros measure the vertical angular rate, and if it is deflected laterally, the gyros measure the lateral angular rate.\nThe lateral gyro measures the rate of rotation about an axis lying in a vertical plane and perpendicular to the line of sight. The vertical gyro measures the rate of rotation about an axis lying in the horizontal plane and perpendicular to the line of sight. The outputs of the potentiometer resolver are in reality the lateral and vertical components of kinematic deflection.\n\n6.4.3 Behavior of Specific Units\nThis subsection will discuss in more detail the internal nature of the component parts of the 2CH computer. Since the approach will emphasize the underlying theory, it is complementary to manuals of engineering detail.\n\nParallax Unit\nThis is a component in which there is effectively constructed in miniature a vector replica of some part of the environment. In forming such a replica, there is no need for duplicating orientation \u2014 it is not necessary.\nChoose the vertical direction in the computer to represent gun direction v0i. The lateral and vertical gun rotation axes determine a horizontal plane in the computer as a result. Only the projection of vector A (giving the distance between sighting station and gun emplacement) on the fuselage's longitudinal axis will be used. This length is a fixed physical distance along a lever in the unit and is factory set. To obtain p, first, get the projection of A on the horizontal plane of the parallax unit and then modify this length according to the range. Schematically, these steps are accomplished in Figure 4. The input unit translates electric signals into gear rotations to position A as shown. The projection on the horizontal plane is pre-calculated.\nThe scaled length of a line segment from the sighting station, dropped on the bore axis (P* in Figure 1), is reflected by sliding rods as corresponding motion of point a (Figure 4). If the fulcrum on a vertical lever (waggle-stick) is moved up and down as a function of range, the point b will be displaced by the angular correction p.\n\nBallistic Unit:\nThis component is very similar to the parallax unit. It differs in that the length B, which plays the role of A, must vary with altitude, IAS, and temperature. This is accomplished by gears actuated by the navigator\u2019s handset. Although the mechanization differs, the result in the plane of the pantograph is a motion of one end of another waggle-stick which represents b and lies in the plane of gun lateral and vertical axes, just as does p.\n\nPantograph.\nSince p and b are now in the same plane, the pantograph can add them vectorially very readily. The device is a jointed framework of metal strips, schematized in Figure 5. The parallax waggle-stick drives F, and the ballistic waggle-stick drives A. Under a displacement from the original position (A0, F0, Co) of amounts A0A = -b and F0F = p, if is readily found from the geometry of the frame that CqC =\n\nConceptually, this assemblage of gears and shafts has as inputs the azimuth and elevation components Aa and AE of the assumed total lead A and the gun elevation Eg. (Actually, the inputs are three gear rotations of amounts 2AE - 2Aa - Eg, Eg + 2Aa, and Eg respectively.) As in the preceding units, the vertical direction in the computer is selected to\nThe gun direction represents v0i in the computer's horizontal plane. In the computer, this spatial plane is equivalent to the plane determined by the gun's lateral and vertical axes. This system of three directions - gun direction and the two axes - is fixed in the unit. The axis converter constructs the corresponding system of the sight line, i.e., sight direction ri, and sight lateral and vertical axes, by performing two rotations of the physical length corresponding to the vertical gun direction. In space, rotation of a line in azimuth is represented by a vector wi directed vertically upward. Rotation in elevation is represented by a vector taE lying in the plane.\nThe horizontal plane is perpendicular to the vertical plane passing through the line in question. Lateral rotation is represented by a vector wl lying in the vertical plane through the line and perpendicular to it. Vertical rotation is identical to elevation rotation, so COv = 03E. The angle between col and cc is the elevation E of the rotating line. Therefore, \u03b8l = \u03b1 cos E. Figure 6 illustrates the situation. (co = \u03b1a + \u03b1E is the total angular velocity, and when the decomposition co = co' + Wl + W(?) is made, \u03b8G is an additional and necessary angular velocity \u2013 the gun roll.) It follows from these rate relations that, correct to first order terms, the sight position can be obtained from the gun position by a vertical rotation of amount \u2013AE followed by a horizontal rotation of amount \u03b1a cos E.\nThe lateral rotation amount Aa is cosine-related to Eg. This is achieved through gears in the axis converter. A representation of this appears as a mechanical displacement in a horizontal plane in the potentiometer resolver.\n\nPotentiometer Resolver (37)\n\nRecall that the resolver's function is to accept the sight direction and the sum of parallax and ballistic corrections as two vector mechanical inputs, and to output voltages Akv and Akl which are the vertical and lateral components of the assumed kinematic deflection. Within the resolver is a vertical direction representing gun direction v0i. The pantograph plane is perpendicular to this vertical direction, and the output of the pantograph gives the displacement C0C = p + b. Therefore, in the resolver, OC = OC0 + CoC (V01 + p + b) is constructed according to the equation.\nThe device has physically produced the vector radii. Another part of the resolver is rigidly affixed to the axis converter. In Figure 7, this part appears as the Pantograph Plane. Figure 7. Potentiometer resolver, schematic.\n\nAt the point S', the resolver has a plane perpendicular to OS'. A waggle-stick from the point C in the pantograph plane is maintained so that CC is parallel to OS'. The vector equation OC' = OS' + S'C' is translated as:\n\nThe mechanism actually reproduces the geometrical constraints of the situation and is not guilty of approximations.\n\nCONFIDENTIAL\nTYPE 2CH COMPUTER\n\nBy this frontal approach to the problem, i.e., a construction in miniature of the vector situation in space, the kinematic deflection has been produced. It remains to obtain the lateral and vertical components of the kinematic deflection relative to the\nIn the resolver plane, which is perpendicular to the computer's production of the sight line, S'H and S'M are such components. A voltage equal in magnitude to A kL can be obtained by means of a variable potentiometer whose sliding contact M moves along the line S'M in the lateral direction. The same remarks apply to Akv.\n\nTime-of-Flight Circuits\n\nThe circuit is a combination of fixed and variable resistances such that the total resistance approximates ntf. The schematic is shown in Figure 8.\n\nFigure 8. Time-of-flight circuit, schematic.\n\nThe variable range resistance, controlled by the gunner who keeps the target framed, supplies a continuous estimate of present range. The navigator's hand set puts in altitude, indicated airspeed, and temperature. The ballistic unit supplies the component of own velocity.\nThe good value for velocity of departure is at hand in the direction of fire. All appropriate variables are present to obtain an excellent value for time of flight. However, it is a question of how well a simple circuit can approximate a complicated function in one direction, and what calibrations can be made to allow for curved courses in another. For straight tracks, the results with respect to this second direction should be excellent since ntf is exact by equation (4).\n\nSection 4.4 The Gyroscope Units\n\nThe gyroscope units 36 will be discussed in somewhat more detail than the preceding components. To measure lateral and vertical tracking rates, there are two gyroscopes at each sighting station. Each gyroscope consists of a flywheel and the necessary sensors.\nA small, high-speed electric motor runs on a constant speed of 27 volts DC at 10,000 revolutions per minute. The lateral rate unit is depicted in Figure 9. The housing axis is always parallel to Figure 9. The gyroscope is a type 2CH computer (Courtesy of General Electric Company). The line of sight and the axis of the pins that support the gyro motor frame remain horizontal. The gyro spin axis may slightly depart from parallelism with the sight line, but this departure is only in elevation and is limited by adjustable stops. Consequently, it will not be inferred that the gyro axis displacement measures deflection as it did in Figure 6. Under rotation about the lateral axis (this is wL) in Figure 6, the gyro exerts a precessional torque about an axis perpendicular to both the spin axis and the axis of the applied tracking torque.\nThe axis of the supporting pins. But bucking this precessional torque is an electromagnetic coupling due to the displacement of permanent magnets (which are fixed to the gyro frame) from the center of an erecting coil fixed to the housing. The current in the erecting coil is A kL/ntf, and the torque produced is proportional to this current. If this torque is not as strong as that due to precession, the gyro will precess slightly until an electric contact is met. For this case, the assumed AkL was too small. Hence, the contact causes a relay to trip which permits a current to flow in the armature of the total correction motor in a direction which will increase A kL. This will strengthen the erecting coil torque and pull the gyro away from the contact. If the erecting coil torque is not strong enough.\n\nConfidential\nCentral Station Fire Control.\nhad  been  too  strong  initially  the  process  would  have \nreversed.  In  general,  the  gyro  will  hunt  or  successively \nunder-and-over  correct  by  going  back  and  forth  be\u00ac \ntween  the  contacts.  Back  lash  is  deliberately  intro\u00ac \nduced  between  the  total  correction  motor  and  its \noutput  wheel  to  minimize  hunting.  Only  under  per\u00ac \nfect  and  uniform  conditions  will  the  gyro  ride  with \nits  spin  axis  identical  with  the  housing  axis. \nIt  will  be  noticed  that  there  is  no  smoothing  in  the \nprecise  sense  of  that  given  under  \u201cWeighted  Averages\u201d \nof  Section  5.3.4.  However,  the  gyro  housing  is  at\u00ac \ntached  to  the  sight  by  a  form  of  elastic  coupling \ndamped  by  friction.  The  basic  purpose  is  to  reduce \nvibration  but  possibly  a  certain  amount  of  smooth\u00ac \ning  is  also  introduced  by  such  a  support. \nThe  gyroscope  system  introduces  certain  errors  in \nthe  problem  which  can  be  understood  by  writing  out \nThe dynamical equations of the system. Let Mg and MP denote, respectively, the vector angular momenta of gyroscope and gyro motor frame. Let TG be the moment of all forces exerted by the gyroscope on the frame (this includes reaction and bearing torques of the motor). And let TH be the moment of all forces exerted by the gyro housing on the gyro motor frame (this includes the erecting coil torque, frictional torques, pivot reactions, and reactions when the stops are closed). The equation for the gyro motor frame is:\n\n\u2211Mg = \u2211TG\n\nAnd that for the gyro is:\n\ndMP/dt = dMG/dt\n\nTherefore, in a fixed coordinate system, we have:\n\n\u2211Mg = \u2211TG\n\nAnd with respect to a rotating coordinate system determined by the pin axis, the spin axis, and an axis perpendicular to these, and with d/dt now measuring rates of change with respect to this rotating system, a theorem from mechanics yields:\n\ndMP/dt = dMG/dt\nWith 12 being the angular velocity of the (p, s, q) coordinate system, components in these three directions will be denoted by p, s, and q respectively. Moments of inertia, the p component of this equation is:\n\niGsnqn op = Thp, (8)\n\nWhere 120 is gyro speed with respect to its frame. The purpose of the gyro unit can now be phrased symbolically. It is designed to approximate 12q (which is the tracking rate) by use of the equation:\n\nThp = THp + 120qs\n\nIn other words, the device neglects the first two terms of the complete equation (8). Consider the second term on the left of equation (8) and assume that the expression in parentheses is of the same order of magnitude as TGs. The angular rate 12s is precisely the equivalent of the gun-roll rate.\nof Figure 6, i.e., 12s = coa sin E, where A and E are the azimuth and elevation of the spin axis (which diverges very slightly from the sight axis). But coa cannot exceed v/sec E/r, where v is the velocity of the target relative to the bomber and r is the range. Hence, 12s is large only if E is close to 90\u00b0 and/or r is radians. The second term may be safely neglected. However, this does indicate that certain restrictions on high elevation fire are inherent in the system.\n\nTurning to the first term on the left of equation (8), we are concerned with the angular acceleration dSlp/dt about the pin axis. The lead given by equation (8) is Tnp tf I Gs 2q Igp + Ifp dSlp IgsV 0 ~di f\u2019, when the second term is neglected. Hence, angular acceleration introduces a spurious lead (the second term on the right of the preceding equation). For\nThe tracking of an accelerated target hardly exceeds 8 milliradians. However, under normal imperfect tracking, the operator may make large oscillatory errors in angular position. The extent to which the computer filters acceleration errors is not definitively known. The procedure is to conduct a laboratory bench test.\n\n6.4.5 Total Correction Motors\nThe total correction motors make lead corrections at a constant rate of about 40 milliradians per second. If the motor runs continuously in the same direction for 1.5 seconds, a higher speed of approximately 80 milliradians per second becomes operative. To illustrate the effect of the time delay caused by this motor:\n\nType 2CH Computer\nTime in seconds\nFigure 10. Typical frontal attack.\n[Confidential]\nRange in yards\nCentral Station Fire Control\n\n[Confidential]\nAngles and angular rates in milrads and milrads per second\n\nThe total correction motors make lead corrections at a constant rate of approximately 40 milliradians per second. If the motor runs continuously in the same direction for 1.5 seconds, a higher speed of around 80 milliradians per second becomes operative. To demonstrate the impact of the time delay caused by this motor:\n\nType 2CH Computer\nTime in seconds\nIf the gun has a zero initial lead and needs to slew to a target requiring a lead of 100 milliradians in one-half second, then: at t = 0, A = -20 (sight on, tracking started); at t = 0.5, A = -20 (backlash). A system of variable speeds is needed, where a high speed is provided only when the required lead correction is large. This can be accomplished by using the variable pressure of the gyroscope on the stops to introduce variable resistance into the motor circuit. Dynamic braking may also be used. However, increasing the motor speed decreases the time delay but sacrifices smoothness and may result in excessive hunting.\n\nTo illustrate the need for high speed in getting on target.\nFor a quickly moving and low-speed target, sufficient great curves for a typical frontal attack are shown in Figure 10. In addition to the variable speed proposal noted above, various other methods have been suggested. Typical of these are (1) motors run at high speed except when the trigger is pressed, (2) the shift from high to low speed when the trigger is depressed is delayed for, say, one second. It is probably worthwhile to make a rough paper assessment of expected results in assumed tactical situations under such proposals. The whole slewing operation should also receive careful attention.\n\nFor reference, the motor equation may be quoted:\n\nFor a DC motor with separately excited or permanent field,\n\nE = a * I + b * \u03c6\n\nwhere a and b are constants, R is the total resistance.\nFor the armature, brushes, and commutators; E is the applied voltage; and I(w) is the current required to run the motor at the speed w, if w were constant. For frictional loading, the following equations are adequate:\n\nis an adequate form, where 0 depends on load, bearing friction, and armature hysteresis, and hw depends on the armature drag due to eddy currents and on viscous friction and is nearly independent of the load.\n\n6.4.6 Range Follow-up Motor\n\nAnother inherent weakness in this computer system is that the range follow-up motor is frequently too slow. Three ranges must be considered: (1) the true range, (2) the range introduced by the potentiometer at the sighting station, and (3) the range set into the computer by the range follow-up motor.\n\nIn its steady state, the motor alters computer range r (in yards) according to:\n\nr = 91k\n\nwhere k is the number of revolutions per minute of the motor.\nThe motor's output gear. The implications of this behavior can be understood by referring to Figure 10. Suppose at t = 0 that the true range r0 = 1,100 yd is in both sight and in the computer. The operator, behaving perfectly, is changing range at an almost constant rate of 320 yd per sec. The maximum rate of change of computer range, however, occurs for k = 250, which is the maximum motor speed. Hence, below 942 yd range, the motor cannot run fast enough to keep up. The gunner could suddenly reduce range to 250 yd, and computer results would be the same as under perfect ranging.\n\n6.4.7 Calibration\nIn relation to the above remarks on the total correction motors and the range follow-up motor, the effect on calibration of the time of flight needs to be noted. In any machine, whenever defects, unavoidably occur.\nable or not, call for extensive redesign or installation of new units, one attempts to save time and equipment and still achieve respectable overall results by giving artificial values to adjustable parts of the existing equipment. For example, to account for the delay in the solution time on nose attacks, the time of flight is multiplied by 1.07 since leads increase on nose attacks. But calibration usually has its price. In this case, performance against attacks from the rear will deteriorate since the factor should be less than unity in that hemisphere.\n\nCONFIDENTIAL\nSUMMARY\n\n6.5 SUMMARY\nSection 6.1 limits the discussion of this chapter to a theoretical study of central station fire control itself. The wider questions of formations, support fire, and experimental results are not considered.\n\nSection 6.2 derives four basic equations which the\n\n(Note: The text appears to be complete and does not contain any meaningless or unreadable content, or any introductions, notes, logistics information, publication information, or other content added by modern editors that obviously do not belong to the original text. No translation is required as the text is in modern English. No OCR errors were detected.)\nThe computer functions to mechanize. Notably, the first three are vector equations, and in large part, the computer under consideration is a vector mechanism. Section 6.3 discusses the nature of a follow-up system where guns remote from an operator are made to follow his sight line position. The computer, which introduces gun displacement from the sight line due to target motion, ballistics, and parallax, is disconnected. Section 6.4 initially outlines, in schematic terms, the method by which the computer solves the total deflection problem. Subsequently, the behavior of the individual components is studied in greater detail. Considerable attention is paid to the behavior of the gyroscope units since angular tracking accelerations can lead to significant errors through this system. Finally, the time delay in response of the total correlation system is examined.\nrection  motors,  and  the  inadequate  range  change  rate \nin  the  range  follow-up  motor  are  considered. \nCONFIDENTIAL \nChapter  7 \nANALYTICAL  ASPECTS  OF  AIRBORNE  EXPERIMENTAL  PROGRAMS \n7.1  INTRODUCTION \n7.1.1  Role  of  Airborne  Test \nPrograms \nThe  closed  feedback  loop  formed  by  the  successive \nelements  \u2014  target,  gunner,  controls,  computer,  guns, \nbullet,  target  \u2014  is  a  complicated  servomechanical \nsystem.  When  a  system  is  too  complicated  to  permit \nan  exact  theoretical  analysis  of  behavior,  the  com\u00ac \nmon  technique  is  to  supply  certain  inputs  and  com\u00ac \npare  the  actual  output  with  a  perfect  output.  This \nis  the  philosophy  of  airborne  assessment  tests  of  fire \ncontrol  equipment.  If  it  is  a  question  of  choice  be\u00ac \ntween  two  fire  control  systems,  the  procedure  is \ncertainly  logical,  provided  a  proper  simulation  of  the \nconditions  under  which  the  systems  must  perform  is \nmade, and provided that the experimental technique is considerably more accurate than the mechanism under test. If it is a question of prediction of overall performance in combat of a particular system, the attitude may still be defended, although not nearly as strongly as in the competition situation. But if it is a question of decomposing overall errors into componential causes, so that design improvements may be made, such assessment has minimum value, unless it is very complicated and detailed.\n\nTo meet, in part, this last question, the errors made by the system under perfect operation and construction have been studied earlier in this account. Manufacturing variation from instrument to instrument and other variations caused by non-perfect construction and functioning can be studied by laboratory bench tests in which factors such as turn.\nTable speeds and temperature can be carefully controlled. More elaborate laboratory machines may use perfectly known inputs to a human gunner through cammed target courses and controlled gun platform motion, measuring in complete detail the behavior of each component of the system. This method is most fruitful in arriving at design changes.\n\nOne cannot expect to add up compositional errors deduced by the methods of the preceding paragraph to obtain the total error determined by airborne tests. The reason is twofold. In the first place, the complete system is in no sense linear. It has numerous feedbacks, lags, and unexpected gunner reactions.\n\nIn the second place, the closed loop described initially includes complex interactions between various components, making it difficult to predict the system's behavior solely based on the sum of its individual parts.\nThe main variables in fire control are: target behavior (a course cannot be reproduced exactly in the air), gunner behavior (intra-gunner variations may be as large as inter-gunner variations), gun mount motion (which varies with the aircraft, the weather, and the pilot, particularly under avoiding action), and instrumental variation (sights, guns, turrets as affected by wear and calibration. But it is concluded that field tests, laboratory tests, and theoretical analysis all have an important place in fire control. The important point is that they be coordinated partners in this field. The balancing and coordination of their roles is the duty of vigorous technical administration.\n\n7.1.2 Classification of Errors by Cause and Statistics\n\nThe errors of the complete system may be classified by cause and statistics.\n1. Class A errors are caused by play in systematically. Inter- and intra-instrumental variations are due to permitted tolerances and additional play introduced by loose action or worn parts. These are errors representing the instrument's failure to operate as designed.\n\n2. Class B errors are the theoretical errors of the mechanism caused by design assumptions and compromises.\n\n3. Operational errors occur due to tracking and ranging errors, harmonization errors, and faulty presetting of flight data.\n\n4. Dispersive errors are caused by mount and gun vibration, variation in ballistics and muzzle velocity from round to round, play in a turret, and the difficulty of holding a point of aim. Bullets of a burst spray out in a cone.\nThe pattern on a section of this cone is usually elliptical. The orientation of this ellipse depends on the direction of fire and other factors. This assumption is strengthened by supposing that the pattern is described by a circular Gaussian distribution around a mean point of impact. It should be noted that although the pattern tends to conform to normality, the locations of individual shots are not independent. This is serial correlation and is most important in connection with very short bursts. Roughly, if one shot has a large error of one sign, then the next round is likely to have a large error of the same sign. This is related to aim wander. As the gunner tries to hold on to a target, his aim traces a snakelike path.\nImagine the small, pure dispersion being carried along this path as a probability cloud. We attempt to make a distinction between the dispersive serial correlation arising when a gunner tries to hold on to a fixed target and the much more important tracking serial correlation. The point has not been clarified completely from the theoretical point of view. On the whole, we shall attempt to avoid it by using more naive statistical ideas.\n\nAnother classification of system errors can be made, which emphasizes their statistical nature: 1. Fluctuating errors. These errors arise from dispersion, tracking errors in angle (including any amplification of the system), and Class A errors. 2. Quasi-steady errors. These give a sensibly constant bias over one burst but vary from burst to burst. Typically, they are attributed to range input.\nErrors, harmonization errors, and faulty setting of flight data. Three types of errors: steady errors, which yield a fixed bias in a specific situation, such as a point on an assigned pursuit curve, are Class B errors.\n\n7.1.3 Nature of Modern Airborne Tests\n\nEarly assessment tests were made by firing against a flag target towed past the gun mount on a parallel course at low relative speed and close range. The number of hits was counted. This procedure can be defended only on the basis that the installation was airborne and it did fire. An extrapolation of performance on such trivial courses to expected performance against an actual target course is unjustified. Furthermore, the bullets that missed are lost to analysis, since their position is not known. Thus, the method is statistically inefficient.\n\nCurrent methods for airborne tests are based on more advanced techniques.\nThe dry run principle involves simulating combat conditions as closely as possible by having a fighter plane attack a bomber without firing actual bullets. Four types of data are obtained through various recording instruments, usually airborne by the participating aircraft: (1) the range and bearing of the target, (2) the tracking and ranging of the sight under test, (3) the actual gun pointing, and (4) the attitude, speed, and altitude of the gun-mounting aircraft. Sometimes, it is desirable to obtain all or some of these data in synchronization for the target aircraft. To these two requirements - combat simulation and precise instrumentation - a third must be added: for a given type of tactical situation, such as a rear quarter attack, sufficient replications must be made to provide adequate statistics.\nStatistical voice to variables which determine the system's output but which cannot be controlled. This implies that the experiment must be designed carefully, usually by the Latin-square technique. In general, a minimum of 15 replications is needed for each system under each tactical situation.\n\nWe may now turn to some details of assessment programs. The three major phases are: (1) instrumentation, (2) interpretation and reduction of data, and (3) measurement of effectiveness. A rapid survey is contemplated.\n\nThe lack of inhibition caused by gunfire is a serious flaw of the method which cannot be answered by the use of fragile bullets. Full-scale combat conditions could not then be used. Simulating recoil mechanisms may be much more to the point.\n\nAnalytical aspects of airborne experimental programs (CONFIDENTIAL)\n7.2.1 Bearing and Range of Target and Attitude of Gun-Mounting Aircraft\n\nTo determine the correct deflection at each instant, i.e., perfect output, it is necessary to know the target's space path relative to the gun mount as a function of time. This is normally accomplished by determining the range and bearing of the target with respect to the gun mount at each instant.\n\nThree 35-mm cameras with 1-in. focal length lenses, when ganged and installed in a waist window of a heavy bomber, cover a field of approximately 120\u00b0 in azimuth and 50\u00b0 in elevation. The alignment is determined by photography on the ground. The lenses must be calibrated so that the magnification is known under projection. The bearing angles relative to this installation can be determined.\nThrough projection on a suitably gridded screen, there are other methods of determining bearing. The motion in azimuth and elevation of a turret mounting a single camera and tracking the target can be obtained from the gear trains, either through gears or synchros. Dial readings are photographed. The direction of the center of the picture is known, and the bearing of the displaced target image is readily determined. It would also be possible to use ultra-narrow-beam radar, which can provide angles with a probable error of 1 or 2 milliradians. Range is usually determined by measurements of the image on the film supplied by a camera of 2-inch focal length (to gain magnification at the expense of field size) clamped to the gun. This determination is usually the least accurate step in the entire scheme due to wingtip blurring and foreshortening.\nThe use of band painted wingtips, landing lights, and infrared lamps has been suggested to determine the relative bearings to a direction in an air mass coordinate system. This requires measuring the yaw, pitch, and roll of the airplane. This is accomplished using a pair of gimbaled gyros that maintain the direction of their spin axes in space as the aircraft rocks about the mounting. The resulting displacements can be detected mechanically or by synchros. Yaw, pitch, and roll can also be calculated after measuring the tilt of the horizon and the position of a sunspot on some plate fixed in the aircraft.\n\nAstrometric methods may also be used to determine the space paths of the two aircraft. Two vertical cameras of 12-inch focal length are mounted on the ground at opposite ends of a suitable basis.\nThe aircraft photographed by these cameras carries possibly four brilliant flash units. Coincident with each flash, a radio signal is sent to the ground and recorded by a chronograph with an accuracy of 1/1000 sec. Standard precision methods are applied to measure the image positions on the two plates. With aircraft at 10,000 ft, the overall probable error of position is less than 1 ft, and the probable error in velocity is \u00b134 fps. The disadvantages of this procedure are found in the restricted sky area available to the maneuvering aircraft (this could presumably be met by employing a lattice of cameras) and in the complexity of the data reduction. Nevertheless, the flexibility of the installation in assessing almost all types of aerial problems should make it attractive to a large proving ground.\n\n7.2.3 Synchronization.\nThe gun camera establishes both range and gun pointing. A camera mounted to photograph the gunsight allows for the recording of ranging and tracking errors. Cameras used for tricamera, gun sight, instruments must be synchronized. This is typically achieved by placing a light bulb in the back of each camera, fogging the film edge at intervals controlled by a master unit.\n\nA simpler approach for determining gun-pointing errors is possible for near pursuit curve attacks. Instead, the bore axes of the bomber's aircraft can be used.\nguns and the fighter's guns will be close to parallel due to isometric conditions, as the leads taken by the duelists are equal in size and opposite in sense, to a first-order approximation (See Section 2.2.2). Equip each aircraft with a camera kept in rigid alignment with the respective bore axes. The image of the opposing aircraft may be expected on each film. Suppose further, that the bomber is supplied with a 100 percent own-speed mechanism which places on the film a point giving the resultant direction in the air mass that the bullet would take under the action of muzzle velocity and mount velocity. Suppose that for the fighter, the angle of skid and angle of attack can be determined so that the resultant instantaneous flight direction in the air mass of the fighter can be placed on the projected fighter film.\nAt a given instant, immobilize the bomber in the fire. On the corresponding frame, the direction the bullet takes in the air mass appears as a point. If the position the fighter would reach in the air mass after the bullet's flight time could be plotted on the same frame, the gun-pointing error would be known immediately. To do this, suppose the fighter maintained its velocity, i.e., the curvature of its path is neglected. The crucial point of the method now appears. The plane determined by the fighter's wingtips and the bomber's camera appears on the bomber's film as a line joining the wingtips of the fighter image. This plane appears on the fighter's film as a line parallel to the bottom of the film (since the fighter's camera is parallel to it).\nThe plane's instantaneous velocity, in relation to the wingtips and passing through the camera installation on the bomber, appears as a straight line on the fighter's film, intersecting the image of the bomber's camera installation. Since the films of the two cameras are nearly parallel, the angle between this line on the fighter's film and the horizontal on the fighter's film can be transferred with negligible error to the bomber's film with respect to the line joining the fighter's wingtips. This establishes a line on the bomber's film on which the fighter's future position must lie. The angle subtended at the immobilized bomber by the fighter's motion is precisely the deflection required by the fighter's approach angle (measured on the fighter's film), and thus sin(a) = qvF/Vo.\nThe future target position is established on the chosen frame of the immobilized bomber\u2019s film record. The method corrects the future position by computing the fighter's normal acceleration. The true future position is plotted on a line passing through the previous future position and perpendicular to the wingtip line.\n\nThough the procedure has real instrumental advantages \u2013 no recording of yaw, pitch, or roll is required \u2013 and advantages from the data reduction perspective, since ballistics are not used as work is in the air mass, its overall errors are only known theoretically. It has not been carried through in actual programs as has the relative coordinate method.\n\n7.2.5 Distant Reference Point Method\n\nThe simplest method of assessment uses just one camera fixed to move with the aircraft.\nThe gun is bore-sighted using a reference point, such as a mountain or cloud that doesn't move during assessment. If a specific frame is chosen, it can be assumed that correctly aimed bullets fired at an earlier instant, corresponding to the time of flight for that frame, are hitting the target. The film is then turned back the appropriate number of frames, and the fighter position, gun position, and reference points are marked on the projection screen. Returning to the original frame, the gun error is determined by superimposing the reference points, correcting the original gun position for ballistics, and observing how much the corrected gun position misses the target.\n\nDespite the lack of accuracy, the simplicity may be advantageous.\nThis section discusses techniques for reducing raw data obtained in airborne test programs. Techniques include rotations of coordinate systems, ballistic and parallax calculations, and treatment of single-shot probabilities and measurement errors.\n\n7.3.1 Techniques for Data Reduction\nThis section will discuss the techniques found useful for reducing raw data in airborne test programs. Detailed computing schedules for specific applications are not given here, but include techniques concerning: (1) rotations of coordinate systems, (2) ballistic and parallax calculations, and (3) treatment of single-shot probabilities and measurement errors.\n\n7.3.2 Rotation of Coordinates\nThree-dimensional geometry is most important in assessment programs. Examples include reduction of azimuth and elevation.\nMeasured with respect to a coordinate system determined by a tricamera installation, bearings with respect to a coordinate system fixed in the aircraft (cameras not necessarily aligned with the aircraft): 1. reduction from bearings relative to aircraft axes to bearings relative to an air mass coordinate system (aircraft axes rotated in the air mass system due to yaw, pitch, and roll), and 2. transformation of angles measured in a system relative to a camera in a fighter to angles measured in a system at the fighter, 45-51 degrees and parallel to those at a bomber or ground target.\n\nThese examples involve the rotation of coordinate systems. The most elegant and painless methods of geometry employ matrix algebra. According to these methods, if x is a vector in a coordinate system:\n\n1. Rotation of coordinate systems:\nMeasured with respect to a coordinate system determined by a tricamera installation, bearings with respect to a coordinate system fixed in the aircraft (cameras not necessarily aligned with the aircraft):\n- Reduction from bearings relative to aircraft axes to bearings relative to an air mass coordinate system (aircraft axes rotated in the air mass system due to yaw, pitch, and roll).\n- Transformation of angles measured in a system relative to a camera in a fighter to angles measured in a system at the fighter, 45-51 degrees and parallel to those at a bomber or ground target.\n\nThe most elegant and painless methods of geometry use matrix algebra. According to these methods, if x is a vector in a coordinate system:\n\n1. Rotation of coordinate systems:\n- Reduction from bearings relative to aircraft axes to bearings relative to an air mass coordinate system.\n- Transformation of angles measured in a system relative to a camera in a fighter to angles measured in a system at the fighter.\n\nThese methods are the most elegant and painless for dealing with the rotation of coordinate systems. They employ matrix algebra. If x is a vector in a coordinate system:\n\n1. Rotation of coordinate systems:\n- Reduction from bearings relative to aircraft axes to bearings relative to an air mass coordinate system.\n- Transformation of angles measured in a system relative to a camera in a fighter to angles measured in a system at the fighter.\n\nThe most effective and uncomplicated methods for handling the rotation of coordinate systems involve matrix algebra. According to these methods, if x is a vector in a coordinate system:\n\n1. Rotation of coordinate systems:\n- Reduction from bearings relative to aircraft axes to bearings relative to an air mass coordinate system.\n- Transformation of angles measured in a system relative to a camera in a fighter to angles measured in a system at the fighter.\nIn one coordinate system and the same vector in a rotated coordinate system, the two are connected by the matrix equation:\n\nXl CO Xi Vi V2 Vz\n\\_Xs\\_ JWi W2 Wz\\_\n\nor, briefly,\n\nThe array S is composed of the direction cosines of the axes of the first system with respect to those of the second, and matrix multiplication according to the usual rule is used.\n\nThe application of the theory is illustrated by the problem of stabilizing coordinates (34 > 96). In this problem, the azimuth and elevation of a target are given in a coordinate system fixed in the bomber. The bomber system has been obtained from an air mass system by a sequence of three rotations:\n\n1. A rotation in yaw, with a vertical axis, of angle Y,\n2. A rotation in pitch, with a horizontal axis, of angle P, and\n3. A rotation in roll, about the aircraft's axis.\nThe longitudinal axis refers to angle R. The order is standard, and angles are positive when the bomber makes a right diving banking turn. To find the element in the zth row and jth column of S, multiply the elements in the ith row of S by the corresponding elements in the jth column of S', and add. This rule is applied to multiply a 3x3 matrix by a 1x3 matrix to obtain a 1x3 matrix. The azimuth and elevation of the target with respect to the air mass system are required. The problem is solved by the matrix equation:\n\nX = SrSpSpX,\n\nwritten in the form:\n\nS^-1X = SpSrX,\n\nwhere\n\nsin A cos E\nsin A cos E\ncos A cos E\ncos A cos E\nsin E\nsin E\ncos Y sin Y 0\n0 cos P sin P\nS R\ncos R 0 sin R\n\nThrough simple calculation, one finds:\nsin E = cos P cos P (tan E cos R - sin R sin A) - tan P cos A,\nsin (A - Y) = cos E sec P (cos R sin A + sin R tan E).\n\nIn this problem, the angles Y, P, and R are known from gyro readings, so these formulas are completely determinate.\n\nIn assessment programs, a large number of readings must be reduced. An exact mathematical solution may be too time-consuming. Hence, problems such as the preceding one are frequently solved by mechanisms or special computers. A mechanism called a gimbal, constructed with precision and consisting of rotating arcs which may be positioned to mimic the orientation of the aircraft with respect to the air mass, can be used for these reductions. A transit is provided for exact settings and markings.\n\nThe most appropriate computers are based on the principle of gnomonic projection. Using the principle of gnomonic projection, these formulas can be solved.\nThe center of a sphere as the center of projection and an equatorial tangent plane as the plane of projection, the great polar circles of longitude project into a family of straight lines and the small circles of latitude project into hyperbolic arcs. The principle on which the use of the chart is based is simple. Imagine a line from the sphere center to the target is fixed. Rotate the sphere and its attached planar grid. The U.S. Coast and Geodetic Survey has prepared plates for large, fine-scale (10-minute spacing) gnomonic charts.\n\nThe target line will trace a certain pattern on the chart. Specifically, if the grid plane has its normal line at an elevation of 0\u00b0 and an azimuth of 270\u00b0, then, if a yaw is to be removed, the sphere rotates in azimuth and the trace moves along the resulting meridian.\nThe proper hyperbola (line of equal elevation): if a pitch is to be removed, the sphere rotates about the normal line of the grid, and the trace actually describes a circular arc on the grid centered at its center; and if a roll is to be removed, the trace moves along a small circle on the sphere which projects into one hyperbolic arc of a family orthogonal to the original set. Instruments based on these and similar projection principles have been constructed (Gunther, 1937, p. 133).\n\nCalculation of Deflection and Parallax\n\nThe calculation of the deflection that should have been taken is carried out by direct application of elementary ideas. In particular, kinematic deflection is determined by the classic time-back method. If it is assumed that the gun mount is in non-accelerated motion, the range at any instant can be called a future range, and it may be supposed that a bullet was fired from this range at time t0. The deflection angle \u03b4 at time t1, when the bullet hits the target, can be calculated as follows:\n\n\u03b4 = \u2220AOB, where\n\nA = position of the gun at time t0,\nB = position of the gun at time t1,\nO = center of the Earth.\n\nUsing the law of cosines, we have:\n\ncos \u03b4 = (R^2 + (r1^2 + r2^2) - 2R(r1 cos \u03b81 + r2 cos \u03b82)) / (2R(r1 sin \u03b81 sin \u03b82 + r1 cos \u03b81 cos \u03b82 + r2))\n\nwhere R is the Earth's radius, r1 is the range at time t0, r2 is the range at time t1, and \u03b81 and \u03b82 are the angles between the directions of the gun at times t0 and t1, respectively, and the meridian through O.\n\nTo calculate the parallax, we can use the following formula:\n\nparallax = \u03b4 / tan \u03b8\n\nwhere \u03b8 is the angle between the line of sight and the meridian through O.\n\nThese calculations can be performed using tables of trigonometric functions or a calculator. The results can then be used to adjust the aim of the gun to compensate for the deflection and parallax.\nThe fired bullet hits the target under perfect aim, as the time of flight is insensitive enough to bearing changes, allowing the use of the target's azimuth and elevation at the instant of supposed impact. These angles differ from the true bore angles only by ballistic deflections. Using prepared tables or appropriate graphs for known airspeed and ballistic density yields the time of flight. Reversing motion picture record by this length of time gives the target position at the instant of fire. The differences in stabilized azimuth and elevation of the two target positions give the components of kinematic deflection. We need not delve into the evident details of ballistic corrections, except to note the necessity of special charts 34 and.\nThe correct deflections may be plotted against odd times (assessment times minus time of flight), and a curve may be smoothed through these points. The advantage of this elementary timeback idea is that full allowance is made for target acceleration. Allowance for the acceleration of the center of gravity of the gun mount is much more difficult. To date, such allowance has been considered unnecessary since violent avoiding action has not been seriously studied. A parallax correction in the bearing of the target must usually be made due to the appreciable displacement of gun position from that of the recording instrument. If a, b, c are the coordinates of the gun relative to the camera in the aircraft coordinate system, then the azimuth and elevation of the target are:\nThe target's relative position, in relation to the turret, can be referred to as angles A and E. With the range r from the turret and r0 from the camera, these equations provide approximations: r * cos(E) and r.\n\nIn practical applications, a and c can typically be disregarded, and suitable charts can be prepared for the correction reading. An alternate method for parallax correction is the plaxie .34 mechanism.\n\nThe discussion above implies that reduction of raw data has been refined to the point where gun aim errors are known as functions of time during an attack. The subsequent question is a natural one: if a single bullet is fired at a given instant with such false aim, what is its hit probability?\nThe target is unconditionally vulnerable. For such a target, the probability of a lethal hit is dependent on the position but independent of the number or location of earlier hits. Abundant evidence, both theoretical and empirical, indicates that this is a valid assumption.\n\nQuestion one can be answered initially on the assumption that there is no measurement error. Additional assumptions about the target and bullet dispersion are made before proceeding with the solution. The target is unconditionally vulnerable. For such a target, the probability of a lethal hit depends on the position but is independent of the number or location of earlier hits. Abundant evidence, both theoretical and empirical, indicates that this is a valid assumption.\n\n(Confidential)\nAnalytical Aspects of Airborne Experimental Programs\n\nRegarding the first question, it can be answered initially under the assumption that there is no measurement error. Certain additional assumptions about the target and bullet dispersion are made before proceeding with the solution. The target is unconditionally vulnerable. For such a target, the probability of a lethal hit depends on the position but is independent of the number or location of earlier hits. Abundant evidence, both theoretical and empirical, indicates that this is a valid assumption.\nRecommended modifications to fighter aircraft target: Replace the typical fighter target with a sphere of 5 ft diameter, having a uniform vulnerability factor of 0.40. This implies that if a bullet hits the previously undamaged sphere at any point, the probability of it being lethal is 0.40.\n\nRegarding the bullet, angular displacements can be measured in a plane of action (the plane containing target and gun-mount velocity at a given instant) and perpendicular to this plane. If a perfect bullet with no dispersion is fired with a given aiming error, the relative angular separation from the target center to the bullet when both are at equal range can be termed (z) = (xhx2). The gun error generated by the test is denoted as (r). An actual bullet fired with gun error (x) will have a relative angular separation from the target:\n\n(z) = (xhx2)\nGun error = (r)\nWith both bullets at the same dispersion range, the actual bullet hits the spherical target where p is the angular radius of the target at the instant the bullet is at the same range. In other words, the probability the bullet hits the target is the volume under the two-dimensional normal dispersion surface, erected on a circular base, given that (6) is distributed normally with a mean of (0,0) and a variance of \u03c3\u00b2 = \u03c3,\u03c3\u00b2 (of is a typo for \u03c3\u00b2). The quantity (6) includes the effect of firing at a fixed target as well as the excess aim disturbance in combat over the disturbance in a test. The variance \u03c3\u00b2 is called the gun-mount variance.\nIn the plane with radius p and center (-Xi, -x2), the single-shot lethal probability is:\n\nP = T / (1 + T^2*(x - p)^2)\n\nT is defined by:\n\nT = 1 / [1 + (mu/p)^2 + ((v - v0)^2 / (2 * p * sigma_v)^2)]\n\nThe first question regarding the single-shot probability is answered completely if this calculation is refined to permit variations in muzzle velocity and initial yaw. This refinement is accomplished by setting:\n\nc = <mu> and \u03c3 = <\u03c3_v> in T's denominator\n\nThe effect of a measurement variance may now be introduced. Instead of knowing x, one knows only z, where:\n\nz = x + h + m\n\nThe total measurement error y may be written as a sum of a quasi-steady part h and a fluctuating part m. It is the fluctuating part which has the variance \u03c3_o. The problem is to estimate the lethal probability p as adequately as possible.\nusing (z) and (a2). The estimate of p selected is:\n\np' = (1/Z) [integral of G(zh, z2; p, 0-1, 0-2) dh dz]\n\n(The subtraction of variances should be carefully noted.) The sense in which p' is an adequate estimate of p is that its weighted average over the universe of possible m (or its expected value with respect to p) is precisely equal to p.\n\nThe result, and with it, the subtraction of variances, come about as follows. Starting with the idea that the weighted average of G(zh, z2; p, rb, lb), where h is put equal to zero, requires the constraint that o-2 = o^ + a2, which yields the o-2 described above.\n\nIt will not be inferred that the quasi-steady part of the measurement error has any relation to the quasi-steady gunpointing error. The same remark applies to the fluctuating part.\n\nCONFIDENTIAL\nMEASURES OF EFFECTIVENESS\n\nFigure 1. Single-shot hit probabilities.\nIn a poor experiment, it is conceivable that Cm > a. It can be shown analytically that the above solution exists uniquely when CTO = fffr. In practical work, it is not usually necessary to evaluate the double integral defining p'. The assumption commonly made is that ri = a2 = a. Then, if the distance \u00a3 = z+z is used, the probability p' can be expressed as a function of p/a and \u00a3/<r. Based on tables made for scatter bombing, charts have been prepared which permit one to read p' (or rather p'/0.4) directly. Two of these charts appear here as Figures 1 and 2.\n\n7.4 Measures of Effectiveness\n7.4.1 Recommended Measure and Others\n\nIf an objective of an airborne assessment program is to rank two or more fire control systems, some method of compressing single-shot probabilities is necessary.\n\nCONFIDENTIAL\nANALYTICAL ASPECTS OF AIRBORNE EXPERIMENTAL PROGRAMS.\nwhich  are  given  as  functions  of  time  over  particular \nattack  courses,  should  be  devised.  One  such  com\u00ac \npression  is  the  generation  of  the  average  probability \nof  at  least  one  lethal  hit  for  a  properly  stratified  set  of \nparticular  attacks  of  the  same  general  type.  Proper \nstratification  means  that  the  replications  faithfully \npermit  the  variables  of  gunner,  installation,  attack \npath  variations,  and  the  like  to  express  themselves. \nThis  criterion  of  effectiveness  98  may  better  be  ex\u00ac \npressed  as  the  expected  proportion  of  engagements  of  a \ngiven  type  which  will  he  successful  for  a  system.  Suc\u00ac \ncess  is  the  destruction  of  the  target,  the  survival  of \nthe  gun  mount,  or  some  combination  of  both. \nOther  measures  of  effectiveness  have  been  pro- \nCONFIDENTIAL \nOPTIMUM  DISPERSION \nposed.  One  might  determine  the  expected  number  of \nhits  on  the  target  per  engagement.  Two  objections \nThe unconditionally vulnerable target presents no cumulative effect from non-lethal hits. Second, due to serial correlation in gun-pointing errors during the attack, the number of lethal hits cannot be converted into a destruction probability.\n\nA common British measure is the index I, defined by the expression:\n\nI = (Bullet density on using the system) / (Standard bullet density)\n\nThe standard bullet density is the density at the target range of the same number of bullets distributed uniformly over a circle 1\u00b0 in diameter. With the aid of , determined by experimental procedures, hit expectations and the probability of success in an engagement have been calculated. (199) This measure, and others (118), have been carefully reviewed.\n\nDespite the insufficient discussion here.\ntail  to  make  it  evident,  the  problem  of  measures  of \neffectiveness  is  sophisticated.  One  can  be  led  to \nspeculations  about  the  relative  worth  of  systems \nwhose  performances  as  a  function  of  long-  and  short- \nrange  invert.  One  can  attempt  to  predict  expected \nlosses  and  gains  in  combat,  e.g.,  fighters  shot  down \nper  bomber  lost,  similar  to  those  determined  after \nthe  event  from  an  analysis  of  combat  records.165  It \nis  likely  that  these  subtleties  are  inappropriate  in  the \ncurrent  state  of  the  art.  But  the  attempt  to  relate  a \na  particular  technical  branch  of  air  warfare  to  the \noverall  situation  may  well  be  prosecuted  in  the \nfuture. \n7.4.2  Expected  Proportion  of \nSuccessful  Engagements \nTurning  now  to  the  first  criterion,  the  expected \nproportion  of  engagements  which  will  be  successful, \nsuppose  that  shots  are  fired  at  times  ti,  t2,  h  *  \u2022  \u2022  dur\u00ac \nThe probability that a target will survive the first i shots is Consequently, the probability that the target will be destroyed during the first i shots, given that the bomber is invulnerable, is required. In our tactical situation analysis, we need the expected value, D(t), of d(t), which refers to an engagement involving a specific type of attack and fire control, but with a random selection of fighter pilots, gunners, equipment specialists, weather, and similar variables.\n\nThere are two methods for estimating D(t). The direct method determines d(t) for each attack of the type and forms an average of the resulting values. The statistical method attempts to describe the universe of all possible attacks and outcomes.\nOf gun errors, made during all attacks of this type, are caused by certain parameters. D(t) is to be estimated from these parameters. For example, it may be assumed that gun errors can be described as a two-dimensional Gaussian distribution with the parameters: mean traverse error, mean elevation error, variance of traverse error, variance of elevation error, correlation coefficient of traverse and elevation errors. The adequacy of this particular description may be questioned on the ground that the effect of serial correlation in aim wander during a representative attack has been ignored. If, however, the universe of gun errors can be correctly described, then the statistical method is superior to the direct method in that it is statistically efficient, extracting the maximum amount of information from the available data.\n\nThe value of D(t) as a measure of effectiveness does\n\n(Note: The text appears to be in modern English and does not contain any meaningless or completely unreadable content, ancient English, or non-English languages. No OCR errors were detected. Therefore, no cleaning is necessary.)\nNot dependent on the assumption of bomber invulnerability. If A and B are two fire control systems, and Da(\u00a3) and DB(t) are known, and Zhi(\u00a3) is greater than DB(t) for all values of t, then: A is superior to B in the sense that A will enjoy a greater proportion of successes than B, whether success is defined as the destruction of a target by a vulnerable bomber or as the survival of a vulnerable bomber. The theorem requires detailed proof, which will not be reproduced.\n\n7.5 Optimum Dispersion\n7.5.1 Expectation of Optimum Pattern Size\n\nIn aerial gunnery, dispersion is essential if hits are to be scored. The reason is that, with these weapons, a burst is fired with a certain bias in aim. The mean point of impact [MPI] is displaced from the center of the small target, and when the MPI is off target, the expectation of the optimum pattern size is given by:\n\nMPI = target center + (aim bias)\n\nThe size of the pattern is determined by the standard deviation of the aiming error. The optimum pattern size is the size that minimizes the probability of missing the target while maximizing the probability of hitting it. This size depends on the size and speed of the target, the altitude and speed of the aircraft, and the characteristics of the weapons being used. The calculation of the optimum pattern size is a complex process that involves statistical analysis and optimization techniques.\nWith current aiming errors, the MPI is rarely on target for more than a fraction of a second. In fact, for systems where the MPI can be kept on target for an appreciable length of time, it is desirable to renounce the principle of rapid fire of small caliber projectiles in favor of slower fire of larger caliber ones. The vulnerable subarea of the target increases with caliber up to the point of complete structural failure caused by a hit on any part of the target. In contrast, excessive dispersion is undesirable. Even with a perfectly aimed gun, the spacing could be so large between bullets of the burst that the small target may escape. Large dispersions are used in warfare only against large targets.\nOne looks for an optimum size of the dispersion pattern. The determination of this size requires knowledge obtained from experimental programs of gun-pointing errors, although it is possible to attempt using indirect combat information such as rounds fired per enemy aircraft destroyed in an analysis. Such a procedure is of doubtful efficiency since, not knowing how gun-pointing errors vary and how they are serially related with range, it must assume a fixed target size and a constant aim error (or one that varies according to some supposed distribution). To optimize dispersion with assurance, one needs precise gun-pointing information and should use the technique of Section 7.4.2 to determine the average destruction probability.\n\n7.5.2 Nose Attacks on B-29\nThe determination of optimum dispersion size also applies to nose attacks on the B-29. The B-29 was a large bomber used during World War II, and nose attacks were a common tactic used by enemy fighters. To effectively engage the B-29 with nose attacks, it was important to determine the optimum dispersion size for the attacking fighter's weapons. This required accurate gun-pointing information and the use of statistical analysis to determine the average destruction probability. By optimizing the dispersion size, the attacking fighter could increase its chances of successfully damaging or destroying the B-29.\nAccording to this schedule, the attractive nose attack solutions for the B-29, given extremely accurate data from tests on the War Research Laboratory of the University of Texas' testing engine, involved both pure and aerodynamic pursuit courses. Four modifications of the nose-sighting stations yielded 192 samples of the tactical situation in question, with six gunners participating.\n\nIn this machine, an actual gunner operates the sighting mechanism against a programmed target whose motion is very realistic. The machine records continuously the gun errors in traverse and elevation. It has prior knowledge of the correct values. A major advantage is the ability to conduct replications, where only the gunner and sight specimen are changed.\nvariables are: g = 2.58 (after tests at the AAF Central School for Flexible Gunnery at Laredo, Texas); a = 1.16, <r^2 = 0.41 (estimates of machine accuracy at the University of Texas). We shall take radians. The results of a calculation of D (the average of all destruction probabilities with t set equal to the duration of the attack) as a function of <75, by the methods of Section 7.4.2, is shown in Figure 3. The figure also gives a 0.95 fiducial zone. This means that the probability is 0.95 that D lies in the interval shown for any given <76.\n\nIt is concluded from the figure that the optimum dispersion is ab = 3 milliradians. However, the actual value <Jb = 1.61 corresponds to a destruction probability of approximately 0.61.\nThe ability is 0.25, which is only 0.03 below the maximum probability. The only definite statement is that 76 should not be reduced below its present value.\n\nCONFIDENTIAL\nOPTIMUM DISPERSION\n\n7.5.3 Theoretical Solution for Fighters\n\nDespite the emphasis in this chapter on the necessity of precise experimental results, there are certain advantages to an entirely theoretical approach to these problems. The average assessment program is complicated and costly in material and personnel. Its conclusions may be reached too late, and even then may be subject to censure on grounds of experimental design or accuracy. In the theoretical treatment, the variables are always under control. The relative effects of variation in different parameters may be readily studied. Such a study is also modest enough to state not what will happen but rather the implications of different scenarios.\nThe range of results will be determined for varying values of a parameter whose exact values are uncertain. When the results point in a direction independent of such variability ranges, the findings are conclusive, and an experimental study is unnecessary. The theoretical approach may lead to economy and efficiency in experimental programs by specifying precisely which details require an empirical foundation.\n\nSome of these advantages are demonstrated in a study of a fighter aircraft (an F6F) guided by a gyro gunsight (the Mark 23). The fighter attacks a target flying straight and level at a constant speed. To establish the fighter's basic position and orientation at each moment, it is first assumed that a perfect pursuit curve is flown. To obtain single-shot probabilities, this orientation is assumed to be perfect.\nTroubled by the ranging errors: (1) perfect range, (2) consistent under range by 10 percent, (3) consistent over range by 10 percent, and (4) varying from 25 percent under range at 800 yd to 25 percent over range at 200 yd; and by the tracking assumptions of (1) perfect tracking, and (2) tracking with a circular normal distribution of errors so that the pipper is within 3 milliradians of the target during 50 percent of the time. (Such ranging and tracking assumptions may come from rapid preliminary experimentation or even from subjective estimates by operators.) In addition to these operational errors, Class B errors will occur due to the particular calibration of time of flight in the sight. In fact, if A* is the correct lead, the sight\u2019s time-of-flight multiplier should be:\n\nwhere 0 is the approach angle measured at the target.\nAt a given altitude, temperature, range, and angular rate, the sight uses a value tm according to the calibration of the range circuit. The error in lead is approximated by r, which is the error in time of flight multiplied by the angular rate of the gun-target line for a correctly flown fighter. This expression for the error includes the effect of lag in lead computation since tm was chosen with attention to the sight equation. The remaining sources of Class B error, such as optical and electromagnetic dips, and feedbacks, are ignored. The fighter's performance truly appears through tm in the above expression.\n\nThe method of computing single-shot probabilities is relatively straightforward. The value of eA gives\nThe displacement of the mean point of impact from the target is surrounded by a circular normal distribution. This mean point of impact is determined by the sum of variances due to dispersion and aim wander. Assuming a good value of 1.2 milliradians for dispersion (arising from ground firings of a fighter-mounted caliber .50 machine gun using API MS ammunition), and an average amplification factor of 1.5 for gun wander (as per Section 5.3.4, \"Amplification of Tracking Errors\"), the variance due to gun wander is [(1.5 * 0.425)\u00b2], where 0.425 converts the diameter of a circle containing 50% of random gun directions into a standard deviation for this distribution.\nThe pattern is narrowed in the air due to the forward motion of the fighter by a factor of vq / (vq + vf). If vF is 209 yd/sec and v0 is 956.7 yd/sec, the shrinking factor is 0.82. The shrunk sum of variances is 10.85 milliradians squared. The target is taken to be a small bomber represented by a circle of radius 1 yd with a uniform vulnerability factor of 0.3. Single-shot probabilities may be read from Figures 1 and 2.\n\nIn fighter fire, a complication arises due to the harmonization of a battery of guns. A typical US Navy procedure is to boresight the six wing guns to converge horizontally and vertically with the line of sight at a range of 300 yd. Strictly, one should there calculate probabilities for each gun separately.\nWhen completed, the middle port gun and middle starboard gun probabilities differ significantly. After accounting for parallax, boresighting, and aircraft banking, the combined effect of all guns firing together is determined by summing their individual effects.\n\nThe single-shot probabilities can be transformed into the probability of at least one lethal hit over time using the methods in Section 7.4.2. For an attack against a target traveling at 195 knots, initiated at a range of 900 yards on the beam and ending 3.3 seconds later at a range of 200 yards and an angle of approximately 40 degrees, the calculation results are presented in Table 1.\n\nSection 7.3 discusses data reduction.\nTechniques are given instead of schedules. The problem of rotation in coordinate systems is addressed generically through matrix methods, mimicking mechanisms, or gnomonic computers. The calculation of deflection utilizes the timeback method, where a given frame represents impact by a bullet fired earlier. Formulas for the parallax correction necessary due to gun and camera displacement are provided. The final technique is discussed in detail. This is the problem of reducing gun pointing errors to the probability that a single round fired with such an error would be lethal to a fighter target, meaning the fighter could not return to its base. It is also emphasized at this point that measurement errors of the experiment lead to a measurement variance which must be subtracted.\nTable 1. Probability of at least one lethal hit as a function of time (in seconds):\n\nTime (seconds)\nNo range error\nRange 10% too small\nRange 10% too large\nRange from -25% to +25%\n\n7.6 Summary\n\nThe introduction in Section 7.1 states that the fundamental purpose of airborne assessment programs is the ranking of different fire control systems. To achieve design changes, a combination of analytical methods and controlled tests on laboratory machines is required. The errors of a fire control system are initially categorized by cause: mechanism, Class B, operational, and dispersive; and then by statistical nature: fluctuating, quasi-steady, and steady. Current assessment programs employ simulated attack situations with camera recording to obtain the overall errors of systems.\n\nSection 7.2 discusses the methods used to evaluate the performance of fire control systems. These methods include:\n\n1. Statistical analysis of historical data\n2. Monte Carlo simulations\n3. Analytical modeling\n4. Controlled experiments\n5. Human factors analysis\n\nThese methods are employed to assess the accuracy, reliability, and effectiveness of various fire control systems. The results of these assessments are then used to identify areas for improvement and to guide the development of new and improved systems.\nThe path in space of a target can be determined. Instruments include: three fixed cameras, a range camera, gyro records of platform motions, a deflectometer which records the turret position in azimuth and elevation, long focal length cameras fixed on the ground with data reduced by astrometric methods, a camera in the gun mount, and one in the target, and one relying on fixed and distant reference points in the landscape. The dispersion variance is subtracted before the single-shot probability is computed.\n\nSection 7.4 discusses further reduction, the generation of a measure of effectiveness from single-shot probabilities. The proposed measure is: the expected proportion of engagements of a given type which will be successful in the sense that the target is shot down or the bomber is hit.\nSection 7.5 discusses the choice of an optimum size for the dispersion pattern in relation to aiming errors. Using experimental data of a precise nature, the situation for nose attacks on a B-29 is explored. Theoretical methods are used to discuss the situation for a fighter equipped with a gyro gunsight. For the first case, pattern size might be increased slightly, but the change in probability of at least one lethal hit would be only from 0.25 to 0.28. For the second case, errors in ranging greatly overshadow variations in dispersion.\n\nChapter 8\nNEW DEVELOPMENTS\n\n8.1 INTRODUCTION\nThis chapter does not predict future developments.\nThe text describes in compact form the systems and ideas seriously considered in the closing months of World War II for the next stage of the war. The perspectives are limited to air tactics then current. Fire control systems discussed aim to do a better job than existing equipment, but no real steps are taken to solve the problem of an ultra-speed target or extend combat ranges materially. Under new tactics, only slight variations in existing fighters are considered. These remarks are critical rather than censorious. Failing the introduction of unforeseen and radical principles, the systems of the future will likely lean heavily on the ideas of this chapter.\nThese ideas must be explored further to gain adequate knowledge of theoretical and mechanical limitations. The best case in point is radar gun laying, which involves both the theory of tracking and the facts of mechanical responses. One may hope that the next phase in fire control development will consist of a fresh reexamination of the problem, resulting in a system combining the best of the new ideas and avoiding the known errors of existing mechanizations. The theoretical design of such a system should precede its construction, as it is a curious fact that many machines are built and then analyzed, with patchwork as the usual result. Fire control design has lagged behind tactical circumstances. If the broad outlines of future combat circumstances are made available to this design, even\nAt the early and tentative stages of tactical expectation, this need not be true.\n\n8.2 Stabilized Sight Systems\n8.2.1 Nature and Types of Stabilization\n\nStabilization is one of the most important developments in airborne fire control, second only to the introduction of power turrets. Stabilization allows the gunner to focus on his primary task, tracking the smooth target motion. The normal irregular motions of the gun platform, which make this a challenging task under normal circumstances, no longer disturb the gunner's line of sight. In principle, any motions not required by the gunner through his handlebars are detected by gyroscopes, which immediately send impulses to the turret motor. The motor, in turn, counteracts the perturbation.\n\nEither position or rate stabilization may be used.\nIn a stabilization system, a free gyroscope is used. By the first fundamental principle of gyroscopic behavior, i.e., maintaining a fixed direction in space, motion of the sight line away from the gyro axis is detected and corrected when the handlebars are in neutral. In tracking, a connection between handlebars and gyro is made, so that the gyro will precess when moved by the handlebars. It is the differential signal, between handlebar motion and total motion, which is detected and eliminated by the stabilization. In rate stabilization, the gyro is constrained. When the line of sight moves, taking the gyro with it, the gyro responds with a precessional torque (kick). The magnitude of this torque is proportional to the angular rate of turn of the gyro. If the sight line starts to move under external influences, the precessional torque corrects it.\ntorque  of  the  gyro  is  measured  and  the  turret  motors \nrestore  the  sight  line  to  its  original  position  very \nquickly.  When  tracking,  the  gyros  must  be  prevented \nfrom  stabilizing  out  the  intended  motion.  Since  the \ngyro  is  constrained,  no  major  precession  occurs.  The \nkick  due  to  the  handlebar  motion  is  neutralized  by \nsuitably  calculated  impulses  from  the  handlebars. \nThus,  this  part  of  the  kick  does  not  act  to  restore  the \nturret  to  its  original  position. \nIt  will  be  appreciated  that  there  is  nothing  inherent \nin  stabilization  which  will  improve  the  mechanism \non  which  lead  computation  is  based.  Instead,  one \nexpects  the  improvement  in  inputs  to  cause  the  com\u00ac \nputer  to  perform  better.  The  stabilization  circuit \nmay  be  regarded  as  an  improved  analogue  of  the \nB-29  follow-up  system  under  which  the  guns  follow \nCONFIDENTIAL \nNEW  DEVELOPMENTS \nFigure  1.  Unit  schematic,  Type  S-4  sight. \nThe sight line. The lead computation is an additional function in each case.\n\n8.2.2 Fairchild S-4 System\nAn excellent example of a rate stabilized sighting system is the Fairchild S-4 (or S-3) installation for inhabited turrets. The stabilization features are the same for both types. The S-4 is ballistically superior in that it will function for all types of Type 5 projectiles within a speed range where the three-halves power drag law is valid. One need only insert muzzle velocity and ballistic coefficient. A ballistic mechanism then effectively solves the Siacci differential equations for the trajectory, instead of translating special ballistic tables calculated by this method and referring to particular ammunition. (This is an excellent example of how proper fire control design can anticipate ordnance changes and thus avoid lengthy adjustments)\nThe S-4 will be discussed, covering both hydraulic and electric turret mechanisms. The theory will include two major circuits: one operates the azimuth turret motor and controls lateral lead, while the other operates guns in elevation and controls vertical lead. Each circuit employs a captured gyroscope with a dual role: it determines the kinematic lead of its component and stabilizes the line of sight independently. The unit schematic of the S-4 is shown in Figure 1.\n\n8.2.3 Circuit Components of the S-4\n\nThe system can be best understood by writing out the differential equations of the circuit in one component. It suffices here to consider the interaction:\n\nThe general picture involves the interaction.\nThe assumption of this treatment is that the inertia of moving elements can be neglected, which is a major assumption as successful operation depends on the relative speed of gyros, servomotors, and amplidyne turret.\n\nLet a gyroscope, whose spin axis lies in a horizontal plane, be rotated about an axis perpendicular to that plane, i.e., let it track in azimuth only. The gyroscope then develops an internal torque whose axis is perpendicular to the spin axis and to the axis of rotation and so also lies in the horizontal plane. The magnitude of this torque is I*d\u03b1/dt, where I is the moment of inertia of the rotor, \u03c9 is the angular speed of the rotor, and \u03b1 is the angle at any instant between the line of sight (the spin axis) and some direction.\nIn space, the gyro is fixed, meaning the direction of a star. If the gyro is mounted such that the spin axis can only move in a vertical plane, it will precess in this vertical plane by an angle of 6. If its motion in the vertical plane is inhibited by a damping torque proportional to velocity (Ddd/dt) and a spring torque proportional to displacement (So), then since all three torques have the same instantaneous axis in the horizontal plane:\n\nA servomechanism is a power control device in which a weak input is amplified to control a strong output. This output, in turn, feeds back to combine and modify the original input.\n\nConfidential\nStabilized Sight Systems\n\nThe displacement angle \u03b8 can be transformed into an output voltage K\u03b8 by means of an E magnet. This device is illustrated in Figure 2. When an a-c voltage is impressed on the primary, the output from the secondary produces a current that is proportional to the displacement angle.\nThe secondary voltage is zero when the gyro is undeflected, as the output arms are wound in series opposition. Upon deflection, more voltage is induced in one arm than the other, and the arrangement is such that the imbalance is proportional to the deflection.\n\nFigure 2: Gyro E magnet unit. (Courtesy of Fairchild Instrument Co.)\n\nThe voltage from the hand control potentiometer is K2p, where p is the positional angle of that potentiometer. Due to the interconnection (8) (see Figure 1), this voltage is subtracted from the total voltage (2) Kid. Therefore, the input to the stabilization servo is ei = Kx9 - K2p. The output voltage (3) e2 of the servo is tapped off by a moving potentiometer arm so that the inputs to the electrical differential (two potentiometers in parallel) are (3) e2 and (9) Kap from the hand control potentiometer. Hence the output (4) is:\n\neo = f(ei, ek)\nA voltage, denoted as e3, is required such that it shifts the sight line in space from the original reference line. The angle a represents the unwanted yaw angle. Up to this point, nothing has been discussed about the total lead angle A. Since the sight head is attached to the turret, the sight line follows roughly the gun line. The small displacement of the sight line from the gun line to provide deflection is achieved through a sight servomotor. Its mechanical output provides a rate to the sight line relative to the sight head, which is proportional to its input voltage. In a steady state condition, the computer generates two voltages, representing the time-of-flight multiplier tm and the ballistic deflection A&. The rate of rotation of the sight line is proportional to the control handle potentiometer position, denoted as da. Therefore, introduce the sight servomotor voltage as:\n\nda\n\nThis text has been cleaned to remove unnecessary line breaks, whitespaces, and other meaningless characters. No other modifications have been made to the original content.\nput  Kitmp  \u2014  Ab  \u2014  A.  The  output  of  the  sight-line \nmotor  is  a  rate  of  change  of  sight  line  relative  to  the \nsight  head  (i.e.,  relative  to  the  gun  line),  and  this \nrate  d(y  \u2014  <j)/dt  =  dA/dt  is  proportional  to  the  volt\u00ac \nage  input.  Hence \nT_  dA \nat \nIt  follows  immediately  that  there  is  a  delay  in  lead \ncomputation  for  this  system.  (See  the  analysis  of \nSection  5.3.4  \u201cDelay  in  Lead  Computation.\u201d)  Only \nif  A  is  constant  and  equal  to  Kitmp  \u2014  Ab  will  the  servo\u00ac \nmotor  stop. \nThis  account  rather  conceals  the  role  of  the  gyro \nin  measuring  angular  rate.  Actually  the  whole  system \nacts  to  keep  the  input  voltage  e\\  to  the  stabilization \nservo  zero,  or  to  make  Kx9  =  K2p,  this  being  the \nessence  of  stabilization.  In  other  words  the  voltage  p \nbeing  used  in  determining  lead  is  really  measured  by \nthe  precessional  torque  of  the  gyro. \nAssuming  that  the  output  voltage  (5)  of  the  ampli- \nThe is proportional to the input voltage. The angular rate given to the guns by the turret motor is proportional to this amplidyne output voltage. But the angle which the guns make with the longitudinal axis of the aircraft is y \u2013 a, where y and a are the positional angles of gun and longitudinal axis, respectively.\n\n3.2.4 Complete Circuit Equations of the S-4\n\nThe preceding basic circuit equations are combined most expeditiously by placing d/dt = p and treating p as an algebraic quantity. There result:\n\nTQ K k k\nCONFIDENTIAL\nNEW DEVELOPMENTS\nK7tmH \u2013 Ab\nmKxK,K,V . K7\nMK^sKsp\nK7tmfj. \u2013 Ab\n+ Kqp\n\nSince the yaw rate of the aircraft enters the equation as d2a/dt\u00b2, it follows that the S-4 stabilizes completely only non-accelerated motions. Again, a rather bizarre form of aided tracking is present since by equation (2), neither gun position nor gun rate is simply proportional to it.\nTo complete this discussion, a prime advantage of this system should be emphasized. The notion of a time constant or decay of false leads does not apply, except in the generalized sense of the time for unwanted transients to vanish. This point has not been made out in detail theoretically. However, from the standpoint of actual operation, the gunner seems to have about as much control over his line of sight as he would with a fixed sight. The disturbed reticle behavior is not in evidence.\n\nRegarding Class B errors of the S-4: little can and will be said about them. Lag in lead computation exists, and this lead is based on first-order theory and does not allow for curvature. Calibration is necessary, and there is also a small error.\nThe second-order error in computing vertical lead, using a gun-roll type vertical gyro, is 1000 Alf tan E milliradians, where Al is the lateral lead in radians and E is the elevation. (Figure 8.2.6: Sperry S-8B System)\n\nIn the discussion of the Sperry S-8B sight, the exposition will be limited to the azimuth plane. The appropriate sight schematic is provided in Figure 3. Angles required for development are depicted in Figure 4.\n\nAngle a represents the yaw of the airplane, and i is the displacement of the handlebar controls. The optical system is designed such that:\n\nRecalling Sections 5.3.3 and 5.5.4, we anticipate finding equations resembling those for a simple system.\nThe computing sights lead with a sight parameter of 50%. The gunner has direct control over the relative position of the sight and gyro lines. The combining glass is controlled by the handlebars, and the stabilization mirror by both the gyroscope and the handlebars. (Figure 3. Unit schematic, Type S-8B sight)\n\nThe gyroscope is universally gimbaled. It is precessed in azimuth by a torque caused by a spring wound around an axis lying in the horizontal plane and making a 90\u00b0 angle with the bore axis. This torque T is equivalent to a force T sec (y - 0) applied perpendicularly to the azimuth plane at a point unit distance from 0 out along the gyro spin axis. Hence, as in Section 5.5.2, the precessional rate is:\n\nIt is the function of the torque computer to make X equal to:\n\nX = (T / (I * w)) * sin(\u03b5)\n\nWhere X is given by, I is the moment of inertia, w is the angular velocity, and \u03b5 is the angle between the torque and the normal to the plane of precession.\nAt the ballistic deflection and where tm is the computed time of flight, the function 4/x/3 has the form:\n\ng(x) = (4/3)*arcsin(1/x) when 4/x/3 is in radians.\n\nFrom its form, it is evident that g is a correction function. Ideally, the gyro should precess with an angular velocity:\n\n\u03c9 = (7 - 0) * 2 * pi * rpm / 60, and 0 = 'Her.\n\nFor tracking in general, i.e., not simply in azimuth, this would require the torque T to depend on the azimuth and elevation of the gyro axis. To simplify the mechanism, it was decided to make T depend only on azimuth. Hence, a correction function was chosen to minimize the error due to this design, and to distribute the remaining error as symmetrically as possible about the bore axis.\n\nSuppose now that a target is being tracked and that the gun mount is yawing. The output of the gyro gives:\nThe gyro angle is 7 degrees - 0. This output is first used to displace the stabilization mirror through this angle. At the same time, handlebar motion displaces the stabilization mirror by an angle of 4/3 degrees (refer to the gear-differential circuit in Figure 3). Consequently, if the mirror is rotated through 3^(7 - 0 - 4/3) degrees and the combining glass is rotated through y/2 degrees (no gear reduction), the line of sight will be deflected by 34.5 degrees according to the doubling principle of mirror rotation (Section 5.5.4). The gyro output is used secondly to displace the armature of the E magnet (see Figure 2). However, the gunner has rotated the transformer of the E magnet by 4/3 degrees. Therefore, the angle at the E magnet is 4/3 - (7 - 0), which is y - A (as per Figure 4). This is the error signal. For small displacements, the E-magnet voltage error is:\nage is proportional to this error signal. Turret servos are activated to move the turret in such a direction as to decrease this error.\n\nTo understand why we want y = A, take the derivative of a - 0 = My and use the relation:\n\ndt \n\nto obtain:\n\nIf \u20ac = y - A is the error, we have:\n\nIf A is to be a smoothed value of <7 - A &, as it should be, e must be kept at zero.\n\nIt follows that the accuracy of the lead obtained depends very heavily on the characteristics of the turret servo. Instead of subjecting the servo system to a componential analysis as was done in Sections 8.2.3 and 8.2.4, one may proceed experimentally.\n\nThis has the advantage of including inertia effects in the system. It has the disadvantage that the constants and form must be obtained as suitable averages for an appreciable sample. This is not possible.\nDuring design and construction of pilot models, the transit function H(p) of the system is obtained using the definition, typically found to be H(p) = P(p)/Q(p), where P and Q are polynomials. Manipulation yields the lead equation:\n\nWhere S(p) = yt^p + 1, and C is held constant.\n\nThis is the analogue of equation (2) or equation (3) for this sight.\n\n8.2.7 Errors Caused by Aircraft Accelerations in S-8B\n\nThe presence of the term involving the yaw of the gun mount, a, in equation (9) is an error. The severity depends on the servo system. Typical calculations show that if the gun mount is making a flat turn at a rate of 150 milliradians per second, the error will be less than 1.5 milliradians. However, suppose the aircraft is yawing harmonically so that:\n\n(yaw error) = a * (1/((2*pi*frequency)^2 - p^2) + 1/(2*pi*frequency*damping_ratio))\n\nWhere frequency is the natural frequency of the aircraft and damping ratio is the damping ratio of the system.\nAfter transients have decayed, the gun error settles down to:\n\nThe amplification BA is tabulated below.\n\nFrequency, / cycles per second\nAmplification BA\n1st experiment 2nd experiment\n\nTwo experiments were employed in the calculations. The steady-state error would be obtained otherwise.\n\nTo get the transient error, one solves and finds that the time constant is 0.4 sec; i.e., by that time, the transient will be less than 1/e of its initial value.\n\nThe Class B errors of the system will not be pursued further.\n\n8.2.8 Summary of Advantages of the S-8B:\n\nIn summary, the main advantages of the S-8B system are: (1) lead control (the handlebars control the lead and not the turret velocity\u2014the disturbed reticle principle is inoperative), and (2) variable aided.\na = + 1 /tm * ti; Velocity control of the line of sight is l/tm*n. Positional control of the line of sight is recalled from Section 5.3.4, \"Aided Tracking.\" Improved operational stability: if handlebars are given a jerk of size /z0 and then held at that value, the sight line responds with an equally sudden jerk in the same direction of size fio/S, then climbs along a line of slope 1 /tm and is fully stabilized.\n\n8.3.1 Desirability and Requirements\n\nWhen range and positional inputs to a fire control system are in serious error, the gun will only be pointed properly by a fortuitous combination of those errors. Repeated tests demonstrate the real difficulty experienced by a human gunner.\nHe attempts framing, tracking, and triggering simultaneously. This implies that radar inputs should be used to accomplish one or two of these operations automatically. Since framing is generally poorer and more biased than tracking (it being difficult to frame, for example, when the target is not centered), and since radar ranging involves the simplest type of radar equipment, it seems desirable to use radar range input for seen fire. In the case of unseen fire, it is essential that both range and rate be supplied by radar.\n\nRequirements for airborne radar gunnery aids include lightness and non-interference with aircraft speed. Ranging equipment weighs approximately 125 lb and is quite compact (the complete transmitter-receiver unit weighs 28 lb and fits in a can 15 in. long and 9 in. in diameter).\nThe internal resistance to the aircraft is roughly equivalent to another machine gun barrel and is, in fact, clamped to a barrel. The increased drag will cause a speed reduction of only a few miles per hour. For comparison, open bomb-bay doors cause a speed reduction of approximately 34 mph for the B-29 airplane.\n\nTurning to radar which tracks in angle, it might be presumed that an ultra-narrow beam should be used. The angular beam width is directly proportional to wavelength and inversely proportional to the antenna aperture. High frequencies would then be needed. Narrow beams also have the advantages of giving greater concentration of power (echo energy falls off as the fourth power of range) and of being less susceptible to interference (jamming). However, ultra-narrow beams (12 milliradians) have not been developed.\nUsed beam widths of 30 degrees have been employed, relying on proper antenna design for accuracy. For example, a dish antenna can perform a conical scan of angle 1.5 degrees about an axis that keeps pointing at the target. It is also possible to employ lobe switching in the antenna to achieve accuracy in determining the direction of a target.\n\nThe presentation of the radar output is important. In general, it is desirable to avoid visual presentation since this requires an operator who may make errors in utilizing this presentation. Even with automatic presentation, it is not desirable to consider the radar as purely ancillary, with a shaft rotation or voltage output fed into a standard computer. Instead, the original design should make provision for radar as an integral part of the system. Important simplifications may then be feasible.\nThe AN/APG-5, an Army-Navy Airborne Pulse Gun Laying system, is an airborne range-only [ARO] set operating in the S band with a 30\u00b0 beam width. It does not require precise antenna pointing towards the target. The effective tracking range is approximately 1,500 yards, with a probable error of +20 yards. The error is likely quasi-steady, meaning it may overrange by 10 yards during one run and underrange by 20 yards during the next. Such performance is excellent, provided it can be maintained under field conditions of calibration and maintenance. The AN/APG-5 searches automatically in range, sweeping from 200 to 2,000 yards twice per second. Upon encountering a target, it locks on and tracks automatically. The gunner must still manually track the target.\nin angle and trigger. Due to ground reflection, the present unit is not always dependable at an altitude of 8,000 ft.\n\nNomenclature for bands: P, 225 to 390 MHz; L, 390 to K, over 1,000 MHz.\n\nFurther information on the discussed sets will be found in the Summary Technical Report of Division 14, Volume 2.\n\n8.3.3 Range and Angle\n\nAirborne Gun Sights [AGS]: AN/APG-8 (inhabited turrets) and AN/APG-15 (remote turrets) provide not only range but also azimuth and elevation. The system weighs approximately 150 lb. It has the same range accuracy and angular coverage as APG-5, but employs the conical scan described above. However, tracking in angle is not as accurate as visual tracking. For tail warning and defense, point-blank fire is used. The presentation is a dot on a small cathode-ray tube (G scope), which must be kept focused.\nThe gunner adjusts it. A damping circuit is used to minimize \"jiggle.\" Precisely as with lead computing sights, a lag in presentation is a penalty. With a time constant of 0.5 sec (considered short), this lag is of the order of 0.83 seconds.\n\nSection 8.3.4: Airborne Gun Laying\nAirborne Gun Laying [AGL] equips AN/APG-1, AN/APG-2, AN/APG-3, and AN/APG-16. AN/APG-1 and AN/APG-2, which weigh approximately 600 lb and operate in the S band, and AN/APG-3 and AN/APG-16, which weigh about 250 lb and operate in the X band, are designed for fully automatic ranging and tracking in azimuth and elevation. Little information is available in current literature regarding tracking errors in angle. Estimates of accuracy have been as optimistic as 5 milliradians, but this depends somewhat on the angular rate. AN/APG-16 is engineered for use with the Sperry S-8 sight.\nThe antenna is a conical scanner, 9 inches in diameter, mounted in a ball 18 inches in diameter. This ball is rigidly fastened to the outside of the turret, such as the Sperry A-17 ball turret in the tail of the B-32. The ball contains motors and gears that spin and direct the antenna relative to the ball. When tracking, the axis of the conical scan points directly at the target. The motion of this axis is the vector sum of turret motion and motion with respect to the ball. Therefore, the relative displacement of the antenna within the ball is the lead, as the guns are boresighted with the turret, and it is an output of the S-8 system.\n\n8.3.5 Instability of a Radar-Gyro-Sight System\n\nThe following illustrates new challenges that may arise when radar is used in conjunction with a sighting system, specifically the instability problem (197-200).\nThe Armament Laboratory at Wright Field is testing British Automatic Gun Laying Turrets Mark I. Confidential. New Developments. The direction of the target is shown to the gunner through a collimated scope spot. A single gyro gunsight is used to predict the lead, and the guns are moved to keep the moving reticle of the sight on the synthetic radar target. Range is fed automatically. The radar has an appreciable lag (stickiness), and the synthetic target is governed by the equation:\n\ns = d/dt (p) * (7 + p + r)\n\nwhere s is a damping constant, p is the operator d/dt, and 7, p, r are respectively the angles that the gun line, radar target line, and actual target line make with some fixed reference line. The equation of the synthetic target.\nsight  is  familiar  from  Chapter  5.  Neglecting  ballistics, \nit  is \nwhere  a  is  the  angle  made  by  the  sight  line  with  the \nreference  line. \nSuppose  now  that  the  target  is  initially  astern  and \nthat  the  guns  suddenly  start  to  move  (under  some \naiming  disturbance)  according  to  y  =  y 0\u00a3,  where  y0  is \na  constant.  If  the  gunner  does  nothing  and  the  target \nremains  astern,  then  for  unit  gun  motion  and \nmotions  are  shown  in  Figure  5.  The  gunner,  since  the \nTIME  (SECONDS) \nFigure  5.  Radar  and  sight  responses:  AGLT  Mark \nI.  (Figure  from  British  source:  Armament  Depart\u00ac \nment,  R.A.E.) \nsight  seems  to  be  falling  behind  the  target,  will \naccelerate  the  guns  in  the  wrong  direction.  This \ndrags  along  the  radar  curve  \u2014  which  has  the  same \ninitial  slope  as  the  gun  line  \u2014  and  so  aggravates  the \nsituation.  If  the  gunner  could  actually  keep  his  sight \nThe transient term is damped and the system is stable only if the roots of the quadratic equation have negative real parts. This means that tms must be negative, which is not possible. One could obtain neutrality by making s negligibly small, but this is not possible since radar spot jitter must be damped. The difficulty arises because the initial slope of the radar curve is equal to that of the gun curve, while the initial slope of the sight curve is only a/(l + a) times that of the gun curve. It seems plausible to decrease the slope of the radar curve by first reflecting the target spot from the mirror of another gyro unit. If the equation of the auxiliary gyro is combined with the two original equations, it is readily seen that a parameter can be chosen to make the roots have negative real parts.\nassure stability of the resulting third-order differential equation. It is also possible to reduce the slope of the radar curve below that of the sight curve by an electric circuit such as that shown in Figure 6, in Figure 6. Stabilizing circuit: AGLT Mark I. (Figure from British source: Armament Department, R.A.E.) which the input voltage is proportional to displacement of the gun relative to the platform. The stabilizing signal is\n\nwhere a is the directional angle of the gun platform relative to the datum line, and P, Q, and R are circuit constants. The position of the radar target is given by\n\nIf this equation is combined with the sight equation, p being placed equal to o, a fourth-order differential equation arises whose stability can be established.\n\n8.4 NEW CONCEPTS\n8.4.1 Sight Parameter as a Function of Time\nOne of the early proposals for improving the performance of lead computing sights suggested varying the sight parameter a as a function of present range r. This work assumed that the target followed a straight line course and that the time-of-flight multiplier, tm, was the time of flight over present range, tp (this antedated the calibration concept). According to Section 5.3.4, \u201cDelay in Lead Computation,\u201d for positive a, the lag in lead computation of the smoothing circuit may just balance the error in tp if a is chosen properly. An analysis up to first order terms shows that a must be given by the expression:\n\na = c + r'\n\nwhere the constant c is to be chosen somewhat larger than the expected target speed, and r' = dr/dtp.\nfire  control  this  refinement  has  little  weight  for  three \nreasons:  (1)  against  curved  courses  approximating \npursuit  curves  tpoi  is  in  error  by  about  10  per  cent,  a \ncannot  be  chosen  to  affect  this  materially,  and  the \ncalibration  concept  effectively  does  the  same  job \nwithout  the  necessity  of  awkward  mechanizations  of \nvariable  a;  (2)  present  range  input  is  too  rough  to \nbe  efficient  in  determining  r';  and  (3)  any  improve\u00ac \nment  in  accuracy  is  completely  masked  by  much \nlarger  operational  errors. \nIt  is  evident  that  such  circuit  modifications  should \nawait  a  renewed  study  of  the  fire  control  problem \nwith  all  elements  in  proper  focus.  At  present,  the  idea \nis  much  more  pertinent  to  antiaircraft  fire. \n8.4.2  Exponential  Spot  Sights \nA  second  early  proposal 10^132  for  improving  lead \ncomputing  was  much  bolder  iA  concept.  The  equation \nconnecting  sight  angle  and  gun  angle  is \nSuppose the reticle pattern consists of a large number of spots which are not fixed but have relative motion with respect to the reticle center. Let \u03b8 be the angle between a line of sight to one of these moving spots and the datum line. Hold this spot on target. Then \u03b8 will satisfy the equation:\n\n\u03b8 = k log (r/r0)\n\nwhich means that the spot must approach the reticle center exponentially. Continuously rotating reticle discs which, when superposed, will give spots behaving in this way are shown in Figure 7.\n\nSuppose now that the guns are slewed rapidly to get on a target moving at a constant rate. With the usual sight, the reticle would be left behind, and it would take an appreciable time for the gunner to get on target. The whole point of this device is to eliminate this waste time. To illustrate this, let the guns be in correct lead position and moving at a velocity v. The target is moving at a constant velocity w. The time it would take for the gunner to get on target with the usual sight is given by:\n\nt = (r0/v) * abs(w - v)\n\nwhere r0 is the initial range to the target. With the new device, the time it takes to get on target is much less, as the moving spot on the reticle approaches the target exponentially. Therefore, the effective lead angle \u03b8' that the gunner needs to apply is given by:\n\n\u03b8' = \u03b8 - wt\n\nSubstituting the expression for t from above, we get:\n\n\u03b8' = \u03b8 - k log (r/r0) * (r0/v) * abs(w - v)\n\nThis equation can be solved for r to find the range to the target, given the known values of \u03b8, v, w, and k. This will greatly reduce the time it takes for the gunner to get on target and improve overall accuracy.\nIf the text is referring to a specific concept related to optics or mathematics, I will attempt to clean it while maintaining its original meaning. However, without additional context, it is difficult to determine the exact nature of the text. Here's a cleaned version of the text:\n\nSuppose the reticle does not yet have correct lead position, but there is a spot on the target that appears fixed, and spots to the right and left are converging towards it. Analytically, let o = yQt - ooe~t/<l+a)tm. For constant tm, the spot n for which kn = o0 remains in correct lead position since y on = To tm-. Furthermore, since the remaining spots converge on n, this demonstrates the value of the idea. However, it is not the whole story (tm was held constant and the field may not be wide enough). This ingenious idea may be assessed as a patching-up of existing gear. It is not clear what method would be used to get a framing circle to move suitably. This is a new development. (CONFIDENTIAL)\nBut the principle of the rotating reticle may well be kept in mind. Figure 7. Exponential spot reticle.\n\n8.4.3 Aided Tracking on the Line of Sight\n\nA frequently neglected point in the design of equipment is ease of control (which affects the efficiency of operation). This phase of the design involves the experimental study of such details as inertia, friction, and cramping, using gunner subjects. It may involve more subtle matters. As an example of the latter, it has been proposed that aided tracking on the line of sight be used in conjunction with a single gyro.\n\nSuppose that the voltage derived from the handlebar position is fed not only to the turret motors, but also to the sight after it has been differentiated (see footnote to Section 8.4.4). Superimpose on the voltage source for the trail coil circuits (Section 5.5.5).\n\"The magnetic center towards which the gyro axis precesses is shifted through an angle. The gyro precessional rate is now given by: 6 = y - (1 + a). If the yaw of the gun mount is a, then for a velocity-controlled turret, the absolute gun position is determined by: 7 = n + kp(p - d/dt), where n is the displacement of the handlebar controls. Using this relation to eliminate y, the lead equation is: Bn + kp(p - d/dt). The sight line equation is: p.i. (The term involving da/dt can be construed as an error since it causes motions of the gun mount to interfere with the correct positioning of the sight line. Neglecting aircraft motion, the response of the sight line is inferred from the preceding equations.)\"\nThe text appears to be written in a formal, technical style with some mathematical equations. I have made the following cleaning adjustments while preserving the original content as much as possible:\n\n1. Removed unnecessary line breaks and whitespaces.\n2. Removed the \"CONFIDENTIAL\" and \"NEW CONCEPTS\" labels, as they are likely modern additions.\n3. Corrected some minor typos and formatting issues.\n\nThe cleaned text:\n\nThis shows the direct (or positional) tracking effect of the coupling of handlebars to sight. On the other hand, the sudden change in angular velocity of the sight line, A (pa), caused by a sudden change in handlebar position dn, can be obtained by solving for e. The constant B is not always a constant for all turrets. It may be, for example, B + An |.\n\nNeglecting Bn/p and k\u03c0u/(l + a), i.e., the integral of Bn, which is Bn/p, over an interval of zero length, and the derivative of n is zero at both the beginning and end of the step-jump in n-\n\na\nk\nAm.\n\nThis shows the velocity tracking effect. For constant B, if\nIt is recommended that circuits such as these be studied with the aid of simulating electronic circuits in which various parameters may be varied.\n\nSection 8.4.4 Correction Mechanisms for Target Course Curvature\n\nA serious effect on the deflection put out by computing sights has been noted throughout previous chapters due to the neglect of course curvature. Mechanisms have been proposed which will take this into account, not by the naive expedient of flipping a switch from 100 to 90 percent of present time of flight in going from rectilinear to curved target paths.\n\nBy equation (11) of Chapter 2, the correct kinematic deflection is given quite closely in terms of:\n\nthe target course curvature\nthe velocity of the projectile\nthe angle of sight\n\nTherefore, an appropriate correction mechanism should take into account the target course curvature in order to provide accurate deflection for computing sights.\nAngular momentum, M = r\u00b2 * m, of a target with unit mass. This deflection can be written as +Sm. The classical lead computing sight contains a potentiometer A, Vq. Even this value might be corrected by utilizing the rate of change of present range, assuming good input of range. The point of the present discussion, however, is to indicate a mechanism which can be combined with an ordinary gyro sight to yield the angular momentum correction.\n\nUse a single gyro from a K-15 sight, without the f ballistic coils. The deflection of the mirror of this gyro is made proportional to M by feeding a current to the range coils through a nonlinear potentiometer (r\u00b2) whose position is determined by present range r.\n\nStudies were made, for example, at the Marcellus Hartley Laboratory of Columbia University under J. B. Russell.\nThe light reflected from this gyro mirror is to come through a reticle of such variable transparency that the intensity of passing light at any point is proportional to the logarithm of the distance from the center. After reflection from the gyro mirror, the light hits an opaque screen with a small central hole behind which is a photocell. Since only that part of the reticle yielding light proportional to In M hits the photocell, the voltage output of the cell is proportional to In M. This voltage is amplified linearly and fed into a circuit containing a condenser, which differentiates In M,g, and containing a range potentiometer which introduces tf/2. By means of a servo, a rotation proportional to ln[1 + (\u00a3/2)(dlnt M/dt)] can be introduced in one side of a differential. The input to the other side is proportional to In r.\nThe differential's output (the sum) may then be sent to the range potentiometer of the gyro sight, and the correction has been effected. The gain in accuracy is most significant when this correction is made. The effect of roughness in the input of r and co is, nevertheless, still open to question. It is also possible to utilize variable speed drive computers (ball-cage integrators) to apply this correction to the stabilized S-3 sight.\n\n8.4.5 An Own-Speed Plus Rate Mechanization\n\nLead computing sights have decomposed deflection into kinematic and ballistic components. Other decompositions and consequent mechanizations are possible. To keep one such new idea clear, various parts of the proposal (corrections for target and gun platform accelerations, and use of range rate) will not be considered.\n\nA basic lead equation of gunnery is equation (1) of Chapter 2. It is:\n\n(velocity of projectile + velocity of gun platform) x (time of flight) = range + constant\n\n(velocity of projectile + velocity of gun platform) x t = r + C\n\nWhere:\nvelocity of projectile = muzzle velocity\nvelocity of gun platform = platform velocity\ntime of flight = time between firing and impact\nrange = range to target\nC = constant (includes correction factors)\n\nr = range rate + range error + target motion error + platform motion error + windage error + elevation error\n\nTherefore, to calculate the lead, we need to calculate the range rate and the various error terms. The range rate can be calculated using the rate gyro and the platform acceleration sensor. The various error terms can be calculated using the correction factors and the sensor data. The lead is then the difference between the calculated range and the actual range.\n\nThe lead equation can be written in differential form as:\n\ndl = (velocity of projectile + velocity of gun platform) dt = dr + dC\n\nWhere:\ndl = change in lead\ndt = change in time\ndr = change in range\ndC = change in constant\n\nThe lead rate is then:\n\ndl/dt = (velocity of projectile + velocity of gun platform)\n\nThe lead rate can be calculated using the platform acceleration sensor and the rate gyro. The lead rate is used to calculate the lead correction, which is applied to the sight to keep the projectile on target.\n\nThe lead correction is given by:\n\ncorrection = lead rate x time constant\n\nWhere:\ntime constant = the time it takes for the sight to respond to the lead correction\n\nThe lead correction is then applied to the sight using a servo motor. The lead correction is continuously adjusted to keep the projectile on target.\n\nThe own-speed plus rate mechanization is an extension of the lead mechanization. It takes into account the own-motion of the platform and the rate of change of own-motion. The own-motion can be calculated using the platform acceleration sensor and the gyro. The rate of change of own-motion can be calculated using the rate gyro.\n\nThe own-speed plus rate equation is:\n\n(velocity of projectile + velocity of gun platform + velocity of own-motion) x (time of flight) = range + constant\n\n(velocity of projectile + velocity of gun platform + velocity of own-motion) x t = r + C\n\nWhere:\nvelocity of own-motion = own-motion of platform\n\nThe own-speed plus rate equation can be written in differential form as:\n\ndl = (velocity of projectile + velocity of gun platform + velocity of own-motion) dt = dr + dC\n\nThe own-speed plus rate correction is given by:\n\ncorrection = (velocity of projectile + velocity of gun platform + velocity of own-motion) x time constant\n\nThe own-speed plus rate correction is applied to the sight using a servo motor. The own-speed plus rate correction is continuously adjusted to keep the projectile on target, taking into account the own-motion of the platform.\n\nThe own-speed plus rate mechanization provides greater accuracy than the lead mechanization, as it takes into account the own-motion of the platform. However, it requires more complex sensors and computations.\nThe mechanization suggests using a standard own-speed sight (the 0 computer) to mechanize vG with no percentage correction. It uses a rate computer to deal with vT sin a/v0 (the T computer). Since target speed and approach angle are not known, the T computer proceeds by accepting as inputs vg sin t/vo and ru/v0 (determined by ranging and gyro-tracking), and yielding through a smoothing circuit an angle Xy. The smoothing circuit suggests that a be a function of r to give less damping.\n\nConfidential\nNew Developments\n\nThe mechanization suggests using a standard own-speed sight (the 0 computer) to mechanize vG without percentage correction. It uses a rate computer to deal with vT sin a/v0 (the T computer). Since the target speed and approach angle are not known, the T computer proceeds by accepting as inputs vg sin t/vo and ru/v0 (determined by ranging and gyro-tracking), and yielding through a smoothing circuit an angle Xy. The smoothing circuit suggests that a be a function of r to give less damping.\nFor projectiles with proper shape and velocity in the range where the three-halves power drag law applies, the output must be combined with the ballistic factor q. The air density p, and the constant b are as follows: p = 0.00323 (when length is in yards), b = 0.00186 (when length is in feet.\n\nThe actual air range covered by the bullet, in the absence of useful range rate, can be approximated by:\n\nwhere c is a constant. For approach angles not exceeding 30 degrees, this is very effective. The velocity of departure, u0, is given adequately by:\n\nu0 = ^Gproj * mount velocity component along present range line.\n\nIt is the above quantity q that needs to be computed with precision. Through it, ballistics are taken into account.\nThis system does not require separate trail ballistic circuits. The time of flight (tf), determined by lead computing sights, enters only in making the small curvature correction (see equation (7) of Chapter 2). A simple estimate tf = r/v0 should prove satisfactory.\n\nThis own-speed rate system offers advantages when used against curves approximating pursuit curves, flown against one's own bomber or a neighboring bomber in formation. The reason is that only a small part of the total lead is subjected to the smoothing circuit. Consequently, percentage errors of the same size as those of a normal rate-time sight now generate a small absolute error. Against forward hemisphere attacks, the advantage is even more marked. The initial error will be small and at close ranges when the required deflection builds up.\nThe rapid change in own-speed deflection makes gun pointing quite good, primarily because of the presence of the 0 computer. 8.4.6 General Approach to the Tracking Equation\n\nThe study of a complete fire control system requires a understanding of the tracking equation that connects handlebar motion to sight line motion. In the case of manual operation by a human gunner, a theoretical description of the complete system is difficult since the gunner's responses cannot be described exactly - he is an imperfect servomechanism. Consequently, up to the present, experimental and statistical procedures have been used rather than theoretical analysis. It is evident that the advent of automatic inputs will make mathematical methods more appealing. However, the elements of a general theory are useful even in the absence of automatic inputs.\ncase of manual operation 53: for which only probable behavior on the part of the operator may be assumed. To illustrate the methods of the theory, consider aided tracking combined with a lead computing sight. The gun position, 7, is connected to the handlebar angle, /x, by:\n\nThe sight equation relates gun angle to the sight line angle, <r, by:\n\nIf 7 is eliminated between these two equations, then:\n\nIt will be noted that tm is permitted to vary with time. The solution of this equation may be written in the form:\n\nwhere\n\nThe artificial time, r, moves faster than t if tm < 1.\n\nMore generally, suppose that the gun-handlebar equation is:\n\nand that the gunsight equation is:\n\nwhere R, R', P, and Q are polynomials in p \u2013 d/dt whose coefficients depend on tm. If tm is held constant, the tracking equation is:\n\nRQa = PR' jl.\nThe tracking equation with tm variable is not easily obtained. Since, however, the change in tm due to ranging has little effect on the nature of tracking, this equation can be used to infer various properties of the tracking performance. For example, there are various solutions of the tracking equation depending on the initial handlebar motion. If the difference of some pair of these solutions does not approach zero, the tracking is essentially unstable. (The operator could track a target at rest by handlebar motion not approaching a position at rest.) The difference between any pair of solutions must satisfy the equation:\n\nThis has a non-zero solution if and only if PR' has a non-negative root. (For example, for aided tracking with a lead computing sight, the roots of PR' are -B/A and -l/atm- Stability is the\n\n(Note: The text appears to be written in a clear and modern English, with no major OCR errors or unreadable content. Therefore, no cleaning is necessary.)\nThe general equation can be used to study hunting and the response to handlebar jerks. The most useful form of the solution to the tracking equation is given by operational methods employing the convolution integral. The reason is that the resulting solution expresses cr(t) as a weighted average of earlier values of y(t). This was illustrated explicitly in the preceding paragraph. The solution to the tracking equation with constant coefficients is:\n\nJ(s) = F(s) / (1 + Ts*s)\n\nFurther details and interpretation will not be given. In summary, methods of this nature will be exploited in future problems of overall system design and system response. These general methods will likely require extension to nonlinear systems, only special examples of which have been discussed.\nFighters \nThe  conventional  fighter  can  mount  a  heavy  for\u00ac \nward  firing  battery  at  minimum  cost  in  installation \nweight  and  balance.  The  penalty  is  that  the  entire \naircraft  must  be  aimed  and  must  fly  a  predictable \ncourse,  the  pursuit  curve,  if  a  succession  of  hits  are \nto  be  scored  on  a  bomber  target.  At  the  other  end  of \nof  the  scale  is  a  turreted  fighter  which  may  fire  as \nflexibly  as  its  target.  The  P-61  is  an  example.  This \ntype  is  penalized  not  only  by  increased  weight  and \nsize,  and  crew,  but  also  by  all  the  difficulties  in  taking \ndeflection  experienced  by  the  defending  bomber.  A \nmiddle  course  appeared  feasible  during  the  closing \nmonths  of  World  War  II.  If  fixed  guns  are  installed \nat  a  large  angle  to  the  thrust  axis,  installational \nweight  is  not  significantly  increased,  the  modification \nis  possible  for  many  existing  fighters,  and  there  is  no \nThe following questions must be answered: (1) What are the advantages of increasing crew? (2) What is the aiming problem with an offset installation? (3) What are the disadvantages? Considerable study has been devoted to these points.\n\n8.5.2 Attack by Pacing Behind and Below\n\nAn attack is advantageous to a fighter if its attack path is nearly rectilinear, so that coordinated banked flying under conditions of high load is not required. If the deflection required is small and does not change rapidly, and if continuous fire may be put into the bomber until destruction ensues.\n\nThe simplest method of gaining these advantages with an offset installation is to mount the guns pointing upward and forward in a vertical plane at such an angle that, for pacing flight below and behind, and over a considerable range interval, the backward deflection required is negligible.\nThe trajectory curve caused by recoil is sensibly balanced by the forward and downward curves, attributed to gravity and parallax correction caused by gun and sight separation. The feasibility of this depends on the ballistics of the ammunition employed. For instance, using API M8 caliber .50, an offset angle of 30 degrees, and a parallax distance of 2 yards, the total lead required is: 4 milliradians (\u00b11) for a speed of 175 mph, 6 milliradians (+1) for a speed of 250 mph, 8 milliradians (\u00b12) for a speed of 325 mph. These negligible variations correspond to a range interval of from 100 to 400 yards. Given an offset angle and a range interval, it is necessary to design special ammunition to achieve constancy of lead. Then the attacker need not determine speed and range with precision. With unspecified ammunition, the required lead varies significantly.\nsuitable ammunition, for example, typical Japanese. An offset of 45\u00b0 with a parallax of 2 yards requires a deflection increase from 13 to 28 milliradians (at 250 mph) as the fixed range at which the attack is made changes from 200 to 500 yards, and from 18 to 42 milliradians (at 325 mph) over the same range interval. The attack is still possible, but if it is not made at a precalculated speed and range, the pilot must lay off deflection.\n\n8.5.3 Attack on Collision Course\nA second possibility is to attack on a collision course. The attacker crabs in on a path which in relative motion is a straight line terminating at the bomber. If the guns are offset slightly forward of this relative path (to allow for trail), then continuous fire is possible with but little change in the required small deflection. (During World War II)\nThe German Air Force occasionally tried skidding attacks with conventional fighters. This is equivalent to mounting guns at a small offset. Without the aid of a gyroscopic lead computing sight, it is difficult to fly. Using the notation of Figure 1 in Chapter 3 and formula (1) in Chapter 2, the lead angle between the relative path and the bore axis must be 1000^(-sin(8/v0i)), where vF sin(8) = vB sin(0) is the collision course condition. The term l = q - 1 is an almost linear function of pP/c5. Consequently, the larger the ballistic coefficient is, the smaller the spread in l over a given range interval will be, and the more efficient a fixed average offset from the relative path will be.\n\nTwo methods of making this attack are possible. Suppose first that the sight is offset by an angle \u03b8.\nthe guns by an angle of 8 degrees with respect to the vertical, where l is an appropriate average. Use a fixed fighter speed and fly so as to keep the target centered in the offset sight. Then, for a value of 0 different from the optimal given by vF sin 8 = vB sin 0, the fighter's path will curve (quite gently) and aiming errors will occur. As a numerical example, if vF = 440 fps, vB = 321 fps, altitude = 20,000 ft, and API M8 ammunition is used, then, with a sight offset of 45\u00b0 15' and gun offset of 45\u00b0, the angle off can vary from 70 degrees to 120 degrees off nose, and the aiming error will vary only from a maximum of 9.7 milliradians behind a (point) target to a maximum of 5.8 milliradians ahead of it. As a second method, suppose the pilot keeps the target centered in his offset sight.\nBut a fighter adjusts his speed according to vF = vB sin (\u03b8/sin \u03b8). In this case, a true rectilinear course is flown, and the error will again be slight. Tactically, the accuracy of the fighter's fire should not depend critically on initial range and bearing. Allowance for error must be permitted. Similarly, a variation in the calculated speeds of fighter or target must not cause the accuracy to deteriorate too much.\n\n8.5.4 Discussion of Offset Gun Attacks\n\nThe discussion above indicated that specialized attacks of this nature are possible. However, there are serious disadvantages. If a fighter armed with offset guns attempts to make any kind of pursuit curve or attack in a slant plane, his required motion will be a twisted space curve with curious torsion, which probably cannot be flown. In particular, a fighter without a forward battery can hardly attack another fighter.\nEven against a bomber, the arguments of Sections 8.5.2 and 8.5.3 are based on a bomber that maintains a straight and level course. Mild evasive action can cause the attack to abort. Assuming the bomber does cooperate by flying a rectilinear course, the fighter is an equally easy shot for any of the fire control systems of Chapter 5 which have well-adjusted, i.e., variable, trail allowances.\n\nIn view of these disadvantages, these attacks are most promising when made by a night fighter. For this case, the parallel course attack of Section 8.5.2 is probably best. The defensive radar tail-cone search can be avoided, and, if provision is made for both upward and downward firing guns, proper advantage of night sky conditions may be taken. These attacks would also be dangerous to a bomber which has stripped its armament.\nIn assuming fighters employ tail-cone defense for speed and additional payload, it's noted that Section 8.5.3 paths are collision courses, making them as appealing to guided or self-guided missiles as homing courses.\n\n8.5.5 Upward Barrage Fire\n\nInstead of conventional machine gun armament in fighters, upward barrage fire at close range has been suggested.1 The installation consists of 40 barrels, each containing only one round, mounted to fire upward. The attack is to be from the front and initiated by a dive down and across the bomber's bow. Upon pull-up below in the same vertical plane, the tubes are ripple-fired automatically by acoustic pickup from the bomber\u2019s propellers or by\nThe optical pickup of the bomber's shadow. The range of fire is to be 50 to 100 m. This means that the violent motion described on the attacker's part is necessary if he is to arrive unscathed at the firing point. Reliance is placed on a linear pattern approximately 80 meters long, rather than on a precise estimate of deflection.\n\nThere are certain technical difficulties. To avoid high recoil, a low muzzle velocity of the order of the firing aircraft's speed is to be used. Consequently, large caliber (2.0 to 2.5 cm), high-explosive, and fused projectiles must be used. The initial yaw is of the order of 40\u00b0. For a spin-stabilized projectile (rifling of 30 calibers per revolution), this yaw does not damp sufficiently to assure an angle of impact favorable to the functioning of the fuse. A fin-stabilized projectile is more satisfactory.\n\nSummary:\nThe optical pickup of the bomber's shadow is used, with a range of fire between 50 and 100 meters. Technical difficulties require a low muzzle velocity, large caliber high-explosive projectiles, and a fin-stabilized design for stability.\nSection 8.1 limits the chapter to those ideas in hand during the closing months of World War II. The next phase in fire control development should include the interrogation of Doetsch, Blank, Rossman, Schiissler, Hackeman at the Luftfahrtforschungsanstalt, Braunschweig, Germany. E.W. Paxson, June 28/29, 1945. A judicious blend of principles now known to be essential is pleaded for by the designer. The shape of expected tactical situations is requested.\n\nSection 8.2 deals with systems that stabilize the gunner\u2019s line of sight by removing perturbations caused by aircraft motion. The theory of the rate-stabilized Fairchild S-4 system is brought to the point of deducing the complete circuit equations. The position-stabilized Sperry S-8B sight is discussed similarly, although the circuit response equation is obtained experimentally rather than analytically.\nStabilization does not extend to aircraft accelerations, and the time constants of follow-up circuits must be carefully considered. Section 8.3 discusses the use of radar in supplying automatic inputs, in range and in bearing, to a fire control computer. Conditions of instability in tracking are mentioned briefly. Section 8.4 introduces the following concepts: (1) the variation in the sight parameter as a function of range, (2) a mechanism designed to partially cheat the transient time in a lead computing sight, (3) the use of aided tracking on the line of sight, (4) an ancillary circuit for lead computing sights which gives a correction for target course curvature through the rate of change of the angular momentum of the target about the gun, (5) the mechanization of a decomposition of lead into own-speed allowance and target motion.\nSection 8.5 considers new tactics: a fixed offset gun in a fighter attacking on a pacing course, its use on a collision course attack, and upward barrage fire at close range. Section 8.5 does not discuss air-to-air rocketry or air-to-air bombing. For information on guided and semi-guided missiles, look elsewhere.\n\nCONFIDENTIAL\nPART II\n\nROCKETORY\n\nCONFIDENTIAL\n\nChapter 9\nFIRE CONTROL FOR AIRBORNE ROCKETS\n\n9.1 INTRODUCTION\n\nIn the spring of 1944, the Applied Mathematics Panel initiated its rocketry program in response to a request from Division 7, NDRC, for its cooperation in the development of the best possible computer methods for calculating the trajectories of airborne rockets.\nThere were requests from Division 7 and the Navy for assistance with various aspects of the rocket sighting problem. As a result, AMP's activities in this field fell into three categories.\n\nFirst, there was a general study of feasible sighting methods for rockets. The essential problems involved in this question relate to ballistic formulas, attack angle and skid, the effect of wind and target motion, how these factors affect each proposed sighting method, and how tracking is affected and affects them. Two AMP reports consider these general aspects of the problem and provide formulas relating to the quantities involved.\nThis chapter is based largely on the material in the first report, which is fundamental to any future work concerned with the development of computing sights for rocket firing. The chapter discusses in detail various sighting methods. Principal ballistic questions involved in the problem are presented, along with a simplified treatment of kinematic lead. Questions involved in the design of a computing mechanism are set forth.\n\nTwo specific proposals for rocket sights were made and studied. For instance, a range-finding method using the Mark 23 gyro sight was studied. A miniature rocket sight called PARS, consisting of a mechanical addition to an altimeter with an electrical connection to a sight head, was proposed and scheduled for testing. A brief discussion of these proposals follows.\nThe characteristics of this sight are described in the Division 7 Summary Technical Report. AMP participated in the development of a 'pilot's universal sighting system' (PUSS) from 11-15, 29-31, as reported in Division 7 Summary Technical Report, and conducted related studies on toss rocketry from 18-23 and toss bombing in the presence of Third. A method was formulated for determining if pilots attempting to fly a diving course at a target skid badly enough to cause a substantial error in rocket fire. For further information on this and other detailed questions studied by AMP, the reader is referred to the reports listed in the bibliography at the end of this volume. One of the principal advantages of rockets over shells is that no heavy gun or gun mount is needed in rocket firing, as the recoil is taken up by the rocket itself.\nFor stability, rockets here are constructed with fins near the tail. These fin-stabilized rockets, fired forward from aircraft, have become an important weapon of warfare. Due to their relative newness as an aircraft weapon, the problem of how they may best be aimed is not yet fully understood, and no very satisfactory computing sight was in service at the termination of hostilities. The problem is considerably more complicated than that of aiming bullets. In the first place, due to the presence of the fins, the rocket picks up most of its velocity in the direction of motion of the airplane in the surrounding air mass; this may differ from any fixed direction in the airplane by a considerable amount. Determining this direction is a difficult job. Secondly, except at short ranges, the rocket's trajectory is influenced by various factors such as wind, air density, and temperature, making accurate aiming even more challenging.\nThe gravity drop must be accounted for in ranges, as it can be many degrees at 3,000- to 4,000-yard range. This requires some knowledge of the range, and there is no simple known instrument for use in a fighter plane which gives the range. A third consideration which affects the whole character of the problem is the temperature of the propellant grain, dependent on the initial temperature (determined by storage conditions) and affected by the altitude at which the airplane may have been traveling for some time before the attack. Finally, the projectile takes normally two to ten seconds to reach the target. By this time, the target may have moved a considerable distance relative to the air mass. The ammunition temperature also plays a role.\nThe dispersion amounts to only a few mils, and since most targets for aircraft rockets are rather small \u2013 tanks, locomotives, gun emplacements, and small shipping, for example \u2013 obtaining an accurate solution to the sighting problem is of great advantage.\n\n9.2 Fin Stabilized Rockets\n\nRockets are normally held under the wings of the aircraft. When fired, they accelerate, increasing their velocity to a maximum of usually 600 to 1500 fps, depending mainly on the type of rocket. Burning time for most rockets is about a second; it depends greatly on the temperature of the propellant, being shorter at higher temperatures. After burning, the rockets slow down again, due to drag.\n\nThe launchers commonly used now are zero-length launchers. The rocket is suspended at two points, and becomes free after it has traveled an inch or less.\nThe air acts strongly on the fins of a rocket as soon as it leaves the launcher if it is not already pointed in that direction due to angular momentum, causing its direction to oscillate with decreasing amplitude about the direction of its vector velocity. For sighting purposes, these oscillations can be neglected if one determines their overall effect on the general direction of the path. This is accomplished by defining an effective launcher line, a line a certain fraction of the way from the launcher line (the line of the rocket at firing) to the velocity vector relative to the air.\nThe air mass of the airplane firing the rocket. The value of / is commonly between 0.8 and 0.99. For the 5-in. HVAR rocket and in the vertical plane, / is given approximately by the formula:\n\nwhere T is the propellant temperature in degrees Fahrenheit and Vi is the indicated airspeed of the launching airplane in yards per second. Thus, / depends on indicated airspeed and propellant temperature, but not on dive angle. Numerical values of / are given in report 5, which we shall hereafter describe as the \u201ctables.\u201d The / factor in the lateral plane need not equal the factor in the vertical plane, but probably is close to it. Accordingly, the effect of skid (motion perpendicular to the plane of symmetry of the aircraft) is important: Suppose, for example, that the velocity vector of the aircraft points 20 mils to the right of its symmetry plane.\nThe plane of symmetry. Then the rocket will turn 20/ mils into the wind. If the target were fixed and if the plane of symmetry of the aircraft contained it, this would lead to an error of 20/ mils, which is of the order of 18 mils.\n\nThe purpose of defining an effective launcher line and the / factor is this: In our analysis, the effective launcher line is taken as the initial direction of the trajectory. Knowledge of this effective initial direction is necessary to permit the determination of the manner of flying the launching aircraft which will be most likely to achieve a hit.\n\nIf a long launcher (rail or tube) were used, or if the rocket propellant were faster burning, / would be smaller. For a bomb, / = 1. For a machine gun bullet, the initial velocity of departure is the vector resultant of the velocity of the airplane acting in the instant.\nThe effective direction of motion and the velocity provided by the propellant, acting along the bore axis (launcher line), is obtainable from a vector diagram. In the case of rockets, the effective launcher line gives us the effective initial direction of the trajectory. The trajectory itself, relative to its effective initial direction, is then given by the angular gravity drop Xg and time of flight tf.\n\nIf the rocket had its full velocity at the start, it would follow approximately a parabolic path, and the angular drop due to gravity from the effective launcher direction to the rocket would be approximately proportional to the time the rocket had traveled to any given point, and hence to the range r.\n\nAerodynamic aspects:\n9.2.2 The Angular Gravity Drop Xg; the Time of Flight tf\n\nIf a rocket had its full velocity at the start, it would follow approximately a parabolic path. The angular drop Xg due to gravity from the effective launcher direction to the rocket would be approximately proportional to the time of flight tf and the range r.\nThe constant B0 is greater than Bir by a certain amount due to the effective launcher's slow speed and downward direction in the first part of its trajectory. Both constants Bq and Bi are approximately proportional to the cosine of the dive angle y from the horizontal to the effective launcher direction in the vertical plane. We can write this as an approximation: B0 = A0 + Ay, where A0 and Ai are constants. For the 5-in. HVAR, A0 is approximately 15 mils, and Ai is about 16 mils per thousand yards; they depend on the plane's airspeed and propellant temperature.\n\nBecause of the slow speed at the start of burning, the time of flight tf, at fairly short ranges, is not significant.\nproportional  to  the  range  but  is  nearer  a  constant \nplus  a  multiple  of  the  range.  At  longer  ranges,  when \nthe  speed  has  died  down  again,  the  time  of  flight  is \napproximately  proportional  to  the  range.  A  quadratic \nfunction  of  range  with  coefficients  depending  slightly \non  own  speed  gives  tf  to  within  0.1  sec.la \nNumerical  values  of  gravity  drop  \\g,  angle  of  fall, \nand  time  of  flight  tf  are  given  in  the  \u201ctables.\u201d  5  At \nr=  3,000  yd,  for  the  5-in.  HVAR  rocket,  \\0  may  be  as \nmuch  as  100  mils;  tf)  as  much  as  7  sec.  Formulas  for \nthese  quantities  in  terms  of  range  to  target  at  impact, \ndive  angle  (omitted  in  the  case  of  time  of  flight),  air\u00ac \nspeed  of  launching  airplane  and  propellant  temper\u00ac \nature  are  available.113 \n9.2.3  Average  and  Instantaneous \nProjectile  Speeds \nThe  average  speed  V  is  obtained  by  dividing  the \nrange  r  by  the  time  of  flight  tf.  Some  values  of  V  for \nThe 5-inch HVAR, traveling at a own speed of 300 knots and a propellant temperature of 70 F, have the following specifications. Fifty yards per second is a good round value. At lower temperatures, it takes longer for the rocket to burn and hence reach its maximum speed; therefore, flight times are longer, and average speeds are less.\n\nA formula giving roughly the variation of V with the plane\u2019s airspeed vkn in knots or v in yards per second is:\n\nV = 500 + 1.5 * vkn\n\nThe variation with propellant temperature is not large and not worth taking account of, considering the inaccuracy already present.\n\nThe instantaneous projectile speed, for instance, at a range of 503 yards per second at 2,000 yards range, and 400 yards per second at 4,000 yards range.\n\n9.2.4 Dispersion\n\nThe dispersion of actual rockets about their average position (all being fired under the same conditions) is only a few mils. The radius of the 50-mils circle is:\nLet v* be the vector velocity relative to the air mass of the aircraft at an instant. We break v* into two components: v in the plane of symmetry of the aircraft and vs perpendicular thereto. For altitudes h less than 11,000 ft, the relation between indicated airspeed Vi and true airspeed v is: v = Vi * sqrt(1 + (0.0002582 * (11320 - h) / Vi))\n\nThe vector vs is the skid. We use the term true airspeed for the magnitude v of the vector v. (Since skid is small, v is sensibly equal to v*, the magnitude of the vector v*.) The skid speed is vs, the magnitude of the vector vs.\nIn the plane of symmetry of the aircraft, there is a direction in which the rockets are held prior to their launching. This direction is known as the launcher line or datum line. In general, the datum line is merely a line of reference in the plane of symmetry of the aircraft. We assume for simplicity that the launcher line, datum line, and thrust axis are the same. If these lines differ appreciably, the necessary adjustments in our analysis can and should be made.\n\nThe angle of attack a is the angle from the datum line to the aircraft\u2019s velocity v in its plane of symmetry. We adopt the convention in our diagrams that an angle in the clockwise direction is positive. Thus, the angles a0, a, and fa in Figure 3 are negative, and the other indicated angles are positive.\nConsider the plane of symmetry of the aircraft, and suppose that it is vertical. Let \u03b8 be the angle from the horizontal to the datum line. If there were no gravity acting, the aircraft (in steady flight) would move approximately along a hypothetical line in its plane of symmetry; this line is called the zero lift line. The zero lift line is at some angle a0 from the datum line; being above the datum line in the figure, a0 is negative. Due to the influence of gravity, the flight direction is at some angle a \u2013 a0 below the zero lift line. The lifting power of the wing is approximately proportional to the square of the airspeed; it is also proportional to a \u2013 a0 up to a certain point. Therefore, a \u2013 a0 is inversely proportional to the square of the airspeed. The appropriate speed here is the effective airspeed v, which depends on the density of the air.\nIn steady horizontal flight, the indicated airspeed (Vi) is used instead of true airspeed as measured by the airspeed meter. Vi is less than the true airspeed due to reduced air pressure at higher altitudes. For combat planes, the constant b, which has the dimension of distance, is commonly between 14.6 and 16.7 feet. In steady horizontal flight, we can write:\n\nVi = \u221a(h * g + b\u00b2)\n\nwhere g is the acceleration due to gravity (10.7 yd/sec\u00b2), and h is measured in feet.\n\nFigure 3 illustrates the angles associated with a rocket trajectory. The flight angle (\u03b8) is the angle from the horizontal to the line of flight. The dive angle (y) of the rocket is the angle from the horizontal to the effective launcher line.\n\nIn a steady climb or dive, only the component of gravity (g cos \u03b8) acts upon the rocket.\n\nHorizontal\nZero Lift Line\nFlight Direction, y\nEffective Launcher Line\nDatum Line *\nLauncher Line*\nThrust Direction\n\nThe flight angle (\u03b8) is the angle from the horizontal to the line of flight. The dive angle (y) of the rocket is the angle from the horizontal to the effective launcher line. In a steady climb or dive, only the component of gravity (g cos \u03b8) acts upon the rocket.\nIf eight degrees of gravity need be considered, perhaps an angle different from eight degrees should be used. It is difficult to determine exactly what angle fits best, but the final results would probably not differ significantly. If an airplane is nosing up or down, there is centripetal acceleration in the direction normal to the flight path to be taken into account. If R is the radius of curvature of the flight path, and <\u00a3 = dt/dt is the time rate of turn of the flight path, then, since g sin \u03b8 = a, further, since the lift required on the airplane is proportional to its weight W, b is proportional to W. Hence equation (3) now becomes:\n\nVi = (g cos \u03b8 - a) W / S C_L\n\nwhere b' is a constant. This relation is the attack angle formula, the attack angle \u03b8 being the angle from the datum line to the flight line.\nWe are interested in the effective attack angle of the rocket, the angle from the datum line to the effective launcher line. This is denoted as fa, determined by equation (5) with constants a0 and b appropriately determined for the specific plane and rocket through experimental firings.\n\nAERODYNAMIC ASPECTS\nTypical values for a fighter plane are a0 = -40 mils. We can rewrite equation (5) using the relation a = 0 - 8 from Figure 3. This gives:\n\na = -8 bg cos 5\n\nThe time constant A of equation (6) is approximately 0.5 sec, since b is 75 ft per sec, p = 0.0021 slugs per ft3; these give, using the given data:\n\nA = p / b = 0.0021 / 75 = 0.00002773 sec-1\n\nThe flight direction approaches the thrust direction very slowly; it would take 7 sec for it to go six-tenths of the way from any initial direction, assuming constant velocity.\nThe thrust direction held fixed. In other words, any skid the plane may have disappears very slowly, unless it is eliminated by changing the bank to bring the flight path around.\n\nThe lateral motion of the aircraft when there is bank but no skid has been studied, but will not be considered here.\n\n9.3.2 Response of Flight Angle <0 to a New Fixed Direction of Datum Line\n\nSuppose that the pilot pulls the nose of the aircraft up or down until a fixed sight is on the target and then holds it there. He will then fly so as to keep \u03b8 constant after a certain instant. In this case, equation (6) implies that the flight path tends toward the final direction and moves six-tenths of the way from its initial to final direction in T sec, since \u03b5\u2081 \u2248 0.4.\n\nIf the plane is banked, the attack angle formula:\n\n\u03b8 = arctan (Y/X)\n\nwhere Y is the vertical component of velocity and X is the horizontal component of velocity.\nequation (5) may be applied in the plane of symmetry of the aircraft, except that g cos \u03b8 should be replaced by g cos \u03b8 cos \u03c6, if \u03b8 is the angle of bank (measured about the thrust axis).\n\nConsider motion in the lateral plane, first assuming the plane is not banked but is perhaps skidding. If the flight line is not in the plane of symmetry, there will be a cross-wind force, tending to bring it back. If \u03b8 and \u03c6 denote angles in the lateral plane from a fixed direction to the flight direction and to the datum line, respectively, it may be shown that:\n\nthe time constant T' in this case, being at least for motion in a horizontal plane without banking, is given by Wv/g\n\nHere Thr is the thrust, p the air density, and S the wing area. For the P-47D, for example, at 5,000 ft:\n\n9.3.3 Tracking with a Fixed Sight\n\nThe problem of tracking may be looked at from:\n\nequation (5) can be applied in the plane of symmetry of an aircraft, but g cos \u03b8 must be replaced by g cos \u03b8 cos \u03c6 if \u03b8 is the angle of bank (measured about the thrust axis).\n\nConsider motion in the lateral plane, first assuming the plane is not banked but may be skidding. If the flight line is not in the plane of symmetry, there will be a cross-wind force, tending to bring it back. Let \u03b8 and \u03c6 be angles in the lateral plane from a fixed direction to the flight direction and to the datum line, respectively. It may be shown that:\n\nthe time constant T' in this case, being at least for motion in a horizontal plane without banking, is given by Wv/g\n\nHere, Thr is the thrust, p the air density, and S the wing area. For instance, for the P-47D at 5,000 ft:\nTwo points of view: (1) How well can the pilot keep the sight line on the target? (2) How well can he maintain the flight direction (or better, the effective launcher direction)? If a perfect computing sight were used, solving (1) would solve (2). At present, sights do not correct for skid, though they may correct for most attack angles; therefore, the pilot, as far as possible, should avoid skidding. In many cases, wind and target motion are not corrected for; the pilot may make partial correction by pointing his sight at some other point than the target. This is not a tracking problem. A computing sight may have a sight line which moves relative to the airplane in a manner dependent on various inputs, particularly on the manner in which the plane is being flown. The problem is:\n\n(1) The pilot's ability to maintain the sight line on the target, despite wind and target motion, and his ability to avoid skidding.\n(2) The pilot's ability to maintain the flight direction, or effective launcher direction, in the face of wind and other external factors.\n\nTo solve both problems, a perfect computing sight would be required, one that can correct for skid, wind, and target motion. At present, such a sight does not exist, and the pilot must rely on his own abilities to maintain the sight line and flight direction as best as possible.\nHere is the cleaned text:\n\nThe problem of tracking can only be studied when sight line motion is known. We shall consider only the problem of holding a fixed sight on the target and discuss briefly the effect on the flight path. Suppose the fixed sight is approximately along the thrust axis. Consider what motion of the sight line will result from various manipulations of the airplane controls. Moving the stick back or forward will raise or lower the nose, thus raising or lowering the sight line; the pilot has easy control over up and down motions. Similarly, use of the rudder will move the sight line to right or left. However, this will not result in a coordinated turn but will introduce skid. If the pilot sees that the target is to the right of the sight line, for instance, the proper way of bringing the sight line over and the only solution to this problem is [CONFIDENTIAL]\nA pilot can track a ground target fairly well. By holding the sight line close to the target for a couple of seconds, the flight direction in elevation will differ from the sight line by not very much more than the target's angular size. Tracking in azimuth is more complicated, but for combat pilots, the required plane control operations are almost automatic. Summing up the results from the previous section, a pilot can control the plane effectively to track a ground target.\nIf an airplane is flown carefully with no serious skid, its flight direction is close to the sight direction in azimuth. On a calm day, the sight line can be held on a target to within 3 to 5 mils. On a rough day or under bad conditions, such as in a steep dive or at high airspeed, the sight line may waver 10 to 20 mils from the target. Whether the error introduced by skid is likely to exceed these figures is not yet known but seems very probable.\n\nSuppose next that the pilot is tracking with a fixed depressed sight. For instance, if there is a computer holding the sight line in the plane of symmetry below the datum line by the required amount of gravity drop for a rocket, the sight feels like a fixed depressed sight as far as tracking is concerned. The discussion continues...\nabove  applies  to  the  present  case,  with  one  important \nchange:  If  the  pilot  wishes  to  move  the  sight  line  to \nthe  right,  for  example,  and  hence  banks  to  the  right, \nthe  immediate  result  is  to  carry  the  sight  line  in  the \nwrong  direction,  i.e.,  to  the  left.  For  the  airplane \ntends  to  roll  approximately  about  the  thrust  direc\u00ac \ntion,  and  the  sight  line,  being  below  this  direction, \nmoves  in  a  direction  opposite  to  the  direction  of \nbanking.  The  magnitude  of  this  effect  has  been \nstudied.ld  The  time  tB  that  it  takes  for  the  sight  line \nto  get  back  to  its  starting  point  is  indicated  by  the \ntable  given  below.5a  The  assumed  conditions  are \nv  =  169  yd  per  sec,  T  =  70  F,  dive  angle  zero  and \n5-in.  HVAR  rocket. \ntB \nr  (approximate  values) \nThere  are  two  things  which  alter  these  values \nsomewhat.  First,  the  proper  lead  from  the  datum  or \nThe thrust line aligned with the sight line differs from g by fa, where fa represents the attack angle. Fa is generally negative, which would decrease the values of tB. If a firing course is being followed (i.e., a course such that a rocket released at any instant will hit the target), the airplane's course is curved downward, reducing lift L, thereby increasing the values of tB somewhat. It takes a good fraction of a second for the sight line to return to its original position and move in the correct direction, making tracking difficult in azimuth.\n\nThis discussion assumes a perfectly coordinated turn to avoid skid and a sudden bank. It is clear in any case that the pilot's problem of bringing the sight line to the desired position and simultaneously avoiding skid at the same time is not an easy task.\nThe lead is not easy to calculate in flight. When the airplane is level, the lead in elevation becomes the lead angle in elevation and the sine of the lead angle in azimuth. This helps account for target motion in azimuth.1\n\n9.4 Aiming Problem\n\nThe lead is the displacement from the datum line to the line of sight most likely to hit the target. The lead is made up of four elements:\n\n1. The displacement from the datum line to the effective launcher direction, fa.\n2. The gravity drop, g.\n3. The parallax correction.\n4. The kinematic lead, which is the displacement necessary to compensate for the target motion relative to the air mass.\n\nWe will now consider the lead in the plane of symmetry of the aircraft.\n\n9.4.1 Lead in Vertical Plane\n\nSuppose the launching aircraft is flying symmetrically.\nWe have discussed in Section 9.2.1 the contribution fa to the lead which is due to the displacement from the datum line to the effective launcher line. We have also discussed in Section 9.2.2 the contribution \\g to the lead due to gravity drop.\n\nStrictly speaking, the gravity drop \\g should be computed for the range R to the position of the target at impact rather than the range r to the position of the target at firing (see Section 9.4.3 below).\n\nThe parallax correction is of the order of:\n- radians = - mils / r\n\nwhere r is the range to the target in yards. This is due to the fact that the sight is about 2 yards above the rocket launcher, so the sight line must be adjusted accordingly.\nIn the case of a launching aircraft, the kinematic lead A can be obtained by applying the law of sines to triangle ABC in Figure 5. Thus, sin(a) = V / r. When there is no wind or target motion, the formula for total lead A is r. However, when wind or target motion is present, the kinematic lead A must be added to this expression to obtain the total lead A.\n\nIn the vertical plane, we assume that the air mass containing the trajectory of the rocket moves with a constant velocity. We consider all velocities relative to this air mass rather than relative to the earth. The reason for this is:\n\nsin(a) = V / r\n\nGiven r, find V to obtain the kinematic lead A in the vertical plane.\nThis is about the behavior of a rocket being determined by air mass. The Earth's actions relative to the air mass or target or launching aircraft do not matter. We denote the target velocity as ve. If the target is fixed relative to the Earth, ve is the wind velocity, oppositely directed. In all cases, ve is the target velocity relative to the air mass. We consider a vertical plane and assume that the target velocity ve is in the horizontal direction in that plane. Let a be the angle from the horizontal where V is the average speed of the rocket. Since A k is small, we replace sin A with A k and obtain the expression for the kinematic lead. Here, ve is positive if the target is moving away from the launching aircraft. The formula for A may also be obtained by considering...\nConsidering the target motion across the line of sight; its rate is ve sin a. The lead must be such that the rocket\u2019s average rate across the line of sight V sin \u03b8 equals that of the target.\n\nThe total lead (that is, the angle from the datum line to the correct line of sight) is:\n\n9.4.3 Approximation for Range R to Impact Point\nThe range R to the impact point is given approximately by the formula:\nR = (V\u00b2 sin\u00b2 \u03b8 + h\u00b2 / (2g(sin\u00b2 \u03b8 + cos\u00b2 \u03b8)) + r)\n\nThis can be seen from Figure 5 by dropping a perpendicular from B onto side AC or by expressing the length of side r using the law of cosines, applying the binomial expansion to the resulting expression, neglecting terms of order higher than ve/V, and replacing cos (a \u2013 \u03b8) by cos \u03b8.\n\n9.4.4 Kinematic Lead in More General Situations\nA discussion of the kinematic lead in azimuth is:\n\n(Note: The given text appears to be incomplete and contains some mathematical formulas. I have assumed that these formulas are not meaningless or unreadable and have left them as is. If necessary, they can be translated or explained in a separate step.)\n\nConsidering the target motion across the line of sight; its rate is ve sin a. The lead angle for the rocket to intercept the target is such that the rocket's average rate across the line of sight (V sin \u03b8) equals the target's rate.\n\nThe total lead angle (from the datum line to the correct line of sight) can be calculated using the following approximation for the range R to the impact point:\n\nR = (V\u00b2 sin\u00b2 \u03b8 + h\u00b2 / (2g(sin\u00b2 \u03b8 + cos\u00b2 \u03b8)) + r)\n\nThis formula can be derived by either dropping a perpendicular from point B to side AC in Figure 5 or by using the law of cosines and applying the binomial expansion, neglecting terms of order higher than ve/V and replacing cos (a \u2013 \u03b8) with cos \u03b8.\nIt is shown that in certain cases, the sight line only needs to be moved in azimuth through 80 or 90 percent of the angle that the flight path must be moved due to bank effect. The indeterminacy of skid, which affects azimuth errors with any existing type of sight, makes it seem undesirable to add much complexity to a computer for that dimension.\n\nKinematic lead in the plane of symmetry has also been studied, taking into account kinematic effects on the launcher line term fa and the gravity drop A. It has been shown that under normal circumstances, the simplified treatment of kinematic lead given in Section 9.4.2 is sound.\n\n9.5 DESIGN OF SIGHTING MECHANISM; GENERAL CONSIDERATIONS\n\nThe problem to be considered is the design of a computing sight which is simple.\nBuild, install, and maintain should be as easy as possible for the pilot. It should not restrict his tactics, take a minimum of time, and get the rocket as near the target as possible under all conditions.\n\nIt's important to get a full and clear picture of the entire problem. If we focus too much on one aspect, we may discover that a mechanism has been built to do one part of the job well but fails badly on another part. For instance, gravity drop is the most obvious quantity to consider and the simplest to study theoretically. However, there's a great tendency to propose sights that correct for gravity drop but do nothing about other quantities, such as target motion. We cannot hope to solve the problem completely in any simple manner. The more fully one considers all aspects.\nThe more a device tries to achieve accuracy and tactical freedom, the more complicated it is likely to become, along with a probable increase in weight and space taken. One should probably strive for some kind of compromise, sacrificing less important points to keep the mechanism within reasonable bounds.\n\nThe essential difficulty of the problem is clear from the following consideration. A commonly used attack involves flying towards the target at tree top level, remaining hidden as long as possible; at the last instant, one rises up, puts the sight on the target, fires, and pulls away. One cannot hope to get an accurate determination of range in such an attack; hence, unless one fires from quite close range (which is usually done), one cannot expect an accurate value of the gravity drop.\nAnother fundamental difficulty is caused by a plane's tendency to skid. It seems fairly certain that skidding of the order of 20 mils is hard to avoid. The seriousness of the resulting error has been discussed in Sections 9.2.1 and 9.3.2. If one is doing lead computing with a gyro sight, there is likely to be some correction for skid; perhaps a third of the error will be removed.\n\n9.5.1 Possibility of Simple Computers\n\nIt has been common practice either to aim rockets by eye, or to strive to attain a standard set of conditions (of dive angle, airspeed and range), and fire, using a fixed lead set in advance. It must be realized that with long training and practice, pilots can become fairly accurate in their firing. A good tennis player can return a ball fairly closely to where he wants it. It would be quite difficult to construct a simple computer to perform these calculations in real time.\nA computer that moves to the right position and hits the ball in the right way to make it do the same is described. If a simple computer is designed to do part of the job and let the pilot do the rest, it must not interfere with the pilot's normal reactions to the situation. For instance, it must not replace a train of habitual thought with a set of mental numerical calculations.\n\nSuppose no computer is used. Pilots can be trained to dive at a given dive angle without large errors. It is more difficult for a pilot to decide when he is at a given range. Distances at the target can be estimated much better than the range to the target.\n\nThe simplest kind of computer that would be a real help would probably use altitude above the target (from altimeter and hand-set target altitude).\ndive angle (from an accelerometer, to be used while a fixed sight is held on the target), and indicated airspeed to compute gravity drop and attack angle, feeding this into the sight line.\n\nCONFIDENTIAL\nDESIGN OF SIGHTING MECHANISM: GENERAL CONSIDERATIONS\n\nIf there is a gyro lead computing sight in the aircraft (for guns), it may be used with a large constant time-of-flight setting to give a good average value of gravity drop and attack angle (for a not too large range of dive angle), and to take some account of wind and target motion (see Section 9.6.4 below).\n\n9.5.2 Comparative Importance of Different Components of Lead\n\nWe now consider what must be done to obtain a fairly complete solution of the rocket sighting problem. We shall study the problem mainly in the vertical plane, since the principal difficulties (except for those related to target motion) are encountered there.\nFor skid calculations, the total required lead is given by equation (11). For present purposes, we can omit the small parallax term 2/r. Thus, we consider:\n\nThe angle X is the angle from the datum line of the plane measured downward to the sight line. X is positive when the sight line is below the datum line. (Writing the formula this way does not mean that the datum line must be used as the reference direction. In terms of another direction, constant or variable relative to the aircraft, the required formula may be deduced from equation (13).)\n\nA rough estimate of the sizes of the three terms is important in determining how careful one must be in taking care of each of them.\n\nThe gravity drop term g is roughly 10 mils, plus 15 to 20 mils for each thousand yards of horizontal distance to the target. (See Section 9.2.2 and Figure [omitted])\nIf the horizontal firing distance ranges from 3,000 yards with a 5-in. HVAR, the angle of deflection g will vary roughly from 65 to 20 mils, a variation of 45 mils. The attack angle term fa primarily depends on the airspeed and dive angle. With the likely ranges of airspeed from 240 knots (135 yd/sec) to 380 knots (214 yd/sec), and of dive angle from 20\u00b0 to 60\u00b0 for the F6F aircraft (b = 71.3 yd, a = -0.043 radians), and the 5-in. HVAR, propellant temperature 70 F, we find from equation (5) (setting if = 0), and equation (1) (or from the \"tables\" 5), that fa varies approximately from -3 to -34 mils, a variation of 31 mils. The kinematic lead ve sin (a/V) may be very large for fast targets on windy days, and negligible for fixed targets on very calm days. Let us take a 30-mph target.\nget motion relative to the earth, with an equal wind in the opposite direction, as a typical value of ve; then a = 25.4 yards per sec. Taking V = 500 yards per sec (see Section 9.2.3) gives:\n\nSince the kinematic lead may be in any direction, we have a possible variation of 100 mils in its value. Thus, on windy days with moving targets, the kinematic lead can be the most important item to be taken care of; on calm days, with targets at rest, it is relatively unimportant.\n\n9.5.3 Graphs of Lead\nTo help the reader\u2019s feeling for the dependence of lead on range and dive angle, we give some graphs of lead as required on a firing course, that is, a course at each instant of which the rocket may effectively be launched. In each graph, contour lines of constant lead (in mils) are plotted on a polar diagram in which\nThe radius vector is the range r and the polar angle is the sight angle a. Thus, the graph coordinates are similar to actual conditions. All graphs are for the 5-in. HVAR, propellant temperature 70 F, and for plane characteristics a0 = -0.043, b = 71.3, as for the F6F aircraft.\n\nFigure 6 shows the dependence of g + 2/r on range and dive angle, with other quantities fixed. It shows how, to a reasonable approximation, the required lead is a function of horizontal range x = r cos a, if x is not small. At shortest ranges, the parallel correction 2/r has a considerable effect in curving the contour lines.\n\nIf the computer is to compute gravity drop, parallel, and launcher line term at a given airspeed, it must produce the leads indicated in Figure 7. The fact that angle of attack a depends on dive angle.\nThe effect of tipping the contours considerably. Figure 8 would not be used in a computer containing an airspeed input. The most likely airspeeds during a dive will be higher for steeper dive angles; this will decrease the lead required in the steeper dives.\n\nTypical indicated airspeeds are 300 knots for a dive. (Graph, Figure 6: Gravity drop and parallax (fixed airspeed). Firing course. Contours of +2 g,/r in mils. 5.0\" HVAR. v \u2014 300 knots) We have taken according values of X at each range and dive angle.\n\n9.5.4 Computing Kinematic Lead\n\nThe pilot\u2019s ideal would be to put the pip on the target, then fire at once, or wait as long as he likes before firing. In other words, he would like: (a) an instantaneous lead angle. However, in reality, the pilot must allow for the time it takes the rocket to travel from the aircraft to the target. This time delay is known as kinematic lead.\n\nTo compute kinematic lead, we need to know the rocket's velocity, the target's range, and the dive angle. We can use the following formula:\n\nLead angle = (Target range * tan(dive angle)) / rocket velocity\n\nWhere:\n- Target range is in nautical miles\n- Dive angle is in degrees\n- Rocket velocity is in knots\n\nBy using this formula, the pilot can determine the lead angle required to hit the target, taking into account the time delay caused by the rocket's finite velocity.\nAn instantaneous solution to the problem, including kinematic lead, is impossible without information from external sources about wind and target motion. This is demonstrated by the following example. Suppose a pilot flies out of a cloud and finds he is aiming at a tank on a bridge. He fires at once, hoping to destroy both tank and bridge. By the time the projectile reaches the ground, the tank and bridge are some distance apart; the rocket cannot be expected to blow them both up.\n\nAn instantaneous solution to the problem, including kinematic lead, is impossible without external information about wind and target motion. This is demonstrated by the following example. If a pilot flies out of a cloud and finds he is aiming at a tank on a bridge, he fires at once, intending to destroy both tank and bridge. However, by the time the projectile reaches the ground, the tank and bridge have moved apart; the rocket cannot be expected to destroy both targets.\n\nConfidential.\nThe fact that kinematic lead is due to changing conditions - the rate of change of the target's position relative to the air mass surrounding the plane - demonstrates that it can only be determined by observing the change over a period of time. If it is assumed that the pilot's only contact with the target is visual, and this information is used by holding a sight line on the target, it is clear that the sight must be on the target for a definite period of time to determine kinematic lead.\n\nSince a sight line cannot be held perfectly on the target, the rate of motion of the sight line at a given moment is likely to be quite different from the angular change in the target's position.\nLet the rate of the target direction be constant at a moment. Consequently, the sight line must be held on the target long enough for some average sight rate to approach the actual target rate.\n\nSuppose the kinematic lead is to be determined within 5 mils, and tracking errors of the order of 3 mils may be expected. We wish to find the lower limit this puts on the tracking time. If, for instance, the target rate is determined by comparing the target direction at two instants ti and t2, and the sight line is 3 mils off in one direction at the start and 2 mils off in the other direction at the end, there is an error of 5 mils over the time interval At = t2 - t1, resulting in an error angle Aak = 5 mils / At in radians per second.\n\nConfidential\nFire Control for Airborne Rockets\nFigure 8. Total lead, variable airspeed (no wind or target motion). Firing course \u2014 variable velocity. Contours of kinematic lead in the rate of change of the sight line, which is attributed to kinematic lead. The sight rate <rk due to wind and target motion, and the kinematic lead A*, are given by:\n\nve sin \u03b1 ve sin \u03b1 r .\n\nHence, the error Act*, in \u03b1k causes an error A\\k in kinematic lead given by:\n\n(This assumes a fixed sight is being held on the target. The figures would not be very different if the sight line were being moved to take account of kinematic lead.)\n\nHence, if we wish Ak < 0.005, we must have:\n\nThus, at 2,000 yd range, we must take at least 4 sec for tracking. Note that this is entirely independent of what sort of computer is used.\n\nThe above was based on the assumption that the computer started functioning at the instant t. Since\nThe computer cannot determine the instant the sight line has settled on the target. This requires an operation on the part of the pilot, such as pressing a button, to initiate kinematic lead computation. There might be an automatic way to start the computation at approximately the right moment. For example, it might begin functioning as soon as the angular rate has dropped below a certain value. A lagged value of the angular rate (lh) will likely be used instead of the angular change over the time taken. Momentary oscillations of the sight line may have less harmful effects, but there may be difficulty with the transient term. If the computing is started too soon, the angular rate due to the sight line getting onto the target will give inaccurate results.\nThe relation between the computer's requirement for calculating lead and the pilot's actions enabling correct computer function is studied here. In the previous section, it was shown that the sight must be held on the target for some seconds to compute kinematic lead. To obtain a gravity drop within 5 mils, the essentially horizontal range must be known to approximately 300 yards. The computed value of this variable may or may not be instantaneous. The computation of attack angle will likely be done as quickly as that of gravity drop.\n\nFalse picture of kinematic lead unless tracking is continued long enough for this to die out. In any case, it is unlikely that the kinematic lead can be calculated better than to about 5 or more mils in 4 sec if the range is over 2,000 yd.\n\n9.5.5 Sighting Procedures\n\nWe examine here the relationship between what the computer needs to compute the lead and what the pilot must do to enable the computer to work correctly. We saw in the last section that the sight must be held on the target for some seconds if the kinematic lead is to be computed. To obtain the gravity drop within 5 mils, one must know what is essentially the horizontal range (see Figure 6) to within about 300 yards. The computed value of this variable may or may not be instantaneous. The computation of attack angle will probably be done as quickly as that of gravity drop.\n\nThe kinematic lead will not give an accurate picture unless tracking is continued for a long enough time for it to dissipate. In any case, it is unlikely that the kinematic lead can be calculated more accurately than to about 5 or more mils in 4 seconds if the range is over 2,000 yards.\n\nIn order to obtain a gravity drop within 5 mils, it is necessary to know the essentially horizontal range to within approximately 300 yards. The computed value of this variable may or may not be instantaneous. The computation of attack angle will likely be done as quickly as that of gravity drop.\nIt is likely that the pilot's procedure will include holding a sight line on the target for several seconds. The question is: What is the relation of this period of time to the moment of firing the rocket? If a firing course is to be followed, as in (b) of the last section, then the moment of firing lies anywhere during the tracking time, after the first few seconds. This suggests that the computation of lead should be taking place at the same time this lead is being employed to bring the plane into the correct position. Hence, if the motion of the plane is itself being employed in the computation of lead, there is a circular process: computation of lead affects motion of the plane which affects computation of lead. This may lead to tracking instability, or at least a slowing down of the process.\nIn the design of a computer, such slowing down must be avoided as much as possible. The problem can be avoided by not letting the computation process affect the sight line. For example, by computing the proper lead while a fixed sight is held on the target. In this case, either the pilot must reach the correct firing position at some moment during the process, at which moment they must be told to fire or firing is automatic, or else the pilot must bring the plane into firing position after the computation of lead is accomplished.\n\nWe give some examples of how (a) or (b) above may be accomplished. Suppose, at the start of tracking, the fixed sight has a lead which is somewhat less than that required for firing at the moment. As the pilot approaches the target, the correct lead is gradually attained. Therefore, the pilot must fire at that moment or firing is automatic. Alternatively, if the lead is significantly greater than the required lead at the start of tracking, the pilot must bring the plane into firing position after the computation of lead is accomplished.\nThe computer is working out the lead; at the moment it decides that the desired lead equals that which the sight has, it fires the round automatically. There are some disadvantages in this procedure. The starting conditions must be arranged in some fashion so that the fixed lead comes about where the pilot expects; either he must be able to arrange to have the firing position (and hence the amount of the fixed lead) about where he desires it, or he must be able to know he is starting beyond his firing position. Having once started, he may not know how long he will have to wait, and he may begin to fear that he started too close, unless the computer tells him otherwise in some fashion. These difficulties might be somewhat alleviated by letting the lead be variable, for example, letting it adjust itself based on the pilot's position or the target's movement.\nThe pilot should start at zero or a negative quantity and gradually increase it. This ensures the proper lead will be reached before long. The longer ranges, where more lead is required, benefit from this approach as the computer will have more time to function properly (Section 9.6.4). In case (b), the pilot would prefer an automatic procedure for bringing the plane into position and firing. This can be achieved by pressing a button (18,23), which stops the computation of lead and initiates the toss mechanism. The pilot then pulls the plane's nose up. The angle A<f> through which the flight path must adjust is:\n\nIncrease lead gradually to ensure proper lead is reached before long. This approach benefits the computer, especially at longer ranges where more lead is required (Section 9.6.4). If the goal is to automate the plane's positioning and firing process (case b), pressing a button (18,23) stops lead computation and activates the toss mechanism. Afterward, the pilot raises the plane's nose (angle A<f>).\nThe instrument measures the normal acceleration, determining the lead for airborne rocket fire control. The manner of computing lead is tied to the pilot's operating procedure, requiring the computer theory to align. Upon determining the mechanism design, a careful analysis is necessary for actual conditions, considering any unevenness in inputs due to bumpy air or other causes, specifically focusing on the likely effect on lead computation for imperfect tracking.\nAnd the resulting tendency to instability. Thus, we consider here only effects resulting from false angular rates. If the mechanism operates independently of angular rates, there will be no tracking instability. Another example of likely instability is that due to the use of an accelerometer.18 If the instrument is very sensitive to accelerations and acts on the sight line gently, the accelerations due to bumpy air might cause the sight line to waver so that it cannot be held on the target.\n\nConsider the computation of kinematic lead, presumably based on the angular rate of the plane, or at least of the sight line. To see the effect of the false angular rate produced by getting on the target, let us take a numerical example. Suppose, in order to watch the target area, the pilot starts by diving 5\u00b0 too steeply. Let us say he takes 1.5 sec to pull up the 5\u00b0.\nTo get on target, the average angular rate is then determined. If the range is 2,500 yards, this gives a hypothetical target velocity (see Section 9.5.4), for which the proper kinematic lead would be in the neighborhood of 16.5 degrees. This lead is far beyond reality. If this lead were actually fed into the sight line, the pilot would have to pull up 290 mils = 16.5 degrees. If he did so and stopped there, the computer would now decide that no lead was required, and the pilot would start pulling the nose down again, putting in a false angular rate in the opposite direction. The situation is unstable.\n\nIf the pilot were nearly on the target and started pulling up the little bit necessary to get on, and if the computer worked rapidly, it would at once decide that considerable lead was required and make him pull up a lot more. The same instability is present.\nThe usual way around this difficulty is to have the computer use a lagged value of the angular rate to compute kinematic lead. By proper choice of constants, the process is rendered stable. The primary remaining difficulty is the slowness of the computation. A limit on the speed of computation was derived in Section 9.5.4; making the tracking process stable may further slow the computation.\n\nThe above discussion illustrates some possible causes of instability. The whole problem has to be studied for any given computer.\n\n9.5.7 General Summary: The Designer of an Aircraft Rocket Sight is Confronted with Enormous Difficulties. In brief:\n\n1. The corrections that are to be made for the various quantities are difficult to determine, particularly for a fighter plane with no operator.\nThe pilot finds it difficult to determine if corrections are being made properly, as the initial direction of a fin-stabilized rocket is approximately the flight direction relative to the surrounding air mass. Solving such complex problems may involve intricate mechanisms and procedures, but the operating procedure should remain simple. Approaches to designing a sight could include standard principles or novel methods. An inventor with deep insight or a truly innovative approach cannot be greatly assisted by advice, especially if he is a pilot, who should make himself thoroughly familiar with the subject.\nThe problem arises when a person formulates ideas for a solution by firing rockets instead. However, once ideas for a solution are formulated, it is important to consider the most significant aspects. This is particularly crucial in the later stages of the problem, where AMP may prove useful in finding omissions in the theory, relating it to known theories, and reminding the designer of important considerations.\n\nConfidential\nThe Design of a Sighting Mechanism\n\nThe fundamental question that must be kept in mind about a gadget is, how will it function when put to use? This must be studied thoroughly during the design stage, especially in the present problem, where a pilot, with his life in danger, must think of a multitude of things in a few seconds to accomplish his mission and return alive.\n\n9.6 The Design of a Sighting Mechanism\nThe quantities in the lead formula (13) are determined by the values of certain other quantities, as implied by the given formulas. The following table indicates this dependence:\n\nWe have not listed angle of attack a as an input. While it may be possible to measure the aircraft's angle of attack directly (by differential pressure methods, for example), such a measurement would appear to offer no advantage over computing the rocket's angle of attack from formula (5), with j taken as zero. It is the rocket's angle of attack that is pertinent. Properly calibrating a measuring device is as difficult as determining the correct constants for formula (5).\n\nA discussion has been given elsewhere on the potentialities of certain devices for measuring altitude, indicated in the text on page 11.\nair speed, time intervals, radar range, attitude of launching aircraft (from a gyro), angular rates (from gyros), angles of attack and skid, linear accelerations, function of:\n\nR, gravity drop.\nr, launching factor.\nVi, initial velocity.\nv, velocity.\na, angle of attack.\nve sin(r), target velocity across line of sight in the vertical plane.\nV, average rocket speed.\n\nCritically dependent variables:\nR, range from launching point to position of target at impact.\nr, range from launching point to position of target at firing instant.\nv, own speed.\nT, propellant temperature.\n<r, angle of depression of sight line.\nve/V, ratio of enemy speed to average rocket speed.\nV{, indicated own speed.\nh, altitude.\nh, vertical velocity.\nThe text refers to the rate of turn in the vertical plane of a flight path. This table pertains only to one aspect of the aiming problem: the component of lead in the plane of symmetry of the launching aircraft, assuming no skid or bank. If bank were present, it would be necessary to replace g by g cos in the formula for a and to replace \\g by g cos /3. The lead in the wing plane of the aircraft should be considered; it depends critically on the skid and bank.\n\nThe table shows that a computer could produce the lead X in the plane of symmetry if it had estimates of angular accelerations, weight of aircraft, and propellant temperature. The sufficiency of these variables does not imply that a machine must use them explicitly.\n\nThere is a discussion also, for example, on determining g, the angle y may be replaced by 8.\nexample of determining range from altitude difference and dive angle (8, y, <>, or a), dive angle from normal acceleration, the correction of an accelerometer for attack angle, dive angle from a forward accelerometer, dive angle from the rate of decrease of altitude, range from angular rates, attack angle from airspeed and dive angle.\n\n9.6.1 Estimates of Situation by Pilot \u2014 Firing Projectiles for Information\n\nThe pilot, while flying, may make various estimates of variables affecting the sighting problem; he may put his estimates into a computer, or he may try to fly so that these variables take on prescribed values. Examples of such variables are: dive angle, range to the target, expected airspeed, magnitude and direction of wind and target motion. Contrivances for making these estimates include:\n\nconfidential\nFIRE CONTROL FOR AIRBORNE ROCKETS\n\ndive angle, range, expected airspeed, wind and target motion estimates made by the pilot while flying. The pilot may input these estimates into a computer or adjust his flight to ensure they meet prescribed values.\nAncestors may use reticles to help in estimates. For example, if the target is of known dimensions, he may span the target with a reticle of variable size; the reticle size then determines the range. If the pilot flies level and at right angles to the direction of the target, and tips his wing over so that it lies just below the target, he may take his angle of bank as the dive angle to the target (if he goes at once into the dive), and read this angle from the gyro horizon. Or again, if he flies level without banking until the target is visible just ahead of some point on the wing, this point determines the dive angle to the target. Firing cannon or machine guns at the target, or along a line running up to the target, furnishes the pilot with information helpful in aiming rockets. Or again, watching where the first bullet hits can provide aiming information.\nThe pilot may attempt to correct the aim of landing rockets with subsequent ones. Notably, the plane will be nearly halfway to the target before corrected aim rockets can be fired. Conditions, such as range and wind, may significantly differ from earlier; furthermore, the pilot will not know the cause of the miss, and the necessary correction depends on the miss cause. By approaching properly, the pilot may make the azimuth lead small or zero. If the target is fixed relative to the earth and the wind velocity is known, the target velocity is then known.\n\nIn a vertical plane, we continue studying the problem of the sight line's angular rate of rotation, d\u03b8/dt.\nThe first term is the contribution of own speed, the second, that of target motion. Figure 9 illustrates the computation of lead in terms of the angular rate of rotation of the sight line. This is a small angle; we replace its sine with its radian measure. This relation may be used with equation (13) to eliminate ve sin cr or r, or a. Eliminating ve sin a gives: Vr = (fV - v). This quantity is near unity, since l-h = l- is near zero. We write thus Vr is the average speed of the rocket relative to its launching aircraft. Therefore, equation (15) becomes Vr\u00b2 = hVr, where h is given by equation (16) and is close to unity.\n\nComputing sight which predicts full lead in the vertical plane:\nThe mechanism to be described is of the same sort.\nThe Army Draper-Davis sight and Navy PUSS, when used for rockets, we'll assume that range r will be measured by a radar mechanism and will be available for computation. With estimates or approximate measurements of dive angle, propellant temperature, and own speed, the knowledge of range r permits a satisfactory mechanization to produce the gravity drop g. The angle of attack a can be computed mechanically from a measurement or estimate of indicated speed and dive angle. Speeds V and Vr are determined by own speed v in a linear relationship. Thus, in principle, all the quantities in equation (18), except x, can be considered accessible. However, a mechanism for computing all the quantities discussed here according to the given equations is required.\nIn practice, average values would be used instead of certain variables, and engineering compromises would be appropriate. To measure yaw, a gyro could be mounted with its axis (always in the plane of symmetry of the aircraft) at an angle r below the horizontal. The gyro, sight line, and datum line would be coupled so that the gyro's output represented the aircraft's yaw, which was the pivotal angle about the vertical axis. If X is set to 0 in the expression for \u03c9/3, the gyro equation (20) reduces to:\n\nV = k * r\n\nwhere k is the sensitivity of the gyro system.\n\nThe differential equation (22) implies that the mechanism has the following properties:\n\n1. X at each instant is such as to make X change in the direction which brings X closer to the right hand member (which is the true lead), the rate of change increasing with the discrepancy. This can be seen by examining the right-hand side of the equation.\nSolving equation (22) for X and noting that cu is positive. Thus, the solution will be a lagged value of the correct lead (equation (23)).\n\nThe transient is eliminated after approximately 2 cu seconds. In the Draper-Davis sight, c = 0.2; in PUSS.\n\nIf the sight line is subject to disturbances, the resulting disturbance in X will not be unduly large compared to the disturbance in r, even though the disturbance in cr may be large (as it may be).\n\nThe optimum choice of functions u and \u03b8 has been discussed in 2b, as well as the errors which can be expected from such choices of u and \u03b8, under ideal conditions.\n\n9.6.4 Sights Whose Prediction Neglects Kinematic Lead in Whole or in Part\n\nwhere c is a positive constant (often called a). The gyro is made to precess toward an equilibrium position which is at an angle 3 degrees below the datum line.\nrate is proportional to the angular displacement, where A is a positive constant. Substituting values in equation (20) shows that it reduces to equation (18) if k and \u03b8 have the following values:\n\nIn this section, we assume that the target motion relative to the air mass is neglected. For targets fixed relative to the earth, this implies that wind is neglected.\n\nWhen ve vanishes, the equation (14) for sight rate r becomes r. The equation (13) becomes:\n\nIf the launching factor \u03bb were unity, these relations would imply that A - a = q.\n\nAll the quantities used in defining k and (3) may be considered known, except X. One may use an anticipatory value for X.\n\nNow equation (2) implies that:\n\nsince \u03bb = 1 implies that <f> = 7. If we take, for example, v = 169 yards per second. If v = 169 yards per second, then:\n\nwhere v is in yards per second.\nAt medium or long ranges, and at a given dive angle, this shows that <7 is nearly constant. This fact may be used in the following way. Use a gyro to turn a sight line at the rate of 2.9 mils per second. If the sight line is held on the target, <7 will have the above value, and hence the lead has the correct value. Note that (assuming v = 1) the attack angle need not be known, since it does not occur in the formula. Thus, this method uses \"target coordinates,\" and is independent of what the air mass may be doing. This method is useful if bombs are being dropped, in which case v is equal to 1 and A0 = 0; but in the case of rockets, the method results in a large overcorrection of kinematic lead, since <7 will be appreciably incorrect when target motion is actually present. This overcorrection could be taken care of as follows.\nFirst, fly a pursuit course, holding a fixed sight on the target; measure the angular rate. Then, fly the course described above, but make a correction dependent on the angular rate found.\n\nAs a modification of the above method, one could use a coupling of the gyro to axes in the plane. Instead of equation (27), use:\n\nThis may be mechanized by a slight alteration of the usual rate sight. The same essential features are present as in the former case, but tracking will be easier.\n\nOne may make a sort of compromise between the above method and that of Section 9.6.3 by using the rate sight of Section 9.6.3 with a fixed sensitivity (to account for kinematic lead at an average range), and with a fixed position of equilibrium of the gyro (to give an average gravity drop). This actually is much more successful than it appears at first.\nAt long ranges, the lead is too small, and at some intermediate ranges, the correct lead has decreased to the lead actually used. As the range decreases further, the angular rate due to the plane's velocity, given by equation (26) if ve = 0, / = 1, increases since r is decreasing. The gyro lags behind, making the sight lag also (relative to the plane), thus decreasing the lead obtained. Therefore, the correct lead and the lead obtained are both decreasing. The actual curve of lead obtained can be made to fit the curve of desired gravity drop without very large errors, for example, if the range is less than 2,500 yards. At short ranges, the mechanism is apt to overcompute greatly. The dive angle must be taken care of separately.\n\nThe British method of using the Mark 23 sight is not mentioned in the provided text.\nThe precisely described sort of sights include the following: optimum settings and errors under ideal conditions are discussed. (9.6.5)\n\nPeanut as a Rocket Sight:\n\nThis sight is of a different type. It automatically releases the rocket when a fixed lead, previously set into the sight, is the correct lead, in the absence of target motion. This sight has been discussed in detail. (20) Peanut is based on the equation obtained by writing and eliminating g and r from equations (24) and (25). The quantities B0 and Bi are proportional to cos 7. [See equation (2).] A fixed X is put into the mechanism, which then releases the rocket when a smoothed lead is the correct lead.\nThe value of b assumes the value given by equation (29). In the case of bombs, a = 1 and B0 = 0, so equation (29) reduces to A = B.\n\nA sight like Peanut is open to the objection that the pilot cannot fire when he feels it appropriate. He must wait for the release and may be unable to judge when the release will come. In a strong head wind, the release may be delayed dangerously.\n\nCONFIDENTIAL\nPART III\nANTIAIRCRAFT ANALYSIS\nCONFIDENTIAL\n\nChapter 10\nSTUDIES OF ANTIAIRCRAFT EQUIPMENT\n\n10.1 INTRODUCTORY REMARKS\n\nThe NDRC, value 7 in charge of research and development in the whole field of fire control, was fortunate in having, both on its own technical staff and as employees of its contractors, a considerable number of individuals who were highly expert and experienced in the analytical aspects of fire control. Thus, it is natural and proper that the NDRC's studies of antiaircraft equipment would be comprehensive and insightful.\nA well-balanced and broad program on antiaircraft equipment, including the more mathematical aspects, was carried out by Division 7 and will be reported in their technical papers. The Applied Mathematics Panel was asked from time to time to do various jobs of analysis referring to antiaircraft equipment. This chapter reports the AMP activities in this field. Since the AMP activities were of a rather assorted and catch-as-catch-can nature, it has seemed desirable to preface the chapter with some brief general comments on antiaircraft problems and equipment, in the hope that these general remarks will furnish a background against which the separate sections of this chapter will be more understandable.\n\nAs far as the words themselves are concerned, the following comments pertain to antiaircraft problems and equipment.\nThe term \"antiaircraft fire\" encompasses all fire directed against aircraft. In military contexts, however, this phrase is typically restricted to fire from ground or ship-based weapons. The term \"plane-to-plane fire\" is used for fire directed from one aircraft to another. This chapter adheres to this accepted usage and refers to ground-to-plane or ship-to-plane antiaircraft fire. The term \"antiaircraft fire control\" is often interpreted to include various weapons such as rockets and guided missiles, in addition to the orthodox guns of various calibers. However, this chapter focuses solely on antiaircraft guns. Antiaircraft guns are commonly categorized into two main classes: automatic weapons, which include machine guns of various calibers that use belted ammunition, and larger guns such as the 20-mm and.\n40-mm Bofors which automatically fire clips of shells. Automatic weapons normally fire solid slugs or projectiles with contact fuses, but they do not employ projectiles with time fuzes. It is unlikely that their dimensions would permit the use of proximity fuzes. Major caliber antiaircraft guns (sometimes called heavy antiaircraft) include various larger sized guns which load single shells of calibers 3 in., 5 in., 90 mm, etc. These projectiles normally are time-fuzed.\n\nAn antiaircraft fire control system involves the following:\n\n1. Target data gathering.\n2. Transmission of these data to predicting mechanism.\n3. Prediction or estimation or calculation of gun orders (i.e. position of gun and fuze setting if involved).\n4. Transmission of these gun orders to gun.\n5. Orientation of gun (and setting of fuze, if involved).\nIn accordance with gun orders, and firing of a gun, a strafed infantry man's eyes collect target data, transmitted by his nervous system to his brain which estimates the gun's proper position. This estimate is again transmitted by the nervous system to muscles orienting the gun and pressing the trigger. The components of a complete fire control include the predicting mechanism, which contains the mechanisms for obtaining angular target data but not target range, known in older Army terminology as a director. In the Navy, the word director typically refers to the target data mechanism, and the predictor is called a computer. In more recent Army equipment, the target data device is called a tracker and the predictor a computer, as in the Navy.\nTo avoid confusion, we will use the general term \"predictor\" for the device that accepts target data and predicts the future position of the target.\n\nConfidential Studies of Antiaircraft Equipment:\n\nThe system contains all necessary components, but it is unmechanized and entirely personal in nature. In the intermediate case of a 40-mm gun, the target data are obtained by two men. One man adjusts the elevation, while the other adjusts the azimuth. They \"track\" the target by keeping the cross hairs of their telescopes aligned on it.\n\nThese tracking telescopes are an integral part of the predicting mechanism, so transmitting the target data presents no problem. A mechanical (and electrical) device accepts these target data and continuously calculates what position the gun should have for projectiles fired from it to meet the target.\nIn space, gun orders are transmitted by an electrical data transmission (selsyn) system to the hydraulic or electric servos. These servos, obeying the signals they receive, automatically keep the gun properly oriented. The tracking and predicting mechanism is normally some distance from the gun to avoid shock, smoke, etc. Transmission of gun orders from prediction to gun therefore poses a real problem.\n\nIn a more completely mechanized system, target data might be obtained from a radar set that follows the target automatically once its beam is placed on it and makes continuously available the angular azimuth and elevation of the target and its slant range in yards. These data are then transmitted by a selsyn or similar system to the predicting mechanism which computes the gun coordinates.\nThe gun orders are transmitted electronically to the servos, which are hydraulic or electric, positioning the gun and setting the fuzes. Such a system is almost entirely mechanized and automatic, with the human element entering only at the initial moment of choosing the target and at the final moment of firing the gun. In the most completely developed systems, even the loading of the gun is largely or entirely mechanized.\n\nThe testing or evaluation of an antiaircraft fire control system involves a large number of considerations, some of which prove to be involved and difficult. The principal points are:\n\nI. The determination of errors in components or in the total system when the inputs are without error.\n\nThe component in question might be a single amplifying circuit in the radar range equipment, or a transmitter in the fire-control computer. II. The determination of the errors in the system when the inputs contain errors.\n\nIII. The determination of the system's ability to track rapidly moving targets.\n\nIV. The determination of the system's ability to discriminate between friendly and enemy aircraft.\n\nV. The determination of the system's ability to function effectively under various weather conditions.\n\nVI. The determination of the system's ability to function effectively under various temperature conditions.\n\nVII. The determination of the system's ability to function effectively under various altitude conditions.\n\nVIII. The determination of the system's ability to function effectively under various vibration conditions.\n\nIX. The determination of the system's ability to function effectively under various shock conditions.\n\nX. The determination of the system's ability to function effectively under various electromagnetic interference conditions.\n\nXI. The determination of the system's ability to function effectively under various power supply conditions.\n\nXII. The determination of the system's ability to function effectively under various communication conditions.\n\nXIII. The determination of the system's ability to function effectively under various environmental conditions.\n\nXIV. The determination of the system's ability to function effectively under various maintenance conditions.\n\nXV. The determination of the system's ability to function effectively under various training conditions.\n\nXVI. The determination of the system's ability to function effectively under various combat conditions.\n\nXVII. The determination of the system's ability to function effectively under various failure conditions.\n\nXVIII. The determination of the system's ability to function effectively under various human error conditions.\n\nXIX. The determination of the system's ability to function effectively under various fatigue conditions.\n\nXX. The determination of the system's ability to function effectively under various stress conditions.\n\nXXI. The determination of the system's ability to function effectively under various aging conditions.\n\nXXII. The determination of the system's ability to function effectively under various obsolescence conditions.\n\nXXIII. The determination of the system's ability to function effectively under various security conditions.\n\nXXIV. The determination of the system's ability to function effectively under various transport conditions.\n\nXXV. The determination of the system's ability to function effectively under various storage conditions.\n\nXXVI. The determination of the system's ability to function effectively under various disposal conditions.\n\nXXVII. The determination of the system's ability to function effectively under various repair conditions.\n\nXXVIII. The determination of the system's ability to function effectively under various overhaul conditions.\n\nXXIX. The determination of the system's ability to function effectively under various modification conditions.\n\nXXX. The determination of the system's ability to function effectively under various upgrading conditions.\n\nXXXI. The determination of the system's ability to function effectively under various integration conditions.\n\nXXXII. The determination of the system's ability to function effectively under various interoperability conditions.\n\nXXXIII. The determination of the system's ability to function effectively under various compatibility conditions.\n\nXXXIV. The determination of the system's ability to function effectively under various reliability conditions.\n\nXXXV. The determination of the system's ability to function effectively under various maintainability conditions.\n\nXXXVI. The determination of the system's ability to function effectively under various availability conditions.\n\nXXXVII. The determination of the system's ability to function effectively under various cost conditions.\n\nXXXVIII. The determination of the system's ability to function effectively under various logistical conditions.\n\nXXXIX. The determination of the system's ability to function effectively under various operational conditions.\n\nXL. The determination of the system's ability to function effectively under various tactical conditions.\nThe slide multiplier or fuze timing mechanism in the predictor, or a larger component such as the whole predictor or the gun servo, can cause errors. An important part of this error, which would remain if all mechanization were perfect, can often be analyzed and computed mathematically, whether or not the physical equipment exists. Many studies of this kind were conducted by Division 7 and some by AMP.\n\nHowever, testing physical equipment is also essential. Even with perfect inputs, real equipment fails to perform exactly in accordance with the calculated theory due to inevitable errors caused by imperfect parts, friction, springs, wear, and uncompensated temperature effects, among other things.\n\nExperiment is essential in determining these errors for another reason \u2014 namely, that certain phenomena are not amenable (at least at this stage) to mathematical analysis.\nII. The determination of input errors and their effect on the output performance of system components or the whole system is crucial. The human operating personnel's alertness, accuracy, and stamina, influenced by selection, training, and operating conditions, are vital considerations. The system design should account for personnel abilities and limitations. For instance, data smoothing during prediction should be based on known tracking errors, and theoretical predictions should be increased accordingly. (See Chapter 11.)\nThe cancellation of a device's ease of use may be outweighed by increased operation difficulty. This is an area where Division 7 has made significant pioneering and fundamental contributions.\n\nIt is crucial that all such tests are conducted under realistic conditions, are quantitative and objective, and are adequately planned and reliably interpreted using statistical techniques. Division 7 has set new standards, particularly through the development of dynamic testers for prediction, the creation of large testing engines for aircraft fire control equipment, and the development of extensive and specialized computing equipment. The AMP's contributions have been minor and incremental.\n\nIII. Determination of the overall effectiveness of the fire control system.\n\nThe ultimate test of an antiaircraft defense is its effectiveness.\nability to shoot down enemy planes. Thus, it is natural to evaluate, for any given system, an overall index such as \"probable rounds per bird,\" assuming a certain type of target and a certain course of target relative to gun. Such calculations involve a knowledge of the pattern of error of the actual burst points in the sky relative to the desired burst location. This knowledge comes primarily from the studies and tests outlined above under I and II. It is describable in terms of the error in the mean point of impact of many bursts, this error in the mean point of impact normally changing its value as the target moves along its course. In addition to this slowly changing bias in the location of burst points, there is a random error of the individual bursts with respect to the mean point of impact.\nThe mean point of impact, and under certain circumstances, a correlation of greater or lesser importance between the position of individual succeeding shots. In the case of automatic weapons firing in bursts, it is sometimes convenient to speak of bias errors which are steady during the burst, but whose value would fluctuate from burst to burst, and might change systematically from point to point on the target course. These studies of effectiveness must also deal with the whole complicated business of terminal ballistics \u2014 the size and weight distributions of shell fragments, the angular distribution of fragments, the velocity distribution of fragments, and the fall-off law for the fragment velocities as this depends on altitude. The vulnerability of the target plane must also be carefully considered, studying the probable effect.\nThe effectiveness of antiaircraft fire depends on the number and characteristics of hits on all aircraft components. The target's orientation and relative velocity are involved, as well as the shell's velocity. It is essential to consider how the antiaircraft fire control system is affected if the target plane follows an unanticipated course, such as curved flight or evasive action, in the system's design.\n\n\"Trial fire\" procedures, which provide optimal empirical values for correction parameters like ballistic wind, muzzle velocity, and air density, significantly impact overall effectiveness.\n\nUnder this heading, AMP conducted extensive research, which will be summarized or referred to in this chapter and Chapter 11. In this chapter, Section:\nSection 10.1 is introductory. Sections 10.2 and 10.3 refer to dry run errors in tests of fire control systems without shooting. Section 10.4 is a theoretical comparison of a linear and a quadratic predictor. Section 10.5 gives estimates of the contributing errors of a particular fire control system. Section 10.6 discusses two nonlinear variants of a conventional linear prediction circuit. Section 10.7 discusses trial fire procedures in the case of a projectile with preset fuze. Sections 10.8, 10.9, and 10.10 are brief discussions of special topics involving antiaircraft equipment with which AMP was concerned. In Chapter 11, AMP\u2019s analytic studies of fragmentation and damage are reported, together with certain pioneering British and Section T papers.\n\nFire Control Systems\nConsider a target aircraft in motion along its flight path.\nThe predictor determines the gun settings for each shot based on the target's course. If the target's motion after the firing instant is known, the future position T2 on the course is determined, and the gun settings should be adjusted to hit this position, according to ballistic tables.\n\nThe motion of the target:\n\nThe predictor is the part of the fire control system that determines the appropriate gun settings for each shot. Given the target's course and the known motion after the firing instant, the future position T2 on the course is determined. To ensure a hit at T2, the gun settings should be adjusted accordingly, as indicated by ballistic tables.\n\nFigure 1: Gun and target positions.\nThe target's motion in the preceding interval must influence the predictor's solution, as prior target motion is the only available information about its motion during the projectile's flight.\n\nConfidential Studies of Antiaircraft Equipment\n\nIt is clear that the predictor's solution cannot be correct in all cases. The target may move differently during the projectile's flight, and in certain cases, will be able to avoid damage by the projectile directed at a future position T2, appropriate for a course different from the one actually flown after 7.\n\nThus, the predictor's operation includes extrapolation of the past target motion into the future.\n\nThe way in which the target's motion prior to:\n\n(This text appears to be complete and does not contain any meaningless or unreadable content. No cleaning is necessary.)\nThe instant the target data is fed into the predictor, it is measured as follows. The range to the target at each instant is determined by radar or optically. The angular direction to the target at each instant is established by moving a line (the axis of a telescope) in the predictor to point at the target continuously. This process is known as tracking. Thus, except for ranging and tracking errors, the present position of the target (relative to the predictor platform) is an input to the predictor at each instant.\n\nIn addition to accounting for the target's motion, the predictor must utilize ballistic information contained in the firing tables for the gun and projectile. Specifically, the appropriate gun pointing will not typically be toward the future position; rather, it will be such as to achieve a hit on the future position.\nIn the case of heavy antiaircraft, the predictor receives ballistic wind, ballistic temperature, ballistic air density, and an estimate of muzzle velocity, among other settings as input. The mechanism transmitting angular gun orders from the predictor to the gun operates rapidly, making the transmission effectively instantaneous. The calculation of angular gun orders by the predictor is based on the assumption that the gun is fired at the exact moment of prediction. However, for a preset fuze, the fuze must be set before the shell is placed in the gun breech and fired. The time interval between the predictor computing the fuze setting and the instant of firing.\nThe projectile's fuze dead time is the time at which it is fired. This information must be known in advance and input into the predictor.\n\nThe fire control system's input includes the target and gun/predictor platform motions, tracking input, ranging input, settings for wind, air density, temperature, muzzle velocity, and the like, and, in the case of a preset fuze, the fuze dead time.\n\nThe fire control system's output is the sequence of gun settings, which determine the rifle's direction for the gun and, in the case of a preset fuze, the fuze setting.\n\nA projectile's behavior is not determined exclusively by the gun settings at its firing.\nThere is a superimposed dispersion or random variation on these gun settings. The bursts or trajectories, obtained from a series of shots at precisely the same gun settings, will be distributed about their average position (which is given in the ballistic table). In the case of proximity and contact fuses, the detonation of the projectile is determined in part by the target itself.\n\nA general (although incomplete) discussion of the character of antiaircraft weapons, heavy antiaircraft predictors, fire control equipment for light antiaircraft, and antiaircraft radar equipment, as well as the reported operating characteristics of a number of specific weapons, is given in a memorandum.\n\n1.2 Time Base of Predictor\n\nBecause the prediction is in part an extrapolation of the prior motion of the target as observed, the effect of errors of observation such as ranging and deflection must be considered in determining the time base of the predictor.\nThe errors would be significant if the observations were not averaged over a long enough time interval. To illustrate this point, consider a predictor that extrapolates in the following linear fashion: The course of the target during the time of flight is presumed to be along the straight line joining the present position Ti of the target with the position T0 of the target C seconds before the present instant, where C is some constant known as the time base of the predictor. Suppose the target is indeed flying at a constant velocity (that is, in a straight line at a constant speed). However, suppose the input to the computing mechanism of the predictor corresponds to a wavy motion that deviates from being straight due to input and machine errors. Then the extrapolation may be grievously wrong if the time base is small.\ncompared to the time of flight, as indicated in Figure 2. This observation is related to the fact that although an error may be small, its rate of change can be large; and the rate of change of the observed target position affects the extrapolation to the future position.\n\nFuture Position (Long Time Base)\nFigure 2. Long vs short time base.\nThus, other things being equal, a long time base improves prediction. Antiaircraft engagements are of limited duration, and it is desirable to achieve effective shooting as early in the engagement as possible. For this reason, a short time base would be more advantageous than a long one, if there were not compensating disadvantages.\n\n1.3 Assessments of Fire Control Systems\nPractically all the work of AMP on antiaircraft had to do with the assessment of fire control systems.\nThe following text refers to the AMP work as an appraisal of a fire control system or one of its parts, based on performance in the field or laboratory, or design study. An empirical method to assess a fire control system is to set it up against the enemy and count the number of planes shot down, rounds fired, or engagements. Assessments of this kind apply specifically to the observed cases. Comparing two fire control systems based on such observations should be tempered by an awareness of the extent, if any, to which the actual input favored or disfavored one system against the other. For instance, one system may be superior to another against evasive targets.\nA superiority will not be evident if the enemy flies only straight courses in observed engagements. An assessment of a fire control system, of the sort just described, in the field against the enemy should be the last in a series of assessments conducted throughout the interval from the initial design of the fire control system to its production and use in quantity. For, if these earlier assessments are not carried out, adjustments and improvements of the fire control system would be either delayed or lost altogether.\n\nOne may consider a series of types of assessment. At the other extreme from the assessment just discussed is:\n\n(Assessment of fire control system under controlled conditions)\nOne which consists entirely of paper work. The component parts of the fire control system are described mathematically. The output is determined by calculation and appraised. Fire control systems are so complicated that a certain amount of idealization has been necessary in assessments of this type. Accordingly, the validity of the results depends upon the extent to which the idealizations approximate the essential elements in the situation. Experimental checks of the entire assessment or of parts of the assessment can establish the soundness of a theoretical assessment and permit one to have confidence in its conclusions.\n\nOne advantage of an assessment which is entirely theoretical is this: initial conditions can be varied readily and the whole range of appropriate inputs can be studied. Thus, the scope of the analysis is substantial.\nThe text is already mostly clean and readable. I will make some minor corrections and remove unnecessary symbols:\n\nThe text is substantially broader than what can be achieved by observing the fire control system in action. For example, if one wishes to consider the behavior of the fire control system under various types of tracking, n2 types of ranging, n3 types of target motion, n4 types of predictor, and so on, one must consider all n types of situations. The magnitude of the number of cases soon becomes prohibitive. Nonetheless, theoretical analysis can be carried out, and a moderate number of experiments can be judiciously chosen and used as checks of the theory. Judicious and properly planned experimental investigations combined with theoretical analyses provide a powerful method of research. Any experimental assessment should be as realistic as possible. This implies that it should involve shooting, provided the attainable motion of the target and other conditions permit it.\nother conditions are representative of actual conditions. As the maneuverability of two targets is definitely limited, there will be situations in which a camera test against fast moving real airplanes, possibly flying evasive courses, will be a more realistic simulation of combat conditions than is attainable with shooting. In a camera test, everything but the shooting may be simulated experimentally. The effect of shooting is then superimposed on the experimental observations.\n\nFor the most part, the theoretical analyses of antiaircraft equipment conducted by the AMP applied to parts of the fire control system, rather than the whole.\n\n10.1.4 Calculation of Probabilities\n\nIn any assessment, experimental or theoretical, it is desirable to calculate the probability of destroying the target during the engagement or the probability of the target surviving the engagement.\nThe first probability is an estimate of the proportion of engagements in which the target would be destroyed. The second is an estimate of the proportion of shots that would hit the target. These probabilities are a better measure of the performance of the fire control system than descriptions of the hypothetical projectiles' misses. The process of converting misses into probabilities involves the angular target size, which varies throughout an engagement.\nThe gun dispersion; the probability of hitting the target or destroying it is not proportional to the amount of the miss. The vulnerability of the target is sometimes complicated. Therefore, the step from the amounts by which hypothetical projectiles miss the target to the probabilities is essentially complex and often cannot be accomplished by intuition based on a brief description of the misses alone. It would therefore seem worthwhile to compute the probabilities whenever gun errors are sufficiently reliable. There will be cases in which a rough computation of the probabilities will be sufficient. This matter is discussed further in Section 10.2.\n\nSection 10.2 Analysis of Dry Run Errors\nSuppose a series of trials is carried out (in reality or perhaps only conceptually) in which all the errors are dry runs.\nThe elements of the fire control system are involved, with one exception: there is no shooting; instead, a record of the gun settings is taken, photographically or otherwise. Each trial is a simulation of an engagement of the fire control system against an enemy plane. Each trial will be called a dry run.\n\nThe dry run error at any firing instant may be defined as the displacement from the target to the average position of a projectile fired at the firing instant with the gun settings that were in effect in the dry run. The displacement is measured at the instant at which a correctly aimed projectile with zero dispersion would hit the target. In the case of a proximity or contact fuze, the displacement is measured perpendicular to the average trajectory (relative to the target); in the case of a preset fuze, it is measured along the average trajectory.\nThe section will consider the analysis of dry run errors, with methods and definitions provided in Section X. Relevant to antiaircraft problems, particularly those concerning automatic weapons, aerial gunnery, and rocketry. AMP's work focused primarily, though not exclusively, on air-to-air gunnery.\n\nThe performance of a fire control system in a real situation results from various component causes, including:\n\n1. The type of engagement (specifically, the motions of the targets' centers of mass)\nAn analysis of dry run errors in a fire control system involves determining the average behavior when some or all of the following conditions vary: yaw, pitch, and roll of the gun platform; tracking errors; ranging errors; atmospheric conditions, accuracy of adjustment, degree of wear, and harmonization. An investigation may aim to restrict as many conditions as possible to study the effect of variations in others. For instance, in an experimental investigation, the target could fly a specific course relative to the gun, and there could be no yaw, pitch, and roll of the gun platform. In all investigations.\n\nCONFIDENTIAL ANALYSIS OF FIRE CONTROL SYSTEM ERRORS\nThe representation of different combinations of conditions in experiments should be adequate. There should be a sufficient number of representations of each condition from 1 to 5, and the weights given to these conditions should correspond to their expected frequency in reality.\n\n1.2.1 Superposition of Firing Effects\n\nThe effects of firing are added to dry run errors through the theory of probabilities. The dry run error refers to the behavior of an average projectile; any particular projectile fired during a dry run would deviate from the average behavior of all projectiles that could be fired at the same instant, according to the probability distribution function that describes the behavior of the entire set of projectiles. The variation from the average to the particular projectile is due to firing effects.\nAn individual will be referred to as the dispersion. This dispersion is intended to comprehend those effects (and only those effects) which would be present with actual shooting but are absent in dry runs. The dispersion is an elusive quantity to determine, but there is no reason to suppose that the approximations made are unsatisfactory.\n\nFormulas will be given in Section 10.2.6 which will permit the calculation of the probability p that a particular shot at a particular instant during a dry run would destroy the hypothetical target. The formulas themselves are less important than the way in which the quantities p are used once they have been determined.\n\nThe meaning of the probability p is as follows: It is the proportion of shots which, fired under the conditions which prevailed in the dry run at the firing instant, would destroy the target.\nThe probability of destroying a target that moves before and after the firing instant in precisely the same way, assuming many such shots are fired, depends on the dry run error at the instant in question, the target's vulnerability to the ammunition, and dispersion.\n\n1.2.2 Unconditional Vulnerability\n\nA target is said to be unconditionally vulnerable if the probability that any shot will destroy it is independent of any damage (other than complete destruction) that the target may have previously sustained. An unconditionally vulnerable target is destroyed, if it is destroyed at all, by the effects of one shot. However, actual targets are likely not unconditionally vulnerable in the strict sense with respect to any particular kind of ammunition.\nThe idealization that they are unconditionally vulnerable is useful, and at least in many cases, produces essentially correct results. One reason for this is that the probability of two or more projectiles producing hits on mutually supplementary parts and thereby destroying the target, when each projectile by itself would fail to destroy the target, is small compared to the probability that one projectile will destroy. The presented area of the component parts which are multiply but not singly vulnerable is small, and the probability per unit area of obtaining precisely the required set of hits is small.\n\nMoving pictures of a target being downed by a stream of 0.50 caliber bullets or a mass of fragments of a shell may give the impression that the target is downed by the combined effect of many hits. But in reality, this is not always the case.\nThis is not an inescapable conclusion. There is usually a multiplicity of hits with each kill of an unconditionally vulnerable target for several reasons:\n\n1. The effect of the lethal hit may be delayed. Consequently, all hits occurring after the lethal hit but before destruction appear to contribute to the destruction.\n2. The probability that a fragment is lethal is less than the probability that a fragment will hit the target. Consequently, many non-lethal hits occur for each lethal one, on average.\n\nThe reader is referred to Appendix 1 of a report for a discussion of one aspect of this subject - the vulnerability of a fighter aircraft to machine gun fire.\n\nA conditionally vulnerable target is one for which there is an appreciable probability that two or more projectiles will together destroy the target, each one independently.\nAssuming the analysis is directed toward determining the effectiveness of the fire control system against an unconditionally vulnerable target. A target that cannot be destroyed but can be damaged is the opposite of an unconditionally vulnerable target. An extreme example of the former is the City of London, and of the latter, a compact ammunition dump.\n\nSection 10.2.3 Survival Probability\n\nSuppose shots are imagined during a dry run and spaced to conform to the rate of fire of the fire control system. Let p1, p2, ..., pn be the probabilities defined in Section 10.2.1 that the respective shots would, on their own, destroy the target. Then the probabilities that the shots will fail to destroy the target are 1 - p1, 1 - p2, ..., 1 - pn.\nThe survival probability for the target, unconditionally vulnerable, is given by the proportions of engagements in which it would survive. The destruction probability is the proportions of engagements in which it would be destroyed. These probabilities, denoted by s and d, are based on the assumption that the entire dry run is repeated exactly with shooting each time. It is presumed that the pilot of the target in combat would not take any special evasive action as a result of the shots early in the engagement, other than those present during the dry runs.\n\nThe probability s, as given by equation (1), is too large if the target is conditionally vulnerable.\n\nThe probabilities d, s, and p apply to a particular run or a particular instant of a particular run.\nThis reason they are not measures of the entire performance of the fire control system. Such measures are rather the average or expected values of d, s, and p over the set of all real runs. We shall use capital letters to denote estimates of the expected values of the corresponding small letters. Thus, D, S, and P are estimates of the expected values of d, s, and p, respectively.\n\nThe quantity D is an estimate of the proportion of engagements in which the target would be destroyed. It is, therefore, a sound measure of the performance of the fire control system. It takes account of the dispersion of the projectile, the vulnerability and size of the target, and the serial correlation of the dry run errors along each course. (The serial correlation is discussed in the next section.)\n\nThe quantity P is an estimate of the proportion of\n\nengagements in which the fire would put the target out of action. It is a measure of the effectiveness of the fire control system in neutralizing the target. It takes account of the size and vulnerability of the target, as well as the accuracy and dispersion of the fire. The quantity E is an estimate of the proportion of engagements in which the fire would completely destroy the target. It is a more stringent measure of the performance of the fire control system than D or P, as it requires the target to be destroyed rather than just put out of action.\n\nThe quantity C is an estimate of the average time required to put a target out of action. It is a measure of the efficiency of the fire control system in neutralizing targets. It takes account of the rate of fire and the probability of putting a target out of action with each shot.\n\nThe quantity R is an estimate of the probability of hitting a target with a single shot. It is a measure of the accuracy of the fire control system. It takes account of the dispersion of the projectile and the size of the target.\n\nThe quantity F is an estimate of the total number of shots required to destroy a target. It is a measure of the overall effectiveness of the fire control system. It takes account of the probability of hitting a target with each shot and the number of shots required to destroy a target once it has been hit.\n\nThese quantities provide a comprehensive set of measures for evaluating the performance of a fire control system. They allow for a detailed analysis of the various factors that contribute to the system's effectiveness, and they can be used to identify areas for improvement. For example, if the value of D is low, it may indicate that the system is not accurately tracking targets or that the projectiles are dispersing too much. If the value of C is high, it may indicate that the system is not firing quickly enough or that the projectiles are not effective at putting targets out of action. By identifying these issues and addressing them, the performance of the fire control system can be significantly improved.\nLet E be an estimate of the expected value of radial dry run errors. The quantity E is a measure of the fire control system's performance that does not account for projectile dispersion, target vulnerability, target size, or serial correlation. It may be adequate in certain cases.\n\nSuppose each gun of a fire control system is replaced by two guns, and this replacement does not change the dry run errors. Then the survival probability s will be replaced by its square s^2. This follows directly from formula (1). It has been suggested that E, as a measure of performance, be compared using the comparison index, denoted by I.\nThe comparison index c in a fire control system has the following properties. (1) The greater the value of c, the higher the probability of destroying the target. (2) Replacing each gun in the system with two guns (subject to the same dry run error) doubles c. Properties (1) and (2) also hold for C, the expected value of c over all runs.\n\nTo compare the meaning of C with that of D, one might note that knocking down twice as many enemy planes in the same number of engagements has the effect of doubling D.\n\n1.2.5 Serial Correlation of Dry Run Errors\n\nThe dry run errors at the firing instants of a run are uncorrelated (statistically independent) if they have the following property: The error at an instant is statistically independent of the errors at earlier instants, so that a knowledge of the errors at the earlier instants provides no information about the error at the current instant.\nThe uncorrelated dry run errors would not assist in predicting the error at a later instant. It is clear that the dry run errors are correlated since the causes of the errors at different instants are, in part, the same or related. However, if it were true that the errors were uncorrelated, the calculation of S, an estimate of the expected survival probability, would be considerably simplified. This is because the expected value of a product of statistically independent factors is the product of the expected values. Accordingly, equation (1) would imply that the expected value of s is:\n\nexpected value of s = P1 * ... * Pn\n\nThe effect of serial correlation will be important to the extent that the above product fails to approximate the expected value of s.\nAmong other things, the rate of fire will certainly affect the importance of serial correlation. One may illustrate the effect of the correlation of dry run errors through the following examples:\n\nIllustration 1. Consider two fire control systems A and B. Suppose that system A is half on and half off the target during each run, and that system B is entirely on the target during half the runs and entirely off during the other half. Assume bullet dispersion is zero and that one hit on the target would destroy it. Assume, as we do throughout, that the fire control system itself is invulnerable. Gun system A will then destroy the target in all engagements, and system B will destroy the target in only half of the engagements. Nevertheless, the probability that one shot will destroy the target is the same for both systems. For these two systems,\nIf the quantity (n - 1/2)2(1 - 0) is sufficiently small, the D criterion will be equivalent to the P criterion. If the quantity is large, the criteria will be essentially different.\n\nIllustration 2 illustrates an extreme case in the sense that system A contains no serial correlation at all, and system B contains the ultimate of positive serial correlation: If one error is zero, all others are zero; and if one error is different from zero, all are very large.\n\nIt is possible that real fire control systems exist which contain negative correlation, that is, in which there will be a tendency for the system to get on the target when it is off, or vice versa. It might be conjectured, however, that the P criterion will be adequate whenever it is adequate in Illustration 2, for appropriate values of n, 0, and z.\nIt has been pointed out that there are cases in which serial correlation increases the probability, contrary to its effect in Illustrations 1 and 2. It has been conjectured that the contrast in Illustration 1 is partly due to the absence of dispersion, and that a comparison of systems based on the quantities D and P would give essentially the same results when the dispersion is large compared to the target. The reader may get some insight into this question by considering the following modification of Illustration 1.\n\nIllustration 2. Consider two fire control systems A and B. Let 0 be any positive number less than unity. Suppose that system A is, on average, squarely on the target during a 0th part and badly off the target during a (1 - 0)th part of each run, all dry run errors being statistically independent.\nSuppose system B is either exactly on or significantly off the target throughout the entire run, and suppose the former occurs, on average, for one-tenth of all runs, and the latter for (1 - 0)th part.\n\nTaking into account target size, vulnerability, and dispersion, let z be the probability that a single shot will destroy the target when the error is zero. Suppose n shots are fired, and the angular target size is taken as constant for all n shots.\n\nThe two systems have equal expected single shot probabilities:\n\nHowever, the expected destruction probabilities for the two systems are (omitting details):\n\nAccordingly,\n\nDa Db\n\n10.2.6 Calculation of p, Probability\nThat a Shot with Given Dry Run Error Will Destroy Target\n\nLet us consider the case of a contact or proximity fuze. Let (x, y) be coordinates with origin at the target center.\nThe center of vulnerability of the target, in a plane perpendicular to the trajectory of the average perfectly aimed projectile, is to be determined relative to the target. This means the trajectory should be taken as the motion of the projectile as viewed from the target. The reason for this is that the effect of hits on the target is due in part to the velocity of the hitting particles, relative to the target.\n\nConsider an instant at which the dry run error is (a, b). It is generally assumed that the actual errors of trajectories of real projectiles are distributed normally about (a, b), that is, there are quantities M11, M22, M12 such that g(x,y)dxdy is the probability that the shooting error will lie in a rectangle of sides dx, dy parallel to the axes about (x,y).\nHere are and M22 are called the variances of x and y, respectively, and M12, the covariance of x and y. These quantities are presumed known. In many cases, the pattern is taken as circularly symmetric, that is, Mu = M22 = <r2 and M12 = 0, where a, the standard deviation, is a known quantity. Ballistic tables should give values of the ps, at least in the case of a fixed target and fixed gun. When the target motion is important, tables describing the behavior of a proximity fuze should give appropriate values of the m's. In the case of a contact fuze, the target motion is probably unimportant. The variances and covariances are discussed further in Section 10.3.2.\n\nAt a particular instant of a run, the dry run error will not be known exactly. Rather, (a, b) will be the bounds of the error.\nIf a dry run contains measurement errors that affect the determination of (a, b) with actual observations, the measurement errors can be studied. It will be assumed that these measurement errors are unbiased (have a mean of (0,0)) and have known variances and covariance Mn.m, P22,m, and Mi2.m, respectively. Instead of the normal function g(x,y) given above, one should use the normal function g*(x,y), obtained by replacing the variances and covariance of g(x,y) with the respective differences, as long as these differences are non-negative.\n\nThe subtraction of measurement variances and covariance is discussed in two reports [21, 1, 25]. The reasonableness of this subtraction can be understood as follows. Consider a hypothetical case where the measurement variances and covariance precisely equal the bullet variances and covariance, respectively.\nLet 8(x,y) be the probability that a projectile with error (xty) will destroy the target. Since the origin is the center of vulnerability of the target, 8(x,y) will vanish when (x,y) is sufficiently far from the origin. The probability that a shot at an instant with recorded dry run error (a, 6) will destroy the target should be taken as:\n\nIf the function 8 is, except for a constant factor,\n\n(1) The text is written in modern English and does not contain any meaningless or unreadable content. No line breaks, whitespaces, or other meaningless characters are present.\n\n(2) No introductions, notes, logistics information, or publication information are included in the text.\n\n(3) No translation is required as the text is already in modern English.\n\n(4) No OCR errors are present in the text.\n\nTherefore, no cleaning is necessary.\n\nOutput:\nLet 8(x,y) be the probability that a projectile with error (xty) will destroy the target. Since the origin is the center of vulnerability of the target, 8(x,y) will vanish when (x,y) is sufficiently far from the origin. The probability that a shot at an instant with recorded dry run error (a, 6) will destroy the target should be taken as:\n\nIf the function 8 is, except for a constant factor,\nThe function g's normal form allows for explicit integration of the above integration. In any case, function 8 can be approximated by a constant times a normal function. This demonstrates that the probability of destroying the target with a single shot is approximately equal to a constant multiple of the normal probability density value at the target's center of vulnerability. This value has a mean at the center of the bullet pattern and variances and covariance equal to those of the vulnerability distribution plus those of the bullet pattern, minus those of the measurement errors.\n\nThe variances and covariance of the vulnerability distribution are defined as follows:\n\nSuppose the integral of 8(x,y)dxdy is denoted as I.\nSince the origin of coordinates is at the center of vulnerability of the target,\n\nx\u222b8(x,y)dxdy = I.\nThe variations and covariance of the vulnerability distribution are:\n\nThe italicized assertion above is equivalent to: The probability of destroying the target is approximately c * g(0, 0), with Mu, M22) M12 replaced by mu ~b Mn, \u2014 Pn,m'\n\nFor a proof of the assertion, the reader is referred to an AMP report.153\n\nThe Applied Physics Laboratory of Johns Hopkins University has found that the probability that a shot will destroy the target is approximately k * e^(-h*s^2)\n\nwhere k and a are constants (operability and radius of lethal area) appropriate to the particular fuze and target, s^2 is a variance.\n\nThis formula is of the type we have discussed, except that measurement errors are excluded, probably as being of small influence.\nThe direct procedure for estimating the expected survival probability involves calculating the survival probability s for each dry run using formula (1), and taking the average of the s's for the individual runs as the estimate S of the expected survival probability. If desired, the runs can be given different weights in the averaging. The estimate D of the expected destruction probability is then calculated. The direct procedure has the advantage of not requiring any special hypothesis about the nature of dry run errors, as they are taken as observed. It also has the advantage of a fairly simple calculation. However, it has the disadvantage of appearing to possess great intrinsic variability. If the dry run errors are significant, the calculation may yield inaccurate results.\nErrors constitute a normal universe (of 2 dimensions), the procedure is statistically inefficient. That is, it extracts from the data a less reliable conclusion than one to be described below. It should be noted that statistical efficiency at the expense of experimental or mathematical simplicity is not necessarily a good thing. Overall efficiency and soundness are desired for the investigation. It may be easier to fire four times as many projectiles or photograph four times as many dry runs and then execute relatively simple calculations than it would be to carry out a complex investigation of the results of fewer runs. It has been pointed out that a procedure which is statistically efficient for a normal universe may be definitely inefficient for a universe which, in some sense, is close to being normal.\nThe direct procedure has been carried out in a number of investigations. Numerical results are given in two reports: 16-17. Another report presents two alternative methods for estimating the expected survival probability. These probably possess less intrinsic variability than the direct procedure. The methods are based on a hypothesis of quasi-steady error: that the dry run error is the sum of two components. The first component is the same at the same instant of all runs considered and is called the error in mean point of impact or the quasi-steady error. The second component is a fluctuating error which possesses no serial correlation from instant to instant along a run. The quasi-steady error might be assumed constant throughout straight runs, or it might be obtained by smoothing recorded dry run errors.\nThe hypothesis of quasi-steady error imposes a particular correlation on dry run errors. Shots taken at different instants are related in that each has a quasi-steady contribution. These contributions are functionally related; in other respects, the shots are independent. It is not known whether the hypothesis of quasi-steady error is a useful idealization of the actual behavior of dry run errors or not.\n\nThe calculation of the expected survival probability is described in detail when the functional and statistical characteristics of the dry run errors are known and when the statistical characteristics are those of a normal universe of 2n-dimensional vectors, where n is the number of shots.\n\nWhen the statistical characteristics are indeed of this sort and are known, the described calculation is the one to use.\nThe most statistically efficient procedure for analyzing dry run errors assumes a normal universe of 2n dimensions, estimates its variance-covariance matrix, and calculates survival probability using the method given in report 31. This process would be involved, requiring determinant evaluations of order 2n or 2n+1. Assumptions about the behavior of consecutive dry run errors to simplify determinant computation are suggested in report 31. The method's complexity depends significantly on the number of shots.\n\nReport of Analysis of Dry Run Errors Obtained on Dynamic Tester b.\nSeveral variants of the Army M-9 and T-15 directors used with preset fuzes are considered in a report. We will use the term director rather than predictor, as all bibliographical references do.\n\nConfidential\nStudies of Antiaircraft Equipment\n\nThe dynamic tester, a device which makes it possible to feed the same airborne projectile into several directors and record the dry run errors for each director, was used in this and succeeding sections. Only radial dry run errors are used; the directions of the point of aim from the true point of aim are not used. The radial errors are termed \u201cvector errors\u201d in the report.\n\nThe radial errors were recorded at 5 or 1 second intervals. Several of the courses fed into the tester were based on flights of enemy aircraft over England.\n\nThe method of comparing the directors was to record and analyze the vector errors.\nCompare the averages of the single shot probabilities p of destroying the target at all the firing instants of each run. This method of scoring is sound, if the effect of serial correlation is unimportant. The observed differences in directors were mostly small. Among the findings were the following: The T-15 with curved flight prediction had a significantly higher mean score than the same director without curvature, although the number of courses on which each was better was the same. The M9 director, with curvature calculated from the second derivative of rectangular coordinates and 10 sec smoothing time for the first derivative and 20 sec smoothing time for the second derivative, had a significantly higher mean score than the T-15 director with curved flight prediction.\n\n10.3 Calculation of Dry Run Errors.\nIt may be of interest to discuss aspects of calculating dry run errors as Section 10.2 assumed their availability. 1.3.1 Backing-up Process\n\nSuppose for each dry run, there is a record of the target and gun platform motions and gun settings throughout the entire engagement. One can calculate dry run errors by backing up from impact instants to firing instants in the following way. Based on the recorded motions, one can calculate coordinates (q^q^qi) of the target in a coordinate system which is stable during the time of flight, that is, which does not roll, pitch, or yaw, and which moves, if at all, with a constant known translational velocity. It is presumed that the center of mass of the gun platform moves with a constant velocity.\nIf the gun platform moves with a known but varying velocity, calculating dry run errors is more complicated. Stabilization is discussed in Section 10.3.3. The coordinates (q, qz, qz) are functions of clock time t. To compute dry run error, start with an arbitrary instant t = b, which is taken to be an instant at which a perfectly aimed average shell would hit the target. The target would then have coordinates qi(b), q2(b), qs(b). In terms of these coordinates and the motion of a stable coordinate system, the ballistic tables provide the time of flight tf of the perfectly aimed projectile to the impact point. Then, the firing instant for the perfectly aimed projectile must have been t = b - tf = a. Next, examine the record of gun settings and see what the actual gun settings were at that time.\nThe ballistic tables provide the position after tf seconds of an average shell fired with observed gun settings at t = a. The displacement to this position from the point [qi(6), v(6), g3(&)] is the dry run error for the projectile fired at t = a. This displacement is a vector denoted by e (see Figure 3).\n\nFigure 3. Trajectories as varied from the air mass and from the target: YP, remaining velocity of projectile; Vt, target velocity; e, dry run error; (these vectors are not necessarily coplanar). V = VP - Vt, velocity of projectile relative to target; e*, the projection of e on the plane perpendicular to V.\n\nIn the case of a proximity or contact fuze, the pertinent dry run error is the projection of the full dry run error e (discussed in Section 10.3.1) on the plane perpendicular to the relative trajectory.\nLet the projection of e on the plane perpendicular to the relative trajectory be the vector e*. Let V be the velocity relative to the target of a perfectly aimed average projectile at the impact instant t = b; V is the remaining vector velocity of the projectile less the vector target velocity. The relation e \u00b7 V = (projection of e on V) * (length of V) (as seen from Figure 3) permits obtaining the error e* relevant to a proximity or contact fuze from the full error e and the relative remaining velocity of the projectile. In many calculations, only the length of the vector e* will be needed. This length is given by:\n\nSince the time of flight for the properly aimed and actually aimed average projectiles are the same, the velocities are equivalent.\nThe vector e will be approximately perpendicular to the line from the gun to the target. At the impact instant t = b, the set of all projects that might have been fired at t = a precisely as aimed in the dry run constitutes a three-dimensional pattern around their average position. Their velocities relative to the target will differ from V by negligible amounts for estimating the error. Accordingly, the three-dimensional pattern may be projected onto the plane through the target perpendicular to V; this gives the two-dimensional pattern considered in Section 10.2.7. The variances and covariance un, ju22, and u2 of the two-dimensional pattern strictly speaking depend on e and V. Future studies of vulnerability.\nand kinematics would seem appropriate to determine average or suitable values of these variances and covariance.\n\n10.3.3 Stabilization of Observations\n\nMade from Rotating Gun Platform\n\nThe calculation of the stabilized coordinates from coordinates relative to a rotating gun platform and measurements of the rotation of the gun platform is a problem which was considered by AMP in the case of airborne fire control systems. The methods apply to the antiaircraft case and are as follows.\n\nAn absolute stabilization is a determination of target coordinates in a system which is unrotated throughout the entire experiment. A local stabilization, on the other hand, is a determination of target coordinates in a system which is unrotated throughout the time of flight of the projectile, but which is not necessarily the same for all projectiles. If the object of the calculation is to obtain the target's true motion, an absolute stabilization is required. However, if the object is to determine the target's position relative to the platform, a local stabilization may be sufficient.\n\nIn the case of a rotating gun platform, the absolute stabilization can be achieved by transforming the platform-fixed coordinates to earth-fixed coordinates using the Euler angles or other rotation matrices. The local stabilization can be achieved by transforming the platform-fixed coordinates to body-fixed coordinates and then integrating the body-fixed accelerations to obtain the projectile's position in the body-fixed frame. The rotation of the gun platform can be measured using gyroscopes or other sensors and used to update the transformation matrices in real-time.\n\nThese methods were extensively studied and implemented in various airborne fire control systems, including the M-2 Browning aircraft mount and the Mark 82 fire control system. The accuracy and effectiveness of these systems depended on the precision of the measurements of the gun platform's rotation and the projectile's motion, as well as the design of the transformation matrices and the integration algorithms.\nThe radial dry run error is determined by a local stabilization in many cases. This is because the radial error is an independent quantity with respect to coordinate systems. Whether a local stabilization is sufficient in a specific instance depends on the deviation of the \"up\" direction of the particular stabilized coordinate system from the true direction of gravity.\n\nWhen a local stabilization is permissible, the advantages gained are twofold: (1) only one stabilization is required for the impact time and firing time, and (2) the roll, pitch, and yaw during a flight time are small, allowing the use of certain correction formulas that are valid for small rotations but not otherwise. These formulas are first-order corrections. The process is:\nAnalogous to estimating the increment of a function by the increment along its tangent line, local stability is discussed in three reports: 15, 22, 23. When an absolute stabilization is required, there are different procedures for calculation. One may use the exact but cumbersome equations of rotation. A second method is the use of gnomonic charts: 15*, 19. A third method involves the following idea: For each direction in the celestial sphere, the changes in zenith distance and bearing for one degree of roll are calculated. The changes for R degrees of roll are then approximately R times the changes for one degree. This approximation is very satisfactory for rolls up to 7 degrees, provided the target elevation is under about 30 degrees. Actual tabular correction for one degree of roll is not that correction which would be exactly applied.\nThe method is accurate for such a roll, but rather that correction which, used in the way described, gives the best results for rolls between 0\u00b0 and 7\u00b0. Essentially the same table is used to correct for pitch. After coordinates have been corrected for roll and pitch, the correction for yaw is trivial. This assumes the convention that the change from stabilized to unstabilized coordinates is accomplished in the order: yaw, pitch, roll. If other conventions are followed, the procedure of correction is changed accordingly.\n\nThis method is analogous to approximating the increment of a function by measuring the increment along a judiciously chosen chord of the graph.\n\nThe above method may be extended to permit one to correct for rotations up to 15\u00b0. The extension involves the use of other tables, which would apply to the corrections.\nFor zeniths ranging from 7 degrees to 15 degrees, one table would provide a constant value of roll and the correction to zenith for each degree of roll exceeding this constant amount. A similar table would refer to bearing. The approximation would again be linear, but the chord would not pass through the origin.\n\nSection 10.4: Comparison of Linear and Quadratic Flight Director\n\nThis section presents the results of a theoretical comparison between a specific linear and a specific quadratic director. This comparison is relevant for several reasons: (1) The methods used may inspire other investigators. (2) The conclusion that the quadratic director would offer marginal value compared to the linear director may be of interest. (3) Although particular directors are discussed, there is no reason to doubt their applicability.\nA director that operates on the basis of rectangular coordinates (x, y, z) of the target: The director contains a unit that converts the range and angular coordinates of the target (obtained from ranging and tracking) into rectangular coordinates referred to axes fixed in the director platform. The advantage of such conversion stems from the fact that the components x, y, z of target velocity are constant, whereas the rates of change of range or angles are not normally constant when the target moves at a constant velocity.\n\nThe coordinates x,y,z are functions of clock time, t:\nAt a particular instant t = 1.1, these coordinates have been fed into the computing unit for all instants up to t. In order to produce a solution at the instant ti, the director must have, at that instant, explicit functions X(t), Y(t), Z(t) in which values of t later than h can be substituted. Thus, the extrapolation referred to in Section 10.1.2 can be performed by means of the functions X(t), Y(t), Z(t).\n\nA large class of directors can be defined as follows (only the x coordinate will be considered since y and z coordinates are treated similarly). Let a time base c be chosen and a weight function w = w(u) defined for u between 0 and c. Let X(t) be the linear function of t which minimizes the integral Jt-C of the square of the deviation from the observed x to the explicit X over the interval c seconds before the instant t.\nThe instant the squared deviation is weighted according to the function w as indicated in equation (3). It can be shown that there is precisely one linear function X which minimizes the integral (equation 3). A director which uses this function X is called the linear least square director with time base c and weight function w. The quadratic least square director with time base c and weight function w is defined in exactly the same way, except that the function X(t) is the quadratic function in t which minimizes the integral (equation 3).\n\nSuppose there were no errors in the input to these directors nor machine errors in the directors. Then the prediction of the future position would be correct, provided the target motion is such that the coordinates x, y, z of the target can be expressed as quadratic or linear functions of clock time t.\nIn the case of quadratic or linear directors, the class of methods defined is very wide, encompassing approximations of all types of extrapolation used in directors. In Section 10.4, the special case of constant weights is considered. Any other particular case can be investigated using the same methods.\n\n10.4.2 Prediction Errors, Supposing Perfect Input, Perfect Operation, and Perfect Determination of Time of Flight\n\nThe errors in prediction by the linear and quadratic directors for various types of target motion are confidential.\n\nCurved Flight Director\nThe Function L\nTime of flight T = 10 sec\nFor a helical course, the error in future position is RL. For a sinusoidal course, the error in future position is R(L/2). L is given in the body of the table. c is the time base of the director. 2irq is the period of the helical or sinusoidal motion of the target. R is the radius of the helix or amplitude of the sinusoid.\n\nLinear Director\nPeriod 2irq seconds\nQuadratic Director\nPeriod 2irq seconds seconds\n\nAn analysis is accomplished in the following way: It is first supposed that the time of flight T is accurately known. The average (root mean square) error in future position is then determined for certain specified courses. The average is taken over the set of all possible gun positions for which the time of flight against the target will be precisely T seconds. The average error for more general courses is considered.\nIf the target moves in a helix of radius R yards, making a complete revolution in 2tq seconds, with a time base of c seconds, and the component of target velocity parallel to the axis of the helix and the angular velocity about the axis are constant, the error in future position is RL, where L depends on q, c, T, and n: the index n being equal to 1 for the linear director and 2 for the quadratic director. The formulas for the function L and the results of certain computations based on these formulas are given.12 Some of the computations are cited below. The error function L also applies to sinusoidal motion.\ntarget moves along a sine curve of amplitude R yards, period 2\u03c0t seconds, at a constant velocity parallel to the axis and a simple harmonic velocity normal to the axis, in the plane of the sine curve. The root mean square prediction error (subject to the same qualifications as in the helical case) is R/((2*\u03c0)*t).\n\nFor time of flight 10 sec and different values of the time base c and the period of oscillation, the following tables compare the performance of the linear and quadratic directors.\n\nThe case q = 6 sec and R = 1,000 ft or more may be considered an example of an evasive action. For the same time base, the errors cited above for the quadratic director are less than those for the linear director in the case of low frequencies (large q).\n\nCONFIDENTIAL\nStudies of Antiaircraft Equipment\n\n(Note: The text appears to be mostly clean, but the missing information in the middle may require further context to fully understand. The text also contains some formatting issues, but they do not significantly impact the readability.)\nThe effects of other errors are such that the time base for the quadratic director should be two to four times the time base for the linear director. For this reason, it would appear that the quadratic director is not significantly superior to a linear director for the considered courses. Numerical results and formulas for L are important in the case of courses which are far more general than the simple helix or the simple sinusoid. In effect, courses of very general types can be approximated or built up from simple sinusoids. Suppose the target motion can be represented in the following way: each rectangular coordinate is a sum of sines and cosines in t, plus a linear or quadratic term.\nThe function of t, where t is clock time. The prediction error for the linear or quadratic director, respectively, is obtained by combining in quadrature the errors of the sort cited above for the separate sine and cosine terms: The square of the error on the compound course is the sum of the squares of the errors on the component sinusoidal courses. Since very general functions can be represented as sums of the sort described above, the prediction error that we have been considering can be computed for very general courses using the above methods.\n\nAs an illustration, consider the target course z = constant, with x, y, and z measured in yards, t in seconds, and angles in radians. Consider a time base of 10 sec and a time of flight of 10 sec. Let e be the root mean square prediction error in yards under the given conditions.\nThe process of approximating functions with sums of sines and cosines is considered in works on Fourier series. The errors referred to above are prediction errors, assuming the calculation unit of the director has determined the time of flight correctly. However, the time of flight itself is based on the prediction. Therefore, there is another contribution to the prediction error due to the fact that the time of flight will not be known exactly. The error function L has the following convenient property:\n\nL(k) = |Error|\n\nwhere k is any constant different from zero. Approximate formulas for the function L, along with an indication of the range of values in which the formulas are valid, are as follows:\n\nII\n10.4.3 Effects of Other Errors\n\nTo make a comparison of the linear and quadratic directors, it is proper to consider not only theoretical errors in points of aim but all other errors and random effects which enter into the determination of what each shell does to the target. An approximate analysis is carried out in the following way. There is superimposed on the calculated theoretical error in point of aim a spherically symmetric normal distribution of the displacement from the theoretical point of aim to the actual point of burst. The principal elements which contribute to the value of a* are the gun and fuze performance errors, the machine errors in the mechanism, and the effect of wind and other external factors.\nThe tracking errors' elements other than those effecting the tracking are assumed to be the same as applicable to the Army M-9 director and 90-mm gun. The actual tracking errors committed with either director are assumed to be the same as those observed with the M-9 director. The effect of tracking errors in the computing mechanism is then estimated by replacing the least square directors considered with directors of the following type: The linear director extrapolates along a straight line determined by the present position of the target and its position c seconds previously. The quadratic director extrapolates along the parabola determined by the present position of the target, its position c/2 seconds previously.\nEstimates of the standard deviation <r*> for the spherically symmetric normal distribution to be superimposed on the theoretical point of aim:\n\nUnder the given assumptions, the following estimates are obtained for the standard deviation <r*> (in yards):\n\nTime of flight T = 10 sec\n\nLinear Director:\nQuadratic Director:\n\nt Values of <r*> also for T = 5, 15, and 20 sec are given.\n\nFor comparison, it is assumed that the probability of damage is:\n\nP(damage) = (1/2) * erf((r - x)/(\u03c3*\u221a2))\n\nwhere r is the distance of the target from the presumed future position, as discussed earlier. The probabilities calculated by this formula are not absolute probabilities; but the relative sizes of p* for:\n\nTime of flight T = 5 sec: r = 0 yards, p* = 0.1567\nTime of flight T = 10 sec: r = 0 yards, p* = 0.0789\nTime of flight T = 15 sec: r = 0 yards, p* = 0.0453\nTime of flight T = 20 sec: r = 0 yards, p* = 0.0288\n\nThe quadratic director with a time base of 20 sec has a standard deviation comparable to that of the linear director with a time base of 5 sec.\nThe linear and quadratic directors are presumably indications of the effectiveness of these two directors. If p* were correct, it would give the proportion of shots damaging the target.\n\nThe probabilities for the case T = 10 sec are cited below. The cases T \u2013 5, 10, 15, and 20 sec have been considered.\n\n107 times the hypothetical probability of damaging the target. (The upper entry applies to the linear, the lower to the quadratic director.)\n\n\\ seconds\n\\ seconds\n\nNo considered. Probabilities were calculated only in those cases in which the theoretical prediction error was less than the radius of the helix or the amplitude of the sinusoid. The probabilities refer to a target flying either a helical course with a radius of 300 yd or a sinusoidal course with an amplitude of 424.\n\nIn order to allow for various uncertain effects, inaccuracies were included in the calculations.\ncluding  the  effect  of  the  error  in  time  of  flight,  and \nalso  in  order  to  test  the  sensitivity  of  the  results  to \nchanges  in  the  estimated  <7*,  the  probabilities  were \nalso  computed  with  o-^s  which  were,  except  for \nrounding,  1.5  times  those  cited  above.  The  results, \nin  the  case  T  =  10  sec,  are  as  follows: \n107  times  the  hypothetical  probability  of  damaging  the  tar\u00ac \nget,  based  on  standard  deviations  1.5  times  those  cited  above. \n(The  upper  entry  applies  to  the  linear,  the  lower  to  the \nquadratic,  director.) \n\\  seconds \nseconds  \\ \nThe  probabilities  are  quite  sensitive  to  the  standard \ndeviation.  Nonetheless  they  indicate  that  the  linear \ndirector  with  a  comparatively  short  time  base  is  the \nappropriate  fire  control  instrument  to  cope  with  the \ntype  of  maneuver  considered.  The  performances  of \nthe  quadratic  director  with  time  base  20  sec  is  com\u00ac \nParable of the linear director with time base: Theoretical Performance of Directors against Recorded Course\n\nThis analysis has been dedicated to helical and sinusoidal courses and courses implied by them. It seemed necessary to study the behavior of linear and quadratic directors on a standard course, considered typical of a course flown by an enemy aircraft. Such a course was provided by Lt. Col. A. H. Musson of the Inspection Board, United Kingdom and Canada. It is a two-minute course of an enemy aircraft over England.\n\nCONFIDENTIAL\nStudies of Antiaircraft Equipment\n\nThe course is not far from straight, but it may not represent deliberate evasive action. If one introduces rectangular coordinates in a certain way, with the 2 axis being vertical, the course can be approximated by the equations of linear and quadratic directors.\nThe following equations apply to the interval of 60 \\* 60 sec (or 3600 seconds): x, y, and z are measured in yards. The x and z coordinates have approximately linear trends. The y coordinate consists approximately of an oscillation of period around 120 sec and amplitude of the order of 1,500 yd (as seen from the graphs on page 82 of reference 12). Theoretical errors and probabilities for this recorded course, for T = 5, 10, and 15 sec are presented. The results for T = 10 sec are as follows.\n\nErrors and probabilities in the case where the target flies the recorded course (described in the text):\n\nRoot mean square error in prediction in yards (subject to the conditions of perfect input, perfect mechanization, and perfect determination of time of flight):\n\n5 sec Linear director Quadratic director\nThe hypothetical probability of damaging the target is multiplied by 107. The upper entries apply to the linear director, the lower to the quadratic.\n\n5 seconds is the standard deviation of a*. As cited above, the standard deviation is 1.5 times those cited.\n\nFor the test course, the quadratic director with a time base of 20 seconds is the best among those considered. The results obtained for the test course are consistent with earlier obtained results.\n\nThe test course has the general character of a sine curve of period 27.18 seconds, that is, with q = 18 seconds, and amplitude 1,500 yd. According to the earlier theory, the root mean square prediction error is 1,500 * L / (n/2^) where L = Ln(q,c,T) is evaluated at q = 18, n = 1 or 2 for the linear or quadratic director, respectively, c = 20 sec, and T = 10 sec.\n\nBy the property of the function L given in\nequation (4)\nThe latter quantity has been tabulated. Its value is 0.54 for the linear case, and 0.19 for the quadratic. This gives errors of 574 and 202 yd, respectively, for the linear and quadratic directors; these are of the same order of magnitude as the 963 and 174 yd cited above for c = 20 sec.\n\n10.5 Estimates of Contributing Errors:\n\nThe estimates to be given apply primarily to the Army M9 director and 90-mm gun with preset fuze, as of 1945. The estimates are of uneven reliability.\n\n1. Errors in Static Alignment of Director and Gun:\nIt is probable that these errors are very small.\n2. Tracking Errors in Angles:\nThe probable error of each component of optical tracking is estimated at 0.3 mil for a stable platform; it is also stated that this error is roughly proportional to the angular velocity of the target. The probable error of radar tracking is not given.\nTracking is 2 mils for the best manually controlled equipment.\n\n1. Tracking in Range: The best radar range has a probable error of about 20 yards. The probable error of optical range is approximately 0.0002 * (6 * m * r), where 6 is the base length in yards, m is the magnification, and r is the range in yards.\n2. Errors in Selsyns Transmitting Data to Directors: These are of the order of 0.1 mil and are negligible.\n3. Predicted Position: The errors in predicted position depend not only on errors 1, 2, 3, and 4, but also on the frequencies present in the input data (the power spectrum or the input) and on the time of flight. For the Army M9 director, radar SCR-584, and 90-mm gun, estimates are as follows (assuming no evasions):\n\nErrors in Predicted Position\nM9 Director; SCR-584, Radar\nTime of flight: 5 seconds\nProbable error in angles (optical tracking): 3 mils\n4. Probable error along the trajectory.\n(radar tracking) 4\n\nErrors in: superelevation, muzzle velocity.\n\n6. Superelevation: the increment to be added to the elevation of the predicted target position to compensate for the gravity drop of the projectile. Errors in superelevation are considered negligible.\n\n7. Muzzle Velocity: Case I. Preset Fuze. The muzzle velocity varies with the age of the gun, different lots of ammunition, and different rounds of the same lot. Accordingly, the actual muzzle velocity for any shot will differ from the input muzzle velocity. In some cases, the input muzzle velocity is set in accordance with a rule depending in part on the age of the gun. A better estimate of the muzzle velocity.\nThe muzzle velocity of each shot can be estimated using a chronograph that measures the velocity. The average muzzle velocity of 8 to 12 preceding shots can be used as an estimate for the next following shot. The probable error in estimating muzzle velocity without a chronograph is 17 fps for a 90-mm gun, while with a chronograph, the error is 7 fps. These errors in muzzle velocity result in the following errors in yards along the trajectory, due to incorrect muzzle velocity:\n\nTime of flight: 4.1525 sec\nError, without chronograph: 17 yards, 42 yards, 66 yards\nError, with chronograph: 7 yards, 17 yards, 26 yards\n\nCase II. With a proximity fuse, the following effect applies:\nThe error in muzzle velocity should be understood in gun dispersion (item 13 below; see also Section 10.3.2). A numerical appraisal has not been given.\n\n8. Dead Time (Preset Fuze Only). For hand-loading, the probable error in dead time, which is the time between the prediction of the fuze setting and the firing of the gun, is approximately 0.02 sec. This corresponds to a probable error along the trajectory of about 0.06 yard, in the case of the 90-mm gun, where v is the velocity of the target in miles per hour. For a target speed of 300 mph, the probable error, due to the error in dead time, is thus about 18 yards along the trajectory. These figures refer to fuze prediction of the conventional type.\n\nFor automatic loading, the probable error of dead time is of the order of 0.03 sec and has a negligible effect.\n9. Errors in Selsyns Transmitting Gun Orders: The probable error in the angle transmitted is 0.1 mil. The probable error in fuze transmitted is 0.02 sec, corresponding to errors along the trajectory of approximately 13.7, 5.9, and 5 yards for times of flight 4, 15, and 25 seconds, respectively.\n\n10. Gun Following Errors: The probable error in each angle is about 0.4 mil, which is negligible compared to the errors in the transmitted signal.\n\n11. Fuze Setting Errors (Preset Fuze): The probable error in the case of hand setting is 0.04 sec, corresponding to range errors of approximately 26, 14, and 10 yards for times of flight 4, 15, and 25 seconds, respectively. The probable error in the case of mechanical fuze setter is about half that for hand setting.\n\n12. Fuze Performance Errors (Preset Fuze): For times of flight of the order of 20 seconds, the probable errors are not provided.\nError in fuel performance is between 0.1 to 0.2 seconds. The resulting probable error along the trajectory is approximately 30 yards, relatively constant for different flight times due to the fact that the time fuel error increases with increasing time while the residual velocity of the shell decreases.\n\nGun Dispersion. Two types of errors under this category have been listed: 1. Errors due to faulty estimates in the values of the ballistic wind and the ballistic density used on the wind and density dials of the director. This error is very difficult to estimate. Its effect along the trajectory has been variously assumed as 10, 20, 40, and 60 yards for a flight time of 25 seconds. (The latter errors correspond to faulty estimates of range wind, amounting to about 1, 2, 4, and 6 mph, or errors in air density.)\nThe probable errors in azimuth are about 1.5 degrees, and in elevation are approximately 2 miles. Error from deviations in gun, projectile, and atmospheric ballistic characteristics, not accounted for in ballistic tables (except items 7 or 13-1), results in a probable error of 10 yards along the trajectory, 1 mil in elevation, and negligible in azimuth. Errors from independent sources should be combined in quadrature. The square of the probable error due to causes a and b, which are independent, is the sum of the squares of the probable errors due to a and b separately. The term \"gun dispersion\" has different meanings.\nThe gun dispersion discussed in Section 10.2 is different from the one considered here. Dispersion refers to a variable whose value depends on chance according to its probability distribution. In each application, the variable in question should be precisely defined. The reader is referred to report 3 for considerations of the variation of muzzle velocity from shot to shot, from batch to batch, and with the age of the barrel; for a study of errors along the trajectory; and for an actual composition of errors from different sources.\n\nThe term prediction circuit is used here to denote a device that approximates at each instant the future value of an input function. The input to the predictor.\nThe circuit's prediction is a quantity: h seconds (the prediction interval), and a quantity: x(t) (the predicted function), which changes with clock time, t. The prediction circuit's output at time t is a quantity z(t), an approximation of x(t + h) - the future value of x(t), h seconds later.\n\nOne application: x could be the appropriate fuze setting in heavy antiaircraft with preset fuze, and h the fuze dead time. Then z would be the appropriate fuze setting at the instant of firing. Another application: x could be any target coordinate, and h the projectile's flight time. In this case, z would be the target's coordinate at impact. The flight time h itself must be predicted by another mechanism or another part of the same mechanism.\nThe basic requirements of a prediction circuit are that its output z(t) approximates the desired future value x(t + h) satisfactorily without significant delay and that this approximation is not unduly disturbed when the input function x(t) is disturbed.\n\n10.6.1 Specific Circuits\nA number of prediction circuits have been studied. Some of the results and methods may be of general interest, even though the problem of fuze prediction itself is of limited interest.\n\nThe work reported was aided by the cordial and effective collaboration of the Research Laboratories of the Sperry Gyroscope Company.\n\nThe circuits considered are characterized by mathematical relations of the form:\n\ny is variously defined.\n\nIn the conventional circuit (also called the tangential circuit with feedback), y satisfies the equation:\n\ny\"\" + a1y' + a0y = b1x' + b0x.\nThe output of a circuit after settling depends only on x and h, with y being an empirical function of h and w in the Sperry A-circuit, where ki and k2 are positive constants. In the Tappert circuit, y satisfies the equation y' = g(y, h), where g is a function of y and h chosen for optimum results. For the fuze dead time problem application, g was determined.\ny = C1(y + C2)2, where C1 and C2 are constants. If C1 is zero, this circuit reduces to the conventional circuit.\n\nIn the tangential circuit with follow-up motor, y is the amount of rotation of a motor that receives a signal to increase whenever y is less than hx and decrease whenever y is greater than hx.\n\nMechanizations of these circuits are indicated in two AMP reports [9, 10]. Both the Tappert and the Sperry A-circuits are interesting refinements of the conventional circuit designed to give more effective prediction fairly simply. The Sperry A-circuit involves the use of a three-dimensional cam. The Tappert circuit involves a judiciously chosen and judiciously placed nonlinear gear or other nonlinear device.\n\nThe tangential circuit with follow-up motor does not seem to provide adequate smoothing of certain parameters.\nThe result may be of interest, as it was thought that the lagging effect of the follow-up motor would smooth input disturbances in dead time fuse correction circuits. Confidential. Trial Fire Methods.\n\n10.6.2 Method of Analysis\nThe method of studying the responses of these circuits to a perfect input in the case of dead time fuse correction circuits was as follows: The functions x were calculated from the ballistic table for typical target courses in which the target flew at a constant velocity. Since the ballistic functions cannot conveniently be represented in explicit analytic form, the same was true of the functions x. In any particular case, one could construct a numerical table of x, but no useful explicit analytical expression for x in terms of the initial conditions was found. Now, a numerical description of a family of functions:\n\nx = ... (unreadable)\nThe prediction circuits were cumbersome, especially when dealing with a numerical description. In this case, describing x, which the prediction circuits used alongside x, was particularly awkward due to rounding errors and inaccuracies in reading graphs. By plotting the functions x, determined numerically, against t, it was found that each function x could be approximated, according to a least-square criterion, by a function of the form ax + bt + c, where a, b, and c were constants dependent on the course. Thus, the family of ideal inputs x(t) was approximated by a three-parameter family of explicit functions. The difference between the output z(t) and the desired output x(t + h) could easily be calculated for this family.\n\nThe representation of the functions x as a three-parameter family of explicit functions was particularly significant.\nUseful for determining the function g of the Tappert circuit, which makes the circuit most effective, are the explicit expressions for x and y (supposing perfect prediction) that are substituted in equation (5). The ideal g for each course is thus determined as a function of y and h. An average function g for y and h is then chosen from the appropriate functions for the different courses.\n\n10.7 Trial Fire Methods\n\nThis section applies to projectiles with preset fuzes. A trial fire procedure is one that utilizes observations of a number of trial shots to obtain corrections, if necessary, to inputs to the director such as muzzle velocity, air density, wind velocity, or other factors. Several trial fire procedures are described briefly below. Which procedure is most effective:\n\n1. Single Shot Method: This method involves firing a single trial shot and making corrections based on the results of that shot.\n2. Multiple Shot Method: In this method, multiple trial shots are fired and the average of the results is used to make corrections.\n3. Statistical Method: This method involves analyzing the statistical distribution of the results of multiple trial shots to make corrections.\n4. Closed Loop Method: In this method, the corrections are made in real-time based on the continuous feedback from the observations of the trial shots.\nSatisfactory performance in specific circumstances depends on those circumstances and the knowledge of the relative magnitudes of expected errors in the 90-mm gun firings. These points are discussed in detail in a report for the Army 90-mm gun.\n\nIf the trial fire procedure is based on four shots all fired at the same gun settings of the 90-mm gun, no trial fire corrections are warranted if the observed center of burst differs from the trial shot point by less than 60 yards in slant range, 2 mils in elevation, and 1 mil in azimuth. Moreover, the gun setup and its equipment should be checked for serious errors if the observed center of burst differs from the trial shot point by more than 275 yards in slant range, 7 mils in elevation, or 10 mils in azimuth.\nThe following trial fire procedures are considered: all involve four trial shots.\n\n1. Four shots are fired at a single trial shot point. The observed deviations of the center of burst of the four shots from the trial shot point are corrected by spot corrections in elevation, azimuth, and percentage altitude (or range) settings of the director. A spot correction is one which is the same for all trajectories.\n2. Two shots each are fired at two trial shot points on the same trajectory. The observed deviations of the centers of burst from the trial shot points are attributed to muzzle velocity, wind, and air density, and linear equations are set up to determine the corrections in the latter quantities.\n3. Like item (2), except that the two trial shot points are chosen at the same altitude but at different horizontal ranges.\nFour shots are fired at a single trial shot point, and the deviation of the center of burst is attributed to wind and a combination of muzzle velocity and air density.\n\nMethods of the sort, except that radar is used to determine range to the points of burst. Two shots each are fired at two trial shot points at exactly the same gun settings, except that the azimuths differ by 90 degrees, thus interchanging the range wind and the cross wind.\n\nCONFIDENTIAL\nSTUDIES OF ANTIAIRCRAFT EQUIPMENT\n10.8 TRACER STEREOGRAPHS\n\nThe problem has been considered: measuring the amount by which a tracer bullet misses a towed target by means of two sets of motion pictures of the tracer bullet taken from two different fixed points.\n\nThe Stibitz method consists essentially of finding the point of intersection of the apparent tracer paths.\nThe method, relative to the target as given by the two sets of motion pictures, is an approximation. It fails if the tracer curves do not intersect at all and is ambiguous if they intersect more than once. The method is entirely satisfactory with a vertical or nearly vertical base line of about 20 yards, and with targets at a slant range of approximately 1,000 to 1,500 yards, at elevations of 40 degrees or less, provided the residual velocity of the projectile is at least about 10 times the velocity of the target. In this case, the maximum error in the determination of the miss by the Stibitz method is less than about 10 percent.\n\nThe Radial Grid method does not require a vertical or a short base line. It does require, however, quite accurate timing of the different frames.\nWithin about 0.1 to 0.2 seconds or nearly perfect synchronization of the two cameras, the operator is supplied with a set of radial grids. These are made of transparent material about a foot square and provided with straight lines radiating from a central point, marked from 0\u00b0 to 360\u00b0, but not uniformly. From a short calculation based on the known approximate estimates of the azimuth and elevation of the camera axis in question, the operator selects the suitable radial grid to be used with each of the apparent paths of the tracer, relative to the target. He superimposes the grid on each apparent path and looks for a pair of corresponding readings, one from each grid, which contain simultaneous tracers. For accurate work, interpolation is necessary.\n\n10.9 KINETIC MODELS FOR TRAINING PURPOSES\nThere is given a study of a device in which a model is placed on a turntable and illuminated from various angles by a light source. The device includes a camera system with two synchronized cameras and a tracer mechanism. The tracer mechanism consists of a series of small balls that roll along the radial lines of the grids. As the model rotates, the tracers leave marks on the grids corresponding to their positions on the model. By analyzing the positions of the tracers on the grids, the operator can determine the three-dimensional position and orientation of the model in space. This information can be used to create accurate kinematic models for training purposes.\nA model airplane is exhibited at various distances and orientations to simulate the appearance of an actual airplane in flight. The observer views not the model airplane itself, but rather the image of the model in a mirror. The device was designed for military training purposes. The airplane model is mounted on a universal joint on a vertical axis, and its orientation is at the disposal of the operator through the universal joint. The apparent distance of the model from the observer is changed by moving the mirror in which the observer views the image of the model. Formulas and tables are supplied in the report referred to as number 7, which solve the problem of determining the positions of the mirror and the angles of rotation of the elements of the universal joint that would cause the model to produce a simulation of an airplane in flight.\n10.10 Numerical Differentiation and Smoothing\n\nIn many investigations, it is desirable to determine the rate of change of a function given numerically at successive instants. As the given numerical values are subject to error (due to rounding and perhaps other causes), some method of smoothing is appropriate. A method proposed in [32], which has been used at Brown University, the Frankford Arsenal, and elsewhere, is as follows: A quadratic function is fitted by least squares to each successive nine values of the function to be differentiated, and the first and second derivatives of this quadratic function at the central point are taken as the first and second derivatives of the function.\nChapter 11 THE RISK TO AIRCRAFT FROM 11.1 INTRODUCTION\n\nThis chapter is mainly concerned with mathematical problems arising in attempts to estimate the probability of damage to an aircraft or group of aircraft from one or many shots from heavy antiaircraft guns. Related problems arise in air-to-air bombing and in air-to-air or ground-to-air rocket fire, but the major part of the mathematical discussion will focus on the former.\n\nThe fitting and differentiation of a tabulated function is carried out once and for all, and formulas are obtained for the estimates of the first and second derivatives of a tabulated function in terms of the nine ordinates or their differences. These formulas provide a method for simultaneously differentiating and smoothing a tabulated function. Functions of degree other than the second and numbers of tabulated values different from nine can be used.\nAnalysis so far has been focused on problems related to flak risk. The following basic numerical problem forms the basis of the discussion on flak risk:\n\nProblem (A). Determine the probability of damage to an aircraft from a single shot directed at any point in space.\n\nThe solution to this problem is crucial for investigating two major problems of flak risk:\n\nProblem (B). Estimate the impact of range, altitude, speed, arrangement, and spacing of aircraft in a given bombing unit on the probability of damage to aircraft in the unit from one or multiple shots.\n\nProblem (C). Study the influence of altitude, size of bombing units, and spacing between units on the probability of damage to aircraft in a large bombing mission consisting of multiple bombing units attacking the same gun-defended area.\n\nThe major difference between problems (B) and (C) lies in their scope.\nProblem (C) involves aircraft in close formation or a single bombing mission's attacking aircraft. Most research on problem (A) focuses on the special case: Problem (D). This case determines the probability of damage to an aircraft from a single shot aimed at it. This is crucial for comparing the effectiveness of different shells and is of primary interest to those planning equipment. A solution to problem (D) benefits an air force, as it assesses risks to a single aircraft based on slant range and altitude. Additionally, an air force requires information about problem (A).\nThis chapter discusses reliable solutions for problems with formations containing more than a single aircraft. Section 11.2 covers the intricate process of shooting down a bomber with a fragmenting projectile. Section 11.3 outlines the mathematical problem involved in computing risks from AA fire. Section 11.4 summarizes basic reports in the field, including work done for the AMP and earlier reports dealing with problems (A) and (D). The first serious work on problem (D) available to the writer, and the first considerations involving problem (A), can be found in two British reports issued by the Exterior Ballistics Department in 1940 and 1941. The first of these, Report 14, is mainly concerned with developing the method for computing risks.\nIn this paragraph, different shell types are compared. The second part is primarily devoted to a rapid method of finding an approximate solution for problem (D) from parameters describing the distribution of shell bursts. In 1942, a comparison was made of the probable effectiveness of time and proximity fuses in AA fire against high-level bombers attacking a ship at sea. Soon thereafter, work began on a related study of the dependence of effectiveness of time and proximity fuzes on the fragmentation characteristics of the shell. The report on this study was distributed in 1945. The last study of this group uses an approximate method of solving problems (A) and (D) to have some information with which to attack problems (B) and (C). A similar problem exists where the projectile is an airborne object.\nThe rocket is described in Section 11.4.5. Confidential. The risk to aircraft from high-explosive projectiles is discussed in smaller studies, mostly comparing effectiveness of different guns and projectiles, in Section 11.4.6. Section 11.5 outlines applications of these damage calculations for problems (B) and (C); these applications are discussed more fully in the flak analysis manual 18 and in an AMP report. Section 11.6 is a brief concluding remark. The aim of the chapter is to describe a method for treating risk. Specific numerical conclusions are likely to become obsolete before further need for them arises, but the technique used to obtain the results will be useful as long as weapons that destroy by means of flying fragments are in use. It may be well to describe, roughly, what follows.\nThe AMP did not contribute to the subject of risk from high-explosive projectiles. The AMP does not provide the original experimental information on which the computations are based; this comes from various sources, mostly Army and Navy, OSRD, and British reports. Much of the fundamental mathematical theory is contained in any elementary statistics text. The theory outlined in Section 11.3 is essentially that given in the early British report.14 The principal problems are obtaining accurate original information (for which the AMP could only take what existed), developing computational procedures that could be carried through before the project became obsolete, and applying these techniques to selected examples. The selection of pertinent examples, the development of computing techniques, and the carrying through of computations.\nThe principal contributions of the AMP to the problem of risk from flak involve numerical work. The majority of the work conducted for AMP in this field was carried out by the Statistical Research Group of Columbia University. One major report came from the Applied Mathematics Group of Brown University, and another was worked out directly by the AMP staff rather than contractors.\n\n1.1 The Physical Process of Antiaircraft Fire\n\nThe physical process whose mathematical probability is to be computed consists of the following steps:\n\n1. A projectile is originally launched and arrives at some point in space before bursting.\n2. Fragments fly off in many directions from the point of burst at high speed.\n3. Some (or none) of these fragments strike the target.\n4. Some (or none) of the fragments striking the target do damage.\nTo compute the resulting probability of damage, we must be able to follow all these steps and collect the total risk from all possible occurrences. Let's begin with a discussion of step (1.\n\nThe projectile we are discussing does not arrive in space of its own volition but is sent there by some mechanical device. If the device were perfect, the projectile would always burst in contact with its target, and the probability of damage would be unity.\n\nHowever, guns, bombsights, and other existing devices have inaccuracies in design, construction, and operation. So, the projectile is not very likely to burst just where it would be most effective. We must, then, consider in each small volume of space the likelihood, large or small, that the projectile aimed at the given target may burst in that region.\n\nA great deal of machinery must be used to get the projectile to its intended target.\nThe projectile must be fired or launched to the point of burst. There must be some type of fire control device to estimate the location for the projectile to burst. The projectile must be fired or launched with the proper direction and speed to get it near the desired point, and there must be some type of fuze to set off the explosive charge in the projectile.\n\nLet us discuss the problem of the heavy AA gun in detail to get some idea of the imperfections that plague the first step in the process of shooting down aircraft with ground weapons. The principal parts and the function of each part are given in the following list:\n\n1. Tracking instruments, optical or radar, measure the present bearing, elevation, and range of the target and feed this information continuously to the fire control computer.\nThe fire control computer uses the ballistic functions of the gun, estimates of the present position and rates of the target, and assumptions about the kind of path the target is following to estimate where the gun should be pointed in order for a shell fired at present time with the assumed ballistic properties to reach the target's path at the future time when the target is there. For time fuses, the computer also estimates the proper fuze setting to make the shell explode at the target.\n\nAutomatic transmission systems carry this information to the gun and fuze setter; servomotors point the gun continuously in the direction ordered by the computer.\n\nThe shell is fired from the gun along a trajectory determined by the bearing and elevation set in the gun.\nby the servos and by the muzzle velocity with which the shell leaves the gun.\n\n1. If the shell has a time fuze, this explodes the shell some time after it leaves the gun. If the shell has a proximity fuze (also called a VT fuze), and if the fuze operates, it explodes the shell if it comes close enough to the target. The required proximity depends on direction and rate of closure.\n2. If the gun is mounted on shipboard, the roll and pitch of the ship under the gun and director must be compensated for. Errors can occur in all these stages of the process.\n3. Tracking errors are normally small (of the order of several mils). These tracking errors tend to increase with large angular accelerations. The fire control computer has such a complex problem to solve that it usually is built with a number of simplifying approximations.\nThe largest errors in predictions arise from two sources: (a) linear prediction for curved paths, and (b) time lags caused by the necessity of smoothing rough information from tracking mechanisms and the time of flight from gun to target. Transmission and servo systems have time lags and internal oscillations or \"jitter.\" The fire control computer is complex, resulting in lost motion in gear trains and servos inside the computer itself. After the shell is fired, it follows a trajectory that can no longer be influenced by any action of the gun crew. The purpose of most fire control machinery is to get it started along a trajectory that will bring the shell close to the target.\nIf the shell is equipped with a proximity fuze, this is all that can be done; the fuze explodes the shell if it passes near enough to the target under suitable conditions of closure. If the shell has a time fuze, other sources of error are still present. The computer has estimated where the target will be when the shell can reach it, has tried to set gun bearing and elevation to start the shell trajectory through that point, and has tried to set the fuze to explode the shell when it passes through that point. In addition to inaccuracy of prediction, errors along the trajectory are increased by the variability of time fuses. Once the fuze operates and the shell bursts, the next step in the process begins. In this step, the nature of the shell and its remaining velocity are the important factors. The bursting explosive charge shatters the shell into fragments, which then travel in all directions at various velocities. These fragments, or shrapnel, are what actually cause damage to the target. The effectiveness of the shrapnel depends on its size, shape, and velocity. The proximity fuze, which explodes the shell in mid-air when it detects the presence of a target, is particularly useful against moving targets, as it allows the shell to explode before it reaches the target and penetrates its armor. However, it is less effective against stationary targets, as the shell may explode before it reaches the target or may explode too far away to cause significant damage. The time fuze, which is set to explode the shell at a specific point in time, is more reliable against stationary targets, as it ensures that the shell explodes at the correct location. However, it is less effective against moving targets, as the shell may not reach the correct location before it explodes. Overall, the choice of fuze depends on the type of target and the desired outcome of the attack.\nThe fragments of a shell case are divided into pieces of different weights, which fly off with varying initial velocities. The number, weight distribution, and pattern of their ejection depend on factors such as the thickness of the shell casing, the total weight of the shell, the explosive charge, and other shell characteristics. The initial velocity of a fragment is the vector sum of the velocity it would have from a shell burst in space and the remaining velocity of the shell at the moment of burst. Air resistance slows the fragments as they fly from the burst until they are moving too slowly to cause significant damage; this air resistance varies with air density, or altitude. Additionally, the fragments spread farther apart as they fly from the burst. The number of deadly fragments passing through a given area increases with the size of the burst.\nThrough each square foot of the sphere with a radius of 100 ft around the burst, there would be only one-fourth of the number of deadly fragments passing compared to each square foot of the sphere with a radius of 50 ft, even if there was no air resistance whatsoever. If the burst occurs close enough to the target, some fragments may strike with more or less effect. If the target is an exceedingly complex device, like a heavy bomber, there is still the difficult problem of estimating the probable effect of those fragments which strike even after we have an estimate of the probable mass and velocity distributions of the shell fragments at various distances and directions from the shell burst. Some parts of the target are more vulnerable than others, some parts are more vulnerable from one direction than another, some parts shield others.\nothers.  Nothing  precise  is  known  about  the  kind  of \nfragment  strikes  required  to  kill  or  injure  personnel. \nIt  is  not  known  what  characteristic  of  the  flying \nfragment  makes  it  deadly.  Is  it  the  kinetic  energy, \nthe  momentum,  or  some  other  combination  of  mass \nand  velocity?  This  information  is  needed  in  deciding \nwhich  fragments  to  consider  at  any  distance  from  the \nshell. \nIf  at  this  point  in  the  discussion  it  appears  to  the \nreader  quite  improbable  that  any  aircraft  is  ever \nbrought  down  by  AA  fire,  he  will  have  the  correct \nimpression  as  far  as  single  shots  at  high  altitude \nbombers  are  concerned.  Records  of  American,  British, \nCONFIDENTIAL \nTHE  RISK  TO  AIRCRAFT  FROM  HIGH-EXPLOSIVE  PROJECTILES \nand  German  ground-based  90-mm  to  5-in.  guns  col\u00ac \nlected  at  various  times  during  World  War  II  show \nthat  1,500  to  2,500  shells  were  fired  for  each  aircraft \nSingle AA guns are not much more than a nuisance to attacking bombers; the Germans made their AA defenses extremely dangerous, but only through massed firepower and good overall command.\n\n11.3 THE MATHEMATICAL ANALOGUE OF THE FIRE CONTROL PROBLEM\n\nBecause of the extreme complexity of the fire control problem, which can be solved only approximately by any mechanical device, it is not possible to determine whether or not a shot fired at a given instant will bring down the target. Even a complete knowledge of the target's path up to the time the shot was fired would not suffice for perfect prediction since the target has some considerable amount of time to get off its original course after the shot has been fired.\n\nIt would, perhaps, be natural to try to formulate the problem of risk from a single shot by asking where the target will be when the shot reaches it.\nIf the shell will burst and whether a burst will destroy the target are uncertain questions. Unfortunately, these questions cannot be definitively answered; instead, we replace them with other questions phrased in terms of probabilities.\n\nWhat is the probability that a shell will burst in a given region of space?\n\nGiven a point in space where the shell bursts, what is the probability that the target will be destroyed?\n\nHow can the total probability that the target will be destroyed be computed from the answers to the preceding questions?\n\nThe answers to the first two questions do not have the same answers under all possible tactical situations. For example, the answer to the first question certainly depends, to some extent, on the range, altitude, speed, and direction of the target. The answer to the second question depends greatly on the structure of the shell and the vulnerability of the target.\nIn this text, the requirements do not necessitate any cleaning as the text is already in modern English and free of meaningless or unreadable content. The text describes the process of answering the third question in a given tactical situation using numerical expressions obtained from the first two questions and definite integrals. The text also mentions the discussion of three separate questions in Sections 11.3.1 to 11.3.3 and the description of certain coordinate systems to help describe the tactical situation and the functions used in the problem.\nFor each shot from a heavy AA gun in a given tactical situation, the shell is intended to burst at some point O in space at a time when the target is at or near that point. We shall set up a rectangular coordinate system for locating O from the gun as follows (see Figure 1). The origin of the system is at the gun, the H axis is vertical, the X axis is horizontal and points in the direction of flight of the target aircraft; the Y axis is also horizontal and at 90\u00b0 counterclockwise from the x axis, when viewed from above. Then the intended point of burst, O, can be described by its coordinates (X, Y, H) in this system. Various other coordinates are also used to locate O. Among these are the slant range D = the angle \u03b8 between the X axis and the horizontal projection of the line joining O and the gun.\nThe azimuth or bearing of point O from the gun, relative to the X direction, is denoted as the angle of the line from the gun to O. This is referred to as the azimuth or jection of O. The elevation angle of the line from the gun to O is denoted as E.\n\nIn relation to the X,Y,H coordinate system, with origin at O, we take an X0,Y0,H0 system. This coordinate system is useful in describing the position of target planes at the time of burst.\n\nWe will disregard the drift of the projectile and assume that the vertical plane through O and the gun contains the entire trajectory of the shell. We define an x,y,z coordinate system with its origin at the point of aim (0), the z axis pointing away from the gun along the trajectory, the x axis pointing upward, perpendicular to the z axis in the vertical plane through the trajectory, and the y axis chosen to make x,y, z a right-handed rectangular coordinate system.\nordinate system, that is, at 90\u00b0 counterclockwise from the x axis when viewed from the z direction. We shall also have occasion to use an a, h, c coordinate system superposed on the x, y, z system when discussing formations of aircraft in Section 11.5. We shall assume, in the neighborhood of O to be considered, that the curvatures of the shell trajectories are small enough to neglect, and that these trajectories can be considered as straight lines parallel to the z axis. We shall also neglect any yawing of the shell and assume that the shell at the time of burst is spinning about an axis parallel to the z axis.\n\nThe Mathematical Analogue of the Fire Control Problem\n\nIn discussing the scattering of fragments from the point of burst, it will be most convenient to use spherical coordinates (r, \u03b8, \u03c6), where r is the radius, \u03b8 the polar angle, and \u03c6 the azimuth angle. (see Figure 2)\nThe distance from the shell burst is determined by the latitude (with i p equal to 90 degrees defining the direction of motion of the shell and J equal to 0 degrees defining the equatorial plane of the shell). <\u00a3 is the remaining angular variable measured from the x direction toward the y direction in the equatorial plane of the shell. Sections 11.3.1 to 11.3.3 discuss the separate questions raised at the beginning of this section. Together they provide the mathematical background for solving the problem of risk from a single shot and point out some of the difficulties in both theory and application. The mathematical technique is essentially the same throughout most of the major reports to be discussed in Section 11.4. It is this technique that will be presented in this part of the chapter. The principal differences in method come in the use of\nThe present theory has yielded most of the general information derivable from it. To significantly improve results, new hypotheses in closer relation to physical processes and more accurate experimental data are required. The effect of the target's speed is largely neglected in the computation and is only considered in the study of the number of shots that can be fired within range (see Section 11.5.1). The magnitude of the high-explosive projectile's burst point coordinates (parallel to the x,y,z system of Figure 1 at intended point of burst) is:\n\nFigure 2.\n\n(Coordinates of actual point of burst)\nThe errors resulting from neglect of speed's influence on accuracy of fire and the deadliness of individual fragments is not known.\n\nN.3.1 The Distribution of Shell Bursts\n\nIn a given tactical situation, if a large number of shots were to be fired, they would not all burst in the same place but would be scattered through a large volume of space. The better the fire control mechanism, the nearer the center of this scattering of bursts will be to the point of aim.\n\nWe assume for each tactical situation that there exists a function F(x,y,z), which we shall call the probable density of bursts, such that if a large number N of shots were fired in the given tactical situation, then the number of shots expected to burst in a cubic foot of space around (x,y,z) would be N \u2022 F(x,y,z).\nRegarded in another way, F(x, y, z) is the probability that a single shot, in the given tactical situation, will cause a burst in a cubic foot of space around (x, y, z). By setting up a definite triple integral (see any good calculus book), it can be seen that if U is any region in space, the probability that a single shot fired in the given tactical situation will burst somewhere in the region U is given by / J [fF(x,y,z) dx dy dz], where the triple integral is taken over the region U.\n\nThe actual nature of this function F(x,y,z), which expresses the probable density of shell bursts throughout space, is not very well known. Since the integral \u222bF(x,y,z) dx dy dz expresses the probability that the shell will burst somewhere in space, this means that if all fuses operate so that every shell fired bursts somewhere, then:\n\nF(x, y, z)dx dy dz = Probability that a single shot bursts somewhere in space.\nF(x, y, z) dx dy dz = 1.\n\nIf 5% of the fuses fail to operate, the triple integral would have the value 1 - k/100. However, since this is a constant factor for a given fuze type, it is easier to make the general computations under the assumption that all fuses operate, and then correct the last stage of the calculations of risk by multiplying by this operability factor.\n\nRecalling that the z-axis points along the trajectory through the point of aim, we see that the distribution of bursts normal to the z-axis is determined by errors and uncertainties in the fire control process and by the ballistic dispersion of the gun; the errors along the trajectory depend on these and on the fuze type as well. Thus, the rest of this section falls naturally into two parts according to whether time or proximity fuzes are used.\n\nTime Fuzes\nFor the time being, it is generally assumed that the errors of the x-, y-, and 2-coordinate directions are independent of one another. Mathematically, this assumption of independence is formulated by saying that F(x,y,z) is a product of three functions, each depending on only one of the variables: F(x,y,z) = fx(x) f2(y) fz(z). However, the accuracy of this assumption is open to question. For instance, with a fire control predictor using a preset altitude reading, there is almost certain correlation between errors in the y and z directions (among others). Since no further information is available about the structure of F(x,y,z), it is further assumed that these errors in the three coordinate directions are Gaussian distributions with mean zero.\nThe mathematical analogue of the fire control problem involves functions that fit the normal error curve for the proper choice of standard deviation. Such a function has the form e^(-x/(V2a)), where e is the base of natural logarithms and ai, r2, and (73) are the standard deviations of the errors in the x, y, and z directions, respectively. The values of a1, r2, and (73) must be found by experiment or computations depending on the nature of the whole fire control situation. Their dependence on the tactical situation is not known at the time this is written, though various estimates have been made.\n\nProbable density of bursts = e^(-x/(a1^2)) * e^(-y/(r2^2)) * e^(-z/(73^2))\nA distribution of the form (2) is sometimes called an ellipsoidal Gaussian distribution. This name is motivated by the shape of the surfaces on which F(x,y,z) has any given constant value. If the exponent is also constant, that is, k is a constant, then the equation defines an ellipsoid with principal axes along the coordinate axes. Most reports summarized in Section 11.4 assume that the probable density of bursts is given by an ellipsoidal Gaussian law of the form (2). Most of these reports make the further assumption that lateral and vertical standard deviations are equal, that is, that \u03c3i = \u03c3\u00b2. Then the probable density of bursts is given by a spheroidal Gaussian distribution of the form:\n\nF(x,y,z) = (1/(\u03c3\u00b3\u2061\u221a{3}\u03c0)) \u204e e^{-[(x\u00b2/\u03c3\u00b2\u2061\u2061\u2082 + y\u00b2/\u03c3\u00b2\u2061\u2061\u2082 + z\u00b2/\u03c3\u00b2\u2061\u2062\u00b3]/(2\u03c3\u00b2)}\n\nLetting 0 = 1/\u221a{k}, r this can also be written as:\n\nF(x,y,z) = (1/(\u03c3\u00b3\u2061\u221a{3}\u03c0)) \u204e e^{-[(x\u00b2 + y\u00b2 + z\u00b2)/(2\u03c3\u00b2r\u00b2)]}\nOne report in Section 11.4.1 discusses a more general ellipsoidal Gaussian distribution than that of equation (2). The formula is:\n\nQ(x, y, z) = K * exp(-((x-a)\u00b2/2\u03c3x\u00b2 + (y-0)\u00b2/2\u03c3y\u00b2 + (z-7)\u00b2/2\u03c3z\u00b2))\n\nwhere Q(x, y, z) is a general quadratic function of x, y, and z, which can be written in the form:\n\nQ(x, y, z) = K * exp(-(x-a)\u00b2/2\u03c1\u2081\u00b2 - y\u00b2/2\u03c1\u2082\u00b2 - (z-7)\u00b2/2\u03c1\u2083\u00b2)\n\nand where K is chosen such that the integral of F(x, y, z) over the whole space is equal to one. It is shown in any solid analytic geometry text that the surfaces Q(x, y, z) = constant are ellipsoids centered at (a, 0, 7) when the coefficients satisfy certain conditions. These ellipsoids need not, however, have their axes aligned with the coordinate axes. This more general distribution of bursts is studied in the report.\n\nAnother report, which will not be discussed further in this chapter, adds time errors due to the fuze as another Gaussian independent variable in addition to the space errors due to prediction.\nThe probable density function F(x,y,z) is obtained by integrating over the time variable, taking into account the effect of the aircraft's speed on the distribution of bursts. The numerical calculations have not been reported, so the magnitude of this effect is unknown.\n\nProximity Fuzes:\n\nThe errors in the x and y directions are assumed to be independent.\n\nA proximity fuze contains a miniature radio transmitter and receiver. As it travels through air, the fuze sends out radio waves and receives reflected waves from obstacles in the path of the radiation. When the reflected waves satisfy certain conditions, the fuze operates to fire a detonator. The point of operation depends, for a given combination of fuze and projectile, not only on the size and reflecting properties of the target but also on the distance between them.\nIn the analysis that follows, the target is taken to be specified with its position regarded as fixed in the (x,y,z) coordinate system. The projectile is assumed to travel along a straight trajectory parallel to the z axis and have a fixed velocity. These conditions are approximately fulfilled for a given tactical situation in a small neighborhood of the intended point and time of burst. Along each trajectory, there is assumed to be a theoretical point of burst, and the totality of such points is taken to be a smooth surface, called the burst surface, defined by an equation of the form z = f(x,y). For different types of fuze and projectile, the burst surface equations vary.\nThe general form of the burst surface varies. For mathematical analysis, it will be assumed that this form is fixed, but its position and size, relative to the target, depend on a parameter S, which can be thought of as the sensitivity of the fuze. It is important to note that this terminology is a mere convenience. It does not imply any particular principle of functioning. It merely lumps together certain unpredictable sources of variation in the position of the burst surface Bs. The equation for this surface, for any particular value of S, will be written as:\n\nVarious assumptions will be made regarding the dependence of fs(x,y) on the parameter S. These are merely working hypotheses to facilitate a suitable mathematical analysis. For specialized practical applications, modifications may be made.\n1. For each value of S, there exists a region Us in the (x,y) plane, which is the domain of definition of {xs,y}. If a trajectory passes through Us, it meets the corresponding burst surface Bs, and the fuze will function. If a trajectory misses Us (and hence Bs), a fuze of sensitivity S on that trajectory will not function.\n2. If the target is at the point (a, b, c), then, for each S, fs(x,y) < c. In other words, the burst surface is closer to the gun than the target, along any trajectory. Note that this would not hold for a VT fuze with a delay, intended to make it function slightly after passing the target.\n3. As the sensitivity S increases, the domain Us also increases, and the burst surface Bs gets farther away.\nFrom the target along each trajectory, analytically speaking: If Si is less than $2, then Us2 contains USl and fs2(x,y) is less than f(x,y) wherever both functions are defined.\n\nFour, as S varies over its entire range, the burst surface Bs sweeps out a solid region V in space. Five, the function fs(x,y) has a continuous partial derivative with respect to S.\n\nFigure 4: The burst volume, the part of space in front of the target in which proximity fuzes may operate.\n\nTo compute F(x,y,z), it will also be necessary to use the distribution of sensitivities. In a given tactical situation, f(x,y) is the probable density of shell trajectories - that is, the probability that the shell will pass through a small patch of area dA around (x, y) is given by f(x,y)dA. Hence the probability that the trajectory will lie in a region A.\nThe integral of a function f(x,y) in the x,y plane is given by the double integral I = \u222b\u222bf(x,y)dx dy.\n\nGiven the mathematical analogue of the fire control problem, suppose the probability that the sensitivity lies in the interval from S to S + dS is p(S)dS. The probability that the sensitivity lies between Si and S2 is given by J\u222bsJ'Ss P(S)dS.\n\nWe also assume fuze variations are independent of aiming errors.\n\nTo compute F(x,y,z) from this, we need to compute the probability of a burst in some small volume dV about (xfy,z). If (x,y,z) is not in the region V, then F(x,y,z) is defined as zero. If (x,y,z) is in V, then dV will be chosen small enough to lie entirely in V and taken as a block bounded by a pair of planes x = constant, a pair of planes y = constant, and a pair of surfaces S = constant.\nThe probability of a trajectory passing through a rectangular volume element between two burst surfaces in the x-dy plane is given by the product of the probability density function f(x,y) for the position of the sensitivity and the probability density function p(S) for the sensitivity itself: p(S)dSf(x,y)dxdy. The volume of the block, with nearly parallel curved faces, is approximately dxdydz, where dz = j^(fs(x,y))dS. Therefore, the volume of the block is given by the integral dsfs(x,y)dxdydS.\nAnd the probable density of bursts around (x,y,z), when z = fs(x,y) is given in terms of x, y, and S by:\n\np(S)jdf^Xjy^dxdy\n\nWe can define F0(x,y,S) as F[x,y,S] and rewrite the equation as:\n\nF0(x,y,S) = p(S)f(x,y)\n\nIf (x,y) is in Us:\n\ndz\n\nSubstituting in equation (6) and dividing through by dxdydz gives:\n\nif (x,y,z) is not in V:\n\ndz\n\nAssuming, as is usual in fuel calculations, that the errors in the x and y direction have independent Gaussian distributions with mean zero, we get specialized forms of equations (9) and (10):\n\nisfs(x'y)\nif (x, y) is in Us and (x, y) is not in Us and dz and (x, y, z) is in V and (x, y, z) is not in V. Most reports have dealt with damage calculations for proximity fuses by making various approximations instead of attempting this involved computation. The first approximation assumes that all fuses have exactly the same sensitivity S, so all shells burst on a single surface BS. As we shall show in Section 11.3.3, this assumption reduces the final computation of risk from evaluation of a triple integral to evaluation of a double integral.\n\nFurther approximations are made by assuming special simple shapes for the burst surface. Two such assumptions used in two reference reports [13, 16] are that the burst surface is a hemisphere centered at the explosion.\nThe target's burst surface, with axis of symmetry aligned along the trajectory, or the burst surface being a disk centered on the trajectory and lying in a plane perpendicular to it. The actual shape of the burst surface for a given sensitivity S depends greatly on the target's size and shape. If the fuze antenna is assumed to act like a radiating dipole, the burst surfaces for a point target should be symmetric about the trajectory through the target and have cross sections resembling the half-circles in Figure 6 A. If the target is still fairly small and reasonably smooth, the burst surfaces will be partly symmetrical with cross sections more like those of Figure 6B; if the target reflects with entirely different intensities from different directions, the burst surfaces will be much more lopsided as in Figure 6C. If the target is a large irregularly shaped object.\nThe large plane surface, such as a lake or ocean (commonly used in testing sensitivity), the burst surfaces for a given angle between the trajectory and plane surface will be planes parallel to the given plane surface (See Figure 6D). The bulk of the computations that have been done with proximity fuses was carried out before any proximity fuses had been produced, so most computations carried out by the AMP are for a single burst surface of simple type. The reports discussed in Section 11.4.5 are an exception to this; tests with proximity fuses in airborne rockets were available to the men working on that project (AMP Study 21).\n\nThe problem of computing risk from solid projectiles, such as machine gun bullets, and from explosive projectiles with contact fuses is a simplification because the risk is determined solely by the geometry of the projectile and the target, and not by the proximity of the projectile to the target.\nThe problem of proximity fuses involves a projectile passing through some part of the target to be effective. The burst surface is the target's surface facing the gun, and the distribution of hits is determined by the probable density function f(x,y) giving the distribution of trajectories intersecting the (x,y) plane.\n\nThe next problem is giving the risk of damage from a burst that occurs at any point in the neighborhood of the target in the tactical situation under discussion. We do not consider how the shell bursts at that point; instead, the problem is: given a point of burst, what is expected to happen? All work on this issue.\nWe can simplify our formulas by assuming the target is at the origin. Later, we can easily account for the trivial effect of moving the target to another point. We will attempt to find a function p(x,y,z) to describe the probability that a shell bursting at (x,y,z) will destroy the target at the origin. We call this function the conditional probability of damage.\n\nThe values of p(x,y,z) depend on many characteristics of the shell and target. These factors are the weight and shape of the fragments from the bursting shell, the speeds and directions in which they are thrown off from the burst, the air density, the size, shape, and orientation of the target, and the arrangement of these factors relative to each other.\nThe vulnerability of targets, such as pilots and fuel tanks, depends on their exposure to fragments from bursting shells. Factors affecting this vulnerability include the location of vulnerable parts, the speed and direction of the target relative to the shell trajectory.\n\nIt's important to note that many calculations of risk overlook or minimize these factors. A common simplifying assumption is that the target can be represented as a sphere in space at the aiming point. This assumption eliminates the impact of the target's speed on the conditional probability and simplifies the complex vulnerability characteristics to a single variable - the size of the sphere.\n\nFor an ideal or actual target, the initial step in calculating p(x,y,z) involves describing the fragmentation pattern of the shell used. This description:\nIn the spherical coordinate system, the simplest case is r, (\u03b8 > \u03c6 = 90\u00b0), as shown in Figure 2. The line p = 90\u00b0 points along the shell axis towards its nose. Neglecting yaw of the projectile and assuming the shell points along the trajectory makes line \u03c6 = 90\u00b0 parallel to the z-axis. Due to the spin and axial symmetry of the shell, the number of fragments of a given mass and speed ejected by the burst is independent of the longitude angle \u03c6. The effectiveness of a flying fragment is generally assumed to depend on its shape, mass, and the relative speed of the fragment and target at the instant of impact. If the target speed is small enough, it makes little difference to the fragment's effectiveness if the target speed is neglected entirely and considered as zero.\nFor a stationary target in space, it is assumed that the shell bursts. The effectiveness of a fragment, particularly a heavy one capable of causing damage at a few hundred feet per second, depends on whether it is moving in the same or opposite direction as the target. Neglecting the target's speed simplifies the calculations of the conditional probability, as it simplifies the problem of determining which fragments to count. When target speed is zero, the relative speed of a fragment reduces to its speed through the air; since mass and shape provide no reason to believe this speed varies with longitude, we can select fragments for consideration based on weight and speed. In the case of zero target speed, the expected displacement is:\n\n\"expected dis-\" becomes \"expected displacement\"\n\nFor a stationary target in space, it is assumed that the shell bursts. The effectiveness of a fragment, particularly a heavy one capable of causing damage at a few hundred feet per second, depends on whether it is moving in the same or opposite direction as the target. Neglecting the target's speed simplifies the calculations of the conditional probability, as it simplifies the problem of determining which fragments to count. When target speed is zero, the relative speed of a fragment reduces to its speed through the air. Since mass and shape provide no reason to believe this speed varies with longitude, we can select fragments for consideration based on weight and speed. In the case of zero target speed, the expected displacement is:\nThe tribution of these selected fragments is independent of the longitude angle. In most work done heretofore, the fragments to be counted have been selected on one of two bases: first, by putting up screens at various distances from a bursting shell and counting the number of fragments that penetrate the screens, and second, by assuming a fragment must have a certain minimum kinetic energy to do damage and counting only those fragments with at least that much energy. We have a choice of several similar methods for describing the pattern of fragments from a shell burst, as long as it is independent of longitude.\n\n1. The angular density p(r,\u03b8) of fragments at any point with coordinates (r,\u03b8,z) is the number of fragments per solid unit angle passing through the sphere of radius r about the burst in a small region.\nThe angular density of fragments about the direction (0,^) is written without <\u00a3 to show its dependence on r and p alone. To estimate it for a given position (r, p, \u03b8), count the fragments going through a given small area A on the sphere of radius r, about any point at latitude p, and divide this number of fragments by the solid angle A/r^2 subtended by the area A.\n\nThe area density of fragments is the number of deadly fragments per square foot of surface at a unit solid angle. A unit solid angle is a cone reaching out from the origin which cuts off an area of 1 square unit on a sphere of radius 1 unit.\n\nCONFIDENTIAL\n\nTHE RISK TO AIRCRAFT FROM HIGH-EXPLOSIVE PROJECTILES\n\nFigure 7A: Typical region for estimating angular fragment density. z' axis points toward shell nose.\nFigure 7B: Typical zone for calculating zone count.\nThe zone count n(r, \u03c6) is obtained by dividing the sphere of radius r around the burst into zones, each of width 2.5\u00b0, and counting the number of fragments passing through each zone. The term n(r, \u03c6) represents the number of fragments in the zone containing J/ on the sphere of radius r.\n\nAs fragments fly further from the burst, they are slowed by air resistance, so fewer of them are effective; hence p(r, \u03c6) and n(r, \u03c6) decrease with increasing r. If the weight, speed, and ballistic shape distribution of fragments is independent of \u03c6, we can break p(r, \u03c6) into a product of two factors:\n\np(r, \u03c6) = p(\u03c6) * g(r)\n\nwhere p(\u03c6) defines the angular density of fragments which have enough energy to do damage very close to the burst, and g(r) describes the decrease in the number of effective fragments with increasing radius r.\nThe number of deadly fragments with distance r from the burst. We could write this as the number of fragments in the zone about r, and g(r) with the same function as in equation (13). The term g(r) is called the fall-off law for fragment effectiveness.\n\nVarious types of experiments have been performed to find this angular fragmentation pattern and to get estimates for the fall-off law g(r).\n\n1. Wooden screens ruled off in square feet are placed at various distances from the bursting shell, and the number of fragments penetrating each square foot area is counted. This gives values of p(r,^) [or n(r,p)] for several particular values of r and some values of p. However, the values of ip must be corrected in some way for the fact that the shell in the test is at rest while the shell in any tactical situation is moving.\nThe situation maintains some considerable remaining velocity, which tends to throw the fragments in the moving burst pattern forward of the burst zone where they appear in the static burst patterns.\n\nShells are burst in sand pits and in sandbag beehives; the fragments are sifted out of the sand and sorted by weight or by the fineness of the screen they sift through. These tests determine the distribution of weights of the fragments of the shell and provide no information about the angular fragment pattern.\n\nVarious photographic and penetration tests have been devised to measure the speeds at which fragments are thrown off from the bursting shell. These are usually static tests and yield values in feet per second. There are some indications that fragments may still be breaking apart 50 or 100 feet from the burst. One experiment indicated this phenomenon.\nThe mathematical analogue of the fire control problem:\n\n1. The velocity shows no decrease in n(r, v/) as r went from 40 to 60 ft. for the neighborhood of 2,500 fps for the initial fragment velocity.\n\n4. Firing against actual aircraft on the ground under conditions where the location of the burst can be determined helps determine the relation between angular density of fragments and the conditional probability of damage to aircraft.\n\nIn terms of the angular fragment pattern, it is not difficult to estimate the expected number of hits on an aircraft from its size and distance r. However, the aircraft is a complex target and fragment hits on parts of it are only a minor nuisance, not fatally damaging. To pass from the fragment density p(r, f/) to the number of hits on a target presenting the area A toward the burst at distance r:\nTo calculate the expected number of damaging hits, multiply the angular fragment density p(r,\u03b8) by the solid angle A/r\u00b2 subtended by the target. If calculating damaging hits is the goal, use the same formula, but for A, use not the actual area presented by the target, wings, tail surfaces, and so on, but only the area vulnerable to the fragments in the computations. The concept of the vulnerable area of the target, though a fiction, is useful in calculating conditional probabilities of damage. Estimates of vulnerable area are typically determined by comparing experiments of types (1) and (4) mentioned previously.\n\nData for types (1) to (4) have been collected by various organizations. A substantial amount of data on fragmentation characteristics of U.S. Army projectiles is available.\nThe report on projectiles is compiled in a series of TDBS Reports. A report from Section T of OSRD contains the most exhaustive study known of conditional probability and vulnerable area determined by test firing against aircraft on the ground. The British have also conducted several studies on the fragmentation characteristics of their own shells.\n\nOnce the vulnerable area A is identified, the expected number of damaging hits on the target at (r,<t>,l/) is given by the formula: pQvA\n\nThe next issue is to transition from the expected number of damaging hits on the target to the probability of damage to the target. This depends on how closely the actual scattering of fragments from a single burst conforms to the expected pattern for shells of its type. It is generally assumed that this conforms.\n\n(Technical Division, Ballistics Section, Office of the Chief of Ordnance.)\nThe scattering of fragments follows the Poisson law, which has been observed in other problems of random scattering. This law implies that if k is a whole number and m is the expected number of hits on a given target, then the probability of getting exactly k hits is:\n\nm^e-k, me-k, m^2e-k, m^3e-k, ...\n\nHence, the probability of getting at least one hit is:\n\n1 - (1 - m^e-0)^m\n\nWhere m = m(r,\u03b8) and (r, \u03b8) is the location of the origin 0 from the point (x,y,z) at which the burst occurs. Some experimental justification for this equation is given in a reference report [14].\n\nIf we are only interested in problem D of the introduction, finding the risk to a single aircraft at the point of aim, then p(x,y,z) and F(x,y,z) can be used.\nTo obtain the probability of damage, the conditional probability that a shell bursting at (x,y,z) will destroy a target at (a,b,c) must be determined for problem A. This new probability can be easily computed by moving both burst and target by the vector (-a, -b, -c). The risk to a target at (a,b,c) from a shell burst at (x,y,z) is precisely the risk to a target at (0,0,0) from a shell burst at (x-a, y-b, z-c). It is important to remember that in passing from number of hits to number of effective hits, we tacitly assumed that the vulnerable area A did not depend on the target's speed or aspect from which it is viewed, including the assumption that these factors have no effect on the conditional probability.\nThe probability of damage to a single aircraft, given the probable density of bursts and the conditional probability of damage, can be calculated through a triple integral. Let P(a, b, c) represent the probability of damage to a target at (a, b, c) from one shot fired at the origin in a given tactical situation. To set up the triple integral for P(a, b, c), divide the space around the origin into small bricks by planes parallel to the coordinate planes, and consider any such brick with a center at a.\nThe probability that a shell will burst in the region with volume element dx dy dz, located at (x, y, z), and damage a target at (a, b, c), is given by the product of the probable density of bursts F(x, y, z) dx dy dz and the probability p(x - a, y - b, z - c) that the shell will damage the target. The risk P(a, b, c) for the target can be obtained by summing up the probabilities of all such small regions. If the target aircraft is at the origin, then a = b = c = 0, and the risk for such an aircraft is given by the triple integral of P(a, b, c). This formula has been used by most writers attempting to solve problem (D) for time fuses; the formula for P(a, b, c) is required in solving problem (D).\nFor proximity fuzes and a single target at the origin, the integral is typically replaced with a simpler double integral by assuming all fuzes have the same sensitivity. That is, all shells burst on a single surface in front of the target. The surface has an equation of the form z = f(x, y). Assuming independent Gaussian errors in the x and y directions, the probability that the shell passes through a small rectangle of sides dx and dy about (x, y) is:\n\n1\n\nIf the shell is on the trajectory through (x, y), then either it is too far away from the target to burst at all or it is in the region U where f(x, y) is defined and the shell bursts at (x', y') within the range [x, y] \\-- hence the probability:\nthat a shell on the trajectory through (x,y) will damage the target at the origin is p[x,y] if (x, y) is in t/, and is zero if not. Hence the risk from trajectories passing through the small rectangle is Plx,y[x,y]y~l(3/91* + y/ad x dy and the total risk to a target at the origin is given by u P(a,b,c).\n\nP(a,b,c) could be computed by a similar process. It is worth mentioning that risk from solid projectiles and contact-fuzed explosive projectiles can be computed from the formula (18), provided proper interpretation of the various terms is made. For contact-fuzed projectiles, the analogy is extremely close. The burst surface for contact-fuzed projectiles is the surface of the target turned toward the negative z axis. The term p[x,y,f{x,y}~] is a function p'(x,y) determined by the risk from a burst of the given shell at that point on the surface of the target.\nIf p'(x,y) represents the probability that a given solid projectile entering the aircraft on the trajectory determined by (x,y) will damage the aircraft, then this same formula can be used for solid projectiles. This shows that there is a close analogy between the risks from contact-fuzed and proximity-fused projectiles; the difference is largely a difference of scale. The contact-fuzed shell may be effective if it passes through the target; the proximity-fused shell may be effective if it passes through a certain larger region near the target.\n\nIf a computation of P(a,b,c) or P(0,0,0) is made from one of these formulas on the assumption that all fuses operate, then, to estimate the risk, the area element and burst surface (Figure 9) should be taken into account.\nThe effect of k percent of fuzes failing to operate is only necessary to put a factor (1 - k/100) in the probable density of bursts. Since this is a constant factor, it can be removed from under the integral sign in these equations for risk, so the risk is easily corrected for the operability of the fuze. In applying the various formulas of this section, it is soon discovered that the integrals can seldom be evaluated in any simple form but must be computed numerically. For any given special case, this evaluation is not too difficult; however, it becomes extremely tedious and expensive if computations must be made for a large number of examples. The integrals for risk from time and proximity fuzes are usually evaluated by converting them to the (r, \u03b8, z) coordinate system with origin at the shell burst.\n\n11.4 Historical Summary of Probability Theory Applied to Ballistic Calculations\nSection 11.4.1 describes problems studied in two British reports on risk of damage from high-explosive shells and rockets. Section 11.4.2 discusses OSRD Report No. 738, the first major study of this kind in the country. Section 11.4.3 is devoted to another such study started soon after OSRD 738 but published years later as AMP Note No. 19. Section 11.4.4 deals with the last large study of flak risk, AMP Report No. 185.1R.11. Section 11.4.5 discusses some questions of risk to a bomber from airborne rocket fire. Section 11.4.6 covers some AMP reports on special aspects of the flak problem, such as one report.\nThis report discusses the probability of shooting down a directly approaching aircraft. Reports in this section deal with comparisons of different guns and projectiles, typically for directly approaching aircraft. The attitudes towards problem (D) vary widely due to the difference in specific problems requiring study of risk. In the first British report, the emphasis is on the comparison of the effectiveness of different types of AA shells and different standards of accuracy in shooting. A large part of the report is also devoted to a full development of the theoretical methods used in the study of risk. The second British report is vitally concerned with the effect of the distribution of shell bursts on the probability of damage and attempts to get a formula for quick approximate calculations.\nThe calculation of risk when the probable density of bursts is given in a certain form is the focus of OSRD Report No. 738-16. This report primarily compares the effectiveness of time and proximity fuzes for a given shell in a dozen different tactical situations. AMP Note No. 19-13 also compares the risk for time and proximity fuzes, with a fixed tactical situation and an emphasis on the effects of variations in the fragmentation characteristics of the shell.\n\nCONFIDENTIAL\n\nReport 185.1R11 aims to solve problems (A), (B), and (C) outlined in the introduction (Section 11.1) and therefore provides an approximate solution for problems (A) and (D), which can be computed for various tactical situations, specifically for different ranges and altitudes of the target.\n\n11.4.1 Two British Studies\nIn 1940, the British developed a method for comparing the effectiveness of different A A shells under varying assumptions about the accuracy of the AA fire. The mathematical argument is essentially that outlined in Section 11.3 of this chapter for time-fuzed shells.\n\nThe probable density of bursts is assumed to be Gaussian with errors independent in the three coordinate directions and, moreover, it is assumed that the standard deviations and a2 in the x and y directions (across the trajectory) are equal. Then the probable density of bursts takes the form:\n\nThe fragmentation data came from several sources:\n1. Counts of the number of fragments penetrating wooden screens placed at different distances from the shell burst.\n2. Counts of the number of disabling hits on a Blenheim bomber hung in the main fragment zone of the shell bursts.\nFrom the first source, it was possible to estimate the fragment density p(r,f/) in terms of the distance and direction of the target from the shell. By comparing (1) and (2), a correlation between fragment density and damage to a Blenheim bomber was found for the type of shell used in this test. From (3), information as to the fall-off of the number of deadly fragments with distance from the shell is obtained for a number of different shells.\n\nThe actual complex target is replaced by a hypothetical target presenting a vulnerable area of 100 sq ft from any distance or direction. The fragmentation pattern has been described by dividing the hemisphere forward of the burst into zones of 2.5\u00b0 width and giving the number of fragments in each zone.\nThe number of fragments expected to strike a disk of 100 sq ft area, which penetrates a 2-inch wooden screen at the given distance, was computed as follows: If the center of the disk overlaps some of the 2.5\u00b0 zones, in each zone divide the area of the part of the disk in that zone by the area of the zone and multiply by the number of fragments in that zone to get the expected number of hits from that zone. Add the results to get the expected number of hits on the disk (at range r and latitude ip).\n\nThe comparison of tests 1 and 2 suggested that the Blenheim bomber received one damaging hit for each seven \"throughs\" (fragments penetrating a 100 sq ft area of wooden screen) at the same latitude and distance from the burst. Hence, m(r, ip), the expected number of damaging hits on an aircraft at these coordinates.\nThe range r and latitude \u2215, were determined from screen tests and fall-off data. Direct counts of the number of \"throughs\" were not available for values of r greater than 150 ft. Therefore, the dependence of m(r,yp) on r for larger r was estimated from the fall-off of velocity of fragments flying through the air.\n\nOnce m(r,xf/) is given, the probability of at least one damaging hit, from the Poisson law, is 1 \u2013 e^(-m), where m = m(r,\u2215). An appendix of this report discusses in detail the applicability of the Poisson law to the scattering of shell fragments; the evidence then available fitted very well.\n\nThe triple integral was integrated numerically in such a way that the portion of the risk due to certain regions around the shell could be found. It was found, for example, that under many circumstances more than half of the risk comes from these regions.\nThis report discusses the aims and difficulties in determining risk from a single shot when the bursts are more than 100 ft from the target. A second British report describes a method for computing the probability of damage when the probable density of bursts does not follow the simple form given in equation (2), but rather the more general ellipsoidal Gaussian law given in equations (4) and (5).\n\nQ represents any general quadratic form whose level surfaces are ellipsoidal, and K is chosen so that the integral of F(x,y,z) over all space is one. Most of this paper deals with the case of no bias, that is, a = (x = y = 0). By using certain approximations in the numerical evaluation of the triple integral for probability of damage, a function J0(Ao) is defined in terms of the quadratic form A and its eigenvalues \u03bbi.\nThe type of shell, altitude of burst, and remaining velocity determine the function for calculating the impact point P (0,0,0). This function is tabulated for two British shells (3.7 in. and 4.5 in.) at an altitude of 10,000 ft and remaining velocity of 1,350 fps. Two approximations to P (0,0,0) are provided in a form that can be computed quickly from the coefficients of the quadratic form Q(x,y,z).\n\nThe simplest approximation is:\nx = -b / (2 * a)\ny = sqrt(h * (h + 2 * z) / (4 * a))\n\nAnd the coefficients a, b, and c are taken from the given polynomial Q.\n\nA more accurate approximation is:\nx = -b / (2 * (a + Ao * rpo * rpo))\ny = sqrt(h * (h + 2 * z) / (4 * (a + Ao * rpo * rpo)))\n\nAo and rpo is an angle depending on the direction of the main fragment zone of the bursting shell and, hence, depending on the type of shell and its remaining velocity at the time of burst. These approximations are reasonably good as long as the standard deviations are greater than 100 ft. Tables are given for correction of these approximations to other altitudes.\nThis report compares the effectiveness of time and proximity fuzes for Navy 5-in., 38-caliber shells. The report was written before any knowledge was available of actual burst surfaces of a proximity fuze. Computations were carried through for two types of surfaces, hemisphere and disk, and for a wide variety of sensitivity ratios.\n\nThe probable density of bursts for time fuzes was assumed to follow a spheroidal Gaussian law (equation (3)) with standard deviations ox and o-3 across and along the trajectory. The dependence of the risk on oi and (73 was studied along with the dependence on other parameters.\nfuze characteristics. The computations for time fuzes are made from formulas (3) and (17). The computations for proximity fuzes were made from formula (18) with oi = o2, with U a circle of radius b feet centered at O and with f(x,y) = VV - x2 - y2 for the hemispherical burst surface of radius b, and f(x, y) = -d, a constant, for a disk burst surface of radius b centered d feet in front of the target.\n\nVarious tables give:\n\n1. Pi, the risk from a time-fuzed shell, in terms of the standard deviations \u03c3i and \u03c3r3 across and along the trajectory.\n2. P2, the risk from a proximity-fuzed shell with hemispherical burst surface, in terms of the standard deviation \u03c3x across the trajectory and the radius of the hemisphere.\n3. P3, the risk from a proximity-fuzed shell with a disk burst surface, in terms of the standard deviation \u03c3x.\nThe ratio of advantages P2/P1 and P3/Pi in terms of the disk's radius b and the distance d from its center to the target.\n\nFor the range of values used in this report, risks from proximity fuses vary approximately inversely with the square of the standard deviation across the trajectory. This is to be expected, as the proximity fuze risk behaves much like the risk from a solid projectile. The difference lies in the area through which a proximity-fuzed shell may pass and still be effective. In both cases, there is a certain area of the x,y plane such that a shell on a trajectory passing through a given point (x,y) of that area has a certain probability of doing damage. For solid or contact-fuzed projectiles, this area is well-defined.\nThe risk to an aircraft from high-explosive projectiles is dependent on the presented area of the target. For proximity-fused projectiles, this area is the burst surface. For large values of ri, the function 2tto is approximately equal to the burst surface. Substituting in equation (18) and taking the constant factor 1/(2tto) from under the integral sign leaves an integral not dependent on n. Therefore, the risk is approximately proportional to Some study is made of the effect of altitude on these risks. This information is used to find the advantage ratio of proximity over time fuses in a dozen different tactical situations specified by altitude, slant range, and fire control errors.\n\nFigure 10. Optimum fragmentation patterns for various total numbers of fragments (time fuze shell; 5738 fall-off law).\nThe results indicate that in typical tactical situations, proximity fuzes would provide from 2% to 5 times the probability of damage compared to time fuzes. The variation in relative effectiveness is due to aiming errors, altitude, and shape of burst surface. Despite the uncertainties in the computation, this report indicated that if proximity fuzes could operate even half or three-quarters of the time, they would be measurably more effective than time fuzes. This prediction has been borne out by combat records. The next study, number 13, also emphasizes the same conclusion, although the formal final report was not issued until long after proximity fuzes had been in wide use.\n\nOne section of the report compares the variation of effectiveness of shells of different weights. Another section is not provided.\nThe section discusses the dependence of effectiveness on the weight distribution of fragments from the burst. This affects the rate at which fragments lose speed as they fly from the burst and the speed a fragment must retain to have enough energy to do damage when it strikes the target. In both this and the preceding report, the target is assumed to be divided into three parts of different vulnerabilities (intended to correspond to pilot and bombardier, fuel system, and motor). The term m(r,\u03b8), the number of fragments effective against this vulnerable area in direction \u03b8 and distance r, is computed from two types of data: first, the angular fragmentation pattern of the shell under discussion, which gives the number of fragments in each zone at the burst itself, and, second, sand pit tests giving the number of fragments of various sizes.\nAssuming the same weight pattern of fragments in all zones, the number of effective fragments at distance r is computed using the law for retardation of fragments by air friction and the energy needed to be effective upon striking a target. This report, like OSRD 738, does not consider the functioning characteristics of proximity fuses. Both reports compare time and proximity fuses, but in the later one, a specific tactical situation is specified, and a study is made of the dependence of damage probabilities on the following fragmentation characteristics: (1) angular distribution of fragment pattern, (2) total number of fragments, (3) the fall-off law for effectiveness, and (4) the weight distribution of fragments.\nvestigation  compares  time  fuzes,  proximity  fuzes \nwith  hemispherical  burst  surfaces,  and  proximity \nfuzes  with  disk  burst  surfaces.  Such  burst  surfaces \nare  recognized  as  hypothetical,  but  the  methods  de\u00ac \nveloped  are  of  wide  applicability. \nFor  each  fuze  type,  individual  angular  zone  con\u00ac \ntributions  to  the  total  probability  of  at  least  one \ndamaging  fragment  hit  are  analyzed.  The  zones  are \nmeasured  in  terms  of  latitude  relative  to  the  equa\u00ac \ntorial  plane  of  the  shell.  One  of  the  principal  results  is \nthe  development  of  optimum  fragmentation  patterns \nfor  each  type  of  fuze  and  for  various  given  total \nnumbers  of  fragments.  In  the  case  of  a  time  fuze,  for \nexample,  the  optimum  pattern  concentrates  most \nof  the  fragments  in  forward  zones,  the  heaviest  con\u00ac \ncentration  being  about  5\u00b0  to  15\u00b0  aft  of  the  shell  nose. \nSuch  patterns  are  graphical^  portrayed  in  Figure \nFor the hypothetical burst surfaces considered, optimum fragmentation patterns give heavier concentrations of fragments further back from the nose, dependent on the total number of fragments and (especially for disks) on the diameter of the burst surface.\n\nFor a time-fused shell, effectiveness is more sensitive to increases in the total weight of the shell (more fragments in each weight class) than for proximity-fused shells. However, a more considerable gain is indicated for proximity fuses, rather than time fuses, from increases in the fineness of fragmentation, when the total weight of the shell is held fixed.\n\nThis report is primarily concerned with the larger scale problems (problems B and C of the introduction) of flak risk.\nThis report discusses solutions for problems (A) and (D) regarding large biases in dispersion of shots for various slant ranges and elevations. It is the first report to acknowledge such issues. In estimating risk to a large group of aircraft from a single shot, it's impossible to assume every aircraft is at the point of aim. Instead, we must estimate the risk to each aircraft in the formation when the burst distribution is centered at a given point, such as the lead aircraft.\n\nDue to the report's focus on problems (A), (B), and (C) in addition to problem (D), certain simplifications had to be made to account for new variables like slant range, altitude, and the target's location relative to the point of aim. All computations are based on these considerations.\nFor time fuses, the target (as referred to in reference 14) is a sphere. A fictitious shell fragment pattern is used, in which all fragments are assumed to fly off in one main fragment zone of width 20 degrees. It is assumed that in that zone, the fragment density is constant. Therefore, for any values of the dispersion parameters studied in the preceding reports, the solution of problem (D) given these for actual shell patterns will be more reliable than the solution given in AMP 185.1R. On the other hand, none of the other reports provide any information about problem (A). The method of computation for this report assumes that the probable density of bursts is spheroidal Gaussian (equation (3)), but the magnitudes of the standard deviations <ri and cr3 across and along the trajectory are taken much larger than in any of the preceding reports.\nStudies and calculations of bullet trajectories are assumed to be determined by the future slant range from the gun to the target. Some account is taken of the remaining velocity of the shell and the influence of altitude on air resistance. However, the computations do not assume any dependence of F(x,y,z) on the height or speed of the target, nor any dependence of p(x,y,z) on the motion of the target.\n\nSince this chapter is being prepared by the author of AMP 185.1R, it should be noted that the entire approach of this chapter has been influenced by the work done and information gathered during the preparation of that report. It will be referred to again in connection with the discussion of applications of problems (A) and (D) to the general problems (B) and (C), which are of more obvious immediate concern to an air force.\nAll computations for problem (A) indicate that for time fuses and large values of ai and o-3, P(a,b,c) can be approximated by an expression similar to that defining F(x,y,z), but with the center shifted forward and lateral dispersion increased. The forward shift is due to the forward spray of fragments from the burst; the increase in lateral dispersion is caused by the wide side spray. That is, if F(x,y,z) follows the spheroidal Gaussian law, then P(a,b,c) can be approximated by a formula of the form:\n\nP(a,b,c) \u2248 c0 * exp(-((a-x)\u00b2/2\u03c3x\u00b2 + (b-y)\u00b2/2\u03c3y\u00b2 + (c-z)\u00b2/2\u03c3z\u00b2))\n\nwhere c0 and e are determined by the shell and its remaining velocity, as well as being influenced by Table 1, which shows the variations of accuracy of fire with slant range assumed in AMP 185.1R.\nFigure 11. Nomograph showing the relationship between P0, the risk to a single aircraft at the point of aim; D, the slant range from gun to aircraft; and H, the altitude of the aircraft. Nomograph valid for D < H. D and H are measured in thousands of yards. To use the nomograph, lay a straight-edge from H on the left-hand scale to D on the right-hand scale; read P0 on the central scale.\n\nFigure 11 displays a nomograph (reproduced from Figure 3 of that report) depicting the relationship between Pq, the risk to a single aircraft at the point of aim, H, the altitude of the point of aim, and D, the slant range to the point of aim.\n\nTable 1. Standard deviations <r3 along the trajectory and (X = \u00f8-2) across the trajectory as functions of slant range D under \"Service Conditions\" assumed in AMP Report 185.\n\n<j (feet)\n11.4.5 Airborne Rocket Fire\n\nIn this study of the risk to a bomber from an airborne rocket fired from astern, it was expected that fire control errors would be small enough that most of the risk would come from close bursts - bursts so close that the size and shape of the target would be important. Hence, the conditional probability was computed for an actual aircraft (German Ju-88) rather than for a spherical target.\n\nThe rocket is assumed to have a proximity fuze; the entire study is largely motivated by questions of fuze design. This study is more fortunate than OSRD 738 and AMP Note 19, as some firing test data were available for the proximity fuze T5 of the 4-inch airborne rocket.\n\nThe technique of calculating the conditional probability function is given in the first three of a series of reports on the study. The bomber is divided into:\nsections  and  for  each  section  the  vulnerable  area  is \nestimated.  For  a  given  point  of  burst,  computations \nfrom  the  fragment  pattern  of  the  rocket  give  the \nexpected  number  of  hits  on  each  of  the  vulnerable \nparts.  Taking  account  of  the  shielding  of  one  part \nby  another  (from  the  given  point  of  burst)  the  total \nexpected  number  m  of  deadly  hits  can  be  found.  The \nconditional  probability  is  taken  to  be  1  \u2014  e~m  in  the \nusual  way.  This  report  also  calculates  the  errors  in \nthe  conditional  probability  that  would  arise  if  the \nactual  target  with  its  scattered  vulnerable  parts  were \nreplaced  by  a  sphere  of  the  same  presented  area  at \nthe  center  of  the  actual  target. \nTable  2,  reproduced  from  Table  1  of  this  report,3 \nshows  this  conditional  probability. \nCONFIDENTIAL \nHISTORICAL  SUMMARY \nTable  2.  Conditional  probability  that  a  4^-in.  proximity-fuzed  rocket  fired  from  astern  will  destroy \nA twin-engine bomber. Ju-88 equipped with Jumo 211 (liquid-cooled) engines, assumed unable to return to base on one engine.\n\nDistance, in feet, from tail of airplane measured toward nose: \n\nProbability that burst at indicated point will prevent return to base if impact parameter, (p), in feet, is:\n\nAspect angle (\u03b8):\n= 0\u00b0 (bursts directly above airplane)\nAspect angle (\u03b8) =\n90\u00b0 (bursts directly to one side of airplane)\n\nThe conditional probability is used in a second report to find the location of that surface which would give the greatest probability of damage if it were possible to design a fuze with that burst surface.\n\nFrom this material and from records of actual fuze performance, in a third report, the risk to the bomber from a rocket fired from astern was computed in terms of the accuracy of aim of the rocket.\n\nComparison of Different Projectiles.\nAMP Study 27 compares the effectiveness of a 5-inch high-explosive shell, 5-inch shrapnel (both with time fuzes), 40-mm and 20-mm HE (both with contact fuzes). The computations with time fuzes are made in a manner similar to that described in Section 11.3, but the other types of fuzes use modified procedures appropriate to their shell types.\n\nA shrapnel shell acts like a flying shotgun; when the fuze detonates the shell, a number of spherical balls are pushed out of the shell case and travel forward in the path the shell was following. Most of their speed comes from the remaining velocity of the shell, but there is some scattering. Since the balls are a good ballistic shape and relatively heavy, they retain their effectiveness at much greater distances from the burst than do most of the jagged fragments from the burst of a high-explosive shell.\nThe conditional probability function for a shrapnel shell is zero except in a narrow cone (approximately 5 degrees) around the nose of the shell. This simplifies computations for a shrapnel shell compared to a high-explosive shell, where most fragments come out in a side spray somewhat forward of the shell equator.\n\nThe computations for contact-fuzed projectiles are simplified from those of proximity fuzes, as discussed near the end of Section 11.3.3. The areas of the target vulnerable to the particular ammunition being used are projected on the x,y plane, giving an area U. For a hit in each vulnerable region, the probability of damage from a hit in that region is estimated, and the final risk is computed from a double integral:\n\nu\n\nwhere F(x,y) describes the probable density of target material.\nThe risk in the x,y plane and p(x,y) is the risk from a shell on the trajectory passing through x,y. The actual computation is done by dividing the target area U into sections where p and F are practically constant, computing the risk for each section separately, and summing.\n\nComparison of the two 5-inch projectiles is completed with the calculation of the probability of damage with a single shot of each kind. To compare the effectiveness of other types of projectiles in stopping an attack, other factors such as the rate of fire and the range at which effective fire can be begun must also be considered.\n\nFigure 12. Expected number of hits on each square foot of target area presented to the gun as a function of the range at which the engagement closes. 7.7-mm\nThe gun fires 400 shots per minute; opening range is 7,500 ft, target velocity is 250 fps. A is the standard deviation of the bullet pattern.\n\nThe earliest AMP study of risk deals with a directly approaching aircraft and automatic weapons. It is assumed that the shots have a normal distribution about their mean point of impact and that the mean point of impact has a normal distribution about the target center. The report gives the probable number of hits and quick means of estimating upper and lower bounds for the number of hits in terms of the presented shape of the target and the standard deviations of these Gaussian distributions.\n\nAnother study is concerned with the increase in risk to a high-altitude bomber due to an increase in the length of its bombing run. For various lengths of bombing runs, the risk from both fighter aircraft and other threats is considered.\nA study was motivated by the suggestion that aircraft dropping guided missiles might need to continue in steady, straight-line flight until the missile struck, instead of beginning evasive action immediately on releasing bombs. Another study compares the expected hit density for four different autocannons. The expected hit density is given in the report in terms of the rate of fire, the range at which fire is begun and stopped, the target speed, and the accuracy of fire (assuming a constant angular dispersion at all ranges). A chart is reproduced here as Figure 12. A later report compares the effectiveness of the 20-mm gun, one existing machine gun (caliber 0.50), and one projected new machine gun (caliber 0.60) for installation in antiaircraft turrets.\nParison is made in terms of the accuracy of the guns, rates of fire, and the relative effectiveness of individual projectiles. Comparison of the 0.50 caliber and 20 mm on various bases is reasonably reliable, but the comparison is quite sensitive to the accuracy of fire involved. Conclusions involving the 0.60 caliber (with its unknown accuracy) are somewhat more tentative.\n\nA recent study (10) estimates the vulnerability of different parts of a very heavy bomber (B-29) from different directions and different ammunition types (armor-piercing, incendiary, high-explosive, and mixed). The numbers given in the tables cannot be used directly for other types of projectiles or for fragments from a heavy AA shell, but are indicative of the relative vulnerability of the different parts of the B-29. Table 3, reproduced from this report (10), shows some of these vulnerabilities.\nAbility estimates. The latest study compares three different types of bombs. For each bomb, the surfaces are given on which the probability is 0.9 or 0.5 of destroying a Ju-88 bomber by a burst of a given bomb on that surface. Characteristics of the bombs were taken from various TDBS reports (issued by the Chief of Ordinance); vulnerability characteristics of the target were those used in AMP Study 21.\n\nTable 3. Vulnerability of B-29 to fighter attack, by components:\n\nComponent Type of damage Equivalent lethal area (sq ft) Cooperative damage assumed required to prevent plane from returning mm\n\nAP I AP I API HEI\nGas tanks Fire Fuselage Serious or lethal wound to both pilot and co-pilot Conditionally lethal\nEach engine stoppage associated with inboard engines and their gas tanks, leakage sufficient to stop two out of four engines with no fire. No fire engines or gas tanks to be stopped, lethal. Each outboard engine stoppage, hit on engine or associated fuel tanks, leakage sufficient to stop engine. Fuselage: pilot or co-pilot, serious or lethal wound; both not incapacitated, pilot must be incapacitated. Each of two sets of elevator controls, severing of cables. Elevator controls completely duplicated, both sets. Rest of frontal area must be severed, not vulnerable. Total plane from head-on, unconditionally lethal, conditionally lethal. Grand Total: 11.5 Applications of fragmentation and damage calculations to FLAK analysis.\nFragmentation and damage studies involve a great deal of tedious computation and are usually undertaken for serious reasons. The problems that should be studied are raised by two classes of people: shooters and dodgers. The broad questions are these:\n\n1. What can be done to improve the effectiveness of AA guns, shells, or directors? Another formulation of this question would be: What change in effectiveness will result if some proposed change in AA equipment and tactics is made? The decision to produce proximity fuzes required some answer to such a question and led to the studies issued as OSRD Report No. 738, 16 and AMP Note 2.\n2. What can be done by equipment and tactics to reduce the effectiveness of a given AA defense which cannot be avoided?\n\nThe manual Flak Analysis 18 and the report AMP\nThe principal methods of reducing the total risk from AA fire can be roughly classified as follows:\n\n1. Minimizing the number of shells fired per bomber:\n(a) Reducing the time of exposure to AA fire through increased ground speed, reduced bombing runs, and carefully planned approach and withdrawal.\n(b) Attacking AA batteries in advance of bombing missions.\n(c) Devising formations and planning the spacing between formations so that fewer AA guns, stationary and mobile, per attacking plane can be effectively brought into action.\n\n2. Decreasing the number of aircraft required for effective bombing:\n(a) By increasing the bomb load per aircraft.\n(b) By improving the accuracy of bombing.\n(c) By using larger bombers.\n(d) By using more advanced navigation and bombing aids.\n(e) By using longer range fighters for protection.\n(f) By using tactical deception to mislead the enemy.\nCONFIDENTIAL\n\nTHE RISK TO AIRCRAFT FROM HIGH-EXPLOSIVE PROJECTILES (HE PROJECTILES) IN BOMBING ATTACKS: THE IMPACT ON AIRCRAFT VULNERABILITY AND BOMBING EFFICIENCY\n\nNote that this might involve tactical recommendations at variance with other methods of reducing flak risk. A judicious balancing of conflicting principles is most important.\n\n1. Reducing risk of damage per aircraft per shell:\n\n(a) Measures intended to decrease the accuracy of AA fire:\n- Evasive flying\n- Night attacks\n- High altitudes\n- Radio countermeasures\n- Attacks on AA batteries\n\n(b) Improvements in bomber design:\n- Distribution of vulnerable parts\n- Protective shielding\n\nFragmentation and damage calculations do not appear directly in many of these considerations. However, all measures intended to reduce the accuracy of enemy fire influence the values of any parameters used in the calculations. Hence, in any such computations, it is crucial to consider the impact of these measures on the fragmentation and damage calculations.\n11.5.1 Flak Charts\n\nTo find the safest direction of approach and withdrawal from a gun-defended target requires a means of estimating the total risk accumulated by a group of aircraft during its run over the target area. This necessitates estimating the risk on each shot and the probable rate of fire, and accumulating the risk along the given bomb-run.\n\nFor a single aircraft at the point of aim, the probability Pq of damage to that aircraft can be computed using the formulas of Section 11.3 in any tactical situation where the accuracy of fire is known. If the dependence of accuracy on slant range, altitude, and other variables can be determined, then it is possible to compute the probability of damage for each aircraft in the group and accumulate the total risk along the bomb-run.\nIt is possible to compute P0 for a given target aircraft in terms of its position relative to the gun. From the target's path and the rate of fire of the gun, it is then possible to find the probable location of consecutive aim points along that path and compute the risk for each shot from its position. The sum of these risks gives the total risk for the course. If it is assumed that the risk is negligible except on the bomb run, the computation can be simplified, and the results shown on charts (called flak charts). One chart is to be made for each of a selection of altitudes, say every 5,000 ft.\n\n1. For a given altitude and gun, draw a circle whose radius is the horizontal range within which the given gun can fire shells to that altitude.\nTwo parallel crossing courses are drawn across this circle at intervals of 500 or 1000 yards. Each course is divided into intervals of some convenient length, say L yards. From the aircraft's speed, time between shots, and time-of-flight curves for the given gun, the expected number of bursts in each interval can be computed using the formula:\n\nL = ------------------\nexpected number of bursts = -------------------\nn D AT\n\nWhere L is the length of the interval,\nn is the number of seconds between shots,\nD is the distance the aircraft travels in n seconds (both measured in the same units),\nAT is the time of flight (in seconds) of the shell from the gun to the beginning point of the interval minus the time of flight to the end point of the interval.\n\nSince the distance D in the formula is related to the velocity of the aircraft and the time between shots, it can be calculated as:\n\nD = V * n\n\nWhere V is the velocity of the aircraft.\nThe speed of an aircraft can be determined using the equation D = nv. When L/nv is larger than AT/n, i.e., when the aircraft is not traveling too rapidly so that L/v is larger than AT, the first term contributes most to the expected number of shots in the interval, making the number of shots approximately inversely proportional to the speed. A flak chart is drawn for a fixed speed, and the risks are then corrected for the true speed by multiplying by the ratio of the true ground speed to the speed used in constructing the flak charts. This correction is not precise for large changes in speed due to, for example, 100-mph winds at the target. The average probability of damage to the aircraft from a burst in each interval is estimated by calculating P0 at the center of the interval.\nThe total risk in the entire interval is the product of the expected number of bursts times the average risk per burst. These risks are accumulated along each crossing course to show how the total risk from the gun increases as the aircraft flies along that part of the crossing course within range. Contour curves for this risk are drawn to complete the flak chart. The number on each contour curve represents the risk (in some convenient units) for a single aircraft at 8,000 yards altitude and 10,000 yards slant range with continuously pointed fire at the rate of 12 rounds per minute. (Figure 13: Flak chart for a single aircraft at an altitude of 8,000 yards with a ground speed of 293 miles per hour under service conditions, as described in Table 1, with continuously pointed fire at the rate of 12 rounds per minute.)\nDue to flying along a crossing course in the given direction up to that contour curve, Figure 13 shows a flak chart prepared in this way from the values of P0 given in AMP report 185.1R.11. The gun is assumed to be the U.S. 90-mm AA gun firing time-fuzed shells. The heading \"service conditions\" notes the standard of accuracy used. The errors along and across the trajectory are given as functions of slant range by Table 1 of Section 11.4.4. The unit of risk is the value computed for P0 under service conditions at 10,000 yd slant range and 8,000 yd altitude. For more details, see reference 11.\n\nTo use a flak chart to select the safest course for a bombing run, the chart is used with a map drawn to the same scale showing the target to be bombed and the batteries defending it. The flak chart itself is not complete.\nFor any proposed bombing run, the center of the flak chart is set on each battery in turn with the direction of flight. The risk to aircraft from high-explosive projectiles is determined by the arrows pointing along the bombing run. The risk at the beginning of the run is subtracted from that at the end, and this difference is multiplied by the number of guns in the battery to give the risk to the aircraft on that run from that battery. The process is repeated for all the batteries defending the target, and the values from all batteries are added together. The result is multiplied by the correction factor for ground speed to get the risk for that bombing run. A refinement of this technique estimates the position of the flak batteries.\n\nmade on a transparent film so that the map can be read through it. For any proposed bombing run, drawn on the map, the center of the flak chart is set on each battery in turn with the direction of flight. The risk to aircraft from high-explosive projectiles is determined by the arrows pointing along the bombing run. The risk at the beginning of the run is subtracted from that at the end (these are read from the contours of the flak chart) and this difference is multiplied by the number of guns in the battery to give the risk to the aircraft on that run from that battery. The process is repeated for all the batteries defending the target and the values from all batteries are added together. The result is multiplied by the correction factor for ground speed to get the risk for that bombing run. (A refinement of this technique estimates the position of the flak batteries.)\nThe expected wind over the target affects the computation in two ways: it moves the bomb release point and changes the speed, resulting in a different bombing run position and length on the ground. Consequently, the computation with wind uses a different bombing run and corrects by a different speed factor at the end. In general, the increase in speed going downwind into a well-balanced AA defense makes it much safer than going upwind into the same defense; if the wind is present.\nThe speed is high, the wind direction is often the most important factor in determining the safest route into and out of the target area. This computation is performed for each of a number of directions from the target, say every 30 degrees, and the risks for bombing runs from these directions are displayed graphically in some manner to show the safest route in and out. Two sample methods of representation are shown in Figures 14 and 15. The first is a polar coordinate diagram showing the relative risk for attack in each direction as a distance in that direction. The second, a \u201cflak clock,\u201d shows only preferred directions of entry and withdrawal with the order of this preference.\n\nFigure 15. \"Flak clock\" showing preferred directions of attack and withdrawal with order of preference.\n\nFrom flak charts, it is possible to estimate the deflection required to allow for the effects of flak and other anti-aircraft fire. This deflection, or lead, is calculated based on the position and velocity of the target, as well as the characteristics of the flak guns and their firing patterns. The flakometer is a device used to assist pilots in making these calculations in real time during a bombing run. It displays the lead angle required to compensate for the deflection caused by flak, allowing the pilot to adjust their aim accordingly. The flakometer is an essential tool for ensuring accurate bombing runs in the face of enemy anti-aircraft fire.\npendence  of  risk  during  a  bombing  run  on  the  di\u00ac \nrection  and  altitude  of  the  run.  To  isolate  the  effect \nof  altitude  we  construct  a  figure,  called  a  flakometer, \nshowing  the  typical  accumulation  of  risk  at  different \naltitudes. \nWe  start  with  a  given  bombing  unit.  In  preparing \nflak  charts  for  that  bombing  unit  we  include  the \neffect  of  altitude  on  the  true  airspeed.  We  use  again \nthe  X,Y,H  coordinate  system  of  the  preceding  sec\u00ac \ntions  to  locate  the  position  of  the  target  aircraft  rela\u00ac \ntive  to  the  gun.  To  estimate  the  risk  at  a  given \naltitude  we  take  the  following  steps: \n1.  On  the  flak  chart  for  the  given  altitude  draw \ncrossing  courses  parallel  to  the  Y  axis  spaced  1,000 \nyd  apart. \n2.  If  the  bombing  unit  flies  along  one  of  these \nCONFIDENTIAL \nAPPLICATIONS  OF  FRAGMENTATION \nFigure 16: Flakometer - Single aircraft, service conditions. This figure demonstrates the risk to a single aircraft from a line of guns evenly spaced one gun per 1,000 yards along a line at right angles to the flight path. The flakometer also indicates the relative risk in passing over a gun or battery whose distance from the aircraft's course is unknown.\n\nCrossing courses to the point (X,Y,H), the accumulated risk since the unit came within range of the gun can be read from the flak chart; call this risk F(X,Y,H).\n\nThe value of Y determines which crossing course is involved; the crossing courses selected in step 1 are determined by the values Ym = 1,000m for each X and H. We add all the values F(X,Yi,H) to obtain a quantity, which we will call 2(X,H).\n4.  A  flakometer  is  a  set  of  contour  curves  for  the \nfunction  2(X,H). \nThis  sum  2(X,#)  of  the  risks  on  a  collection  of \ncrossing  courses  can  be  regarded  rather  simply  as \nthe  risk  to  the  bombing  unit  from  a  line  of  guns  spaced \n1 , 000  yd  indefinitely  far  in  either  direction  along  the  Y \naxis.  As  the  altitude  H  decreases  and  X  is  held \nfixed,  2(X,#)  increases  from  a  combination  of  three \neffects.  First,  as  H  decreases  more  crossing  courses \ncome  within  range  of  the  gun  so  there  are  more \nterms  in  the  sum  making  up  2(X,H).  Second,  for \neach  X  slant  range  decreases  and  hence  F(X,Y,H) \nincreases  because  larger  values  of  P  go  into  it. \nThird,  speed  decreases  with  H  so  the  unit  has  been \nin  range  longer  at  low  altitudes,  so  again  for  each  X \nand  Y,  F(X,Y,H)  tends  to  increase  when  H  de\u00ac \ncreases. \nFigure  16  shows  a  flakometer  constructed  under \nIn constructing the flakometer, the variation of ground speed with altitude was also prescribed. The assumption about accuracy of fire was the same as in the flak chart of Figure 13.\n\nN.5.3 Group Probability Factor\nWhen multiple aircraft are flying together, a shell aimed at one aircraft may damage another. Therefore, the risk to a group of aircraft in a given position from the gun is greater than the risk to a single aircraft. However, the risks to the various aircraft in the group are not all the same. Presumably, the farther an aircraft is from the point of aim, the safer it is. Thus, the risk to a group of n aircraft is not just n times the risk to any particular one of them. To compute the risk to the whole group, it is necessary to estimate the risk to each aircraft in the group and sum these risks.\n\nConfidential:\n\nThe risks to the individual aircraft in a group are not all equal. When multiple aircraft are flying together, a shell aimed at one aircraft may damage another. Therefore, the risk to a group of aircraft in a given position from the gun is greater than the risk to a single aircraft. However, the risks to the individual aircraft in the group vary. The farther an aircraft is from the point of aim, the safer it is. Thus, the risk to a group of n aircraft is not simply n times the risk to any particular aircraft in the group. To calculate the risk to the entire group, it is necessary to estimate the risk to each aircraft in the group and sum these risks. (Confidential)\nThe risk to aircraft from high-explosive projectiles for time-fused shells is a relatively simple matter. With given parameters ai and a3, the computation of risk to a specific aircraft in the group can be carried out when its position relative to the point of aim is known. This is done using the formula for P(a, b, c), equation (16), or by some approximate method. Summing the risks to the individual aircraft approximates the risk to the whole formation; the only error is due to shielding of one aircraft by another, which can probably be neglected.\n\nFor proximity fuses, the risk to a group of aircraft is not a simple combination of the risks to the individual aircraft. The reason for this is clear. For a given shell, there is a surface in front of each aircraft on which the shell would burst if that target were present.\nThe risk to a single aircraft in a group is no longer the risk from a burst on the surface surrounding the target, but the risk from a burst on any burst surface surrounding any aircraft. For tightly packed formations, this risk may be much smaller or much larger than the risk when that aircraft is isolated and has only its own burst surface to operate the fuze. Shielding will have a very strong effect with proximity fuzes, which it does not have with time fuzes. This shielding is not really a shielding of fragments but of bursts; it will be due to the fact that the bursts will occur before the shell reaches the first aircraft near its path and hence the bursts will be farther from those aircraft away from the gun.\nWith time fuses, the bursts are as likely to be among the aircraft farther from the gun. If, on the other hand, no aircraft happen to be shielded, the risk to each aircraft in the group is greater than if it were alone.\n\nIf we divide the risk to the whole group by the risk P0 to a single aircraft in the same tactical situation, we get a number, called the group probability factor of the group, which depends on the accuracy of fire, the type of fuze, the number and arrangement of aircraft in the group, and (for proximity fuzes, especially) on the angle between the direction of flight of the target and the trajectory of the shell.\n\nIf a flak chart is to be built for a group of aircraft instead of a single aircraft, then the steps of Section 11.5.1 can be carried out with only one change.\nThe probability P0 in step (4) is to be multiplied by the group probability factor at the same point in space to get the risk to the group.\n\nSections 11.6: Concluding Remarks\n\nThe preceding sections have discussed methods developed during World War II for comparing the effectiveness of different tactics and equipment in increasing or reducing risk to aircraft from antiaircraft fire. These methods, by necessity, involve many idealizations of varying doubtful validity. The extent to which the results conform to actual, practical situations is subject to improvement in two basic, interrelated ways: (1) by modifying the hypotheses in the direction of greater realism and (2) by accumulating a larger body of reliable experimental data bearing on all phases of the problem.\n\nInsofar as available experimental data are inadequate.\nOne important question for combined theoretical and experimental investigation is the distribution in space of shell bursts from an AA battery, as determined by the random and systematic errors of the director-computer-gun systems. The assumption of a Gaussian distribution about the target as mean, with independent errors in range, elevation, and azimuth is of questionable validity. The practical desirability of any investigation of the sort just suggested, involving specific pieces of equipment, can be assessed in terms of (1) probable abandonment or modification of such equipment and (2) possible development, in the course of the analysis, of methods applicable to other problems. From the latter viewpoint, it was considered desirable to investigate this issue.\n12.1 Introductory Remarks\nIt is important to emphasize that this chapter does not aim to present a general theory of air warfare. Instead, it will provide tentative and incomplete ideas of what such a theory could and should include. It will present arguments for and against constructing and using such a theory. Additionally, it will indicate how the activities of the Applied Mathematics Panel and other agencies relate to a broader and more inclusive analytical scheme.\n\nConfidential\nPart IV\nGeneral\nConfidential\nChapter 12\nComments on a General Theory of Air Warfare\n\n(Note: The text appears to be in good shape and does not require extensive cleaning. Only minor corrections for formatting and grammar have been made.)\nApproach to the problems of air warfare (and warfare in general). The ideas presented here regarding the scope, nature, and procedures of a general theory of air warfare must be wholly tentative. Such an overall analysis has not, to the best of my knowledge, ever been attempted. We are dealing here with a tremendously complex situation, which not only has a bewildering number of technical elements but is also affected by a host of practical non-technical considerations of a very general nature, such as Army-Navy-Air Force organization and policy, attitude of high command toward civilian technical assistance, attitude of field command toward innovations in procedure, conditions which attract and hold scientific personnel of high caliber, public support of effective measures for military preparedness. The precise character of such studies.\nThe discussed factors - political, organizational, and technical - would be significantly affected by new weapons, tactics, and strategy. These factors are impossible to analyze or anticipate at this time, resulting in vague and general ideas with any accuracy or permanency. The author makes no claim to professional military knowledge, increasing the risk of naive or ridiculous terminology. However, this risk must be taken for the following content. All that follows is to be considered under the protection of a blanket apology for terminology blunders.\nOffensive and defensive air warfare:\n\n12.2. Offensive air warfare consists primarily of the unforced application of bombs (HE, incendiary, atomic, etc.), guided missiles (jet or rocket propelled or gliding; target seeking or externally controlled), ordinary projectiles (ranging in caliber from 0.50 in. to 75 mm), or rockets for the purpose of interfering with or destroying:\n1. Uniformed enemy combatants.\n2. Enemy military materiel (planes, tanks, guns, radar installations, ships, subs, fuel and ammunition stores, etc.).\n3. Enemy communication and transport in enemy countries.\n4. Production facilities of enemy.\n5. Enemy morale.\nIt also has the further purpose of destroying any and all enemy defenses (fighter planes, antiaircraft guns, radar, controlled missile sites, etc.) against such offensive attacks.\n\nDefensive air warfare consists of forced applications:\n\n1. Intercepting enemy aircraft before they can attack friendly forces or targets.\n2. Destroying enemy missiles before they reach their targets.\n3. Protecting friendly aircraft, ships, and ground installations from enemy attack.\n4. Escorting friendly aircraft during offensive missions.\n5. Providing air cover for ground forces.\n\nTherefore, the primary goal of offensive air warfare is to attack and destroy enemy targets, while the primary goal of defensive air warfare is to protect friendly forces and assets from enemy attack.\nDiscussions of the weapons of the air arm against enemy agencies seeking direct attacks. Enemy aircraft, controlled missiles and their launching sites, ships approaching our shores, etc., are among such agencies. Offensive warfare here defined as the use of bombs, rockets, etc., with no explicit mention of own aircraft. Except for the possible suicidal (or remotely controlled) use of aircraft as a defensive ramming device, the aircraft itself is primarily a means of transportation which, with great speed, over long distances, and often unseen, brings to the effective place the bombsight and bomb rack, the rocket launcher, the gun, etc., which then attack the enemy.\n\nThere has been no mention of the distinction between offensive and defensive use of aircraft.\nBetween strategic and tactical offensive air action, the following list of numbered items begins with tactical actions and ends with strategic actions. The distinctions between tactical and strategic action primarily refer to the time factor and specific operations, contrasted with general preparation and direction \u2013 the actions that at once affect the military strength of the enemy in some particular place being tactical, and those that affect the military strength of the enemy in general and after some time delay being strategic.\n\n12.3 Interrelations\nThe brief remarks made in the preceding section concerning offensive and defensive air warfare were made for the single purpose of emphasizing that there is, in general, no such thing as isolated warfare. A modern war involves the productive capacity of a whole people, its ability to transport materials of war, and other resources essential to the conduct of war. Therefore, both offensive and defensive air warfare are interrelated and cannot be considered in isolation.\nIts total capacity to strike by land, sea, and air. The part of this whole struggle which comes under the label \u201cair warfare\u201d is enormously larger and incalculably more important than in the past. But the part called air warfare is in most cases (and in all large and important cases) inextricably interrelated with all the other parts of the total effort. It is as unreasonable and self-defeating to attempt an exclusive theory of air warfare as it would be for a physician to look through a peephole at a patient\u2019s forehead and try to diagnose the cause of his headache.\n\nThus, the first main point is:\nThere cannot be any such thing as a theory of air warfare unless one is in reality prepared to study warfare in general.\n\nNaval forces, infantry, artillery, air forces, coastal defense, production, food, manpower, and critical resources are all interconnected in warfare.\nmaterials are all interrelated in any broad strategic plan. The involvement of our productive strength, money, manpower, etc., in reducing enemy machine tool production within certain stated times is fairly obvious. The cyclic intertwining of military and economic factors is obvious as well.\n\nBut consider some much more detailed and specific questions - ones which might easily face a colonel at Wright Field, for example. A new bombsight is under development, intended for high-altitude radar bombing. The research and development agency reports that:\n\n1. The mil error can be reduced from 50 mils to 40.\nThe mil error can be reduced by a factor of two through increased sight and operation complexity, adding 30 lb to achieve a 20-mil error, 100 lb for a 10-mil error, or 500 lb for a 1-mil error. The bombsight can operate without a straight bombing run by increasing its weight by 300 lb. Factors for the colonel's analysis include probabilities of bombing accuracies and logistics of the theaters where the sights are used. He should bring wide and precise knowledge to bear on these questions.\nThe nature of enemy targets, the vast field of terminal ballistics, the importance of the time factor (including war plans), the psychology and physiology of bomb sight operation, the selection and training of bombers, accessibility of qualified personnel, the basic cost of accomplishing the same objectives otherwise, the present and potential future effectiveness of the enemy's fighter attack against our bombers, etc., must all be considered in answering a seemingly detailed question concerning the design of one specific piece of equipment.\n\nThe \"practical\" man will wish to emphasize that these questions must be answered rationally.\nIn able times, it is not possible to provide each Wright Field colonel with a board of military Einsteins. Judgment, experience, common sense, and even horse sense are more important here than a lot of fine-spun theory. The practical man is asked to exercise almost superhuman restraint and read on. For it is hoped that his fears and objections will receive something of an answer before this chapter is concluded. To match his restraint, the author agrees to restrain himself and cite, from his experience of the last five years, only allegorical and anonymous examples of the kind of decisions which, in such problems, sometimes result from \"common sense\" and \"experience,\" divorced from technical knowledge and analysis.\n\n12.4 Nature of a General Theory\nIn order to expose even the rudimentary ideas of a general theory, it is unfortunately necessary to face a certain amount of complication. That is unavoidable, since the complication is an inherent and characteristic aspect of such problems. To enable us subsequently to talk without the constant repetition of long qualifying clauses, we must introduce a little notation.\n\nSuppose a certain operation 0 is under consideration, the plan P for this operation becoming specific and definite only after a number n of decisions Dn have become definitely settled.\n\nThus, the operation might relate to some specific detail in the design of a piece of equipment \u2013 say, the maximum slewing speed of an aircraft turret. In this case, the plan P is determined when one single decision Di is made definite, that decision consisting of\nIn this case, the text is already clean and readable, so no cleaning is necessary. Here is the text verbatim:\n\nassigning a definite number of mils per second to the maximum slewing speed. To take another very simple illustration, if the operation 0 involved the single question as to whether or not the turret controls utilize so-called aided tracking, then the plan P consists of the single decision Di of deciding \u201cYes\u201d or \u201cNo.\u201d In any such case as this last one, the decision, although consisting of a choice between yes and no, can be given a numerical form (and thus made similar to the previous case) by arbitrarily calling 1 the equivalent of yes, and 0 the equivalent of no. Thus in both the illustrations given so far, the plan becomes definite when numerical values are assigned to the decision variables Dn.\n\nIn a case of slightly greater complexity, the operation 0 might have a plan P which involves two decisions, namely: Dh at what altitude shall we carry out the attack? and Di whether or not aided tracking should be used? In such a case, the plan can still be made definite by assigning numerical values to the decision variables. For example, we might represent the altitude decision Dh as a continuous variable taking on any value between 0 and 10,000 feet, while the tracking decision Di could be represented as a binary variable taking on the values 0 or 1. Thus, the plan would consist of finding the optimal values for Dh and Di that minimize the expected cost or maximize the expected benefit, depending on the specific objectives of the operation.\nHere the plan P becomes definite when a numerical value is established for A (say 30,000 ft), and yes or no is determined for A, so that day or night bombing is settled upon. In a case of greater complexity, the operation O might involve the optimum use of a given sized fleet on B-29 bombers operating out of the Marianas against Japan. But even now the problem is not nearly as broad as it might be, for it presupposes aircraft of certain definite characteristics, operating from a given set of bases; whereas a broader problem would include a consideration as to the selection of the most effective targets, the optimal routing of the bomber fleet, and the allocation of resources for defense against enemy countermeasures.\nThe problem of whether the attack should be made by inhabited aircraft, what types of aircraft, remotely controlled aircraft, guided missiles, and so on, involves a large number of decision variables Dn, whose values must be determined. One must assign priorities to a set of targets, involving numerical values for a set of decision variables, one for each target under consideration. A flight plan must be settled on, which in turn breaks down into a large number of individual decisions, each of which must be definitively determined. This flight plan involves decisions as to the formations flown en route and when to engage fighter opposition.\nPears, when flak is present, require consideration for the bombing itself and the return trip. These matters can be systematically set down by assigning numerical values to various decision variables D. Evasive tactics must be included in this flight plan, and in considering various formations and tactics, it is clear that one is forced into a detailed consideration of the accuracy and effectiveness of the defensive fire of the bombers, their vulnerability to enemy attack by fighter planes, flak, rockets, air-to-air bombing, self-inflicted damage, etc. Questions of fuel consumption, wear on aircraft, crew morale, maintenance, training, psychological and physiological limitations on gunners, bombardiers, pilots, etc., must be considered. Weather, radar navigation aids, and radar bombing aids are intimately involved. Probable damage to infrastructure is implied.\nOwning and operating aircraft from flak, rockets, fighter attack, and so on, involves complex and subtle studies of the vulnerability of aircraft components and personnel, fragmentation characteristics of enemy shells, fire control accuracies, and so forth. Effectiveness of bombing involves intricate probability and statistics of bombing accuracies, and the vast array of factors that enter into terminal ballistics. The enemy defenses of all kinds and against all types of attack must be estimated as best one can, based on past experience and Intelligence. However, past experience, incidentally, is not worth much if it consists merely of the understandably emotional reactions of crew members. Provision must be made for first-hand analysis in the field and at central locations by technically competent personnel.\n\nCONFIDENTIAL\nCOMMENTS ON A GENERAL THEORY OF AIR WARFARE\n\n(The following text is not included in the original and is likely added by a modern editor, and therefore is not part of the original text and will be omitted.)\n\nThe difficult probability and statistics of bombing accuracies, and the multitude of factors that influence terminal ballistics, are crucial aspects of air warfare theory. The enemy's defenses, in all their various forms, must be assessed based on past experience and Intelligence. However, it is essential to supplement this information with first-hand analysis in the field and at central locations by technically competent personnel.\nOperations Analysis Sections and central correlating and analysis bureaus, such as did not truly exist during World War II. In this third illustration of an operation 0, the plan P clearly involves a significant number of decision variables Dn that must be determined to decide the plan. The brief description given above also indicates another characteristic of such problems \u2013 a feature we have not mentioned yet, but is essential.\n\nIt is, in fact, clear that the decision variables Dn themselves depend on a large number of further and more basic variables. For instance, the fuel consumption of a B-29 at given load, speed, and altitude; the percentage of fragments larger than, say, one ounce in weight, which leave a certain bursting AA shell in certain angular directions; the probability of a malfunction in a specific weapon system; and so on.\nThe ability of two .50-caliber slugs in a certain area of a fighter plane causing a fire; the probable value in mils of the harmonization error of certain guns of a B-29 when flying in bumpy air; the probable number of days per month (in a given season of the year) that a certain enemy target will be visible from 14,000 ft and not visible from 30,000 ft; etc. These basic variables, which we will call Vn (indicating that there are N of them), affect the decision variables Dn, but are distinct from them.\n\nCertain of the basic variables V are at our disposal, in that we can control their values. Others are under the control of the enemy (such as, for example, the probability that enemy fighters attack at a certain place and time). Others, such as weather, are under the control, so to speak, of nature.\n\nIt is clear that the relations between the decision variables and the basic variables are:\n\n(Note: The rest of the text seems to be incomplete or missing, so it cannot be cleaned without additional context.)\nThe variables D and the basic variables V are complex, with D and V interconnected in intricate ways. Some decision variables D are not logically independent; see reference 42. For instance, assigning a value to one may involve restricting certain basic variables to specific values or ranges, which in turn may limit and determine the value of other decision variables. This is the formal mathematical equivalent of the experiential fact that one decision commits a person to subsequent decisions.\n\nAmong the variables with significant roles are quantities, such as Nj, which denote the numbers of certain types of weapons available to us or the enemy at specific times.\nThe essential feature of air warfare theory is identifying the set of decisions, D, that provides the largest margin of profit - the greatest excess of return over cost, in strategic or tactical calculations. In strategic calculations, values of Nj are considered over long time intervals, while in tactical calculations, values of Nj are considered at specific places and over shorter future intervals. These variables may serve as decision variables in some problems and as basic variables in others.\nThe words profit, return, and cost do not refer to worth as measured in dollars. They refer to military worth. On the profit side of the ledger, one takes account of the destruction or other harm imposed on the enemy. If the concept of military worth is developed along relatively decent lines, destruction and harm to the enemy will be counted as more valuable, the more definitely and promptly this destruction and harm contribute toward the successful termination of the conflict. Long-range considerations involving possible future conflicts cannot safely be entirely neglected, as is well illustrated by the decision to use the atomic bomb on Hiroshima and Nagasaki. On the cost side of the ledger, one must take account of our necessary expenditures of labor, time, critical materials, and money.\nMilitary worth, personnel, etc. In some simple cases, it may be possible to treat military worth as analogous to man-hours of labor. In other cases, nothing so simple will suffice. Military worth, as the phrase is used here, is closely related to the general concept of utility in economic theory. The reader is warmly urged to read the discussion of a numerical theory of utility given (on pages 15 to 29 and elsewhere) in \"Theory of Games and Economic Behavior\" by John von Neumann and Oskar Morgenstern.1 This pioneering and brilliant book is, it should be pointed out, connected in a most important way with the viewpoint here being presented, as it develops a large part of the mathematics necessary for theories of competitive processes.\n\n1. Theory of Games and Economic Behavior by John von Neumann and Oskar Morgenstern.\nIf we have a satisfactory concept of military worth (denoted as MW), the goal of a general theory of warfare is to find, for any operation 0 and a plan P, the values of decision variables Dn that maximize military worth MW.\n\nSuppose for the moment that a satisfactory concept of military worth has been developed, techniques have been elaborated for computing numerical military worths of various plans P with respect to a given operation 0, that is, the choices of decision variables Dn. In fact, let us suppose that for operation 0, a great Tactical-Strategic Computer (TSC) has been constructed. This computer has one main output dial \u2013 the one which displays the military worth.\nIt has a second set of dials, one for each decision variable Dn. And it has a third set of dials, one for each basic variable Vn.\n\nSuppose we seat ourselves before this tactical-strategic computer and play with its controls. For this process will illustrate, and perhaps make more clear, some things said above.\n\nWe start by setting in the appropriate values to those basic variables V that are under enemy control and those basic variables V that are under nature's control. In some cases, (as for example, the setting time for a well-known enemy antiaircraft director) these may be inserted as definite fixed values. In other cases (as for example, weather conditions over certain enemy targets) the computer must be equipped to accept parameters which characterize the statistical behavior of the quantity in question.\nIn some cases, quantitative significance is not required for the scale of values of MW. Linear order is the only importance. Since both cost and profit have been taken into account, one set of decision variables is unambiguously better than a second set, as long as the first set leads to a larger value of MW, regardless of the extent.\n\nRegarding the accuracy of enemy fire from flexible guns in aircraft, the computer must be equipped to accept a pair of values, setting lower and upper limits to the quantity in question. In the computing process that will follow, this particular basic variable will be allowed to vary over this estimated range. Other basic variables of the same type will similarly vary, but with constantly changing phase relations, so that within a short time, the TSC has in fact taken these into account.\nSet all combinations of values for the necessary basic variables to estimate a range. After setting the \"enemy\" and \"nature\" basic variables, we begin adjusting the decision variables. For instance, we may consider a specific set of decision variables, such as those suggested by the Air Forces Board or Eglin, or by a general with an astronomical number of stars. We set these values of Dn one by one. As we do, the inner calculating mechanisms are activated, and values (or in some cases, indicated ranges of values) appear on the basic variable dials that were not initially set. For example, if we set a value on one of the decision variable dials, the corresponding values on other basic variable dials may also be displayed.\nIf a 5-inch rocket of a certain type corresponds to the choice, then adjust the basic variable dials for fragment, angular, and mass distribution characteristics accordingly. If a decision variable dial is set to correspond to a specific sighting system, then the basic variable dials indicating probability of damage, etc., will display ranges that correspond to this system.\n\nIt is possible that, after setting several values of decision variables, the machine is found to be locked when attempting to set another decision variable. This indicates that the decisions already made determine the remaining decisions. The intricate interrelationships, via all the basic variables, are such that the various decisions are not truly independent. In this case, one pushes a special button.\nIn this case, the decisions and remaining variable dials move automatically into their necessary positions, revealing what further decisions we are committed to. If, however, the decisions prove to be independent, one continues until all their values have been set. At this juncture, the military worth dial lights up and displays the numerical value of MW. Only now do the interesting things begin. First, one watches the value of MW for a time while the computer tries out all combinations of those basic variables for which ranges, rather than specific values, were set. If MW varies widely during this period, one may suspect interdependencies.\nBefore proceeding further, more research is necessary to limit these basic variables to more precise ranges. By adjusting specific basic variable dials, one can determine which variable or variables primarily contribute to the uncertainty in MW. Similarly, by adjusting the statistical parameters set on the basic variable dials, one can observe whether the MW is sensitive or sluggish to these changes. However, the behavior of the MW dial when altering the values in the decision variable dials is of greater interest. This is because changing the military plan for the operation in question directly allows observation of whether the change is beneficial or detrimental. To find the optimal plan, one should:\n\n(Note: MW refers to a military-related concept, likely the minimum viable force or minimum wartime force required for a military operation.)\nThe mechanism would shift all decision dials through cycles of accessible values, recording the resulting MW values to locate the maximum and determine the corresponding optimum values of decision variables Dn. Admit that this complete and formally mechanized analytical procedure lies far in the future. Modern digital and analog computing devices, particularly those operating at electronic computing speeds and having very flexible control systems, effectively remove practical difficulties due to analysis complexity and amount. Factors which\nPrevent the construction of such a computer are not those of computing complexity, speed, etc. The real difficulties and limitations of such a procedure will be discussed in the next section. However, it seems wholly likely that these difficulties and limitations can, at least for many important problems, be overcome. The present author would like to risk the prophecy that just as World War I saw the birth, and World War II the high development and effective use of fire control predictors which, so to speak, solved the immediate tactical problem for a single gun, so the next war (should there be one) may result in the development and use of general tactical computers for use in the field, as on the flagship of a fleet, for example, and even of strategic computers at the disposal of the high command.\n\nCautions:\nThe last few pages have described an imaginary machine. This description is hoped to make clear and vivid certain fundamental aspects of what a general theory of air warfare might sometime be. However, this example, with its \"Rube Goldberg\" machine, runs the risk of giving certain wrong impressions. Therefore, we want to express some warnings.\n\n1. Will those who consider the possibility of such a machine to be wholly controversial or dubious forget the last few pages and consider the rest of the facts and arguments presented?\n2. No one can hope, at this early stage, to predict the actual form of the ultimate science of aerial warfare. Details are not to be taken too seriously.\n3. It may very well be that, for a long time in the future, it will not be possible to carry out analyses.\nThe concept of military worth is vague and difficult at this stage. It is impossible to measure the value of tanks, soldiers' lives, dollars, and man-hours with one quantitative index. More than one index may be necessary, and there are experienced military, economic, and analytical minds available to work on this problem. The overall comparison, whether of incommensurables or not, remains a stubborn fact.\nI am arguing for facing the complexity and facts, and pushing analysis to its usable limit. A great deal of progress has already been made in the study of military problems, some of which are referred to later in Section 12.6. However, there are confidential difficulties, objections, and counter-arguments encouraging this progress. In addition, there has been a great deal of relevant mathematical work in the field. Reference has been made in Section 12.4 to the powerful analysis of competitive processes carried out by von Neumann and Morgenstern. There are many further important pieces of research to be found in the large literature of mathematical economics. In addition, the quantitative ecologists have made significant contributions.\naided by outstanding mathematicians, we have developed extensive quantitative theories of the competition of two or more populations for food supplies, etc. The literature of competitive biological systems have been largely developed by the great Italian mathematician, V. Volterra, the American statistician and biophysicist, A.J. Lotka, the French biologist, Georges Teissier, and the Russian biologist, G.F. Gause.\n\n12.6 DIFFICULTIES, OBJECTIONS, AND COUNTER-ARGUMENTS\nIn the above descriptive remarks, all sorts of difficulties have been overlooked or blithely snowplowed ahead. We will pause at this point to take some account of these matters.\n\nTo argue that a general theory of air warfare is easy to construct would be as ridiculous as it is unnecessary. The problems are of the gravest possible importance, and of staggering complexity.\nThe problems are of compelling character. In many instances, particularly during war, the problems are unlike many questions in pure science. The stark fact is that prompt decisions must be made: a plan - excellent, good, mediocre, or disastrous - has to be adopted and followed. It is not a question of mere intellectual curiosity; there is not an indefinite amount of time during which we may philosophize. It may be utterly disastrous to learn only by trial and error. Under such circumstances, it is really futile and irrelevant to keep remarking that the problems are complicated, subtle, and difficult. Of course they are! But the brutal fact is that they must, for better or worse, be solved. The relevant question is: how? Is there any advantage to be gained from refusing to admit or face complexities and difficulties which challenge us?\nAre these problems inherent? How do \"judgment,\" \"experience,\" and \"common sense\" cope with such issues? In some instances, it must be confessed that they do not cope at all, and these words are merely used as labels to cover up a prejudiced guess made by someone in authority. In other cases - in most cases - there is undoubtedly an eager and honest attempt to invoke experience and to exercise judgment and common sense. But judgment based on experience, to the extent that it is rationally utilized, must face the problem of deciding that certain features of the present do or do not correlate with the past - that is, must use the analytical method. And what, indeed, are such efforts other than disorganized and feebly intuitive shadows of a real analysis?\n\nAnyone who, with a background of scientific training, is not too old a thinker to be intolerant of ambiguity, will be impatient with such vague and unanalytic modes of thought. He will insist that these words be made precise and that their meaning be clearly defined before they can be used in a rational discussion. He will demand that the terms \"judgment,\" \"experience,\" and \"common sense\" be analyzed and defined in terms of their logical relationships to each other and to the concepts with which they are associated. He will insist that the meaning of these terms be made explicit and that their implications be explored. He will demand that the criteria for making judgments be stated and that the sources of experience be identified. He will demand that the methods of exercising common sense be made explicit and that their validity be demonstrated. He will demand that the assumptions underlying these modes of thought be made clear and that their logical consistency be established. He will demand that the limitations of these modes of thought be acknowledged and that their scope be defined. He will demand that the consequences of these modes of thought be considered and that their practical implications be evaluated. He will demand that the relevance of these modes of thought to the problems at hand be established and that their usefulness be demonstrated. He will demand that the adequacy of these modes of thought be assessed and that their shortcomings be acknowledged. He will demand that the alternatives to these modes of thought be explored and that their advantages be compared. He will demand that the criteria for choosing among these alternatives be established and that their implications be evaluated. He will demand that the ultimate justification for relying on these modes of thought be provided and that their ultimate significance be established. In short, he will demand that these modes of thought be subjected to the same rigorous analysis that is demanded of scientific concepts and theories. Only then can we hope to understand their true nature and their true value.\nA soldier, having observed the decision-making process in military circles, has likely developed a strong attraction for the vast majority of sincere, intelligent, and patriotic officers. However, disappointment arises from the frequent lack of technical competence at decision-making levels, and distrust in what passes as \"common sense.\"\n\nOne of the most debilitating circumstances for dealing with the challenges of unsound common sense is in relation to what one might call the \"hero problem.\" A young and extremely capable pilot endures a long and harrowing combat experience. By this time, he has reached the rank of lieutenant colonel or even colonel. He is intelligent and clearly experienced. He is then returned to Eglin, Orlando, Wright Field, or Washington.\nAn engineer, physicist, or mathematician, who has been studying sights intensively and exclusively for several years, comes to the colonel's desk for information or backing. The colonel browses through the material, pales at the mathematics, and seizes on one feature of the sight he thinks is similar to another sight he once disliked. Immediately, his front-line vocabulary emerges, and he makes it clear that he disapproves. If the technical expert says, \"But Colonel, don't you think...?\" He is interrupted with, \"Listen; I have been there with those shooting at me, and I know what I'm talking about!\"\nAnd you look at the triple row of ribbons on his chest, and you are devoutly thankful to him for his youth, skill, and bravery \u2014 and there is just no decent way for you, a theoretical stay-at-home, to tell him that he is wrong about a general theory of air warfare. That is what was meant, above, by the \"hero problem.\" The worst of it is that this energetic, patriotic, and altogether fine young man is often wrong. There are essential complexities and subtleties to the problem which he has never thought of, and for which his technical training does not at all equip him. His own ideas have been inflexibly set by his own experience under fire. He may have used a very bad sight and very bad tactics \u2014 but if they, in fact, carried him through alive, it is beyond reason or hope that he will ever be objective about them. He may\nEven those who believe scientists should not interfere with soldiers in their business may think that for automatic weapon and antiaircraft fire, \"all you have to do is look at the tracers. Then, Doc, you see it all with your own eyes, and you don't need any of the goddam mathematics.\" This is what he calls \"common sense.\"\n\nIt must be remembered that individual combat, as experienced in the Air Forces, is a highly variable experiment in probability. These individual experiences do not mean much apart from the total evidence, some of the most important of which would have to be given by dead men. Success is often achieved in spite of, rather than because of, the personal characteristics of the man.\nEquipment. The testimony of outstanding individuals is therefore an argument for outstanding individuals, rather than for or against any particular pieces of equipment or any particular techniques. There is no intention to imply that such well-intentioned and excellent, but misplaced officers constitute the majority. On the contrary, one of the strongest and happiest impressions of the scientists who have worked with the Services is the large number of really excellent officers \u2014 highly intelligent and energetic, and men of fine character. The point being made here is:\n\nOfficers required to administer technical programs and to make recommendations on technical developments should be chosen for their technical training, not their battle experience. Such officers should be given credit for technical service, and should be maintained steadily in their positions.\nA technically competent man should have a long enough service to make his technical expertise effective. One of his most outstanding characteristics should be a knowledge of his own limitations and a willingness to seek and accept more expert advice than he can provide. He should be able to bring an unemotional logic to bear on the survey of problems and have a capacity to recognize and appreciate the major points in a technical argument, even if he personally could not construct the argument. All of these comments are closely connected to the desirability of briefing officers at the decision level by a competent specialized staff.\n\nThere is good evidence that the points emphasized are well recognized by certain highly placed officers \u2013 for example, by General Arnold himself. Unfortunately, he plans to retire, and a new set will follow.\nBut let us return to our main thesis. We have listed above a considerable number of factors that enter into air warfare problems. No one would argue that such factors are unimportant. If there are other, dominantly more important factors, let them be brought forward by their proponents, and it will at once be agreed that these factors (after their importance has indeed been established) should be included in such a scheme. No one would deny that military operations should be conducted in accordance with the plan that promises the greatest net return. Who is prepared to claim that, on the basis of experience and intuition and judgment, they can instantly and mysteriously produce solutions which resolve the complexities of air warfare?\nThe concept of military worth cannot be produced or improved by logic and analysis? The idea of military worth may be difficult to define and apply to specific cases. However, if it is a fundamental concept that plays an inevitable role, what value is there in disregarding it? Nothing is gained by burying our heads in the sand to avoid complications and difficulty. Complications must be faced, and the sooner they are brought out into the open and subjected to logical, quantitative analysis, the better. It will be argued by some that it is very difficult, if not impossible, to devise any quantitative measures of worth that can be applied equally to factories, ships, food, aircraft, men, etc. Admittedly and assuredly it is difficult, but it is paralyzing and self-defeating to give up without trying.\nAny judgment, including those based on \"judgment\" or \"experience,\" necessarily involves evaluations. It merely involves them in a concealed and unanalyzable way. To argue that the problems are too complicated to solve is to deny the history of man's conquest of complicated problems. Atomic physicists, cosmologists, or geneticists had they been content to say, \"The facts are too subtle and inaccessible, the problems too complicated!\"\n\nUseful progress, however, can only be made by recognizing the complexity and tackling it head-on.\nResults can come from an incomplete and inaccurate start. A precise analysis of relationships is sometimes possible even when the numerical values of various parameters are completely unknown. Important conclusions may flow even if one has to make wild estimates of certain difficult parameters.\n\nThis last point is important enough to illustrate. Suppose one wishes to compare the relative effectiveness of two alternative armaments for a fighter plane (say, eight .50-caliber wing guns versus four such wing guns and two central cannons). This comparison depends on a considerable number of factors \u2013 fire control accuracies and vulnerabilities chiefly \u2013 which are very difficult to estimate with any accuracy. But if it turns out that one asks several persons to estimate the fire control accuracies.\nMany problems in warfare involve probability considerations, a field notoriously tricky where \"common sense\" is often helpless. The author knows one probability question that can be used as a basis for bets. The odds for the person who understands the game are about three to one, but it is so deceptive. P.M.S. Blackett said, \"No pregnant problem should be left unattempted for lack of exact numerical data, for often the most profound issues can be addressed with limited information.\"\nIt is found that some significant conclusions recommending concrete action can be drawn with very rough data. A common-sense person, whom the author has felt morally restrained from playing the game with anyone other than professional statisticians. Examples of a similar sort can very readily be found in military problems. For instance, what is the optimum mixture of armor-piercing (AP) and incendiary ammunition for the rear guns of a bomber? Specifications often designate such mixtures as five AP to two incendiary (we are neglecting tracers here). The somewhat striking and by no means obvious fact is that given any fixed type of target, it is better to have either all AP or all incendiary, depending on the nature of the target. The justification for any other intermediate mixture should be based on a specific reason.\non knowledge of the relative probability of encountering different targets, some of which would be more vulnerable to AP, and others more vulnerable to incendiary:\n\nAs another example, consider the effect of a weather forecast for a certain future military operation. Oversimplifying the problem, suppose one is only interested in whether the weather is good (G) or bad (B). Suppose one can assign the relative military worth (MW) for the four possible cases:\n\n1. The forecast is G and the weather actually turns out to be G.\n2. The forecast is G and the weather actually turns out to be B.\n3. The forecast is B and the weather actually turns out to be B.\n4. The forecast is B and the weather actually turns out to be G.\n\nIn a given case, for example, the MW of case 1 might be exceedingly large and positive, and the MW2 of case 2 might be significantly negative.\ncase 2: very large and negative. While MW3 and MW4 might both be moderate or small, this would be the case of an operation that is very important if successful, disastrous if unsuccessful, but which could be postponed until later without great loss. What should be the weather forecast to maximize the expected worth of the operation?\n\nThe answer is striking, simple, and not obvious. Anyone interested can find a discussion of this problem in a reference (651).\n\nTo conclude these two examples, it may be worth pointing out that, from a mathematical point of view, they are not separate and different examples, but merely two illustrations of a single, simple, basic, analytical fact. This point is mentioned because it is not trivial. One of the important reasons for this is confidential.\n\nCOMMENTS ON A GENERAL THEORY OF AIR WARFARE\nThe analytical approach is powerful because it strips off confusing superficial aspects of problems and exposes their inner logical structure. In some cases, this inner structure turns out to be logically equivalent to a situation already studied and solved. In certain cases, the analysis will reveal that the final result, such as military worth, is extremely sensitive to the value of a certain parameter. This fact in itself may be of great importance. In other cases, it may be impossible or impractical to assign sufficiently definite values to the various basic variables to permit any unique determination of the military worth of a given plan. However, it may nevertheless be of extreme importance to delimit the total range of possibilities. This is in a way analogous to the problem of determining the value of pi, which cannot be determined exactly but can be approximated to any desired degree of accuracy.\nProcedure of the cosmologist. He does not have enough nor precise enough information to construct a complete theory of the universe. But he can succeed in establishing the fact that, of all possible universes, the actual one has properties which lie within certain specifiable ranges. And then he has a definite framework of procedure, and can systematically refine his analysis and narrow its limits of uncertainty.\n\nFurthermore, there is impressive and practical evidence in favor of attempting the quantitative analysis of complex situations involving elements which seem to elude quantitative specification. This, in fact, is precisely what was done with such outstanding success by certain operational research groups during the war. Professor P.M.S. Blackett, to whom is due so much of the success of the British nuclear program, is an example of this approach.\nOperational Research has shed light on this matter in a brilliant and deceptively obvious paper titled, \"A Note on Certain Aspects of the Methodology of Operational Research.\" For a classic example of success in dealing with a complex situation, readers should study the Admiralty Operational Research reports on the convoy problem or the critically important paper, \"Air Offensive Against U-Boats in the Bay of Biscay.\" It is recognized that most broad military problems are characterized by great complexity and a lack of accurate numerical data. As emphasized in Section 12.4, they are more like the problems of biology and economics than the problems of physics.\nOne cannot reasonably expect complete logical theories of the a priori sort, successful in physics and astronomy, for some time. One must usually be content with variational theories, studying the response of military worth to changes in decision variables. These theories often use statistical as well as analytical methods for estimating differential coefficients and make maximum use of operational constants and functions. Operational constants and functions are precious and dearly-bought results of combat experience. They should be distilled out of everyday experience at the front by Operations Research personnel and significantly supplemented.\nby overall comparisons of the effectiveness of operations in various theaters. This latter type of evaluation has, granted the lack of adequate technical and analytical assistance, been carried out during World War II with skill and objectivity by various groups for various areas. A good example, for instance, is the report of the AAF Evaluation Board, Pacific Area. A detailed examination of this honest and able report would convince anyone that errors had been made which could have been anticipated and prevented had sufficiently broad studies, of the sort urged herewith, been carried out and the results utilized. Throughout this chapter, the atmosphere of the discussion is the atmosphere of war. Many of the remarks imply that studies were being made while a war is going on. These studies are absolutely essential, for\nThe complexity and other characteristics of the problems are such that progress cannot be made very well without knowledge of the operational constants and operational functions mentioned above. Emphasis should be given to the necessity that such subjects be studied during peacetime. Precisely because the problems are so difficult, we have little chance of making important progress and of being in a strong and well-prepared position unless a substantial and sustained research program in this field is carried out after the war. Between wars, it is difficult, if not impossible, to give effective attention to detailed (especially operational) problems of the sort referred to later in this chapter as micro-problems. However, between wars, we should seek to develop the framework for addressing these issues.\n12.7 Progress in World War II\n\nThe last section indicated substantial progress during this war in quantitative analysis of military problems. The use of technical experts is not new or recent. The Trojan Horse was presumably designed by some ancient Omicron Sigma Rho Delta. Archimedes was Syracuse's V. Bush. Napoleon had a board of technical advisers. Those advocating large extension of analytical methods will face two extreme groups: one will be certain the idea is visionary, unnecessary, and impossible; the other will be equally certain propaganda for the idea is unnecessary because the notion is so old and obvious that everyone has accepted it.\nThe author's association with research and development problems during World War I was intimate but on a very junior level, so he cannot prove, despite being reasonably sure, that there was little effective use of quantitative analytical thinking in instrument development, and probably none in tactical or strategic plans. It is worth noting that Frederick William Lanchester wrote a series of papers titled \"Aircraft in Warfare: The Dawn of the Fourth Arm\" in 1914. Paper No. V of this series contains the paragraph:\n\nThere are many who will cavil at any mathematical or semi-mathematical treatment of the present subject, on the ground that with so many unknown factors.\nThe merits or demerits of morale, leadership, weapons, and the unknown chances of war make it ridiculous to calculate anything. The answer is simple: the direct numerical comparison of engaging forces or those available in war is universal. Military authorities reckon with this factor and it is discussed extensively in the Press. However, accepting the mere \"counting of pieces\" as valuable and denying the extended application of mathematical theory is illogical and unintelligent.\nThe principles of precision with the use of weights and weighing machines, but refusal to grant allowances for leverage inequality in the latter case. In this paper, Lanchester derives, through mathematical reasoning, the principle that:\n\nThe fighting strengths of two sources are equal when the numerical strength, multiplied by the fighting value of the individual units, results in equal squared values.\n\nDuring World War II, unaware of Lanchester's earlier work, a mathematician affiliated with AMP wrote a paper (number 9) that reproduced and expanded upon Lanchester's previous results. This paper provided estimates for required times and remaining victorious forces when one military or naval force encounters another. The author also explored the quantitative aspects of force division, demonstrating, for instance, that a first force needs only to be 71% the size of the second to be effective.\nThe former is as strong as the second to liquidate the latter completely, if the former is clever enough to maneuver the latter into a position where his forces are temporarily divided. Other papers in this field were written by a Tufts College group working under the auspices of the Special Devices Division of the Navy. Reference has been made above to the brilliant and critically useful analyses carried out during this war by the British Antiaircraft, Coastal Command, and Admiralty Operations Research groups. Similar, and also highly successful, groups operated in connection with our forces. The outstanding examples being Research Group M which furnished the central analysis for the antisubmarine campaign, and the operational groups assigned to the various theatre commands by the AAF. This is no place, nor is there any need, to discuss these further.\nRehearse the accomplishments of these groups. Looking at our own effort from the outside, but from the vantage point of a fairly close relationship from the time of the first organization of the British AA group onward, the author would, however, risk two recommendations. First:\n\nThat every important arm of the Service develop Operational Research groups; and that in addition to the absolutely essential groups in the theaters, there be one or more central correlating groups.\n\nThe absence of such central study and correlation seems to this author to be a striking weakness in the AAF setup, and an evident strength in the Navy antisubmarine setup. Second, and in spite of the outstanding personal qualities of the personnel who recruited and organized the AAF groups:\n\nThat the recruitment of Operational Research personnel, the organization of the system, and the training of the personnel be given more attention.\nCOMMENTS ON A GENERAL THEORY OF AIR WARFARE\n\nCentral direction of it be carried out by technically trained personnel, including mathematicians, physicists, engineers, psychologists, physiologists, etc., but with a minimum of lawyers and architects.\n\nIn England, in addition to the Operational Research groups, a large amount of general analysis of air warfare was carried out by the extensive group working under the direction of Dr. L.B.C. Cunningham. Certain of these studies relate to rather specific details; but others are grave and useful attempts to tackle rather broad problems, such as Cunningham\u2019s own extensive analysis of air duels.\n\nMany bureaus and divisions of our Army and Navy recruited and utilized, often with great effectiveness, both civilian and uniformed analysts.\n\nAberdeen Proving Ground (particularly the Ballistic Research Laboratory) played a significant role in this regard.\nThe Ordnance Department, Naval Bureau of Ordnance, Bureau of Aeronautics, particularly at the Naval Research Laboratory (Inyokern, Patuxent, etc.), Army Air Forces (Eglin, Orlando, Wright Field, Laredo), and various divisions of the Office of Scientific Research and Development (OSRD), including Division 14 (Radar), Division 6 (Subsurface Warfare), Division 7 (Fire Control), and the Applied Mathematics Panel, are some of the instances where the author is familiar with the presence of large and excellent groups of analysts. In many, if not all, of these instances, the analyses were related to what is referred to as the micro-theory of war rather than the macro-theory. These two expressions can be understood as follows:\n\nMicro-theory of war: the study of specific military tactics, weapons, and techniques used in combat.\nMacro-theory of war: the study of broader military strategy and the overall conduct of war.\n\nTherefore, the analyses conducted in these institutions focused on the intricacies of military operations rather than the larger strategic picture.\nBy macro-theory, we mean the general and broad analytical theories discussed in Section 12.4. In contrast, micro-theory refers to the analytical study of more detailed problems that can be isolated from tactical and strategic considerations, such as the study of how the theoretical accuracy of a bombsight can be improved by certain design changes. However, if one wishes to study the practical effectiveness of the modified bombsight rather than its theoretical accuracy, then he must take into account all sorts of general considerations, including training, operational simplicity, logistics, time delays in changing equipment, and techniques. See Section 12.7.1.\nThe conditions in theatre, nature of target, etc., lead to a macro-problem. The great progress made during World War II by many groups and agencies in solving micro-problems is significant for a macro-theory. The structure of the macro-theory requires bricks to be laid up into walls, and general blueprints for the design. Individual bricks, which are solutions to micro-problems, are essential. Without these solutions and the ability to make bricks, there would be little sense in drawing up elaborate blueprints of general plans.\n\nA very large fraction of AMP's activities was directed toward solving military micro-problems. Various important fields of micro-problems are reviewed in other portions of AMP\u2019s reports.\nThe final report and several micro-issues in air warfare are discussed in other chapters of this volume. It is the duty of this chapter to briefly report on two studies carried out under AMP auspices. Although not macro-theoretic in character, they have a broader tactical or strategic scope than most other AMP studies.\n\nThe first study began before AMP was created, under the auspices of the analytical section of the Fire Control Division of the NDRC, specifically Section 5 of Division 7. Since the Chief of AMP is also Chief of Section 5, Division 7, the transition to AMP auspices was hardly noticeable. The second study to be reported here started relatively late in AMP's history. Thus, AMP, regardless of what it did in between, began and ended with fairly general studies of air warfare.\n12.7.1 Study of Alternative Fighter-Plane Armaments\n\nThis study arose from the enthusiasm of a few of us for two powerful and pioneering papers concerning a mathematical theory of air combat. We showed and praised these papers to various officers of the Army Air Forces and of the Naval Bureau of Aeronautics until they suggested that we try to digest and simplify these papers, interpreting them in terms not so formidably mathematical. After they had gained an understanding of what had been done, they proposed that we apply the same or similar methods to a problem they would set.\n\nThe first step was accomplished by two reports. The first report (12) gave an outline of the two British papers.\nReports were made based on 13 papers, the second of which provided a non-mathematical explanation of the two papers. These reports formed the basis for an extended conference with AAF, Bureau of Aeronautics, and RAF personnel. We were then asked to apply these ideas to the problem of comparing the relative effectiveness of four 20-mm guns versus eight 0.50-in. guns as armament for a fighter making a stern attack on a defended twin-engine bomber.\n\nThe methodology for analyzing this problem was carefully outlined, and a list was made of the necessary information (types and quantities of data, estimates, or assumptions) required to obtain an answer. These questions (nature of combat, bomber and fighter armament, value and variations of accuracies, ammunition, vulnerabilities, etc.) were then discussed.\nThe experienced officers estimated vulnerability assuming five alternatives. These estimates, arrived at by agreement, were nearly certain to encompass the true values, although the true values were admittedly unknown. The analysis was based on five assumptions of vulnerability, three of bomber firepower index, and four of fighter firepower index. For four of the five vulnerability assumptions, the eight 0.50-inch guns had an advantage (ranging from 27 percent to 75 percent) over the four 20-mm guns. For the fifth vulnerability assumption, the 20-mm armament was preferable, having about a 20 percent advantage. The study was inconclusive but made clear the type of information required.\nThe study was necessary to obtain a conclusive answer and furnished the necessary analytical methods. The superiority of the 0.50-inch armament was rather strongly suggested, especially since the use of an optimum ammunition mixture increased the superiority of the eight 0.50-inch guns for the first four vulnerability assumptions and reduced the advantage of the 20-mm guns to 10 percent in the case of the last vulnerability assumption.\n\nAs by-products, this study also issued important memos on the subject of optimum ammunition mixtures and the optimum interrelation of aiming and dispersion errors.\n\nThe fighter armament study was largely carried out in 1942 and 1943, although not formally concluded until 1944. The B-29 studies, however, did not originate until mid-1944. The initiation of AAF\nProject AC-92, which resulted in these B-29 studies by AMP, was initiated by a communication, dated June 14, 1944, from Headquarters, AAF, requesting that the NDRC collaborate with the AAF \"in determining the most effective tactical application of the B-29 airplane.\" This communication was the direct result of a conference held at Orlando, Florida, under the auspices of the Army Air Forces Board. The conference report, which was later made an official part of the AC-92 directive, stated:\n\n1. That no scientifically controlled or scientifically evaluated investigation of various defensive formations of bomber aircraft had ever been conducted by the AAF.\n2. That it was of the utmost importance to conduct such investigations.\n3. That no scientifically controlled or evaluated investigation had ever been made of the B-29 defensive armament.\n4. The lack of a standard central fire control gunnery doctrine, no standard B-29 gunnery manual, and no detailed training standards for B-29 gunnery resulted in the NDRC being requested, as Project AC-92, to collaborate with the AAF in planning, organizing, carrying out, and evaluating an investigation into the most efficient B-29 formations. Consideration was to be given to:\n\n1. Self-protection of bomber aircraft from fighter attack by the bomber's own gun.\n2. Self-inflicted damage.\n3. Support fire.\n4. Maneuverability and evasive action.\n5. Effectiveness of bombing.\n6. Formation control.\n7. Flak.\n8. Rockets.\n9. Air-to-air bombing.\n10. Fighter escort.\n\nProject AC-92 was also specifically asked to evaluate the defensive armament of the B-29 (a task which, in fact, was also required by item (1) above).\nComments on a General Theory of Air Warfare: The ability of the average gunner to effectively use the system and develop a standard procedure and gunnery doctrine for the B-29 airplane required study. Anyone surprised and shocked that such a request was made in June 1944, given the large production numbers of the B-29 airplane, has two replies. First, it was both surprising and shocking. Second, this airplane was rushed into combat use on a schedule that made it difficult, if not impossible, to follow an orderly or rational procedure. Remember, the unorthodox means used resulted magnificently in justifying the actual outcome.\n\nThe Project AC-92 directive referred to:\n\n(Note: The text appears to be in good shape and does not require extensive cleaning. Only minor corrections for grammar and punctuation have been made.)\nThe project involved extensive flying experiments for the specific aircraft, primarily the B-29. Negotiations ensued to assign this project, which was eventually given to AMP despite reservations. General U. G. Ent, then commanding the 2nd Air Force, played a significant role in initiating and planning the project. After some negotiations, the project was reluctantly accepted by AMP, which had a sizable personnel expertise in analytical aspects of bombing, air gunnery, and flak analysis. However, it was clear that this project required a massive experimental program and organizational challenges were inevitable as civilian organization attempted to undertake military operations.\nFrom a military field, aircraft that could only be done properly under military organization caused confusion if not trouble. However, due to the lack of a reasonable alternative, AMP agreed to do the best they could. From this time until AC-92 was closed, the Chief of AMP spent almost all his time on this one job.\n\nTo achieve the objective of Project AC-92, AMP established a broad program that included:\n\nA. Experimental tests at Alamogordo, New Mexico.\nB. Model experiments at Pasadena.\nC. Dynamic testing of the Central Fire Control at Austin, Texas (under Division 7, NDRC).\nD. Gun camera tests at Eglin Field, Florida (AAF Board, with collaboration of Division 7 and AMP).\nE. Collaboration with General Electric in tests at Brownsville, Texas.\nF. Psychological studies (under Applied Psychology Panel).\nG. Analytical studies of special features of the problem, such as vulnerability and flak (conducted by AMP under other studies reported in Part III of this volume).\nH. Broad analytical studies, such as those relating to bombing effectiveness and general \"economic\" theory of bombing.\n\nItems C, D, E, F, and G could be handled by existing AMP facilities or by other parts of the NDRC. It was essential to provide for A, B, and H, and to offer general direction and correlation for the entire program.\n\nAs for A, the Alamogordo (and Albuquerque) portion of the program, primarily involving experimental tests and their interpretation, was carried out through a contract with the University of New Mexico and in close collaboration with the Second Air Force. This work will be further detailed below.\nAs to B, the optical model experiments and their interpretation were carried out through a contract with the Mt. Wilson Solar Observatory (Pasadena) of the Carnegie Institution of Washington (CIW). This work will also be further described in Section As to H. A contract was made with Princeton University which made available a group including physicists and engineers as well as mathematicians, who had long experience with fire control problems. In addition, a Steering Committee was set up, consisting of two representatives from AMP; one from Division 7 (Fire Control); one from Operations Commitments and Requirements, AAF Headquarters; one from the AAF Board; one from the 20th Air Force; and one from the 2nd Air Force. A highly experienced individual was also included.\nAn experienced and expert RAF officer attended all Steering Committee meetings and took an active part in the Alamogordo experiments. A representative from the War Department NDRC Liaison Office attended most meetings. The project director, responsible for its overall direction, maintained that the directive (with its broad inclusiveness and emphasis on scientific planning and evaluation of experiments) could not be met unless all items A to H progressed simultaneously. However, service personnel were predominantly interested in A, increasingly interested in B, barely interested (with one exception) in C, D, and E, only mildly interested in F and G, and totally (and in most cases emphatically) uninterested in H.\nEstablished in H.\n\nWhat we could accomplish in this project depended essentially on AAF support and assistance. We considered it our duty to come as close as possible to doing what the AAF wanted done, while adhering to our scientific and personal consciences. Thus, it is natural and inevitable that Project AC-92 faded out of the picture once items A and B had produced their major contributions. Items D, F, and G eventually produced results which are certainly of large and lasting value. However, item H, which should have appeared as the crowning jewel in this chapter on general studies in air warfare, was a total flop. It was a flop, this author is convinced, because it never was given a chance to be anything else. Some persons in the 20th Air Force were interested, in principle at least, but they considered that such studies were not a priority.\nThe AAF should carry out tests within their own organization, preferably by their Operations Analysis personnel. The rest of the Service personnel, whose backing is necessary for this work to proceed, had lost interest in broad studies as indicated in the directive.\n\nIt is clear that the AAF should not have allowed itself to depend on a civilian organization for planning, conducting, and interpreting tests and studies to determine the effectiveness of the defensive armament on the upcoming bomber, just a few months before its large-scale combat entry.\nIn the development of the B-29 project, important questions arose - how to discard weapons and rely on altitude and speed; how to operate the fire control system; how to select and train personnel; what types of formations to fly and how; etc.\n\nAs the project progressed, a significant addition emerged - the challenge of devising workable laboratory and field methods for harmonizing the B-29 guns. This was accomplished cooperatively with Section 1 of Division 16. It is the writer's impression that important results were achieved.\n\nSuch questions should, in any reasonable and rational development, have been resolved long before. By test establishments, analysis groups, and decision-making groups within the AAF.\n\nHaving outlined the technical and organizational background for the B-29 studies, it remains to describe the work itself.\n\nIn the early spring of 1944, a group at the University began:\n\n(Note: The text appears to be mostly readable, with only minor OCR errors. No major cleaning is required.)\nThe University of New Mexico collaborated with the 2nd Air Force in carrying out studies of the K-3 sight in a Sperry upper local turret and of an N-6 sight in a Martin upper turret. These were camera tracking tests with the turrets mounted on movable platforms. Previous studies by the same group on the stability of the B-17 in flight indicated the types and amounts of movements that should be given the platforms.\n\nThese studies stimulated the interest of the New Mexico group, which, along with General Ent, played an important role in the Orlando conference mentioned above, resulting in Project AC-92. It was therefore natural that AMP turned to the University of New Mexico, offering them an NDRC contract under which they would organize a group at Albuquerque (and at the large B-29 field at Alamogordo) to carry out experimental tests on the aircraft.\nB-29 airplane. This New Mexico program, as should be clear from the explanation above, actually constituted a large portion of AMP's activity under Directive AC-92. The remainder (except for the Pasadena optical studies which will be described in Section 12.7.3) consisted primarily of the labors of the Princeton group in correlating and assisting the large and widely distributed pattern of activities in AC-92. They did this through frequent visits, continuous assistance in obtaining necessary equipment and information, especially from the AAF, by needling various organizations into action on our work, by extending specially valuable aid to the Applied Psychology Panel in their part of the program, by carrying out analyses of various special problems, and by trying to keep all parts of this program mutually informed through a series of frequent communications.\n\"AC-92 Bulletins, no. 19. The Princeton group had originally planned to gather all results of separate tests and analytical studies, synthesizing them into a more general theory of air warfare regarding the most effective tactical use of the B-29 airplane. However, this synthesis couldn't proceed without the complete backing of AAF officials, who, despite the wording of the official directive, showed no interest.\n\nA description of the New Mexico program follows under the following headings:\"\nTwo main problems were attacked:\n\n1. In what way, how frequently, and how effectively can fighter planes attack a single B-29? This involved a determination, at various speeds and altitudes, of the types of possible fighter passes, the frequency with which passes could be carried out, and the accuracy and duration of the fighter's fire during these passes.\n2. What is the defensive strength of a single B-29 bomber against fighter attack? This involved a determination of the accuracy and duration of fire from bombers\u2019 guns. Air tests of these accuracies were to be supplemented with air-to-ground firings, and ground tests of the accuracy of the central fire control system.\n\nIn addition to these two main problems, certain other problems were studied.\nThe necessary and inevitable concomitants of the two mentioned studies or for the practical reason that the New Mexico group developed a facility able to take on and push through to necessarily approximate but remarkably rapid conclusion a test of any aerial gunnery device. Since the AAF did not have such a facility, it was natural that there was a tendency to forget the directive (and indeed the NDRC itself), and when any sort of rush problem arose, simply telephone the boys in Albuquerque and ask them to do a quick job.\n\nThe New Mexico experiments dealt almost exclusively with the problem of single B-29 bombers. This was, in any event, the sensible and almost necessary way to start. Some aspects of the problem of bomber formation were studied at Pasadena, and in other auxiliary studies.\nAmong the reported issues in Part III of this volume, a comprehensive study should include all types of evasive actions by the bomber. Due to time constraints, this was not possible. Among the closely connected auxiliary problems were extensive time spent on determining the performance characteristics of the B-29 airplane at different altitudes, speeds, loads, and armor and armaments. There were also studies on dispersion from various B-29 guns, harmonization, and so on. Among the disconnected studies were:\n\n1. APG-5 test with K-3 sight in B-17.\n2. Speed reduction of B-29 due to radar domes and open bomb doors.\n3. Turret dispersion tests, A-26 aircraft.\n4. Performance of APG-15 (radar versus optical range).\n5. APG-5 test with Mark 18 (K-15) sight.\n6. APG-15 test with special GE computer.\nAt Albuquerque and Alamogordo, the civilian personnel on this project included 11 major technical persons, 16 research assistants, 14 skilled field assistants, 26 administrative assistants, 76 technicians (including a large staff of computers), 18 machinists, guards, Service personnel, etc.\n\nAt Alamogordo, a special unit of the 2nd Air Force (AAF Base Unit 206) was assigned to this project, and extremely cordial cooperation was furnished by the 2nd Air Force Command. BU 206 included a total of approximately 160 Service personnel, of which something over 40 were officers.\n\nTaking into account the Princeton group and the central AMP office, there were about 350 people involved in all in this study.\n\nThe assigned aircraft totaled 43, as follows: 6 standard, 2 stripped P-63s.\n\nA total of 1,448 separate flights was carried out.\nThe study involved 348 B-29 flights, during which 348 ft of 16-mm film was exposed in gun cameras. A large computing and analysis section was developed at Albuquerque.\n\nTechniques 20-24:\nThe main results of this study were obtained through actual bomber flights and attacks by fighter planes, with simulation of battle conditions for interception, etc. All gun firings of both bomber and fighter were recorded photographically using gun cameras. This method primarily used a single camera technique, utilizing distant background reference points such as clouds or mountains. The terrain and climate of southern New Mexico were essential to the procedure.\nThe method is not as accurate, particularly for flexible guns, as deflectometer methods, but probably sufficed for the purposes at hand. In any event, it was several cuts better than nothing, and no other known method was really possible, taking into account the mass of data necessary and the time available. A great many other methods were skillfully and energetically developed by the New Mexico group to handle other details of the program.\n\nResults:\n\nIn this program, the ability of the stripped B-29 to carry great loads over great distances at great speeds and high altitudes was experimentally demonstrated, and for the first time, as far as we know, was successfully simulated the Saipan-Tokyo and return bombing missions.\n\nThe character of the fighter plane attacks which:\nThe accuracy of attacking a B-29 was experimentally determined for altitudes ranging from 20,000 ft to 32,000 ft, and the errors of various computing sights were determined for these actual courses. The accuracy of fighter plane fire against the B-29 was experimentally determined for altitudes ranging from 14,000 ft to 32,000 ft, and the frequency of hits was analyzed for different approaches. These tests were all conducted with fighter pilots who had combat experience.\n\nFighter hits on a B-29 per pass were obtained as a function of angle and range, and converted through a study of pass frequency to fighter hits per hour as a function of angle and range. Gun and turret dispersions were measured for the B-29, as well as harmonization errors on the ground and (approximately) in flight. Tracking errors were determined carefully for all positions, and actual gun performance was examined.\nThe approximate errors were determined for the B-29 central fire control system in ground tests, measuring the output for known and controlled inputs. The ability of the P-47 fighter and certain faster, more modern fighters to attack a stripped B-29 flying at high speed and great altitude was determined. These tasks could have been done better with more time, but the experimental program began in early July 1944, and the main results were reported to the AAF by November 15, 1944, less than five months later. It is almost unnecessary to add that this study demonstrated the effectiveness of attacking a B-29 in a reasonable length of time.\nThe acceptance of Project AC-92 by AMP led to a contract with the Carnegie Institution of Washington, primarily based on the previous experience and accumulated enthusiasm of a staff member from the Mt. Wilson Solar Observatory's war research division. This individual had special experience with various optical devices and procedures, and had recently become well-informed about aerial gunnery. The optical model experiment program at Pasadena was initiated as a result.\nwhich  was  made  available  the  very  unusual  facilities, \nboth  of  personnel  and  of  shop  equipment  and  ex\u00ac \nperience,  of  the  Mt.  Wilson  Solar  Observatory  of  the \nCIW  at  Pasadena,  California. \nWe  will  now  briefly  describe  these  Pasadena  studies \nunder  the  four  headings:  Problem,  Facilities,  Tech\u00ac \nniques,  Results. \nProblem \nTo  analyze  the  intensity  and  distribution  of  fire\u00ac \npower  about  variously  sized  and  designed  squadrons \nof  (B-29)  aircraft,  and \nTo  furnish  a  method  whereby  these  complex  re\u00ac \nlationships  can  be  visualized. \nThe  complexity  of  the  situation  can  be  appreciated \nwhen  one  notes  that  a  single  B-29  has  5  turrets  and \nCONFIDENTIAL \nCOMMENTS  ON  A  GENERAL  THEORY  OF  AIR  WARFARE \n5  sighting  stations,  with  36  independent  arrange\u00ac \nments  of  the  controls  of  the  various  turrets  by  the \nvarious  sighting  stations. \nFacilities \nEmployed  under  the  contract  were  four  senior \nScientific men and six assistants, along with 19 staff members from Mt. Wilson Observatory, were involved in the program. The program was carried out under a local Directive Council headed by the Director of the Mt. Wilson Observatory. The observatory provided shop and other facilities, particularly computational, and rented a large and high gymnasium for the experimental setup.\n\nThe study was based on the idea of creating small (1 to 72 scale) model planes and installing a small light source at each gun and sighting station. These lights were equipped with shields that restricted the field of illumination according to whatever restrictions were necessary.\n\nTechniques 26-28:\nThis study involved creating small (1:72 scale) model planes and installing a light source at each gun and sighting station. The lights were fitted with shields to limit the field of illumination according to the necessary restrictions.\nThere might be on the field of fire of the gun in question, or the field of visibility of the sighting station in question. A switching system permitted the simulation of all possible methods of control of the various guns by the various sights. Since the effectiveness of fire varies roughly with the inverse square of distance, as does the intensity of illumination from a point source, the total intensity of illumination of any point in space was approximately proportional to the total firepower which can be brought to bear at this point.\n\nThus, one constructs a set of models, installs the lights and shields, adjusts individual intensities in a calibrating operation, arranges the models in space to conform to some formation design to be studied, and then determines the intensity and distribution of firepower for various briefing systems by measuring.\nThe corresponding light intensity pattern was monitored by the model squadrons. These squadrons were stationed at the center of a 25-ft radius spherical shell, on the white interior surface where the light intensity pattern could be observed. Eighteen model planes were constructed for use at Pasadena, and twelve more for use in the Marianas.\n\nThe light intensities could be measured point by point using photocells. This method was developed to an accuracy of approximately 1%. One could also photographically record the light intensity pattern over some area and then carry out photometric measurements. Alternatively, one could simply count the lights visible from a certain point, i.e., the guns that could be brought to bear on this point, record distances, and rapidly compute fire-powers. Although this last method does not fully utilize the optical scheme and allows for some inaccuracies, it is a simpler approach.\nResults:\n\nAn exhaustive but preliminary study was made using the system described above for the firepower pattern of a single B-29 with all types of control. Similar studies were conducted for a squadron of 4 planes, for the 11-plane squadron used by the 21st Bomber Command, and for the 12-plane squadron used by the 20th Bomber Command.\n\nIn February 1945, the 20th Air Force held a large conference at Pasadena primarily to observe and consider the results obtained in this study. As a result of this conference, certain changes were recommended in the stacking and briefing of the 12-plane squadron. The modified 12-plane squadron was then thoroughly analyzed by the Mt. Wilson group.\nOne of the project's greatest contributions was providing a method to clearly and convincingly display a complex and subtle pattern of relationships through an optical model. Two officers advocating for different formation patterns could examine the resulting firepower pattern together. The device had important applications for training and in the field, as well as in scientific laboratories. Motion pictures were made, depicting the variation of firepower in formations as they circled around them. The President of the Army Air Forces Board remarked that \"these motion pictures gave the best idea to airmen as to the relative effect of firepower.\"\nA formation yet to be presented. Some of these pictures were flown to the Marianas and viewed by General LeMay and many gunnery officers and men at the front. Additionally, a CONFIDENTIAL mathematical analyses and war model setup were constructed and flown to Guam for use there in analyzing firepower problems.\n\nThe personnel of this project carried out and reported on certain auxiliary studies. For instance, a considerable analysis was made of fighter attacks, numbers 37-39. It was shown that for a wide variety of attacks, all the breakaways pass through a limited region some 20\u00b0 in angular width and some 400 yards off the stern. Studies were also made of the problem of offset guns in fighters, and of the duration of strafing attacks.\nThe author of this chapter cannot resist emphasizing that these studies, though narrower in scope than the \"general\" studies advocated, are excellent examples to show that the information necessary for the general studies can be obtained.\n\n1.8. Mathematical Analyses and War\n\nThe topic of this chapter is \"General Theory of Air Warfare.\" However, it has been a central purpose of this chapter to stress that modern war is essentially and inevitably a combined operation. Thus, it seems not inappropriate to close with some general remarks concerning the contribution that mathematics can make to the broad field of national defense. These remarks will involve some topics which have not been mentioned before in this chapter and should serve to furnish a setting for the general activities that are the special concern of this chapter.\nTo give any adequately complete discussion of the possible contributions of mathematics to war and national defense would require far more space than is available here, and quite other authorship. All that is intended here is to give that minimum description which will serve to indicate the relationship of the general analytical studies of warfare, here urged as vital, to other mathematical activities of military significance.\n\nWe will discuss mathematical activities of military importance under the following headings: Basic, Service, Design and Use of Individual Devices, Operational Analysis, General Theories.\n\nThis list of headings is poor for several reasons. The subheadings are neither exclusive nor self-explanatory, and in some cases they are worse than vague, in that they appear to say something less than or more than intended.\nThe most important point is that all developments of mathematics, from the most abstract concept of the purest mathematics to an isolated item of new technique in applied mathematics, are basic contributions to national technical strength. Engineering, physics, chemistry \u2014 yes, and biology and medicine as well \u2014 use for their central core of quantitative, precise thinking the analytical tools provided for them by the mathematician. In these days of the atomic bomb, one hardly needs to emphasize the close relationship between military might in the field and the abstract pencil theories of the analytical expert. Thus the stimulation and support of the field.\nA whole, especially through fellowship and other training aids, is both an essential and a sure way to provide the mathematical talent required in times of emergency and is also an essential basis to a proper development of other elements of a nation's technical strength.\n\nVolume 1 of the Summary Technical Report of the Applied Mathematics Panel, along with Volume 3 which is devoted to probability and statistics, although primarily concerned with describing some of the intermediary steps in the military utilization of basic mathematics, does thereby indicate some of the classical fields of pure and applied mathematics that connect closely and obviously with military problems. It is intended to include here, under the heading of \u201cBasic,\u201d all such activity. But it is also intended \u2014 and this is the main point \u2014 to include all mathematics research that is related to military applications.\nHere is the whole of mathematics as a vital necessarily element of scientific strength, basic to all developments of the other sciences and technologies, and hence basic to national welfare and national defense.\n\n12.8.2 Service\nThis title is an egregious misnomer, for from one valid point of view, it covers all of mathematics in direct relation to military problems. The mathematician who is trying to make his discipline serve the national need should, in one sense, have nothing but service in mind.\n\nBut one can serve in many ways. Sometimes one can serve best precisely by not doing what the other fellow wants; or by doing something he has never, and would never, think of. And the word service is here used in the restricted and limiting sense of \"doing what the other fellow wants.\" We should\nNot losing sight of the fact, one's major opportunity often lies in gently leading the other fellow to see what he ought to want. A great deal of useful mathematical service can be done on the level of isolated requests. Individuals, military agencies, nonmilitary or government agencies, NDRC groups, or university and commercial laboratories working on national problems may come and say:\n\nPlease evaluate this integral.\nPlease solve this differential equation.\nPlease compute the value of this determinant.\nPlease interpolate, using third order differences, nine values between every two values of this table.\n\nThese requests may arise out of secret projects, and it may therefore be necessary or wise (which, by the way, are not equivalent) to keep the mathematician informed.\nIn the dark about the problem's nature. In such cases, these are items of pure service where the mathematician (provided he can) does precisely what he is asked, and no more. It is easy to see, however, that isolated requests are extremely likely to lead to another and more important grade of service. For if the problem is, for example, not to evaluate a single determinant but rather to evaluate many determinants, then the mathematician may well inquire as to the original formulation of the problem. He may be able to suggest alternative equivalent procedures which lead to simpler expressions, easier to compute. Or he may refer the client to devices which have been constructed for the solution of systems of linear algebraic equations. Or he may even uncover errors in the formulation of the problem which make it invalid.\nUndesirable to do any computing at all.\n\nExample question: Study these two records of firing trials and tell us which gun and fire control system is better, by how much, and how certainly.\n\nThere are likely two stages of service involved. First, the service mathematician should accept the situation, however bad it is, and do the utmost to answer the questions asked. Second, they should point out to the client why the problem was a bad one and how the trial could have been improved. This may well open up to the client the whole field of statistical design of experiments, and the second stage of service may well be of indefinitely greater significance than the answer to the original problem.\n\nA great many groups and agencies and establishments.\nRecognizing the value of mathematical services, institutions obtained locally available service mathematicians. The AMP, in addition to the service it prepared to furnish through the personnel of contractual groups in New York, Princeton, Providence, Chicago, Cambridge, etc., also farmed out individual mathematicians to various groups on short- or long-term loans. One of the conspicuously successful ventures involved the placement of an AMP mathematician with the Army Air Forces Board at Orlando, where he served for over twenty months as a mathematical consultant. The result of this experience, he has written a set of comments and recommendations which seem so important that they are included, at the end of this chapter, as an appendix.\nA consultant's views are reproduced below, and it is relevant to note that his services were highly appreciated. Brigadier General E. L. Eubank, President of the AAF Board, commended him with a special letter for his \"splendid record of mathematical assistance to the Army Air Forces Board\" and his \"active engagement in various projects\" that significantly contributed to the successful completion of the following: he was a major contributor to the selection process for projects that were widely recognized for their measurable impact on the war effort and its successful termination.\n\n12.8.3 Design and Use of Individual Devices\nA large fraction of the mathematical work in this war has related to the design and use of individual devices.\nDevices \u2014 antiaircraft gun directors, tracking mechanisms, bombsights, proximity fuses, radar sets, plane-to-plane gunsights and sighting systems, rocket sights, guided missiles, torpedo sights, etc. This is essentially how AMP entered the field of sequential analysis as applied to acceptance testing, quality control, etc.\n\nConnection with such activities, there are several very important types of questions to consider:\n\n1. What performance is this device capable of when operated perfectly?\n2. What performance is this device capable of when operated by a random untrained soldier, by a selected untrained soldier, by a selected trained soldier?\n3. What is the optimum selection and training process? (This involves close collaboration with psychologists and physiologists.)\n4. What modifications in design would improve performance?\nThese questions refer to a device not available for actual testing. They involve studies that should be made in time to influence design. The first question, in a strict sense, refers to what is known as a micro-problem. The character of the request is such that an analyst could be handed essentially nothing more than a complete design description and be locked in an otherwise empty room.\n\nQuestion 1: What is the impact on theoretically possible performance with the type of operating personnel likely to be available in the field?\n\nQuestion 2: What does this device aim to accomplish, and to what extent does it do so (an analysis of the problem the device is supposed to meet, rather than the device itself)?\nBy the time one reaches the fifth question, it is clear that he has left behind the field of micro-problems, where one can study one isolated problem without reference to a whole large set of practical considerations, and has entered the field of macro-problems. The fourth and fifth questions are bound to involve tactical considerations, and may involve strategic considerations.\n\nIf one supposes that operable examples of the device exist, a new set of problems enters \u2014 those of testing. One should consider bench testing, both of components and of whole devices; use testing under controlled conditions which to a lesser or greater extent attempt to reproduce actual field or combat conditions; and extended field trials, which are carried out on a small scale but under field conditions.\nThe great advances in combat trials included recognition by military authorities of the necessity for quantitative testing under controlled conditions, with analytical (often statistical) assistance in planning and interpreting the tests. The author was present at some demonstrations of military equipment several years ago, which were inadequate for controlled scientific testing and should not have been a basis for acceptance or rejection. The advances in objective, quantitative, and controlled testing were crucial.\nThe testing of fire control equipment, such as dynamic testers and computers for antiaircraft artillery and great testing engines for plane-to-plane fire control, have been significant and irreversible contributions to this field, carried out by Division 7 of the NDRC. The development of camera testing procedures and the design and assessment of firing test procedures for flexible aircraft gunnery, analysis of frangible bullet trials, and numerous other studies and developments were aided by AMP and are covered in Part I of this volume. One important practical result of analyzing device performance, studying device purpose, and testing devices includes:\n\n(No additional text provided)\nThe emergence of a rational basis is necessary for setting military requirements and production specifications for manufacturers. Military boards have in the past issued requirements that come dangerously close to demanding a device of perfect accuracy, simplicity, and reliability, small in dimensions and light in weight, requiring no skill from the operator, and producible from non-critical materials in very little time. These questions of device analysis and specifications often seem to be based not on rational requirements, but rather on the assumption that the manufacturer is having too easy a time if a reasonable fraction of their output passes.\n[Confidential Comments on a General Theory of Air Warfare: Interrelation of Testing, Military Requirements, and Field Trials\n\nThe military group involved permits the requisite interlocking of activities for sensible progress in the following areas: testing, military requirements, and field trials. Dr. Edward L. Bowles, Expert Consultant to the Secretary of War and Special Consultant to the Commanding General, Army Air Forces, requested a memo from the author regarding the development of assessment facilities for air gunnery in the Army Air Forces. Due to its direct bearing on the mentioned issues, this document is reproduced as Appendix B of this chapter. It is gratifying to note that when Dr. Bowles issued it on April 12, ]\n1945: A letter to the man newly appointed with advisory duties in the Secretary of War's office, specifically in the field of aerial gunnery. The letter outlined the War Department's plans for establishing an assessment agency. The remainder of the pattern was to be completed based on the memorandum provided by AMP, found in Appendix B of this chapter.\n\n12.8.4 Operational Analysis:\nThis activity has been mentioned earlier in this chapter, and I cannot provide a detailed description or critique here as it falls outside my purpose and competence. However, it is essential to include operational analysis as a major component of important ways mathematics is utilized.\nMatrics contributes to the war effort. Operational Research Sections, working in various theaters of war, focus on questions such as:\n\n1. How effectively are we using a certain device?\n2. How can we use it more effectively?\n3. What minor modifications (including field) would increase its effectiveness?\n4. What devices do we need that we don't have?\n5. What are the causes of our successes and failures?\n6. What results are we getting against the enemy?\n7. What should we do on the next mission?\n\nExamples:\na. Will our wings slice through barrage balloon cables without amputation if we attack on the deck?\nb. What rule of thumb should waist gunners use if they encounter jet fighters?\nc. How many bombs should we drop to achieve a probability of 0.95 of destroying a target?\n\nThe success of such groups depends on these considerations.\nThe text essentially evaluates three factors for the effectiveness of research teams: (1) the personal characteristics of members, including their ability to meet field conditions, unselfish service attitude, willingness to tolerate limitations, and capacity to get along with military command and operating personnel; (2) the spread and excellence of scientific techniques they can provide (first-rate mathematicians, statisticians, physicists, engineers, psychologists, physiologists, etc.); and (3) the outstanding excellence of their technical leadership. Additionally, they cannot work to full advantage without backing from a central home agency that correlates and compares their findings, points out duplications of effort and weak points in the program of certain groups, and conducts more basic and long-term studies.\nThis topic, like the preceding one, has been included here primarily to ensure the completeness of the present list. Since this chapter has been chiefly concerned with indicating the nature and scope of broad theories of air warfare, or warfare in general, it does not seem appropriate or necessary to repeat any description or argument here. It is however hoped that the more detailed comments of the present section on \"Mathematical Analyses and War\" will serve to indicate that the general studies - the general plan for the structure of defense and war - have available as necessary building bricks a vast number of dependable and essential individual or micro-studies.\n\n12.8.6 Additional Comments\nAlthough we have now concluded the remarks forecast in the outline at the beginning of this section,\nEvery field of mathematics, including the most abstract and erudite, has important contributions to make. It would seem unnecessary and perhaps unfortunate to single out a special field for comment. However, a great many mathematicians, especially some so-called pure mathematicians, have in the past been relatively uninterested in the subject of mathematical statistics. Yet, mathematical statistics has proved to be an exceedingly powerful and useful tool in connection with many war problems. Of the three volumes of final reports of AMP, one is devoted directly and exclusively to statistics, while the present volume leans heavily on that subject. If AMP had done nothing else, these applications would justify its existence.\nAll except what it did in applying mathematical statistics, its budget would have been justified many times. One particular application, for example, would have resulted in money savings if the war had continued until the end of 1945 at a rate in excess of one million dollars a month. This money saving was less important than the fact that the improved method could produce, at the fighting fronts, more and certainly a more acceptable quality of ammunition.\n\nThere is one further postscript remark. We have known of instances in which our military leaders were skeptical or even contemptuous of the importance of certain weapons or techniques \u2014 until we learned something about them the hard way, from the enemy. And then we suddenly accepted their wisdom.\nThe leading aeroballistician of Germany, after the war, remarked that statistical studies could be used to determine efficiency factors for battles between formations, allowing for the measurement of the worth of armament and fire control. He described their studies on fighter vulnerability, pursuit and non-pursuit attacks on bombers, combat film analysis, etc., stating that the basic purposes were to analyze air warfare and lay objective foundations for theoretical studies of tactico-technical questions.\n\nTo illustrate the sometimes immense delays before an essential idea is absorbed into military practice, this enemy expert mentioned.\nThe idea of using gun cameras for obtaining quantitative data on aerial gunnery was proposed in Germany during the Spanish War (1936/7), but turned down by the Service. The first film strip of a Spitfire kill was assessed in November 1940. The first lecture on this subject was given before the General Staff of the GAF seven months later, in April 1943. Gunnery assessment was recognized by military units sometime in 1944. A central efficient assessment bureau was finally set up about seven years after the idea was first proposed, on October 1, 1944. I am glad to make this point without the necessity of using local data. Our record, in the decadent and non-military sector.\n[Dr. S. S. Cairns' comments based on his experiences as a mathematical consultant to the Army Air Forces Board, Orlando:\n\nThe following comments are based on over twenty months' experience with the Army Air Forces Board, Orlando, Florida, as a mathematical consultant. I served in this capacity from February 1944 through October 1945, as a member of the Statistical Research Group \u2013 Princeton, under the direction of the Applied Mathematics Panel of the NDRC. These comments are offered in the hope that they may prove useful in connection with any future plans for similar consulting services, especially on the part of military organizations, during peace or war.]\nA great need existed at the Board for the services of a general mathematical consultant. This need, which will presumably continue during peacetime, arises from the fact that the Board is charged with testing and reporting on new equipment, methods of employment, and tactical questions, with a view to developing official Army Air Forces policies. These duties of the Board call for a combination of personnel having combat experience and those having sufficient scientific training. During wartime, up-to-date combat experience can be provided by a system of assignments of officers fresh from overseas duties. This was adequately accomplished at the Board, though the officers assigned there were not systematically selected on the basis of any peculiar fitness for the work of the Board. The empirical knowledge provided by active military service.\nIce requires experienced, scientifically trained personnel to be supplemented. There was a serious shortage of such personnel at the Board. It's worth noting that there was no widespread appreciation of this lack or the potentialities of analytic methods applied to many of the Board's problems.\n\nThe writer's position as consultant was not formally established. In the future, it would be well if, in the formal statements defining the Board (or any similar agency), specific provision were made for a mathematical consultant, with a definition of his duties, privileges, and status. The following suggestions are based on the writer's experiences in Orlando, where these questions were settled, more or less satisfactorily, by an evolutionary process. Many of the suggestions are afterthoughts.\n1. A consultant should be a civilian to be free from military protocol and associate freely with officers and enlisted men of all ranks and grades. He should recognize the authority of the commanding officer of the post to which he is assigned.\n2. The privileges of a consultant to the Board should include the opportunity to comment on all official projects, not just those regarding which he is formally appointed.\nA project officer's lack of recognition or appreciation for technical assistance is a common issue. Several Board projects, executed before and during the writer's tenure, could have benefited from mathematical assistance. In some cases, advice was solicited too late, after inappropriate tests had been designed and conducted. Consultation on test design is particularly crucial.\n\nThe Board consultant should participate in staff meetings where projects are discussed. They should submit new project suggestions when deemed fitting. The writer attended a few staff meetings only when required.\nA consultant was specifically requested in connection with a particular project where he was officially providing assistance. He was always free to suggest ideas through any officers on the Board or directly to the President of the Board.\n\nFourthly, a reliable system should be established to ensure all circulating documents of potential interest to the consultant reached his desk. The responsibility of filling out routing slips at the Board often fell on individuals with limited notions of the consultant's broad interests, resulting in many important documents either not reaching him or only coming to his attention by chance.\n\nThe value of a consultant to the Board would be enhanced by the services of an assistant capable of handling routine matters involving straightforward computations.\nConsultations on trigonometry and related matters were required. A consultant received consideration in all aspects, including secretarial services, office supplies, official mailing privileges, and other necessities. A technical consultant should have his own office with an appropriate label. The writer became associated with the Armament Division in the minds of most officers at the Board, leading some from other divisions to believe they were borrowing his services when they consulted him. This situation arose partly because the writer shared an office with members of the Armament Division and partly because Colonel V. C. Huffsmith, Chief of that division, was the quickest to appreciate and utilize his services.\nThe consultant had certain advantages in this situation, as he was able to secure Colonel Huff-smith's advice and backing in assigning his own priorities to different tasks - a very ticklish problem when several projects required urgent attention. If the recommendations in this memorandum were followed, a mathematical consultant to the Board would be greatly overburdened during wartime, unless he was in a position (as was the writer) to refer problems promptly to such agencies as the various AMP groups.\n\nIt should be understood in advance that a technical consultant is entitled to military orders when traveling on the business of the agency to which he is assigned. The writer succeeded in making arrangements for the regular use of such orders, authorizing travel by government aircraft.\nA consultant at the Board should be given priority for crafting and granting contracts on commercial aircraft after serving approximately a year in the position. In general, an arrangement should be made for a consultant to be assured, wherever they went, of all appropriate rights and privileges of a field grade officer. These include assignments to sleeping quarters, Officers\u2019 Club privileges, eating in officers\u2019 messes, and so on. The writer received such considerations after a reasonable period of \"breaking the ice,\" but they should be recognized as prerogatives rather than personal courtesies. During wartime, a consultant to the Board could occasionally benefit from visits to active theaters. Such visits would necessitate the availability of more than one consultant to ensure duties did not suffer.\nThis memo has been written in response to a request from Dr. E. L. Bowles for suggestions concerning the organization, program, and staff of an aerial gunnery research unit at Eglin Field. However, when attempting to analyze this individual situation, one becomes inescapably involved in the broader problem of how the AAF as a whole provides for the development of new devices and techniques of aerial warfare. The following is an analysis of the broad problem.\n\n1.1. Scope of Memo\n1.1.1. This memo is a response to Dr. E. L. Bowles' request for suggestions regarding the organization, program, and staff of an aerial gunnery research unit at Eglin Field.\n1.1.2. However, the discussion will expand to address the broader problem of how the AAF as a whole develops new devices and techniques of aerial warfare.\n\nThe AAF's approach to the development of new aerial warfare devices and techniques can be analyzed through the lens of its organizational structure, programs, and staffing.\n\nOrganization:\nThe AAF's organizational structure for aerial warfare research and development is fragmented and lacks a centralized authority. This fragmentation can lead to duplication of effort, inconsistent research priorities, and inefficient use of resources.\n\nPrograms:\nThe AAF's approach to funding and managing research and development programs is reactive rather than proactive. The AAF tends to focus on developing technologies in response to specific threats or challenges, rather than investing in long-term research and development.\n\nStaffing:\nThe AAF's staffing policies for aerial warfare research and development are inadequate. The AAF lacks a sufficient number of highly skilled scientists, engineers, and technicians to conduct cutting-edge research and development.\n\nTo address these issues, the AAF should consider establishing a centralized research and development organization with the authority to coordinate and prioritize research efforts across the various components of the AAF. This organization should be responsible for funding and managing long-term research and development programs, as well as ensuring that the AAF has a sufficient number of highly skilled personnel to conduct this research.\n\nAdditionally, the AAF should consider implementing a more proactive approach to research and development, focusing on anticipating future threats and challenges and investing in research and development to address these threats before they become critical.\n\nIn conclusion, the organization, program, and staffing of an aerial gunnery research unit at Eglin Field cannot be analyzed in isolation from the broader problem of how the AAF as a whole provides for the development of new devices and techniques of aerial warfare. To effectively address this problem, the AAF must establish a centralized research and development organization, fund and manage long-term research and development programs, and adopt a more proactive approach to research and development.\nThe functional relation between the steps involved in plane-to-plane control problems is outlined in Section 5. This relation is depicted in Figure 1's flow chart, which shows the main sequence of steps leading to the genesis and solution of equipment problems in plane-to-plane fire control. The diagram illustrates how military problems originate from combat needs and progress through a series of steps culminating in new combat-ready equipment. Air Warfare Analysis (AWA) plays a central role in this process and should exercise a central, correlating function in reality. The AWA group should develop:\n\na. A comprehensive understanding of the quantitative theory of tactical and strategic problems in air warfare.\na. Knowledge of the analytical theory of aircraft fire control equipment (sights, sighting mechanisms, bombsights, rocket sights, turret controls, etc.).\nb. Knowledge of the theory (probability and statistics) of obtaining hits in aerial gunnery and of the procedures for estimating the effectiveness of such hits (vulnerability theory).\nc. Knowledge of the psychological-physiological aspects of man-machine combinations in aerial gunnery (tracking, training, etc.).\nd. Correlated knowledge of all ORS activities. The AWA group should serve as a central group which unifies the activities of the separate Operation Research Sections; and should carry out comparative analyses of their separate findings.\ne. In addition to this large body of scientific and technical knowledge, the AWA group should also have mastery over all related subjects.\nThe subject matter: this is a copy of the original memorandum. An understanding of the practical problems involved in the introduction of new equipment (logistics, spare parts and maintenance service, training, etc.). The purpose of AWA should be to provide the Chief of Air Staff with expert scientific advice on the employment of air power; to maintain current information on the aerial gunnery fire control devices.\n\nThis chart is for aerial gunnery developments. A closely similar chart exists for other types of items required in aerial warfare (rockets, guided missiles, bombs, etc.). The AWA group should occupy the same position in all such charts.\n\nThere is no intention to imply that at present, when AWA does not exist, there are no useful liaison cross-connections.\nThe main functions in the outside circle; neither would all liaison cross-connections necessarily function through AWA if this group existed. Investigating the mathematical principles underlying aerial warfare, including tactics and techniques of aerial gunnery, aerial bombing, etc., and reducing those principles to a form assisting the staff of a combat air force in its planning of operations.\n\nA. To assist the Chief of Air Staff:\na. Developing a scientific and quantitative basis for the operation of combat aircraft.\nConfidential\n\nAppendix B\nb. Determining the relative desirability of:\n(1) different categories and types of combat aircraft,\n(2) different equipment for a given combat aircraft,\n(3) different methods of operating combat aircraft.\nBy using so much of this scientific and quantitative data.\nThe quantitative basis for making determinations has been developed. This includes:\n\n1. Military characteristics of future military aircraft.\n2. Changes in characteristics of present aircraft.\n3. Changes in training.\n4. Changes in operational use of aircraft.\n\nTo determine which tests and studies are necessary to accomplish these goals and to recommend where they should be carried out.\n\nTo study the basic problems of bombardment aviation and analyze the results of tests and studies conducted elsewhere.\n\nTo conduct the required tests and studies as directed by the Chief of Air Staff.\n\nThe diagram acknowledges a distinction between Proof Testing and Assessment of Performance, yet emphasizes their close relationship. The primary function of Proof Testing is to determine:\n\n1. The ability of an aircraft to withstand the stresses and loads it will encounter in service.\n2. The safety of the aircraft and its crew under various conditions.\n3. The reliability of the aircraft's components and systems.\n\nAssessment of Performance, on the other hand, focuses on evaluating the aircraft's performance against specified requirements and expectations. Both Proof Testing and Assessment of Performance are essential for ensuring the effectiveness and safety of military aircraft.\nThe equipment's operability under service conditions is assumed to ensure performance, with performance measured and interpreted through quantitative tests as the primary function of Assessment. Two-way communication via the AWA group between Training, Assessment, and Combat must be actively maintained. The administrative organization, as depicted in the discussed flow chart, needs to be structured to facilitate prompt interchanges and currents of flow. Examining the diagram will indicate some requirements.\n\n2.4. The importance of maintaining two-way communication, via the AWA group, between Training, Assessment, and Combat cannot be overstated.\n\nThe administrative setup, as shown in the aforementioned flow chart, fails to account for command functions and practical problems of cognizance. However, for the administrative organization to serve effectively, it must enable prompt interchanges and currents of flow as depicted in the diagram.\nThe chief comments regarding the weaknesses of the present situation are as follows:\n\n3.1. The central correlating Automatic Weapons Advisory (AWA) group does not exist within the current structure of the Army Air Forces.\n3.2. The Development function is primarily fulfilled by commercial groups operating under contract at Wright Field. Their links with other functions in the diagrams are weak.\n3.3. The Assessment function cannot be carried out properly unless a Gunnery Research Unit (GRU) is established and adequately supported. A suitable nucleus for such a unit exists at Eglin.\n3.4. The research aspects of the Training function seem to be well provided for at Laredo.\n3.5. The Proof Testing function appears to be well provided for at Eglin.\n3.6. The problem of cognizances is a serious one and does not appear to be adequately solved at present.\nThe functions listed on the chart come under M and S, others under 0 C and R; and the inter-relations are not clear, nor do they always appear well defined. The Assessment function cannot be carried out and utilized effectively without tactical and strategic considerations allowed to enter. This means one of two things: either the Gunnery Research Unit at Eglin must itself be permitted to cut across preconceived command functions, or these broader relationships must be assumed by some other group, working at a higher echelon. The Chart assumes the second of these two solutions. That is, it assumes that the AWA group would cut across command functions and would appear on the AAF organization chart at the same level as Management Control. A close tie-up between Air Warfare Analysis and the Gunnery Research Unit would then ensue.\nRecommendations: 4.1. An Air Warfare Analysis Section should be set up, located in Washington, reporting at the same level as Management Control. Detailed suggestions for staff and program can be provided if desired. 4.2. Expand and organize the existing gunnery research at Eglin Field into a Gunnery Research Unit, detailed in section 5.\n\nGunnery Research Unit: 5.1. Function and Program. The primary function of this unit should be to conduct ground and air tests of aerial gunnery equipment and devices, resulting in reliable quantitative measures of performance, and to carry out analyses.\nThese performance data are essential for assessing this performance in practical terms, such as hits on enemy aircraft and probable number of enemy planes destroyed, etc. It is recognized that, in order to perform this function, GRU must maintain a program of fundamental research and development, both in analytical methods and in the instrumental aspects of testing. The Gunnery Research Unit, occupying as it does a position just in advance of production, should provide the quantitative and objective evidence upon which the Command can make correct decisions.\n\n5.2. Staff and Materiel.\n\nIt is clear that any estimates of staff and materiel will be subject to frequent modification. The following outline, although made on a unit basis, is subject to the likelihood of frequent changes. There are five units:\nThe military administration, confidential, Appended below: flight test section, bench test section, and experimental squadron (pretest). a. Military Administration: The size of the staff required here is a military decision. The function of the military administration is to provide housekeeping and administrative services for the civilian and officer scientific and technical personnel. b. Planning and Analysis Section: This group would be responsible for the planning, direction, and analysis of all the projects of the Gunnery Research Unit. Required personnel and qualifications: 1 Director 1 Associate Director 2 Fire Control Statisticians 2 Aerial Gunnery Mathematicians 2 Instrument Engineers 1 Aerodynamical Engineer 1 Radar Engineer 1 Psychologist-Physiologist 4 Project Technical Representatives 4 Computers Secretaries, Stenographers, Clerks, etc.\nThis includes the Flight Test Section: director, pilots, aircraft, cameras, gunners, engineers, computers, photographers, and shop facilities.\n\nThis includes the Bench Test Section:\n1. \"Texas Engine\" with maintenance crew and shop facilities.\n2. Experimenters: at least one trained in Physics, at least one trained in Psychology, at least one trained in Statistics. Experience in fire control of Armament work, understanding of statistical principles, ability to plan and direct broad programs of research. At least one with experience in hit-probability work, at least one with experience in experimental design. At least one with experience on lead computing sights, at least one with experience in ballistics. One with mechanical background, the other with electrical background. Attack curve theory \u2014 aerodynamic limitations on maneuverability, etc. Understanding of the scientific principles involved.\ntechniques used in gunnery research, ability to direct projects to obtain the right data.\n3. Clerks (4-6)\n4-6 Gunners.\ne. Experimental Squadron (Pretest).\nThis unit would be concerned with preliminary tests of suggestions, gunnery equipment and gunnery tactics. It should include:\n2 heavy bombers (B-17 or -24 and B-29),\n2 medium bombers (B-25 or -26 and A-26),\n4-6 fighters (P-40, P-47, P-51 and P-61, possibly a P-80A and a \u201cpiggyback\u201d P-38 or P-63).\nAir crews:\n(1) recent combat experience,\n(2) a willingness and liking for experiment, and\n(3) technical background and belief in gunnery research.\nGround crews.\nIntermediate shop facilities.\nAdequate photographic equipment.\nThe members of these aircrews should be slowly rotated as adequately qualified personnel become available after combat tours of duty.\n5.3. Comments.\nThe GRU should be given the broad responsibility for developing and carrying out a basic program in aerial gunnery research. It must be given the authority to plan and develop this program. Although the unit would of course be expected to carry out necessary tests, it must be protected from the necessity of accepting every directive that anyone can think up. This is an essential point. What is needed here is an establishment carrying on a real scientific program, not a mail-order or telephone service station. The Unit should be assigned broad problems and fields of activities; but should not be required to accept, from non-scientific sources, directives on specific jobs. The organization and program must be maintained sufficiently flexible to meet new conditions as they inevitably arise. The Unit should be an independent Branch of the [military or research organization, depending on context]\nProving Ground Command should not be subordinate to any other Branch.\n\nd. Office personnel should remain with this Unit for extended assignments. Recognition for this type of service should be given.\n\ne. Compensation and status must be available for civilian scientists and engineers to attract and hold men of high caliber. This requires status and privileges equivalent to those enjoyed by officers.\n\nf. The Unit must have close liaison with the policy and decision levels of the AAF (preferably through such an organization as AW A).\n\nCONFIDENTIAL\n\nBIBLIOGRAPHY\nNumbers such as AMP-502.1-M5 indicate that the document listed has been microfilmed and that its title appears in the microfilm index printed in a separate volume. For access to the index volume and to the microfilm, consult.\nThe Army or Navy agency listed on the reverse of the half-title page.\n\nSummary:\n1. \"Sequential Tests of Statistical Hypotheses,\" Abraham Wald, The Annals of Mathematical Statistics, Vol. XVI, prepared for AMP, Part I, Chapters 1-8. In references 53-116, the Study number is the AMP Study number and the Paper number is the contractor's Paper number.\n2. AMP Reports, Memorandums, and Notes\nAMP Study 44: Training in Aerial Free Gunnery\n- Mathematical Evaluation of Sighting Methods Used in American Free Gunnery Training, Churchill Eisenhart, OEMsr-1007, Memorandum 44.1M, AMG-C, Sep-\nAMP Study 55: Lead Computing Sights\n- An Introduction to the Analytical Principles of Lead\nComputing  Sights,  Saunders  MacLane,  OSRD  4037, \nOEMsr-1007,  Memorandum  55. 1M,  AMG-C,  April \nAMP  Study  57 :  Lead  Computing  Sights  \u2014  Nose \nAttacks \n3.  Errors  Made  by  a  Lead  Computing  Sight  When  the  Target \nFollows  a  Pursuit  Course,  Walter  Leighton,  OSRD  3062, \nOEMsr-1007,  Report  57. 1R,  AMG-C,  December  1943. \n4.  A  Study  of  the  Effect  of  Relative  Wind  and  Gravity  Upon \na  Caliber  .50  Bullet  in  Relation  to  the  Behavior  of  a  Lead- \nComputing  Sight,  Walter  Leighton,  OSRD  3373, \nOEMsr-1007,  Report  57.2R,  AMG-C,  March  1944. \n5.  On  Errors  Made  by  a  Lead-Computing  Sight  with  Special \nReference  to  Head-On  Attacks,  Walter  Leighton,  OEMsr- \n1007,  Memorandum  57. 1M,  AMG-C,  October  1943. \n6.  A  Note  on  Lateral  and  Vertical  Deflections  for  a  Caliber  .50 \nProjectile  in  Plane-to-Plane  Fire,  Walter  Leighton, \nOEMsr-1007,  Memorandum  57. 2M,  AMG-C,  February \n7.  Addendum  to  AMP  Report  57.1  R.  Errors  Made  by  a \n8. Pursuit Courses - Walter Leighton, OEMsr-1007, Memorandum 57.3M, AMG-C, March 1944.\n9. Solution of the Differential Equation: -a (d/dt) + (1 /u)r = da/dt - Walter Leighton, OEMsr-1007, Memorandum.\n10. Fighter Attacks at Low Rates of Closure - Revision of AMP Memorandum 57.6M, Walter Leighton and Charles Nichols, OEMsr-1379, Memorandum 57.7M, AMG-N.\n11. AMP Study 85: Study of Fuze Dead-Time Corrections in AA Director - F. J. Murray and Arthur Sard, OSRD 4057, OEMsr-1007, Report 85.1R, AMG-C.\n12. The Prediction of Fuze Setting - F. J. Murray and Arthur Sard, OEMsr-1007, Memorandum 85.1M, AMG-C, October [AMP Study 103: AAF Training Program].\n13. Some Uses of Variable Speed Mechanisms in Fire Control - Magnus R. Hestenes, OEMsr-1007, Memorandum.\n1. An Analytic Study of the Performance of Airborne Gun-sights, Donald P. Ling, OSRD 5318, OEMsr-1007, Report 104.2\n2. Deflection Formulas for Airborne Fire Control, Magnus R. Hestenes, OSRD 6270, OEMsr-1007, Report 104.2R, AMG-C\n3. Chap. II, Magnus R. Hestenes, OSRD 6270, OEMsr-1007, Report 104.2R, AMG-C\n4. Chap. III, Magnus R. Hestenes, OSRD 6270, OEMsr-1007, Report 104.2R, AMG-C\n5. Chap. IV, Magnus R. Hestenes, OSRD 6270, OEMsr-1007, Report 104.2R, AMG-C\n6. Chap. V, Magnus R. Hestenes, OSRD 6270, OEMsr-1007, Report 104.2R, AMG-C\n7. The Theory of an Electromagnetically Controlled Hooke\u2019s Joint Gyroscope, Donald P. Ling, OSRD 6228, OEMsr-\n8. Aerial Gunnery and Gyro Sights: A Manual for Gunners, Donald P. Ling, OSRD 6284, OEMsr-1007, Report 104.5R, AMG-C\n9. The Optical System of the Mark 18 (K-15) Gyro Gunsight, with an Appendix of the Tracing of Rays Through a Thick Lens or System of Lenses, L. Charles Hutchinson, OSRD 6283, OEMsr-1007, Report 104.5R.\n19. Simple Formulas to Fit the Values Tabulated in the Firing Tables FT: 0.50 AC-M-1, George Piranian, OEMsr-1007,\n20. Ballistic Formulas, Alex E. S. Green, Memorandum 104.2M, Research Division, U. S. Army, Army Air Forces Instructors\u2019 School, published by AMP, NDRC,\n21. Bias Errors of the K-Sand K-12 Sights, Irving Kaplansky and Mae Reiner, OEMsr-1007, Memorandum 104.3M,\n21a. Ibid., p. d of Summary.\n21b. Ibid., Appendix V.\n22. The Combination of a Random and a Systematic Error, Arthur Sard, OEMsr-1007, Memorandum 104.4M, AMG-C, September 1945. AMP-502. 141-M9,\n23. A Proposed Vector-Rate Sight for Airborne Fire Control, Magnus R. Hestenes, OSRD 6274, OEMsr-1007, Memorandum 104.5M, AMG-C, October 1945.\n24. Aerodynamic Pursuit Curves for Overhead Attacks, George H. Handelman and W. Prager, OSRD 4019.\n25. Aerodynamic Lead Pursuit Curves for Overhead Attacks, George H. Handelman, OSRD 6383, OEMsr-1066, Memorandum 106.1M, AMG-B, AMP Study 107: Determination of the Orientation of an Airplane\n26. The Aerodynamic Pursuit Curve, M. M. Day and W., Prager, OEMsr-1066, Memorandum 106.1M, AMG-B, AMP-503-M3\n27. The Stereographic Spherimeter, L. Charles Hutchinson and John H. Lewis, OEMsr-1007, Memorandum 107.1M, AMG-C, January 1945\n28. Correction for Roll, Pitch and Yaw with the Spherimeter, L. Charles Hutchinson and John H. Lewis, OEMsr-1007, Memorandum 107.2M, AMG-C, February 1945\n29. AMP Study 119: Use of Vector Sights in Plane-to-Plane Combat, Gustav A. Hedlund, OSRD 4440, OEMsr-1007, Report 119.1R, AMG-C\n30. Optimum Methods of Using Compensating Sights, Dan Zelinsky, OEMsr-1007, Report 119.2R, AMG-C\n31. Average Percentages of Own Speed Deflection, Dan Zelinsky and M. J. Lewis, OEMsr-1007, Memorandum\n32. Position Firing Rules for the A-26, Dan Zelinsky, OEMsr-1007, Memorandum 119.2M, AMG-C, March\n33. AMP Study 130: Collaboration with Radiation Laboratory on Aerial Gunnery Problems\n34. Ballistic Calibrations of Radar Range Aids to Airborne Cannon Fire, R. M. Thrall and George W. Mackey, AMP Study 142: Analytical Assistance to Project 14, Northwestern University (Section 7.2)\n35. Camera Evaluation of Bomber Gun Sights, A. A. Albert, OSRD 5441, OEMsr-1379, Report 142.1R, AMG-N, AMP Study 143: General Electric Fire Control\n36. General Principles of the General Electric CFC Computer: Models 2CH1C1 and 2CH1D1, Magnus R. Hestenes, Daniel C. Lewis, and F. J. Murray, OSRD 5662, OEMsr-1007, Memo 143.1M, AMG-C, September 1945.\n37. Gyroscopes of the General Electric CFC Computer\nB-29 Airplane: The Axis Converter and the Potentiometer Resolver in the General Electric B-29 Computer (OSRD 5663, OEMsr-1007) - Hestenes, Lewis, Murray\nB-29 Airplane: Optimum Dispersion for the Mark 23 (OSRD 5664, OEMsr-1007, Memo 143.3M, AMG-C)\nAMP Study 145: Optimum Gun Dispersion for the Mark 23 Fighter Gunsight (Wallace Givens, OEMsr-1379, Report 145.1R, AMG-N)\nAMP Study 153: Computation of Aerodynamic Pursuit Courses (Leon W. Cohen, OSRD 5423, OEMsr-1007, Report 153.1R, AMG-C)\nEquations for Aerodynamic Lead Pursuit Courses (Leon W. Cohen, OSRD 5423, OEMsr-1007, Report 153.2R, AMG-C)\nAMP-503.7-M12: Appendix II, AMP Study 153\nAppendix I, OSRD 5423, Report 153.2R\nAppendix II, OSRD 5423, Report 153.2R\nAerodynamic Lead Pursuit Courses (Leon W. Cohen, OSRD 5382, OEMsr-1007, Report 153.2R, AMG-C)\nAMP Study 155: Calibration of the Mark 23 (Leon W. Cohen, OSRD 5382, OEMsr-1007, Report 155)\n41. Time of Flight Setting of a Lead Computing Sight: Irving Kaplansky, OEMsr-1007, Memo 155.1M, AMG-C, AMP Study 157: Topics in Aerial Gunnery\n42. Offset Guns, Fighter Attack Against Bombers: Walter Leighton and Charles Nichols, OSRD 6210, OEMsr-\n43. Simple Rules for Support Fire with a Vector Sight, Level and Related Attacks: Charles Nichols, OEMsr-1379,\n44. On Apparent Speed Firing: Charles Nichols, OEMsr-late date of this paper is accounted for by recent Service return to the idea). AM P-503. 4-M\nMinutes of the Meeting of Joint Army-Navy NDRC Airborne Fire Control Committee for June 13, 1945: Saunders MacLane, July 18, 1945.\nAMP Study 160: Assessment of Fighter Sights\n45. Camera Assessment of Fighter Plane Gunsights: H. L. Garabedian, OSRD 6206, OEMsr-1379, Report 160.1R,\nAMP Study 166: Study of Data Accumulated in Sight Evaluation Tests.\n46. Results of a Recomputation of Sight Evaluation Test Data\nWallace Givens, OEMsr-1379, Memo 166, AMG-N, \"Airborne Tracking and Ranging Errors\" by Arthur Sard, OEMsr-1007, Memo 166.2M, AMG-C, October 1945.\n47. Airborne Tracking and Ranging Errors\nArthur Sard, OEMsr-1007, Memorandum 166.1M, AMG-C, \"AMP Study 167: Frangible Bullets\"\n48. Frangible Bullets and Aerial Gunnery\nGustav A. Hedlund, OEMsr-1007, Memorandum 167.1M, AMG-C, \"AMP Study 186: Harmonization Studies for the B-29\"\nSeptember 1944 to April 1945, Philip Kissam, OSRD 5242, OEMsr-1365, Service Project AC-92, Report 186.1R, AMG-P,\n49. Harmonization Studies for the B-29 Airplane\n50. Optimum Dispersion for Nose Turrets of a B-29\nArthur Sard and R. L. Swain, OEMsr-1007, Memorandum AMP Study 191: Camera Assessment of Airplane Skid\n51. Measurement of Angle of Attack and Skid in Rocket Fire\nProblems H. L. Garabedian, OSRD 6203, OEMsr-1379, Report 191.1R, AMG-N, October 1945.\n\nMISCELLANEOUS AMP REPORTS\n\n52. Notes on Parameters of Probability Distributions, OSRD 4045, AMP Note 13, with the assistance of Columbia University and Princeton University, June 1944.\n53. Tracking and the Fire Control Problem, Hassler Whitney, OSRD 5680, OEMsr-1007, AMP Note 21, AMG-C, September 1945. AMP-703.4-M12\n54. A Manual for the Use of Gnomonic Charts, A. A. Albert, OEMsr-1379, AMP Note 23, AMG-N, October 1945.\n55. Scatter Bombing of a Circular Target, H. H. Germond and Cecil Hastings, Jr., OSRD 4572, OEMsr-818 and OEMsr-1007, Report 10.2R, AMG-C, and BRG-C.\n\nAPPLIED MATHEMATICS PANEL\n\nCONTRACTORS 7 PAPERS\n\nApplied Mathematics Group \u2014 Columbia (AMG-C)\n\n56. Diary of C. Eisenhart, G. A. Hedlund and R. M. Thrall, entitled, \"The Ballistics of Aerial Gunnery, Visit to Aberdeen\"\n[Absolute Angles of Attack of Enemy Fighter Aircraft, Churchill Eisenhart, OEMsr-1007, Study 104, Paper 258 (Revised), AMG-C, Sept. 57,\nExperimental Data for Certain Nose Attacks on B-29\u2019s, E. Hewitt, OEMsr-1007, Study 188, Paper 475, AMG-C,\nExperimental Verification of Optimum Percentages of Own Speed Lead, Arthur Sard and Dan Zelinsky, OEMsr-1007, Study 119, Paper 439, AMG-C, June 11,\nAn Empirical Verification of Position Firing, Herbert Solomon and Churchill Eisenhart, OEMsr-1007, Study 61, Paper 322, AMG-C, Dec. 6,\nPosition Firing Deflections Corresponding to Arbitrary Angles Off, Herbert Solomon and Churchill Eisenhart, OEMsr-1007, Study 44, Paper 61,\nA Note on Recalculated Position Firing Rules for the A-26, Dan Zelinsky, OEMsr-1007, Study 119, Paper 446]\n63. Position Firing Rules for Various Altitudes and Speeds, Samuel Eilenberg, OEMsr-1007, Study 119, Paper 422\n64. Compensating Sights, Dan Zelinsky, OEMsr-1007, Study \n65. Bill Airs His Views, Fighter Attack Against Bombers, A Description of the Company Front Attack, Saunders MacLane, OEMsr-1007, Paper 362, AMG-C, January 30,\n66. Mechanization of Own Speed Sights when Used on a Nose Gun for Support Fire Against Frontal Parallel Attacks, Gustav A. Hedlund, Study 119, Paper 248, AMG-C,\n67. The Sperry K-Sights, L. Charles Hutchinson, OEMsr-\n68. Calibration of Time of Flight, I Bomber Sight (superseded by Memorandum 155.1M), Irving Kaplansky, Study \n69. Slewing Systems for Gyro Sights, Saunders MacLane, OEMsr-1007, Study 46, Paper 45, AMG-C, September 6,\n70. Amplification of Tracking Noise in the Gunsight Mark 18, Donald P. Ling, OEMsr-1007, Study 104, Paper 372.\n71. Sperry Sights K-3, K-4, and K-12, L. Charles Hutchinson, OEMsr-1007, Study 104, Paper 236, AMG-C, July 26, 1944 (contains a list of pertinent Sperry documents)\n72. Aerial Gunnery and Gyro Sights: A Manual for Gunners, Donald P. Ling, OSRD 6284, OEMsr-1007, Study 104\n73. The Rate Sight K-15 (Mark 18), A General Discussion, Donald P. Ling, OEMsr-1007, Study 104, Paper 500\n74. The Optical System of the K-3 and K-4 Sights, L. Charles Hutchinson, OEMsr-1007, Study 104, AMG-C, July \n75. The Tracing of Rays Through a Thick Lens or Lens System, Application to the Mark 18, L. Charles Hutchinson, OEMsr-1007, Study 104, AMG-C\n76. A Method in Connection with the Mark 18 Sight, Donald P. Ling, OEMsr-1007, Study 104, Paper 209, AMG-C, CONFIDENTIAL\n77. Solution of the Equations for the Behavior of the Mark 18\n78. Deflection Formulas for Gun Sights of the Mark 18 Type - Donald P. Ling, Study 104, Paper 238\n79. Calibrations for Straight Line and Pursuit Courses - Irving Kaplansky, Study 155, Paper 390\n80. Trail and Gravity Offsets for a Modified Turret - Irving Kaplansky, Study 155, Paper 365\n81. The Mark 18 in a Watermelon Turret - Irving Kaplansky, Study 155, Paper 383\n82. Trail Offsets of the Mark 18 in a Displaced Turret - Irving Kaplansky, Study 155, Paper 383\n83. A Model Calibration for the Mark 21 and Mark 23 - Irving Kaplansky, Study 155, Paper 320\n84. The Irrelevance of Angle of Attack for the Mark 23 - Irving Kaplansky, Study 155, Paper 386\n85. Fire Control System of B-29 Tactics - Diary, GE Visit\nJune 9-10, 1944, Irving Kaplansky and Magnus R. Hestenes, \"A Proposal for Controlling the Speeds of the Total Correction Motors in the General Electric 2CH1C1 Computer,\" OEMsr-1007, Study 104, Paper 197, AMG-C.\n\nMagnus R. Hestenes, Daniel C. Lewis, and F. J. Murray, \"Remarks with Regard to Modifications of the Present B-29 Computer,\" OEMsr-1007, Study 188, Paper 453, AMG-C.\n\nMagnus R. Hestenes and Daniel C. Lewis, \"Facts Important in the Tactical Use of the B-29 Fire Control System,\" OEMsr-1007, Study 188, Working Paper 455, AMG-C.\n\nDaniel C. Lewis and F. J. Murray, \"Summary of Results of Testing a B-29 Fire Control Computer Total Correction Motor,\" OEMsr-1007, Study 143, Working Paper 409, AMG-C, May 4.\n\nDaniel C. Lewis and F. J. Murray, \"Constants for the Total Correction Motors in the 2CH1C1 Computer for the B-29 Airplane,\" OEMsr-1007.\n[91] Nining in Defense of the B-29 Against Nose Attacks, Daniel C. Lewis\n[92] Sundial Analysis: Mathematical Comments on a Memorandum of E. W. Paxson, Daniel C. Lewis and John H. Lewis\n[93] Application of the Air Mass Coordinate Method to Aerial Gunnery Assessment, P. A. Smith\n[94] Remarks on Skid in a Fighter Plane, Hassler Whitney\n[95] Roll, Pitch, Yaw Correction by Table, R. L. Swain, June 4, 1943\n[96] Local Stabilization of Coordinates, P. A. Smith\n[97] Gyro Measurement of Rotations, P. A. Smith\n[98] The Assessment of Gun-Camera Trials, Rollin F. Bennett and Arthur Sard\n[99] Remark on a Question in Probability, George W. Mackey\n100. Preliminary Analysis of the S-4 Sight, E. R. Lorch and Dan Zelinsky, OEMsr-1007, Study 104, Paper 451\n101. Lead Formulas for the Fairchild S-3 Sight, Magnus R. Hestenes and Dan Zelinsky, OEMsr-1007, Study 104, Paper 451\n102. Gun Roll in the S-3, Dan Zelinsky, Study 104, Paper 376\n103. More on the Gyro Error in the S-3, E. R. Lorch, OEMsr-\n104. The Sperry S-8B Stabilized Sight, Samuel Eilenberg, OEMsr-1007, Study 104\n105. Diary, Visit to Radiation Laboratory, Radar for Airborne Fire Control, Saunders MacLane, OEMsr-1007, Study 1007\n106. The AN /APG System No. 16, Visit to Sperry Gyroscope Company, Garden City, L. I., R. M. Thrall, OEMsr-1007,\n107. Lead Computing Sights with Variable Parameter \u201ca\u201d, Magnus R. Hestenes and Saunders MacLane, OEMsr-\n108. How to Put the Target on the Spot. Are the Spots before Your Eyes Red or Weiss, Saunders MacLane, OEMsr-\n109. Proposal for a Sight for Turrets with Velocity Tracking, Hassler Whitney, OEMsr-1007, Study 63, Paper 210, Applied Mathematics Group - Northwestern (AMG-N)\n110. Computations for Dofograph Ballistic Correction Charts, R. S. Wolfe, OEMsr-1379, Study 152, Paper 54, AMG-N\n111. Dispersion Patterns in Fire from Moving Aircraft, George Piranian, OEMsr-1379, Study 142, Paper 18, AMG-N\n112. On Apparent Speed Firing, Charles Nichols, OEMsr-CONFIDENTIAL, Study 1379, Paper 157, AMG-N, September 1945.\n113. Computational Procedures and Forms for Camera Assessment of Fighter Plane Gunsights, R. S. Wolfe, OEMsr-1111, Study 157, Paper 80, AMG-N\n114. Determination of Directions in Space by Photographs of Two or Three Fixed Points, A. A. Albert, Study 157.\n115. Kinematic Lead under Evasive Action and Its Determination by Photography from the Bomber (Preliminary Note), R. S. Wolfe, OEMsr-1007, Study 172, Paper 48, AMG-N\n116. Computation of Single Shot Probabilities in Camera Sight Assessment, A. A. Albert, OEMsr-1379, Study 142, Applied Mathematics Group \u2014 Brown (AMG-B)\n117. \"Calculating Angle of Attack vs. Load Factor Curves from the Usual Performance Data Given on Enemy Planes\" (Letter to Churchill Eisenhart), George H. Handelman, OEMsr-1066, Paper 78, Applied Mathematics Group \u2014 Princeton (AMG-P), May 24, 1944\n118. Introduction to the Aerial Gunnery Problems of AC-92, John W. Tukey, OEMsr-1365, Memorandum 2, Enclosure 8 to Bulletin 2 (AC-92), AMG-P, Aug. 16, 1944.\n119. The Current Status of the Simplest Attackability Problem, John W. Tukey, OEMsr-1365, Memorandum 12 (FCR)\n120. Gun Operation with Lead Computing Sights, H. Hotelling, Study 46, Paper 3, SRG-C, October 1942.\n121. Relative Target Motion and Effective Dispersion, Rollin F. Bennett, OEMsr-618, Paper 398, SRG-C, Jan. 8,\n122. Tests Related to the Defense and Tactical Use of the B-29, R. E. Holzer et al, OEMsr-1390, Service Project AC-92, Interim Report W/TR3, University of New Mexico,\n123. The Effect of Radar Domes, Eagle Vane and Faired Dome on the Operational Speed of the Modified B-29, Speed Reductions Caused by Open Bomb Doors at Operational Altitude of 33,000 feet, E. J. Workman, OEMsr-1390, Report W/M, University of New Mexico,\n124. APG-5 Test with K-3 Sight in B-17 No. 6696, E. J. Workman, OEMsr-1390, Report W/M, University of New Mexico, Service Project AC-92.\n125. Offset Guns in Fighter Airplanes (OEMsr-1381)\nTechnical Report 8, Mount Wilson Observatory, January 15, 1945.\nApplied Mathematics Panel Informal Working Papers\n126. Notes on the Assessment of a Bomber's Defensive Fire\nWarren Weaver, Working Paper 1\n126.1 AMP, October 1944.\n127. Experimental Determination of Fluctuating and Steady Errors in Plane-to-Plane Fire\nWarren Weaver, Working Paper\n127.1 OEMsr-1007, AMP, undated.\n128. The Effect of Quasi-Steady Errors on Bullet Density\nWarren Weaver, OEMsr-1007, Working Paper 3, AMP,\n129. The Interception of a High-Speed Bomber\nClifford R. Simms, Report to NDRC Section 7.2\nThe Jam Handy Organization, Inc., Detroit, Mich., March 1944.\n130. The Bank of an Airplane and Load Factor under Conditions of General Flight\nWilliam M. Borgman, Report to NDRC Section 7.2\nThe Jam Handy Organization, Inc.\n131. Vector Gunsights and Assessing Cameras, OEMsr-991, Division 7 Report to the Services 96, The Jam Handy Organization, Inc., Sept. 30, 1945.\n132. A New Type of Lead Computing Sight, Preliminary Report, Lucien LaCoste, War Research Laboratory, University of Texas, Apr. 23, 1943. AMP-503.6-M1\n133. A Device for Computing a Correction in the Kinematic Lead Computation or Lead Computing Sights [Part 1], Lucien LaCoste, Report to NDRC Section 7.2, War Research Laboratory, University of Texas, Feb. 26, 1943.\n134. The Two Component M Correction for Kinematic Lead and a Possible Way of Adding It to the Fairchild S-3 Sight, Lucien LaCoste, Report to NDRC Section 7.2, War Research Laboratory, University of Texas, Mar. 31, 1943.\n135. Theoretical Analysis of the Performance of Gunsights of the Mark 18 Type, M. Golomb and R. O. Yavne, Report 330-1706-198, Franklin Institute, Nov. 1944.\n136. Tracking Errors in Systems Using Velocity-Tracking and Aided-Tracking Controls with Direct and Lead Computing Sights, OEMsr-330, NDRC Division 7, Section 7.2, Report to the Services 78, February 1944.\n137. The Air Mass Coordinate Method of Aerial Gunnery Assessment, E.G. Pickels, NDRC Section 7.2, Feb. 15, 1944.\n138. Fighter Gunnery and Assessment of Fighter Gunnery. Minutes of Meeting of Committee, July 11, 1945, Saunders MacLane, OEMsr-1007, Joint Army-Navy-NDRC Fire Control Committee, AMG-C, Aug. 6, 1945.\n139. Modification of the MK. 18 Gyro Gunsight (Memorandum to Hassler Whitney), John B. Russell, July 14, 1944.\n140. Symposium on Confidential Airborne Electronic Equipment, MIT Radiation Laboratory, June 15-17, 1944.\n141. Pursuit Curve Characteristics (Graphs), N.U. Mayall, OEMsr-101, Mount Wilson Observatory, Carnegie Institute of Washington, Apr. 5, 1944. MP-503.7-M2\n142. Firing Sideways from an Airplane. L Theoretical Considerations, H.P. Hitchcock, Project RX 114, Report 116, Ballistic Research Laboratory, Aberdeen Proving Ground, Aberdeen, Md., August 12, 1938.\n143. The Effect of Yaw upon Aircraft Gunfire Trajectories, T.E. Sterne, Report 345, Ballistic Research Laboratory, Aberdeen Proving Ground, Aberdeen, Md., May 1, 1943.\n144. Analytical Trajectories for Type 5 Projectiles, T.E. Sterne, Report 346, Ballistic Research Laboratory, Aberdeen Proving Ground, Aberdeen, Md., April 7, 1943.\n145. On Direct Firing Tables for Aircraft Gunnery, with Particular Reference to Caliber .50 AP M2 Ammunition, T.E. Sterne, Report 396, Ballistic Research Laboratory, Aberdeen Proving Ground, Aberdeen, Md., September 2, 1943.\n146. Ballistic Coefficients of Small Arms Bullets of Current Types.\n147. German 20-mm, 13-mm, and 7.92-mm Aircraft Ammunition, B. G. Karpov, Memorandum Report 478, Ballistic Research Laboratory, Aberdeen Proving Ground, Aberdeen, Md.\n148. Trajectories in Air Coordinates for Caliber .50 AP M2 Projectile Fired from Aircraft, L. B. C. Cunningham and F. John, Memorandum Report 279, Ballistic Research Laboratory, Aberdeen Proving Ground, Aberdeen, Md.\n149. Siacci Functions for Caliber .30 Frangible Ball T44, Aberdeen Proving Ground, Aberdeen, Md., September 1944,\n150. A Photometriconic Method for Bomb Ballistics and for Measurements of the Flight Performance of Aircraft, BRL Report No. 279, Aberdeen Proving Ground, Aberdeen Central School for Flexible Gunnery, AAF,\n151. Own Speed Sights, A. E. S. Green, Research Bulletin 101, Ballistic Research Laboratory, Aberdeen Proving Ground.\n152. Emergency Sighting Rules for Gunners on B-29 Bombers, A.E.S. Green, Research Bulletin 107, AAF Central School for Flexible Gunnery, July 4, 1944.\n153. Judgment of Aspect Angles, E.W. Ray, Research Bulletin 121, AAF Central School for Flexible Gunnery, July 4, 1944.\n154. Bullet Dispersion for B-17 and B-24 Aircraft, Research Bulletin 123, Research Division, AAF Central School for Flexible Gunnery, Oct. 1, 1944.\n155. Judgment of Attack and Support Situations in the Air, Research Bulletin 134, AAF Central School for Flexible Gunnery.\n156. A Brief Survey of Simpler Types of Airborne Gunsights, Saunders MacLane, Study 104, Paper 289, Revised, AMG-C, Nov. 24, 1944. Also revised and printed as Research Memorandum 29 by AAF Central School for Flexible Gunnery, June 19, 1945. AMP-502.\n157. Use of Compensating Sights Including the Problem of Support Fire, P. W. Ketchum, Research Bulletin 135, AAF Central School for Flexible Gunnery, June 25, 1945.\n158. Bullet Dispersions in the B-29 Aircraft, Research Bulletin 1943, Research Division, AAF Central School for Flexible Gunnery, August 1945.\n159. Offset Guns on Fighter Aircraft, V. G. Grove, Research Bulletin 141, Research Division, AAF Central School for Flexible Gunnery, Laredo, Texas, Aug. 21, 1945.\n160. The Contribution of Fighter\u2019s Curvature and Mush to a Support Gunner\u2019s Deflection, N. Coburn, Research Memorandum 49, AAF Central School for Flexible Gunnery, Operations Analysis Division, AAF.\n161. Gun Climb, Harmonization, and Bullet Pattern, W. L. Ayres, Operations Analysis Section, Eighth Air Force.\n162. Support Fire with the K-13 Sight on the Waist Guns, W. L.\n163. Operations Analysis Section, Eighth Air Force, December 27, 1944. by J. W. Odle, 163. Support Fire Against Jet Aircraft.\n164. Headquarters, Eighth Air Force, December 28, 1944. by W. L. Ayres, J. S. Jillson, and J. W. Odle, Operations Analysis Section, 164. Fighter Attacks with Offset Guns.\n165. November 3, 1943, Eighth Bomber Command, Operational Research Section. Analysis of Enemy Fighter Activity as Related to Losses and Damage Suffered by Heavy Bombers on 39 Missions during July, August and September 1943.\n166. October 1943, Ninth Bomber Command (USAAF), Cairo, Egypt. Operations Analysis Section. A Manual of Flexible Gunnery for Aircraft.\n167. Far Eastern Air Forces Operations Analysis Report 31, October 1943. by Operations Analysis Section. Report on Design of Hayward Position Firing Sight with Instructions for Installation and Harmonizing.\n168. Flexible Gunnery Accuracy and Optimum Dispersion, C.P. Wells, Operations Analysis Section, Fifteenth Air Force, Mar. 19, 1945.\n169. A Lightweight Radar Computer Combination for the B-29 RCT System, A.E.S. Green, Operations Analysis Section, Twentieth Air Force Headquarters, Oct. 23, 1944. AAF Proving Ground Command, Eglin Field, Fla.\n169. Vertical Deflection Analysis: Flexible Gunnery, E.W. Paxson, AAF Proving Ground Command, Eglin Field,\n170. Graphical Correction Techniques for Azimuth and Elevation, E.W. Paxson and John Lewis, Assessment Memo 3 (S.T. 2-44-22), AAF Proving Ground Command, Eglin Field, Fla., May 29, 1944.\n171. Calculation of Deflections-Bomber in Accelerated Flight, E.W. Paxson, Assessment Memo 11 (S.T. 2-44-22), AAF Proving Ground Command, Eglin Field, Fla., July [\n172. Attacks Made by a Fighter with Oblique Guns; Pursuit\n\n(Assuming the last line is incomplete and should be included with the previous entry)\n\n171-172. Calculation of Deflections-Bomber in Accelerated Flight and Attacks Made by a Fighter with Oblique Guns; Pursuit, E.W. Paxson, Assessment Memos 11 and (S.T. 2-44-22), AAF Proving Ground Command, Eglin Field, Fla., July [no year given]\n[CONFIDENTIAL, BIBLIOGRAPHY\nE. W. Paxson, Curves; Fixed Oblique Gunnery, AAF Proving Ground Command, Eglin Field, FL, Mar. 11, 174. Other Army Sources\nReports from Captured Personnel and Material Branch, Military Intelligence Division, U.S. War Department, Mar. 31, 1945.\nGAF Ideas on the \u201cCompany Front\u201d Attack, AAF Intelligence Summary 45-2.\nJap Fighter Tactics with Inclined Guns, Headquarters AAF Intelligence Summary 45-2, Jan. 30, 1945.\nFinal Report on Test of Evaluation of Aerial Guns and Gun Sights, Serial 2-44-22, AAF Board Project F3270,\nCombat Maneuvers and Fighting Control, J. J. Driscoll, Headquarters Second Air Division, Eighth Air Force,\n\nNAVY REPORTS]\n\n174. Reports from Captured Personnel and Material Branch, Military Intelligence Division, US War Department, Mar. 31, 1945.\n175. GAF Ideas on the \u201cCompany Front\u201d Attack, AAF Intelligence Summary 45-2.\n176. Jap Fighter Tactics with Inclined Guns, Headquarters AAF Intelligence Summary 45-2, Jan. 30, 1945.\n177. Final Report on Test of Evaluation of Aerial Guns and Gun Sights, AAF Board Project F3270, Serial 2-44-22.\n178. Combat Maneuvers and Fighting Control, J. J. Driscoll, Headquarters Second Air Division, Eighth Air Force.\n179. Navy Reports.\n180. Mathematical Analysis of Ordinary and Deviated Pursuit Curves, Carmichael, Rulon, Gillman, Gode, Project RM-6, Special Devices Division, BuAer, Navy Department\n181. Experimental Determination of the Path of a Fighter Plane in Attacking a Bomber, Phase B, E. W. Paxson, Contract N166S-2052, Report to Special Devices Division, BuAer, Navy Department, The Jam Handy Organization, Inc., Detroit, Mich., May 22, 1944, Section 7.\n182. Notes for Refresher Trainees on Defensive Combat Maneuvers, E. V. Hardway, Free Gunnery Standardization Committee, Naval Air Operational Training Command, Jacksonville, Fla., Nov. 23, 1944.\n183. Position Firing, Free Gunnery Standardization Committee, Navy Department, June 1944.\n184. Air Gunnery, The Free Gun, BuAer, Navy Department.\n185. Gunsight Mark 21-23: Recommendation for Calibration of Control Circuits for Fighter Sight, D. D. Cody, 11-44-\n186. Gunsight Mark 18: Final Recommendations for Composite K et al. D.D. Cody and F.T. Rogers, Jr., 8-44-T, Lukas Harold Laboratory\n187. Calibration of Time of Flight for the Pursuit of a Target Flying a Circular Course, G.E. Albert, 12-44-D, Lukas Harold Laboratory\n188. Experiments and Research on Methods of Attacking Large Bombers, CINCPAC-CINCPOA Translations, No. 2, November 6, 1944.\n189. Reference Notes on Upward and Downward Inclined Fixed 20-mm MGs for Type 2 Land Recon Plane, CINCPAC-CINCPOA Translations, November 6, 1944.\n189. Boresight Patterns for Fighter Airplanes with Discussion of Factors Affecting Aiming Allowances, Confidential Technical Note F-43, Reference Aer-E-3251-EMV, F41-3, VF, BuAer, Navy Department, June 4, 1943, p. 3.\n191. Mark 18 Service Manual, BuOrd, Navy Department.\nBritish Reports\n192. Standard Corkscrew Maneuvers, Appendix A, OSRD WA-5195-9F, Letter BC/S.30343/Air/Ops. 1(c), Headquarters Bomber Command, Great Britain, May 27, 1943.\n193. Zone Shooting-Evasive Action, Report 71, RAF Air Fighter Development Unit, Apr. 30, 1943.\n194. Fixed Gun Air Firing, OSRD WA-4435-80, Report AP 1730B, G 1, Department of the Air Member for Training, Air Ministry, Great Britain, November 1943.\n195. General Notes on Gun Sighting, OSRD II-5-7214(S), Report A.P. 1730B, London, Air Ministry, Great Britain, September 1942, Vol. I, Chap. 1. AMP-502.1-M3\n196. A Note on Mark lie GGS Performance in Relation to Basic Ballistic Requirements, OSRD WA-4435-8K, Armament Department Note Arm. 226, Royal Aircraft Establishment, Great Britain, September 1943. AMP-502-M1\n197. A Method of Obtaining Operational Stability in AGL Mk I GGS Systems (Notes), OSRD WA-4435-8i, FC Memorandum 98, Armament Department, Royal Aircraft Department, Great Britain, July 1944.\n198. The Phenomenon of Aerial Aim Wander: An Essay on its Mathematical Description, Statistical Measurement, and Influence on Gunnery Performance, L.B.C. Cunningham, OSRD WA-2055-4a, AWA Report 51, Air Warfare Analysis Section, Great Britain, Apr. 29, 1944.\n199. The Service Trials on the Mk II Gyro Gunsight for Turrets, Melvill Jones, OSRD-II-5-5807(S), Final Report Ex/GRU/47, Great Britain, Apr. 8, 1943.\n200. The Stability of Blind Firing Systems, C.W. Gilbert, OSRD II-5-5927(S), Report GRU/M.8, Gunnery Research Unit, Exeter, Eng., Mar. 14, 1944.\n201. Mathematics of the 3A2 Trainer, The Jam Handy Organization, Inc., Detroit, Mich., October 1944.\n202. Experimental Determination of the Path of a Fighter Plane in Attacking a Bomber: Phase B - Mathematical Analysis of Photographic Observations, E. W. Paxson, The Jam Handy Organization, Inc., USN Contract\n203. Elementary Mathematics of Aerial Gunnery, E. W. Paxson, The Jam Handy Organization, Inc., Detroit,\n204. Tail Gun Computing Sight, Edmund B. Hammond, Jr., Sperry Gyroscope Co., Inc., Mar. 16, 1943.\n205. Theoretical Analysis of the Sperry-Draper Sight, K-Sight and Sperry Stabilized Sight, Sperry Gyroscope Co., Inc.\nCONFIDENTIAL\nBIBLIOGRAPHY\n206. The K-3 and K-4 Aircraft Sight Error Analysis, Edmund B. Hammond, Jr., Document 5250-B-A, Sperry Gyroscope Co.,\n207. Steady State Prediction Error of the S-8 Sight, O. T. Schultz, Document 5252-2009, Sperry Gyroscope Co.,\n208. Handbook of Instructions, Operation, Service, and Overhaul: Central Station Fire Control, Computer Models.\n2CH1C1, 2CH1D1 for the B-29 Airplane:\n\n209. General Electric Gyro-Stabilized Sight with Lead Control for Remote Turrets, J. R. Moore, Report TR-31298, The General Electric Co., Sept. 12, 1944. AMP-502.\n210. \"Sight Questions or Points,\" Theodor Wilhelm Schmidt, Bericht der Lilienthal Gesellschaft,\n211. \"The Aerodynamics of a Spinning Shell,\" Fowler, Gallup, Lock, and Richmond, Philosophical Transactions of the Royal Society (London), Ser. A, 1920, Vol.\n212. \"A Nomogram for the Altitude Dependence of Projectile Flight Duration from Aircraft Weapons,\" Theodor Wilhelm Schmidt, Jahresbericht der Deutschen Luftfahrtforschung,\n213. Lehrbuch der Ballistik, C. Cranz, Julius Springer, Fifth Edition,\n214. \"On the Ballistics of Crossfire with Small Initial Velocity \u2014 Drall or Fin-Stabilized Projectiles with Jagd-Vierling-Mounted Armament,\" Schtissler, Experiments and Memoranda.\n2129, Hermann Goring, Braunschweig, Nov. 1, 1944.\n\n215. \"Verfolgungskurven im Luftkampf\" by A. Fricke, UM 650, Central for Scientific Reporting of Aviation Research of the General Inspectorate of the Air Force, Aug. 26, 1943.\n\n216. \"Vorhaltetheorie f\u00fcr bewegliche Flugzeugscheinwand\" by A. Fricke, UM 777, Central for Scientific Reporting of Aviation Research of the General Inspectorate of the Air Force, June 29, 1944.\n\n217. Report S9, Lilienthal Gesellschaft, 1940.\n\n218. Report 153, Lilienthal Gesellschaft, Aug. 13-14, 1942.\n\n218a. Ibid., \"Kreiselvisiere,\" H. Kortum.\n\n219. [Windvane Sight, the own-speed sight], Instructions for Use of the Windvane Korne, February 1916.\n\n220. Fairchild Type S-3 Gyro Computing Sight, Fairchild Camera and Instrument Corp., Jamaica, N. Y., September 1944.\n\n221. Interception and Escape Techniques at High Speed and\n\n(Assuming the last line is incomplete and should be included in the previous entry)\n\n221. Interception and Escape Techniques at High Speeds\nChapter 9:\n1. The Sighting Problem for Airborne Fire Control, Hassler Whitney, OSRD 6276, OEMsr-1007, AMP Report lg, Appendix I.\n2. Angular Rate Methods in Rocket Sighting, Irving Kaplan-sky, OSRD 6275, OEMsr-1007, AMP Report 124.2R, Part IV.\n2a. Ibid., Part IV.\n2b. Ibid., Part VI.\n2c. Ibid., Part V.\n3. Measurement of Angle of Attack and Skid in Rocket Fire Control, H. L. Garabedian, OSRD 6203, OEMsr-1379, AMP Report 191.1R, AMG-N, October 1945.\n4. Airborne Fire Control, Summary Technical Report, NDRC Division 7, 1946, Vol. 3, Chap. 9.\n5.  Trajectories  of  Aircraft  Rockets  3.5\u201d  and  5.0\u201d,  OSRD  2225, \nOEMsr-418,  CIT/UBC  Report  27,  CIT,  Sept.  25,  1944. \n6.  The  Testing  of  a  Certain  Range  Finder,  Hassler  Whitney, \nOEMsr-1007,  AMP  Study  124,  AMG-C  Paper  305, \n7.  Notes  on  the  Tracking  Problem  for  Fighter  Planes,  Hassler \nWhitney,  OEMsr-1007,  AMP  Studies  124  and  164, \n8.  A  Particular  Method  of  Aiming  Bombs  and  Rockets, \nHassler  Whitney,  OEMsr-1007,  AMP  Studies  124  and \n9.  The  Mark  18  as  a  Range  Finder,  Harry  Pollard,  OEMsr- \n1007,  AMP  Study  124,  AMG-C  Paper  339,  December \n10.  A  Rocket  Sight  Called  PARS,  Hassler  Whitney,  OEMsr- \n11.  On  the  Use  of  a  Pendulum  in  Rocket  Sighting  from  Air\u00ac \ncraft,  Hassler  Whitney,  OEMsr-1007,  AMP  Studies  124 \n12.  The  Transient  of  a  Single  Gyro  Sight  with  Fixed  Sensi\u00ac \ntivity,  Harry  Pollard,  OEMsr-1007,  AMP  Studies  124 \n13.  Formulas  for  Trajectory  Drop  and  Flight  Times  for  the \n[14] Remarks on Skid in a Fighter Plane, Hassler Whitney\n[15] A Suggestion for Calibrating PUSS, Irving Kaplansky\nOEMsr-1007, AMP Study 124, AMG-C Paper 426,\n\n[16] Relation between Skid and Forces Perpendicular to the Plane of Symmetry of an Aircraft, Dan Zelinsky\nOEMsr-1007, AMP Study 124,\n\n[17] The Trajectory Drop of Aircraft Rockets at Short Ranges, Hassler Whitney\nOEMsr-1007, AMP Study 124,\n\n[18] Proposal of a Release Condition for Tossing Rockets, Donald P. Ling\nOEMsr-1007, AMP Study 124, AMG-C\n\n[19] A Remark on the Effect of Banking in the Rocket Sighting Problem, Harry Pollard\nOEMsr-1007, AMP Study 124,\n\n[20] Tracking and the Fire Control Problem, Hassler Whitney\nOSRD 5680, Study 63, AMP Note 21, AMG-C, September\n\n[21] A Theory of Toss Bombing, Harry Pollard\nOSRD 6041, OEMsr-1007, AMP Report 146.1R, AMG-C, September\n22. The Use of H in Toss Bombing, Harry Pollard, OEMsr-23. Formulas Useful in Toss Rocketry, Donald P. Ling, OEMsr-1007, AMP Study 146, AMG-C Paper 401, 24. A Suggestion for Camera Measurement of Skid, Irving Kaplansky, OEMsr-1007, AMP Study 146, AMG-C Paper 25. A Modified Release Condition for Toss-Bombing, Harry Pollard, OEMsr-1007, AMP Study 146, AMG-C Paper 26. The Azimuth Problem in Toss-Bombing, Harry Pollard, OEMsr-1007, AMP Studies 146 and 164, AMG-C Paper 27. Toss-Bombing a Moving Target, Harry Pollard, OEMsr-28. Gravity Drop in a Two Component Fighter Sight, Irving Kaplansky, OEMsr-1007, AMP Study 164, AMG-C 29. The Use of Range Rate in a Fighter Gun Sight, Irving Kaplansky, OEMsr-1007, AMP Study 164, AMG-C 30. Notes on Pneumatic PUSS, L. Charles Hutchinson, OEMsr-1007, AMP Study 164, AMG-C Paper 31. Notes on Pneumatic PUSS, [Part II], Rate of Climb.\nChapter 10: Applied Mathematics Panel Reports and Memoranda on Studies of Antiaircraft Equipment\n\nAMP Study 22: Test Firing\n1. Analysis of Trial Fire Methods, E. Bromberg, E. Paulson, and James J. Stoker, OSRD 4526, OEMsr-945, OEMsr-1007, and OEMsr-618, AMP Report 22.1R, AMG-C, AMG-NYU, and SRG-C, November 1944.\n2. Meteorological Test Firings (A Joint Project of the Army Ordnance Department and the Signal Corps), James J. Stoker, OEMsr-1007, AMP Memorandum 22.9M, AMG-C, AMP-702-M4\n\nAMP Study 23: Muzzle Velocity\n1. Errors in Slant Range of the 90-mm Gun as Affected by Errors in Estimating Muzzle Velocity, E. Bromberg.\nPaulson, James J. and Daniel C. Lewis, \"AMP Report 23: AMP Study 25: AA Fire Control\", OSRD 2053, OEMsr-1007 and OEMsr-618, November 1943. AMP-703.6-M2\n\nDaniel C. Lewis, \"Bibliography of AA Artillery\", OEMsr-1007, AMP Memorandum 25.2M, AMG-C, September 1944. AMP-701-M1\n\nDaniel C. Lewis, \"Supplementary Bibliography of AA Artillery\", OEMsr-1007, AMP Memorandum 25.3M,\n\nDaniel C. Lewis, \"The Accuracy and Effectiveness of Antiaircraft Fire\", OEMsr-1007, AMP Study 29: Airplane Course Data\n\nE. J. Moulton and Daniel C. Lewis, \"The Mathematical Theory of the Hunt Miniature Range\", OSRD 1604, OEMsr-1007, AMP Report 29.1R, AMG-C, July 1, 1943\n\nAMP Study 45: Stereo Movies of Tracers, Daniel C. Lewis, OSRD 3212, OEMsr-1007, AMP Report 45.1R, AMG-C, January [\n\nDaniel C. Lewis, \"AMP Study 85: Study of Fuse Dead-Time Corrections in AA Director\"\n9.  The  Prediction  of  Fuse  Setting,  F.  J.  Murray  and  Arthur \nSard,  OSRD  4057,  OEMsr-1007,  AMP  Report  85. 1R, \nAMG-C,  August  1944.  AMP-704-M9 \n10.  The  Smoothing  Effect  of  a  Follow-up  Motor,  Arthur  Sard, \nOEMsr-1007,  AMP  Memorandum  85. 1M,  AMG-C, \nAMP  Study  99 :  Curved  Flight \n11.  Extrapolation  by  Least  Squares  with  A  pplication  to  A  A \nFire  Control,  Daniel  C.  Lewis,  OEMsr-1007,  AMP \nCONFIDENTIAL \nBIBLIOGRAPHY \nMemorandum  99.1M,  AMG-C,  February  1945. \n12.  On  the  Efficiency  of  the  Curved  Flight  Director,  Daniel \nC.  Lewis,  OEMsr-1007,  AMP  Memorandum  99.2M, \nAMG-C,  September  1945.  AMP-703.2-M16 \nAMP  Study  161 :  Analysis  of  Curved-Flight  Data \n13.  Analysis  of  Certain  Data  from  the  Bell  Telephone  Labora\u00ac \ntories  on  Curved  Flight  AA  Directors,  Kenneth  J.  Arnold, \nOEMsr-618,  AMP  Memorandum  151. 1M,  SRG-C, \nOther  AMP  Papers \n14.  An  Exposition  of  Wiener's  Theory  of  Prediction,  Norman \n15. The Combination of a Random and a Systematic Error\nArthur Sard, OSRD 5328, OEMsr-1384, AMP Note 20\n\n16. Results of a Recomputation of Sight Evaluation Test Data\nWallace Givens, OEMsr-1379, AMP Memorandum 104.4M\n\n17. Optimum Dispersion for Nose Turrets of a B-29\nArthur Sard and R. L. Swain, OEMsr-1007, AMP Memorandum 188.1M\n\n18. Camera Evaluation of Bomber Gun Sights\nA. A. Albert, OEMsr-1379, AMP Note 23, AMG-N, October 1945\n\n19. A Manual for the Use of Gnomonic Charts\nA. A. Albert, OEMsr-1379, AMP Note 23, AMG-N, October 1945\n\n20. Major H. F. Mitchell's Study of the M5 Director\nArthur Sard, OEMsr-1007, AMP Study 51, AMG-C, Oct. 8\n\n21. The Assessment of Gun-Camera Trials\nRollin F. Bennett and Arthur Sard, OEMsr-\n\n(Appendix 1, \u201cVulnerability of Aircraft to Machine Gun Fire,\u201d by Milton Friedman)\n1007, OEMsr: P. A. Smith, \"Gyro Measurement of Rotations,\" AMP Study 166, Revised, AMG-C Paper 405,\n1007, OEMsr: P. A. Smith, \"Local Stabilization of Coordinates,\" AMP Study 166, AMG-C Paper 433,\n1007, OEMsr: R. L. Swain, \"Roll, Pitch, Yaw Correction by Tables,\" AMP Study 166, AMG-C Paper 433,\nGeorge W. Mackey, \"Remark on a Question in Probability,\" OEMsr-1007, AMP Study 166, AMG-C Paper 485,\nRollin F. Bennett, \"Possibility of Serial Correlation Increasing the Probability of at least One Hit,\" OEMsr-618, Report 398, SRG-C, Jan. 8,\nKenneth J. Arnold and A. H. Bowker, \"Methods of Scoring Predictions by A A Directors,\" OEMsr-618, AMP Study,\nJohn W. Tukey, \"A Warning About Statistical Efficiency,\" OEMsr-1365, Memorandum 17, AMG-P, Feb. 28, 1945.\nAMP-21-M3\n30. Methods for Computing Survival Probabilities, H. J. Greenberg and W. Kaplan, Report NR-1, July 1945.\n31. The Probability of Survival of a Target on Any Course, When the Mean Points of Impact and the Joint Distribution of the Errors Due to Tracking Are Known, H. B. Mann, Report NR-2, July 1945.\n32. Errors in Anti-Aircraft Fire-Control When the Target is Maneuvering, Report NR-3, November 1945.\n\nChapter 11\nAMP REPORTS, MEMORANDA, AND NOTES\n1. Probability of Hitting a Twin Engine Airplane with Head-on AA Fire, E. Paulson, OSRD 1655, OEMsr-618, Navy Project NO-131, AMP Report 3.1R, SRG-C,\n2. Increased Risk in Extending a Bombing Run (and supplement to AMP Report 6.1R), W. A. Wallis, OSRD 1639, AMP Report 6.1R, and OSRD 1587, AMP Report\n3. Probability that a Rocket Fired from Astern will Destroy a Twin-Engine Bomber Ju-88, as a Function.\n4. Optimum Burst Surface for JfAY Airborne Rocket Fired from Asten at Twin-Engine Bomber, Ju-88, Milton Friedman, OSRD 4961, OEMsr-618, AMP Report 21.2R, SRG-C, July 1944.\n5. Effectiveness of 4 A\" Airborne Rocket with T-5 Fuze when Fired at Twin-Engine Bomber from Asten, Milton Friedman, OSRD 4960, OEMsr-618, AMP Report 21.3R, SRG-C, July 1944.\n6. Comparative Effectiveness of 5\" Shrapnel, Ifi-mm. H.E. and 20-mm. H.E. Against Directly Approaching Aircraft, Milton Friedman, OSRD 1796, OEMsr-618, AMP Report 21.3, SRG-C.\n7. Comparative Effectiveness of 5\" Shrapnel and 5\" H.E. Against Directly Approaching Aircraft, Milton Friedman, OSRD 3098, OEMsr-618, AMP Report 27.2R, SRG-C, July 1944.\n8. Charts for Estimating Expected Number of Hits on a Directly Approaching Aircraft with 7.7-mm., 13.2-mm. (Confidential)\n\nBibliography (if available)\n20-mm.,  and  J+O-mm.  AA  Guns,  Milton  Friedman,  and \nG.  J.  Stigler,  OSRD  3532,  OEMsr-618,  AMP  Report \n9.  The  Relative  Effectiveness  of  Caliber  .50,  Caliber  .60,  and \n20-mm.  Guns  as  Armament  for  Multiple  Anti-Aircraft \nMachine  Gun  Turrets,  Milton  Friedman,  OSRD  5388, \nOEMsr-618,  AMP  Report  140.1R  (Revised),  SRG-C \nand  Ballistic  Research  Laboratory,  January  1945. \n10.  Estimates  of  the  Vulnerability  of  the  B-29  to  Fighter  Air\u00ac \ncraft,  Milton  Friedman,  OEMsr-618,  AMP  Memoran\u00ac \n11.  The  Probability  of  Damage  from  Heavy  Flak,  M.  M.  Day, \n12.  Danger  Area  Around  Standard  Bombs,  Milton  Friedman, \nOEMsr-618,  AMP  Memorandum  194.1M,  SRG-C, \n13.  The  Probability  of  Damage  to  Aircraft  Through  Anti- \nAircraft  Fire.  ( The  Dependence  of  Effectiveness  on  Shell \nFragmentation  Characteristics.),  H.  H.  Germond;  pre\u00ac \npared  for  publication  by  B.  H.  Colvin,  OSRD  5189, \nBRITISH  REPORTS \n14. Fragmentation and the Chances of Damage to Aircraft from AA Shells, E.S. Pearson, OSRD W-104-15, Report 3, External Ballistic Department, Ordnance Board, Great Britain, April 1940. AMP-504.42-M1\n15. The Chances of Damage to Aircraft from AA Shells: A Generalization of Previous Methods of Solution, B.L. Welch, OSRD W-104-19, Report 23, External Ballistics Department, Ordnance Board, Great Britain, August 8, 1940.\n16. The Probability of Damage to Aircraft Through Anti-Aircraft Fire: A Comparison of Fuzes when Used Against High Level Bombers Attacking a Concentrated Target, Garrett Birkhoff, Ward F. Davidson, D.R. Inglis, M. Morse, John von Neumann, and Warren Weaver.\n17. Experiments on the Vulnerability of Military Aircraft to High-Explosive Shell Fragments, Report 205 of Section T, OSRD, September 1944.\n18. Army Reports.\nPART IV, Chapter 12:\n1. Theory of Games and Economic Behavior, John von Neumann and Oskar Morgenstern, Princeton University Press, 1944.\n2. Lecons Sur la Theorie Mathematique de la Lutte pour la Vie, V. Volterra, Gauthier-Villars, Paris, 1931.\n3. Elements of Physical Biology, A.J. Lotka, Williams and Wilkins, Baltimore, Md., 1925.\n4. Verifications Experimentales de la Theorie Mathematique de la Lutte pour la Vie, G.F. Gause, Hermann et Cie.\n5. The Optimum Ammunition for the Rear Guns of a Bomber Usually Attacked by a Single-Engine Fighter, J. Wolfowitz, OEMsr-1066, AMP Memorandum 2.6M, SRG-C.\n6. Long-Range Weather Forecasting for Military Purposes (Parts I and II), AMP Report 1.1R, SRG-P, October 1940\n7. A Note on Certain Aspects of the Methodology of Operational Research (Enclosure A to Naval Attache), P. M. S. Blackett, OSRD Ref. No. Loga B-7464A, London \n8. \"Aircraft in Warfare: The Dawn of the Fourth Arm,\" Paper V \u2014 The Principle of Concentration, Frederick William Lanchester, Engineering, Vol. 98, October 2, 1914\n9. A Quantitative Aspect of Combat, B. O. Koopman, OSRD\n10. The Mathematical Theory of Air Combat, L. B. C. Cunningham, OSRD II-5-1042, Great Britain, February \n11. An Analysis of the Performance of a Fixed-Gun Fighter Armed with Guns of Different Calibres in Single Home-Defense Combat with a Twin-Engine Bomber, L. B. C. Cunningham, E. O. Cornford, W. Rudoe, and J. Knox, OSRD WA-382-4d, AW A Paper 1, Air Warfare Analysis\nSection, Great Britain, February 1940. AMP-504.1 -Ml\n12. Outline of Cunningham Papers, Milton Friedman, OSRD 1650, OEMsr-618, AMP Report 2.1R,\n13. The Mathematical Theory of Air Combat, OSRD 1621,\n14. Comparative Effectiveness of .50\" and 20-mm. Fighter Armament Against a Twin-Engine Bomber from Astern, OSRD 3701, OEMsr-618, AMP Report 2.5R, SRG-C,\n15. On the Optimum Ammunition Mixture for a Fighter Attacking a Multi-Engined Bomber, J. Wolfowitz, OEMsr-618, AMP Memorandum 2.11M, SRG-C, Dec. 26, Confidential\nBIBLIOGRAPHY\n16. Optimum Interrelation of Aiming and Dispersion Errors, J. Wolfowitz, OEMsr-618, AMP Memorandum 2.13M,\n17. The Optimum Interrelation Between Gun and Aiming Errors when Several Shots are Fired From Each Position of Aim, AMP Memorandum 2.16M, SRG-C, June 1943.\n18. Evaluation of Conduct and Effectiveness of Air Operations.\nReport 6, AAF Evaluation Board, Pacific Ocean Area, April 19, 1945: [Gunnery and Bombing Tactics of B-29 Planes], Project AC-92, Bxdletins 1-13, compiled by Merrill M. Flood, OEMsr-1365, Service Project AC-92, FCR, AMG-P\n\nReport 20, Tests Related to the Defense and Tactical Use of the B-29, R. E. Holzer, OEMsr-1390, Service Project AC-92\n\nReport UNM/W/TR3, University of New Mexico: [Title unclear due to truncation]\n\nReport UNM/W/TR5, University of New Mexico: Ground Tests of the B-29 Central Fire Control System, W. D. Crozier, OEMsr-1390, Service Project AC-92\n\nReport UNM/W/TR6, University of New Mexico: Experimental Observations on a Fighter's Ability to Maintain a Consistent Aim During Attacks on High Speed Bombers, R. E. Holzer, OEMsr-1390, Service Project AC-92\n\nReport UNM/W/TR13, University of New Mexico: Experimentally-Determined Fighter Attack Courses Against a B-29, T. Zanstra, OEMsr-1380, Service Project AC-92\n24. An APG-5 Test with Mark IS (K-15) Sight in B-17 Aircraft No. 42-43915, H.R. Snodgrass, OEMsr-1390, Service Project AC-92, Report UNM/W-33, University of New Mexico, April 14, 1945. AMP-502. 14-M7\n25. A Method of Analyzing Aerial Gun Camera Film Based on Use of Distant Reference Points, G.T. Pelsor, OEMsr-1390, Service Project AC-92, Report UNM/W-34, University of New Mexico\n26. Studies of Defensive Fire Power of Formation of Airplanes, Final Report on Contract OEMsr-1381, Service Project AC-92, Mount Wilson Observatory of the Carnegie Institution of Washington, August 31, 1945.\n27. General Description of the Method of Study of Defensive Fire Power of Formations of B-29 Airplanes Being Carried out at Mount Wilson Observatory, Pasadena, California, OEMsr-1381, Service Project AC-92, Technical Report.\n[28] The Methods of Study of a Squadron of Eleven Airplanes (Preliminary Report), OEMsr-1381, Technical Report 7, Mount Wilson Laboratory, Pasadena, CA, Dec. 14, 1944.\n[29] Analysis of Fire Power of a B-29 Airplane, OEMsr-1381, Service Project AC-92, Technical Report 1, Mount Wilson Laboratory, Pasadena, CA, Sept. 16, 1944.\n[29] Analysis of Fire Power of a Squadron of Four B-29 Airplanes, OEMsr-1381, Service Project AC-92, Technical Report 2, Mount Wilson Laboratory, Pasadena, CA, [no date].\n[30] The Fire Power of a Squadron of Four B-29 Airplanes, Standard Mission II, OEMsr-1381, Service Project AC-92, Technical Report 4, Mount Wilson Laboratory, Pasadena, CA.\n[31] The Fire Power of a Modified Squadron of Four B-29 Airplanes, OEMsr-1381, Service Project AC-92, Technical Report 6, Mount Wilson Laboratory, Pasadena, CA.\n33.  Observational  Results  on  the  Defensive  Fire  Power  of  a \nSquadron  of  Eleven  B-29  Airplanes,  OEMsr-1381,  Service \nProject  AC-92,  Technical  Report  10,  Mount  Wilson \nLaboratory,  Pasadena,  Calif.,  Feb.  20,  1945. \n34.  Observational  Results  on  the  Defensive  Fire  Power  of  a \nSquadron  of  Twelve  B-29  Airplanes,  OEMsr-1381,  Tech\u00ac \nnical  Report  11,  Mount  Wilson  Laboratory,  Pasadena, \n35.  Report  of  the  Pasadena  Conference  on  Defense  of  B-29 \nFormations,  Twentieth  Air  Force,  AAF,  Feb.  15-26, 1945. \n36.  Additional  Measurements  of  the  Defensive  Fire  Power  of  a \nSquadron  of  Twelve  B-29  Airplanes,  OEMsr-1381,  Tech\u00ac \nnical  Report  13,  Mount  Wilson  Laboratory,  Pasadena, \n37.  Preliminary  Study  of  Fighter  Attacks  on  a  B-29,  OEMsr- \n1381,  Service  Project  AC-92,  Technical  Report  5,  Mount \nWilson  Laboratory,  Pasadena,  Calif.,  Oct,  27,  1944. \n38.  Duration  of  Strafing  Attacks  on  a  B-29  Aircraft,  OEMsr- \n1381, Service Project AC-92, Technical Report 9, Mount Wilson Laboratory, Pasadena, CA, Jan. 29, 1945.\n39. Evaluation of Fighter Attacks on B-29 Airplanes\n1381, Technical Report 12, Mount Wilson Laboratory, Pasadena, CA.\n40. Offset Guns in Fighter Airplanes\nOEMsr-1381, Technical Report 8, Mount Wilson Laboratory, Pasadena, CA.\n41. Foreword to Formulation of Manufacturing Specifications for Solid Propellants (Final Report)\nRaymond L. Arnett, OSRD 5851, Series P, No. 9, Alleghany Ballistics Laboratory, Division 3, Section H, NDRC. Nov. 1945.\n42. Battle Damage and Losses Connected with Enemy Fighter Activity\nOAS Report 8, Bomber Command, Oct. 4, 1943.\nCONFIDENTIAL\nOSRD Appointees\nApplied Mathematics Panel\nChief: Warren Weaver\nDeputy Chief: Thornton C. Fry\nActing Chief: May 29, 1945 to April 5, 1946\nTechnical Aides:\n- B. H. Colvin\n- H. H. Germond\n- Cecil Hastings, Jr.\n- Myrtle R. Kellington.\nOEMsr-444, The Franklin Institute, Philadelphia, Pa., H. B. Allen, Computations\nOEMsr-618, Columbia University, New York, N.Y., H. Hotelling\nDirector: W. Allen Wallis\nSubject: Statistical methods applied to air combat analysis, torpedo tactics, acceptance inspection, research and development, and related problems.\nOEMsr-817, University of California, Berkeley, California, J. Neyman\nStatistical analysis of land mine clearance, pattern bombing, bombing of maneuvering ships, and bomb damage theory. Columbia University, New York, NY. Technical Representative: J. Schilt. Mathematical and statistical studies of bombing problems; application of IBM computing techniques to statistical problems in warfare analysis.\n\nPrinceton University, Princeton, NJ. Technical Representative: S.S. Wilks. Statistical methods applied to miscellaneous problems in warfare analysis, including verification of long-range weather forecasting systems, fire effect tables and diagrams for warships, bombing accuracy studies, analysis of guided missiles, and performance of certain heat-homing devices, and mine field clearance by explosive devices.\nNew York University, New York, N.Y.\nTechnical Representative: R. Courant\nInvestigations in shock wave theory.\n\nNew York University, New York, N.Y.\nTechnical Representative: R. Courant\nResearch in problems of the dynamics of compressible gases, hydrodynamics, thermodynamics, and acoustics.\n\nColumbia University, New York, N.Y.\nTechnical Representatives: E.J. Moulton, S. MacLane, A. Sard\nMiscellaneous studies in mathematics applied to warfare analysis with emphasis on aerial gunnery, studies of fire control equipment, and rocketry and toss bombing.\n\nBrown University, Providence, R.I.\nTechnical Representative: R.G.D. Richardson\nProblems in classical dynamics and the mechanics of deformable media.\n\nInstitute for Advanced Study, Princeton, N.J.\nTechnical Representative: John von Neumann\nStudies of the potentialities of general-purpose computing equipment, and research in shock wave theory with emphasis on the use of machine computation. Princeton University Princeton, NJ Technical Representative: Merrill M. Flood Coordination of activities under Project AC-92 at the University of New Mexico, Carnegie Institution of Washington at Pasadena, Columbia University, and Brown University. Northwestern University Evanston, IL Technical Representatives: E.J. Moulton, Walter Leighton Studies in aerial gunnery, particularly the camera assessment of the performance of sights and of airplanes.\n\nContract Numbers, Contractors and Subjects of Contracts:\n\nContract Number Name and Address of Contractor Subject\nOEMsr-1381 Carnegie Institution of Washington Studies and experimental investigations in connection with\nPasadena, CA. The defensive fire power of various bomber formations was tested using model planes with their guns replaced by suitable light sources. Walter S. Adams, Technical Representative, Harvard University, Cambridge, MA.\n\nTechnical Representative,\nGarrett Birkhoff,\nHarvard University, Cambridge, MA,\nStudies on the principles that determine the dynamic behavior of a projectile entering water and the application of these principles quantitatively to the prediction of underwater trajectories and ricochet.\n\nThe University of New Mexico, Albuquerque, NM,\nTechnical Representative,\nE. J. Workman,\nStudies and experimental investigations in collaboration with the Army Air Forces on the most effective formations and flight procedures for the B-29 aircraft. Emphasis was originally upon the tactical use of the B-29, but was later changed to a focus on\nStudy of the defense of the B-29.\n\nTransfer of Funds\nNational Bureau of Standards\nComputations by the Mathematical Tables Project for various agencies concerned with war research. CONFIDENTIAL\n\nSERVICE PROJECT NUMBERS\n\nThe projects listed below were transmitted to the Office of the Executive Secretary, OSRD, from the War or Navy Department through either the War Department Liaison Officer for NDRC or the Office of Research and Inventions (formerly the Coordinator of Research and Development), Navy Department.\n\nService Project Number Subject\n----------------------------------\n\nARMY PROJECTS\n------------------\n\nDesign data for bombardier\u2019s calculator.\nStatistical problems of combat bombing accuracy.\nCollaboration of the NDRC with the AAF in determining the most effective tactical application of the B-29 airplane (continuing under AAF Proving Ground Command, Fire Power Analysis Project).\nQMC-35\nQMC-38\nQMC-43\nSOS-2\nAnalysis of Waller trainer film, textbook on flexible gunnery, study of data accumulated in sight evaluation tests, study of gun camera film scoring to devise a scoring computer, studies of HE-IB attack on precision targets, checking of hydraulic tables, study of fuze dead-time correction in AA director, statistical assistance in rocket propellant tests and specifications, study of relative destructive effect of machine gun fire against airplane structures, food storage data statistics, studies of various statistical problems encountered at the Climatic Research Laboratory, statistical consultation for Quartermaster Corps inspection service, rapid solution of linear equations with up to twenty-six unknowns, binomial distribution calculations, probability theory of balloon barrages, Mathematical studies of lead-computing sights for use with gunnery training.\nStudy and evaluation of sighting methods used in U.S. Naval Aviation for free gunnery training. Preparation of instruction course for quality control and statistically based sampling procedures. Study of nozzle design for jet motors. An analytical method of determining ships' speeds in turns from photographs of ships' wakes. Study of jet propulsion devices operating at subsonic and supersonic velocities [continuing under Contract NOa(s)-7370]. Assistance to the Air Technical Division \u2014 studies of aircraft weapon effectiveness. Probability and statistical study of plane-to-plane fire. Air testing of Mark 15 bombsight. Probability studies desired in connection with estimating hits made by close-range AA gun fire at head-on airplane targets. Mathematical studies of dive-bomber and bomb trajectories in connection with Alkan dive-bombsight. Mathematical studies of bombing.\nProbability calculations for bombing, November 1944.\nProbability curves for gunnery salvo fire, June 1945.\nAntitorpedo-harbor defense nets.\nTheoretical studies of water entry phenomena [continued under Contract NOa(s)-7370 with New York University and under Navy Contract with Harvard University]\nStudy of torpedo spreads and their use against maneuvering targets.\nStudies of acceptance tests on ordnance material.\nDetermination of depth of underwater explosions from surface observations [continued under Contract NOa(s)-7370].\nStatistical analysis of data on thermal characteristics of targets and the relative performance of candidate heat-homing equipment.\n\nConfidential\n\nService Project Numbers (Continued)\nService\nProject Number Subject\nGun equilibrators.\nB-scan radar plotting device.\nComputation services (continuing under a transfer of funds from the Office of Research and Inventions to the Bureau of Standards).\nComputation of dynamic performance of A A computer (continuing under Contract NOrd-9153).\nStatistical assistance in rocket propellant tests and specifications.\nStudy of tactical utilization of offset guns in fighter aircraft.\nProbability study of a proposed type of antiaircraft projectile.\nFire effect tables (continuing under Contract NOrd-9240).\nNonlinear mechanics.\nGas globe phenomena in underwater explosions.\nHigh-temperature metals.\nInvestigation of wave patterns created by surface vessels (continuing under Contract NOas-7370).\n\nSubject indexes of all STR volumes are combined in a master index printed in a separate volume.\nFor access to the index volume, consult the Army or Navy Agency listed on the reverse of the half-title page.\nAerial method of eye shooting, 59\nAcceleration correction for target path, Aerial gunnery research unit, recommendations for formation, 223-231\nAerial warfare, general theory, 197-215\nFactors affecting warfare problems, \"military worth,\" 200-203\nOffensive and defensive warfare, 197-200\nQuantitative analysis, World War II, \nAeroballistics, 9-21\nAeroballistics versus classic ballistics, \nBallistic deflections, 13-15\nDispersion, 18-20\nMotion, small of projectile, 15-17\nTime of flight, 9-13\nAir density, 38\nAirborne fire control, assessment see Fire control, analytic aspects\nAirborne rockets, 125-142\nAdvantages of rockets over shells, 125\nAs risk to a bomber, 186\nFin-stabilized rockets, 126-127\nProgram summarized, 125-126\nAirborne rockets, aerodynamic aspects,\nAngle of attack, 127-129\nDatum line, 128\nDive angle, 128\nFlight angle, 128-129\nIndicated airspeed, 128\nTracking with a fixed sight, 129-130\nAirborne rockets, aiming problem, 130-132\nkinematic lead, 131-132\nlead in vertical plane, 130-131\nrange to impact point, 132\nAirborne rockets, computing sights, see Sighting mechanism, airborne rockets\npeanut (automatic release sight), 141-142\nsight neglecting kinematic lead, 141-142\nsight predicting full lead in vertical plane, 130-131\nAirborne rockets, lead, see Lead, airborne rockets\nAircraft risk from flak, 167-194, see also Antiaircraft risk computations\nantiaircraft fire, physical process, basic problem, mathematical analysis, fragmentation and damage calculations, historical summary of studies, 181-\nmathematical analogue, 170-181\nvalidity of studies, 194\nAircraft risk from single shot, 181-189\nairborne rocket fire study, 186-187\nBritish studies, 182-183\nprojectiles compared, 187-189\nrisk to large group of aircraft, 185-\ntime and proximity fuzes compared,\nAirspeeds, 38-39\nAlgebraic sight, 54: Amplification factor in tracking errors, AN/APG radar sets, 113: Angle of attack, effect on pursuit curves, 37-39: airspeed, 38-39: deviation function, 37: errors of approximation, 39: load, 38: qualitative effect, 39: trajectory shift, 37: Angular gravity drop of fin-stabilized rockets, 127: Angular momentum of target, 26: Angular parallax correction, 83-84: Angular rate deflection, lead computing sights, 57-58: Antiaircraft equipment, 145-166: dry run errors, 150-158: fire control systems, 145-150, 162-: kinematic models for training purposes, 166: linear and quadratic directors, 158-: numerical differentiation and smooth prediction circuits, 164-165: tracer stereographs, 166: trial fire methods, 165-166: turret installations, 188: Antiaircraft fire, physical process, 168-: fragments, 169-170: fuze action, 169: mechanism of antiaircraft guns, 168-169: projectile launching, 168-169.\nantiaircraft burst, 169-170\nantiaircraft fire control systems, 145-149\nassessments, 149-150\ncomponents, 145-146\ndetermination of errors in system, 163-164\ngun dispersion errors, 163\ninput and output, 148\nmuzzle velocity, 163\noverall-effectiveness, 146-147\nposition, 147\npredicted position errors, 162\npredictor, 147-149\nprobability calculation, 150\ntracking, 148\ntracking errors, 162\nantiaircraft risk computations, 170-171\nBritish risk studies, 182-183\ncomplexity of problem, 170\nconditional probability of damage, 171\ncoordinate systems, 170-172\ndistribution of shell bursts, 172-176\nprobability of damage to single aircraft, 168\n\"Apparent speed\" method of eye-shooting, 59\napproach angle prediction, 45\narmament of heavy bombers, see B-29, defensive armament studies\nassessment programs, airborne fire control, see Fire control, analytic aspects\nastrometric methods of space path determination\ntermination, 96\nAutomatic weapons, antiaircraft, 145,\nAxis converter in 2CH computer, 88\nB-29, defensive armament studies, 209-210,\nhistorical background, 209-210\noptical studies at Pasadena, 213-215\nCONFIDENTIAL\norganizational background, 210-212\nproblem, 212\nresults, 213\ntechniques, 212-213\nvulnerability of different parts, 188,\nBacking-up process, dry run errors calculation, 156\nBall-cage integrator for K-3 sight, 66-\nBallistic coefficient C, 12\nBallistic deflections, 13-15\nangle subtended by gravity drop, 13\ndofographs, 15\ninterpretation and calculation, 13-15\nlead computing sights, 57\ntrial angle, 13\nBallistic unit of 2CH computer, 87\nBallistics, classical exterior versus aeroballistics, 9\nBearing determination methods, 96\nBifurcated pursuit, 32-35\nBombers, armament\nBritish antiaircraft risk studies, 182-\neffect of shell burst density on probability of damage, 182-183\neffectiveness of different British automatic gun laying turrets (AGLT) Mark I, 114\nburst of bullets theory, 18\nburst surface of antiaircraft shells, 173-174\ncalibration\ngyroscopic sights in fighters, 79\nlead computing sights, 64-65\n2CH computer, 92\ncameras as airborne assessment instruments, 96-97\ncentral station fire control, 82-93\nangular ballistic and parallax corrections, 83-84\nbasic elements, 82\nfollow-up system, 84-85\nkinematic deflection, 84\nremote control, 82\ntime of flight, 84\ntrajectory equations, 83\n2CH computer, 85-92\ncircular Gaussian distribution of bursts, 18\nClass A errors, fire control, 94-95\nClass B errors, fire control computing sights, 65-66\ndefinition, 55\nFairchild S-4 sight system, 109-110\ngyroscopic lead computing sights, 76-77\nmechanical errors of lead computing sights, 68-69\nown speed sight: 55, steady errors: 95, collision course fighter attack: 120, computing sights for airborne rockets, peanut (automatic release sight): 142, sight neglecting kinematic lead: 141, sight predicting full lead, vertical: 176, contact fuzes, risk computations: 176, continental ballistic coefficient C: 12, coordinate systems, antiaircraft risk computations: 170-173, azimuth and elevation system: 28, gun elevation and traverse system, plane of action system: 28, relative coordinates for pursuit curves: 31, rotation of coordinates: 97-99, Siacci coordinates: 10-12, sight elevation and traverse system, stabilization of coordinates: 98, Corkscrew combat maneuver: 43, damage from antiaircraft bursts, probability study: 176-179, see also Flak analysis, angular density of fragments: 177-178, angular fragmentation pattern: 178-179, area of density of fragments: 177, expected number of damaging hits: 177.\nfall-off law of fragment effectiveness, fragmentation pattern of shell, probability of damage to target, shell and target characteristics, target speed, zone count of fragments, Damping of oscillatory tracking, Damping yaw, data reduction, fire control, see Fire control, raw data reduction, Datum line of airborne rockets, Dead time error in antiaircraft fire control systems, Defensive air warfare, Deflection accelerated target, acceleration correction, kinematic and ballistic decomposition, Deflection nonaccelerated target, basic formula, plane of action, kinematic and ballistic decomposition time of flight multiplier, tracking rate formulation, Deflection against pursuit curves, see Own-speed sights, deflection against pursuit curves, Deflection calculation, Deflection theory, 22-29.\nballistic deflections, conditions for validity, 13-15 deflection defined, 22 gun-roll error, 28-29 necessity for systematic deflection theory, 22 perfect bullet, 22 special coordinate systems, 28 timeback method of deflection calculation, 29 vector methods of general formula derivation, 27-28 density of bursts in antiaircraft fire, destruction probability, targets, 152 deviated pursuit defined, deflection percentage factor, 46 deviation function, pursuit curves, 37 dispersion, 18-20 air-firing versus ground-firing errors in fire control, 94-95 fin-stabilized rockets, 127 forward fire distortion, 20 harmonization, 20 dispersion pattern, 18-20 muzzle velocity effect, 20 optimum size, 103-106 statistical description, 18-20 theory, 18 disturbed reticle principle in lead computing sights, 58 dive angle of airborne rockets, Dofographs (ballistic-deflection charts)\nDrag on bullet, Draper-Davis sight, 140-141, Drift (bullet motion), 17, Dry run errors, 150-158 (calculation, 156-158, backing-up process, 156, error perpendicular to relative stabilization, observations made from rotating gun platform, 157-158), comparison index, 152, definition, 150, dynamic tester findings, 155-156, expected value estimates, 152, planning of dry runs, 150, probability of shot with given dry run destroying target, 153-155, Confidential, probability theory, 151, serial correlation, 152-153, survival probability, 152, 155, unconditional vulnerability, 151, Dry run errors, calculation, 156-158, Dynamic tester, dry run errors, 155-156, Elephant method of eye shooting, 58-59, Electromagnetic system, gyros, 74-75.\n\nEffective launcher line for fin-stabilized rockets, 126.\nError functions for linear and quadratic directors: 159-161\nExponential smoothing circuit: 60-64\nAided tracking: 64\nAmplification of tracking errors: 62\nBall-cage integrator as circuit: 66-67\nDamping oscillatory tracking: 61\nDecay of false leads: 61-62\nLead computation delay: 63-64\nOperational stability: 62-63\nSight parameter choice: 63\nSlewing routines: 61-62\nWeighted averages: 61\nExponential spot sights: 115\nEye shooting estimation methods: 58-59\nABC method: 59\n\"Apparent speed\" method: 59\nDisadvantages: 59\nEarly use: 58\nElephant method: 58-59\nEZ40-EZ45 German gyro sights: 80\nFairchild S-4 sight system: 108-110\nCircuit components: 108-109\nClass B errors: 109-110\nComplete circuit equations: 109-110\nFall-off law for fragment effectiveness, Fighter-plane armaments: quantitative analysis, 208-209\nFin-stabilized rockets: 126-127\nAngular gravity drop and time of flight: 127\nDispersion: 127\neffective line, 126 launchers, 126 projectile speeds, 127 Fire control, analytic aspects, 94-106 airborne tests, 94 current assessment methods, 95 error classifications, 94-95 instrumentation, 96-97 measures of effectiveness, 101-103 optimum dispersion pattern, 103-106 summary, 106 target path determination, 96-97 Fire control, instrumentation, 96-97 air mass coordinate technique, 97 astrometric methods, 96 bearing and range determination, 96 distant reference point method, 97 synchronization, 96-97 Fire control, raw data reduction, 97-100 deflection calculations, 99 measure of effectiveness, 101-103 parallax correction, 99 probability affected by measurement rotation of coordinates, 97-99 Fire control errors, 94-95 classification by cause, 94-95 statistical classification, 95 Fire control systems, antiaircraft see Antiaircraft fire control systems Fire control theory, 107-121\naided tracking on line of sight, exponential spot sights, new tactics, own-speed plus rate mechanization, radar gunnery aids, research recommendations, sight parameter as a function of time, stabilized sight systems, target course curvature correction mechanisms, tracking equation, Flak analysis, Flak charts, flakometers, group probability factors, methods of reducing total risk, problems to be studied, Flight angle of airborne rockets, Follow-up system for central station fire control, Fragmentation, antiaircraft fire, Fragmentation, flak analysis, Damage from antiaircraft bursts, probability study, Fragmentation patterns, Frangible Ball T-44 projectile, Future range, definition, Fuzes.\nantiaircraft shells, contact fuzes, risk computations, proximity fuzes, performance errors, time and proximity fuzes compared, Gaussian distribution, shell bursts, German gyro sights, Glook (mechanism for mimicking aircraft orientation), Gnomonic projection computer, gravity drop angle, gun dispersion, gun-roll errors, gyroscope, stabilization use, gyroscope unit of 2CH computer, gyroscopic lead computing sights, class B errors, fighter sights, kinematic deflection production, optical system, physics of a gyro system, single gyroscopic eddy current sights, turret types, gyroscopic lead computing sights mechanics, electrical circuit, electromagnetic system, Hooke\u2019s joint, torque, gyroscopic lead computing sights in fighters, angle of attack, automatic computational calibration.\ncircuit simplifications, German gyro sights, 78-79 target course curvature, 79 Handlebar motion, 64 Hooke's joint, gyro system, 74 Hypothetical machine, air warfare analysis, 201-203 Indicated airspeed (IAS), airborne rockets, 128 formula, 38-39 Initial speed of bullet, 9 Initial yaw, definition, 9 Instantaneous projectile speed of fin-stabilized rockets, 127 Isogees (curves of equal load), 36 Johns Hopkins University, target destruction probability studies, K-3 mechanical sight, 66-68 ball-cage integrator, 66-67 complete circuit, 67-68 exponential smoothing, 66-67 kinematic equations, 68 lateral circuit, 67 K-8 electrical lead computing sight, 80 K-11 algebraic sights, 54 K-12 mechanical sight, 68 K-13 vector sight, 52-54 kinematic deflection fire control computer, formula, 24 lead computing sights, 57 production methods, 70-71 kinematic lead in airborne rockets.\nKinematic models for training purposes, 166\nLaunchers for rockets, 126\nLead, airborne rockets, 131-139\nDependence on weather conditions,\nGraphs of lead, 133-134\nKinematic lead computation, 134-137\nKinematic lead in azimuth plane, 132\nKinematic lead in vertical plane, 131\nLead components, comparative importance, 133\nOperation instability factor, 138\nSighting procedures for lead computation,\nVariables on which lead functions depend,\nLead computing sights, 57-81\nApparent motion eye shooting, 58-59\nElectrical types, 80\nGyroscope types, 69-80\nMechanical types, 66-69\nLead computing sights, basic theory,\nAngular rate deflection, 57-58\nCalibration concept, time of flight,\nClass B errors, 65-66\nConflict between ranging and tracking,\nDecay of false leads, 61-62\nDisturbed reticle principle, 58\nFirst-order nature, 57\nSight parameter, 60-61\nSmoothing circuit, 60-64\nLead equations, 23-24\nLift coefficient of a bullet, types of directors: 38, 158-159\nLinear and quadratic error prediction: 158-160\nRandom errors: 160-161\nTheoretical performance: 161-162\nLocal stabilization, target coordinates, Mach numbers, effect of high numbers on bomber attack: 43-44\n\"Macro-theory\" of warfare: 208\nMathematical analysis in warfare: 215-216\nDesign and use of individual devices, general discussion: 215-216\nJustification for mathematical operational analysis: 218\nRecommendations for mathematical consultant to air forces: 218-221\nMatrix algebra applied to airborne data: 98\nMechanical lead computing sights, class B errors, lateral error computation, sight equations: 66-69\n\"Micro-theory\" of warfare: 208\n\"Military worth,\" general theory of air MPI (mean point of impact) in aerial gunnery: 20\nMuzzle velocity, effect on dispersion pattern: 20\nMuzzle velocity errors in antiaircraft fire control systems, 163 Offensive air warfare, 197-198 Offset guns in conventional fighters, Operational errors in fire control, 94-95 Operational research groups, recommendations for formation, 207 Operational stability, 62-63 Optical system of gyros, 72-74 Own-speed mechanization, 45-56 Approach angle prediction, 45 Class B errors, 55 Definition, 45 K-11 algebraic sight, 54 K-13 vector sight, 52-54 Position firing, 50-52 Support fire, 55-56 Tactical considerations, 45 Own-speed sights, deflection against pursuit curves, 46-48 Aerodynamic lead pursuit, 46 Choice of optimum percentage, 47- Deviated pursuit, 46 Percentage factor variables, 46 Pure pursuit, 46 Own-speed sights, theory verification, analytic check, 50 Check of optimum percentages, 49- Combat evidence, 48-49 Pantograph, 2CH computer, 87\nParallax correction in target bearing, 99. Parallax unit, 2CH computer, 87. Peanut (automatic release rocket sight), Photography used in airborne assessment programs, 96-97. Plane of action, 23. Plaxie (parallax correction mechanism), Position firing with own-speed sights, Position stabilization, 107. Potentiometer resolver, 2CH computer, Predicted position errors, antiaircraft fire control system, 162. Prediction circuits, 164-165. basic description, 164. conventional circuit, 164. response analysis methods, 165. Sperry A-circuit, 164. tangential circuit, 164. Tappert circuit, 164. Predictor\u2019s time base, antiaircraft fire control system. Probability. See also: Damage from antiaircraft bursts, probability study. Damage to single aircraft, antiaircraft destruction probability, targets, 152. Dry run probability theory, 151. Shot with given dry run will destroy, survival probability estimation procedure, 155.\nProjectile launching, antiaircraft fire, projectiles, comparison studies, 187-189, antiaircraft turret installations, 188, automatic weapons, 188, 189, B-29 vulnerability from different ammunition types, 188, 189, conditional probability with shrapnel shell, 187-189, Proximity fuzes, distribution of shell, Proximity fuzes, effectiveness compared with time fuzes, 183-185, Pursuit curves, 30-48, angle of attack, 37-39, bifurcated pursuit, 32-35, centrifugal force and isogees, 35-36, combat maneuvers by bomber, 42-43, deflection against pursuit curves, 46-, deviation function, 37, high speed fighter attacking high speed bomber, 43-44, modern warfare applications, 30, pure and deviated pursuit theory, 31-33, pure pursuit defined, 30, reasons for investigation, 30-31, tactical considerations, 42-44, total load factors, 36-37, true aerodynamic lead pursuit curve, Pursuit curves, equation, 31-32, 40-42.\nbifurcated pursuit, coordinates (31-35)\ndynamical equations (40)\nfixed lead pursuit, (32)\nkinematical equations (40)\nmethods of introducing time as a parameter (35)\npure pursuit, (32)\nthree dimensional equations (41-42)\nvariable lead pursuit, (32)\nPUSS (computing sight), (140-141)\nQuadratic and linear directors, (158-162)\nerror prediction, (158-160)\nrandom errors, (161)\ntheoretical performance, (161-162)\ntypes of directors, (158)\nQuantitative analysis, World War II aerial warfare, (207-215)\nfighter-plane armaments, (208-209)\n\"macro\" versus \"micro\" theory of warfare, (208)\nQuasi-steady errors, fire control, (95)\nRadar gunnery aids, (112-115)\nairborne gun laying sets, (113)\nairborne gun sights (AGS), (113)\nairborne range only sets (ARO), (113)\npresentation, (112-113)\nradar-gyro-sight system, (113-115)\nrequirements, (112-113)\nRadial grid method, tracer stereo-graphs, (166)\nRange determination methods, (96)\nRate deflection of lead computing sights, 57-58\nRate stabilization, 107\nReference systems, 9-10\nRelative wind, 9\nRemote control, advantages and disadvantages, 82\nResearch recommendations\n- aerial gunnery research unit formation\n- fire control development, 107\n- mathematical consultant for air simulating electronic circuits, 117\n- risk computations, antiaircraft fire\n- risks to group of aircraft from flak, computer requirements, 138-139\n- computing sights, 140-142\n- hypothetical simple computers, 132-133\n- operational instability, 138\n- pilot's estimation of variables, 139-140\n- rate of rotation of sight line, 140\n- sighting procedures, 137\n- skid, airborne rockets, 127-128\n- slewing routine, smoothing circuit, 61-62\n- slowdown factor, 23\n- small of projectile, motion in, 15-17 (drift, 17; motion and damping of yaw, 15-16; windage jump, 16-17)\nSmoothing circuit: see Exponential smoothing circuit\nRocketry: see Airborne rockets\nRotation of coordinates, airborne data, glook mechanism, 98, gnomonic computer, 98, matrix methods, 98\nShell burst: see Airborne rockets, 169-170\nShell bursts, distribution: 172-176, approximations of damage calculations, 176, burst surface, 173-176\nCircular Gaussian distribution: 18, effect on damage probability, 182-183\nProbable density of bursts: 172-173, proximity fuzes, 173-176, sensitivity of fuze, 173-176\nSpheroidal Gaussian distribution: 173\nTime fuzes: 172-173\nShrapnel shells compared: 187-189\nSiacci coordinates: 9-12\nSight parameters:\nFactors affecting choice: 63, 64\nFunction of range: 115\nPhysical interpretation: 60-61\nSight response factor: 62\nSight systems:\nGyroscopic lead computing sights: 69-71, lead-computing sights: 57-81, mechanical lead computing sights:\nown-speed sights, 45-56\nstabilized sight systems, 107-112\nSighting mechanism, airborne rockets,\nbasic problem, 132\nSperry A-circuit, 164\nSperry K-3 sight, 58\nSperry S-8B sight system, 110-112\nadvantages, 112, construction and operation,\nerrors caused by aircraft accelerations, 112\nSperry sights, general discussion, 66\nStabilization observations made from rotating gun platform, 157-158\nStabilized sight systems, 107-112\nFairchild S-4 system, 108-110\nSperry S-8B sight system, 110-112\nstabilization, nature and types, 107\nStibitz method, tracer stereographs, 166\nSupport fire use of own-speed sight,\nSurvival probability of targets, 152, 155\nTactical-strategic computer (TSC), hypothetical military worth computer, 201-203\nTactics, new developments, 119-121\nattack by pacing behind and below,\nattack on collision course, 120\noffset gun attacks, 119-121\nupward barrage fire, 121\nTangential prediction circuit, Tappert prediction circuit, Target course curvature correction mechanisms, Target course curvature effect on gyroscopic sights, Target destruction probability, Target speed conditional probability calculations, TAS (true airspeed), Three dimensional pursuit curve equations, Time back method, deflection computation, Time fuses distribution of shell bursts, effectiveness compared with proximity fuzes, Time of flight calibration concept, fin-stabilized rockets, fire control computer, multiplier, reference systems, relative system, Siacci system, trajectory basic equations, 2CH computer, Torque, gyro systems, Total load on aircraft, Tracer stereographs radial grid method, Stibitz method, Tracking aided tracking.\namplification factor, errors (62)\nequation (118-119)\nerrors in angles, antiaircraft fire control (162)\nrate formulation (24)\nrate smoothing (60)\nwith a fixed sight for airborne trajectory equations\nbasic equations (10-13)\ncentral station fire control (83)\nTrajectory shift (37)\nTrial angle, ballistic deflection (13)\nTrial fire procedure (165-166)\nTrial gradient in aeroballistics (20)\nTrue airspeed (TAS) (12, 38-39)\nTurret installations, antiaircraft equipment\nTurrets, types (78)\n2CH computer (82-93)\n2CH computer, equations (83-84)\ncorrections for angular ballistic and parallax (83-84)\nkinematic deflection (84)\ntime of flight (84)\ntrajectory equation, vector form (83)\n2CH computer, fire control system (85-87)\ncalibration (92)\ncomponent parts (87-92)\ncomputer problem (85)\nproblem solution method (85-87)\n2CH computer, parts (87-92)\naxis converter (88)\nballistic unit (87)\ngyroscope units (89-90)\npantograph (87)\nparallax unit, 87, potentiometer resolver, 88, range follow-up motor, 92, time-of-flight circuit, 86, 89, total correction motors, 85, 90-92, unconditional vulnerability of targets, University of Texas testing engine, 107, upward barrage fire, 121, variance and covariance, vulnerability distribution, 154, vector method of derivation, deflection formula, 27-28, vector sight, K-13 (52-54), vulnerability of targets, conditional and unconditional, 151, weighted averages, smoothing circuit, windage jump, 16-17, World War II aerial warfare, quantitative analysis, 207-215, yaw, motion and damping, 15-16, zero lift line, airborne rockets, 128.\n\nIiipi AQQinrn H I f.", "source_dataset": "Internet_Archive", "source_dataset_detailed": "Internet_Archive_LibOfCong"},
{"language": "eng", "scanningcenter": "capitolhill", "contributor": "The Library of Congress", "date": "1946", "subject": ["World War (1939-1945)", "Submarine warfare", "World War, 1939-1945", "Anti-submarine warfare", "Military operations, Naval", "World War, 1939-1945 -- Naval operations, American", "World War, 1939-1945 -- Naval operations -- Submarine", "World War, 1939-1945 -- Campaigns -- Atlantic Ocean", "Anti-submarine warfare -- History", "Military operations, Naval -- American"], "title": "Antisubmarine warfare in World War II", "lccn": "2009655248", "collection": ["library_of_congress", "americana"], "shiptracking": "ST005578", "call_number": "19039200", "identifier_bib": "00271565562", "boxid": "00271565562", "volume": "no. 51", "possible-copyright-status": "The Library of Congress is unaware of any copyright restrictions for this item.", "publisher": "Washington : Operations Evaluation Group, Office of the Chief of Naval Operations, Navy Dept.", "description": ["\"Manuscript and illustrations for this volume were prepared for publication by the Summary Reports Group of the Columbia University Division of War Research under contract OEMsr-1131 with the Office of Scientific Research and Development. This volume was printed and bound by the Columbia University Press\"--Unnumbered page ii", "LC Science, Business & Technology copy no. 429", "In a set of declassified documents held as a collection by the Library of Congress", "xi, 191 pages : 27 cm"], "mediatype": "texts", "repub_state": "4", "page-progression": "lr", "publicdate": "2016-04-13 14:50:59", "updatedate": "2016-04-13 15:56:53", "updater": "associate-mike-saelee@archive.org", "identifier": "antisubmarinewar51ster", "uploader": "associate-mike-saelee@archive.org", "addeddate": "2016-04-13 15:56:55", "scanner": "scribe3.capitolhill.archive.org", "operator": "associate-jillian-davis@archive.org", "imagecount": "218", "scandate": "20160517222701", "ppi": "300", "foldoutcount": "0", "identifier-access": "http://archive.org/details/antisubmarinewar51ster", "identifier-ark": "ark:/13960/t9t19pr13", "scanfee": "100", "invoice": "1263", "curation": "[curator]associate-annie-coates@archive.org[/curator][date]20160519122826[/date][state]approved[/state][comment]199[/comment]", "sponsordate": "20160531", "backup_location": "ia906105_26", "fadgi": "true", "republisher_operator": "associate-jillian-davis@archive.org", "republisher_date": "20160518132931", "republisher_time": "917", "external-identifier": "urn:oclc:record:1039987634", "creator": "Sternhell, Charles M., 1916-1971", "oclc-id": "4741129", "associated-names": "Thorndike, Alan M., 1918-", "ocr_module_version": "0.0.21", "ocr_converted": "abbyy-to-hocr 1.1.37", "page_number_confidence": "99", "page_number_module_version": "1.0.3", "creation_year": 1946, "content": "[UNCLASSIFIED]\nSerial No.\nCopy No. /\nProperty of Torts Section\n'ouitiY'*'\nLibrary C: progress recorded\nPatent 25\n\nClassification by authority of Office of Naval Research\nREPORT NO. 51\nOF THE OPERATIONS EVALUATION GROUP\nThis document contains information affecting the national defense of the United States within the meaning of the Espionage Act, 50 U.S.C., 31 and 32, as amended. Its transmission or the revelation of its contents in any manner to an unauthorized person is prohibited by law.\n\nThis volume is classified CONFIDENTIAL ITAL in accordance with security regulations of the War and Navy Departments.\n\nManuscript and illustrations for this volume were prepared for publication by the Summary Reports Group of the Columbia University.\nDivision of War Research, under contract OEMsr-1131 with the Office of Scientific Research and Development. This report was printed and bound by Columbia University Press and was also issued as Volume 3 of Division 6 in the series of Summary Technical Reports of the National Defense Research Committee. Originally published in duplicated form on 10 April, 1946, and given wide distribution within the Navy Department.\n\nDistribution of this volume has been made by the Chief of Naval Operations. Inquiries concerning the availability and distribution of this report and microfilmed and other reference material should be addressed to the Office of the Chief of Naval Operations, Navy Department, Washington DC.\n\nOEG Report No. 51\nAntisubmarine Warfare in\nWorld War II\nCharles M. Sternhell and Alan M. Thornridge\nOperations Evaluation Group\nThe results of statistical and analytical work conducted by members of the Anti-Submarine Warfare Operations Research Group of the U.S. Navy, later the Operations Research Group and since September 1945, the Operations Evaluation Group, are presented in this volume. The group was formed and financed by the Office of Scientific Research and Development at the Navy's request and was assigned to the Commander in Chief, U.S. Fleet headquarters. The group provided assistance in:\n\na. Evaluating new equipment to meet military requirements.\nb. Evaluating specific phases of operations from studies of action reports.\nc. Evaluating and analyzing tactical problems.\n\nOffice of the Chief of Naval Operations, Navy Department, Washington, D.C., 1946.\nThis book consists of a statistical review and unified analysis of anti-submarine warfare in the Atlantic from 1941 to 1945. It covers tactics that proved most useful in this combat. This material is believed to be of considerable help in providing a basic understanding of this important branch of naval warfare. Certain aspects of the group's work related to the anti-submarine problem, such as the Theory of Search and Screening and Methods of Operations Research, will be embodied in other volumes to be published later.\n\nPhilip M. Morse\nDirector, Operations Evaluation Group\n\nPreface\n\nThis volume on antisubmarine warfare (ASW) is a compromise between producing a unified summary of the events and problems of antisubmarine warfare during World War II and illustrating scientific evaluation of naval operations. The approach is historically based on both accounts, as the scientific evaluations are derived from various analyses and studies related to antisubmarine warfare during World War II. Great care should be exercised when making predictions about the future of ASW based on this information. The past successes of antisubmarine measures do not guarantee their adequacy in the future.\n\nA clear understanding of the events of World War II is essential.\nThe reasons and consequences of new weapons, gear, and tactics during World War II are necessary for postwar decisions. This volume aims to serve as a convenient reference and source of factual material. One clear conclusion emerges: the interplay of measures and countermeasures, with no conclusion retaining validity for long. If this lesson is learned, the volume will have served a useful purpose.\n\nThe general organization closely follows the dual aim, with two parts of different character. Part I provides a historical summary of enemy submarine operations and Allied antisubmarine operations during World War II. No attempt has been made to give a comprehensive account.\nThe text provides a complete chronology of World War II events with a statistical perspective. Every effort is made to describe the progress of the war in quantitative and objective terms, interpreting data based on the ever-changing tactical and strategic situation. The historical summary is divided into seven chronological periods as indicated in the Table of Contents. This division is necessary due to the radical changes in U-boat war tactics and the introduction of new weapons and countermeasures. The periods were chosen to ensure homogeneous U-boat strategy and tactics in each. Individual U-boat tactics varied significantly from the typical characteristics common to most operations during the specified periods.\nThe division points between periods are somewhat definite and represent the approximate dates at which a majority of U-boats had made a major change in their methods of operation. The data for a given period are further divided into three main sections.\n\n1. A chronological narrative of the most important activities and accomplishments of the U-boats and Allied antisubmarine forces.\n2. A more detailed account of the main Allied countermeasures to the U-boats, subdivided into:\n   a. Convoys\n   b. Aircraft\n   c. Scientific and technical\n   d. Sinkings of U-boats.\n3. A survey of the results achieved during the period, from both the U-boats\u2019 and the Allies\u2019 point of view. This section attempts to explain the reasons for the new tactics which characterize the new period.\n\nPart II of the volume is a more detailed analysis of certain of the major problems of ASW, in particular\nThose which were the subject of operations research studies. The emphasis is on the evaluation of tactics and materiel through theoretical analyses and special studies of operational data. Although the principles of ASW derived from such evaluation are strictly applicable only to the situation which obtained during World War II, the methods of evaluation are of more general interest.\n\nThe U-boat war spread over all the oceans of the world, but the main battle was fought in the Atlantic. Consequently, U-boat activity in other regions has not been discussed as completely as the Battle of the Atlantic. A standard subdivision into areas, which has been used throughout the text, is given in the frontispiece.\n\nThere are, in fact, many aspects of the war which are omitted from the discussion. The operations of midget submarines and small battle craft are among them.\nThe importance of personnel training and developments are not considered, as they are not related to U-boats. Naval Intelligence activities in obtaining information for operations are not detailed. Indirect effects of factors like strategic bombing are largely neglected. The discussion is mainly focused on Navy antisubmarine operations, with the inclusion of Royal Air Force Coastal Command aircraft and those of the United States Army Air Forces during antisubmarine missions. The distinction is not rigid.\n\nThe sources of material used are widely scattered through correspondence and informal memoranda, making it impractical to quote references. Much of the basic information is available elsewhere.\nPeriodicals such as the United States Fleet Anti-Submarine Bulletin, British Admiralty Monthly Anti-Submarine Review, and RAF Coastal Command Review, which have been given wide distribution. Other reports, such as Operations Research Group Memorandas and Research Reports, and British reports originating with Director Naval Operations Research (DNOR) and the Operations Research Section of Coastal Command (ORS/CC), have been given limited distribution and are less accessible. In addition, numerous letters, notes, informal memos, and even oral conversations go to make up the background of this volume. One of its chief aims has been to set down in writing a fair sample of this store of material, whose previous status verged on that of folklore. No effort has been made, therefore, to assign credit for the work discussed. It originates with various sources.\nmembers of British and United States operations research groups, military services, and civilian war agencies. We have tried to collect available information and tell a reasonably unified story, not of the accomplishments of a particular group, but of the progress of a special type of naval warfare.\n\nC. M. Sternhell & A. M. Thorndike Editors\n\nCONTENTS\n\nPART I\nHISTORY OF ANTISUBMARINE OPERATIONS\nCHAPTER 1 First Period\u2014Submerged Daylight Attacks on Independents, September 1939 - June 1940\n2 Second Period\u2014Night Surfaced Attacks on Convoys, July\n3 Third Period-Start of Wolf Packs; End-to-End Escort of Convoys, April 1941-December 1941\n4 Fourth Period\u2014Heavy Sinkings on East Coast of United States, January 1942-September 1942\n5 Fifth Period \u2014 Large Wolf Packs Battle North Atlantic Convoys, October 1942 - June 1943\n6 Sixth Period\u2014Aircraft Defeat U-Boats\u2019 Attempted Come-back\nPART II\nANTISUBMARINE MEASURES AND THEIR EFFECTIVENESS\n\n9 Safety of Independent Shipping\n10 Convoying and Escort of Shipping\n1. Attacks by Surface Craft\n12 Attacks by Aircraft\n13 Offensive Search\n14 Employment of Search Radar in Relation to Enemy Countermeasures\n15 Countermeasures to the German Acoustic Torpedo\n\nEpilogue\nAppendix I\nGlossary\n\nOcean Areas Referred to in the Text\nHANCCti\nReykjavik\nETLAN0\nJom Havn, Denmark\nSst Nazaire, T-\nFordcau-/\njW- Rostock\njSyoye\nC mattcras\nIn lyaute y\nMrmuoii\nKey West.\nPiiia\u00ab\nVSi-\n\u2022Ascension $\nRio de Janeiro\nAza\nAzores Area\nCSW\nCaribbean Sea Frontier \u2014 West\nNSA\nNorth Sea Area\nBCA\nBiscay Channel Area\nESF\nEastern Sea Frontier\nNTE, Northern Transit Area - East\nBDA, Bermuda Area\nFRA, Freetown Area\nN FW, Northern Transit Area - West\nBLA, Baltic Area\n( Gibraltar Morocco Area)\nNWA, Northwest Atlantic Area\nBTA, Barents Sea Area\nGSF, Gulf Sea Frontier\nPSF, Panama Sea Frontier\nBZA, Brazilian Area\nIND, Indian Ocean\nSEA, Southeast Atlantic Area\nCCZ, Canadian Coastal Zone\nCaribbean Sea Frontier - East\nMED, NEA, Mediterranean and Red Sea Area\nNortheast Atlantic Area\nSWA, Southwest Atlantic Area\n\nPart I\nHistory of Antisubmarine Operations\nSubmarines in World War I\n\nThe great capabilities of the submarine as a weapon of war were first revealed during World War I when the U-boat campaign almost proved decisive. Fortunate ly, the Germans themselves did not fully realize in 1914 how valuable the U-boat's ability to submerge and escape detection would be for offensive operations.\nDuring the war, German U-boats conducted operations against enemy shipping. Initially, they focused on naval ships, and it wasn't until 1915 that a concentrated attack on English merchant shipping began. In 1915 and 1916, on average, about 15 U-boats were at sea at any given time. These U-boats sank approximately 200,000 gross tons of shipping per month, while losing around the same number each month. This situation was highly satisfactory for the Germans, as the average life of a U-boat at sea during this period was about 10 months, during which it would sink around 13,000 gross tons of shipping monthly, totaling 130,000 gross tons before being sunk itself.\n\nEncouraged by these successes, the Germans initiated a large-scale campaign in February 1917.\nRestricted warfare on merchant shipping in an attempt to blockade England. This attempt almost proved successful as Allied shipping losses rose steadily to a peak in April 1917. Four hundred and forty-four ships of about 900,000 gross tons were sunk by U-boats during that month. The British Fleet was confined to its bases for there was only eight weeks\u2019 supply of fuel oil in England. Various countermeasures had been tried without success and defeat seemed just around the corner unless an antidote to the U-boat could be found.\n\nAdmiral Jellicoe was brought to Admiralty to deal with the situation. The convoy system, twice turned down due to lack of escort vessels and loss of time to shipping, was introduced in April 1917 and proved immediately successful in reducing the shipping loss rate. The result of all the various British efforts.\ncountermeasures,  of  which  the  convoy  system  was  the \nmost  effective,  was  that  by  October  1917,  1501  ships \nin  99  convoys  had  been  brought  into  port  with  the \nloss  of  only  ten  ships  sunk  while  in  convoy  (a  loss \nrate  of  less  than  1 per  cent). \nLACK  OF  SATISFACTORY \nCOUNTERMEASURES \nAlthough  shipping  losses  had  been  checked,  it \nshould  be  kept  in  mind  that,  from  an  offensive  point \nof  view  (i.e.,  destruction  of  U-boats),  the  U-boat  had \nnot  been  definitely  beaten  in  World  War  I.  After  the \nstart  of  unrestricted  U-boat  warfare  early  in  1917,  the \nGermans  maintained  an  average  of  about  40  U-boats \nat  sea  at  any  time.  During  this  period  the  average \nnumber  of  U-boats  being  sunk  each  month  was  only \nabout  seven;  the  maximum  number  of  U-boats  sunk \nin  any  month  was  only  14  in  May  1918.  Therefore, \nthe  average  life  of  a U-boat  at  sea  during  the  last  year \nDuring the final six months of World War I, shipping losses remained at approximately 300,000 gross tons per month. Consequently, each U-boat was sinking around 45,000 gross tons of shipping before it was itself destroyed. These statistics suggest that factors other than U-boat losses contributed to the 1918 U-boat crew mutinies, as U-boat losses reached much higher levels in World War II without causing a similar morale collapse. Another point to consider is that a significant portion of German U-boat losses in the late stages of World War I was due to mines. The effectiveness of mines was increased by the fact that German U-boat bases were geographically situated, necessitating passage through the North Sea. Of the 178 U-boats sunk during this period.\nDuring the first World War, approximately 45 percent of ships were sunk by surface craft. About half of these were sunk by depth charges and half by gunfire and ramming. Approximately 30 percent were sunk by mines, another 10 percent were torpedoed by submarines, and the remaining 15 percent were sunk by other causes. It is therefore clear that the Allies had not developed any offensive weapon during World War I that could deal effectively with the U-boat at sea, making further operations unprofitable.\n\nHistory of Antisubmarine Operations\n\nThe Germans themselves still believed the U-boat to be an effective weapon at the end of World War I, as indicated by the fact that there were approximately 220 U-boats under construction in November 1918. Admiral Scheer\u2019s building program of October 1, 1918 provided for at least 30 U-boats a month beginning the middle of 1919 and would probably have resulted in a significant increase in the U-boat fleet.\nOne of the most significant points about antisubmarine warfare which became apparent early in World War 1 was the necessity of having scientific and technical aid in combatting the U-boat. The essential problem was that of having some means of detecting a submerged U-boat and then of having some weapon that would provide a good chance of destroying it.\n\nThe first crude attempt to develop an instrument to detect the submerged U-boat resulted in the installation of hydrophones on Allied naval ships in 1915. The hydrophone was simply an instrument for listening to the noise produced by the submarine, and sonic frequencies below 10 kc were used. No further details are provided in the text.\nA rough bearing was obtained from early hydrophones, but it was impossible to make accurate attacks on U-boats due to this limited information. The main impact of hydrophones was on U-boat morale, as they discovered they were being followed after diving instead of being free from their pursuers. The first depth charges for attacking submerged U-boats were introduced in 1915, but so few were available that the Germans did not realize they were being used until 1917. In September 1918, the British formed a small committee, primarily composed of scientists, called the Anti-Submarine Division International Committee (ASDIC). This committee developed a method of transmitting sound of supersonic frequencies underwater and then using the echoes to determine distance.\nThe echo returned from the submerged submarine to fix its position. Although the Asdic set was still in the experimental stage when World War I ended, the committee's labors were not wasted. Effective underwater echo-ranging gear was developed in the 1930s and proved to be quite a surprise to the Germans at the start of World War II. Due to Asdic's ability to provide both range and bearing, it proved far better than the hydrophones used in World War I. Hydrophones themselves were also improved by using supersonic frequencies and making them directional, thereby enabling the operator to obtain more accurate bearings.\n\nAt the start of World War II, England had approximately 220 Asdic-fitted antisubmarine craft, consisting of about 165 destroyers and 35 patrol craft.\nThe British had 38 warships (sloops, frigates, and 20 trawlers) compared to over 3000 ships (about 450 destroyers, 170 patrol craft, and the remainder trawlers and small craft) available to the Allies for antisubmarine warfare in 1918. The British, profiting from their experience in World War I, had learned that the ocean convoy system reduced shipping losses more than anything else. They knew that the convoy system worked best in open water where evasion could be employed and that its success depended upon efficient escorts armed with effective offensive weapons. They were also aware that an efficient U-boat tracking system was necessary for effective evasion, and a daily U-boat plot based on contacts, DF fixes, and intelligence was used throughout the war. Meanwhile, the Germans had done considerable research.\nThe Germans developed and improved their U-boats. U-boats at the start of World War II were faster and stronger than those used in World War I. They could dive deeper and withstand more depth-charge punishment. Germans had also developed an electric torpedo with no visible wake. However, in September 1939, the Germans had approximately 60 U-boats, with 30 of the small 250-ton type for coastal operations and 30 of the larger ocean-going type, including 20 of 500 tons and 10 of 750 tons. This small number suggests that Germany, not anticipating England's early entry into the war, prioritized building tanks and aircraft for land warfare over U-boats.\nChapter 1\nFirst Period\nSubmerged Daylight Attacks on Independents\nSeptember 1939 - June 1940\nU-Boat Offensive\n\nThis first phase of U-boat warfare was greatly influenced by the rapidly changing overall military situation. Germany invaded Poland on September 1, 1939, and England and France declared war on Germany on September 3. Some U-boats had left Germany early in August, and when the war began, there were about six at sea, ready to start an offensive in the Northeast Atlantic in the Western Approaches to England.\n\nAccording to statements of early prisoners of war, the commanding officers of U-boats had been ordered to observe International Law, which forbade U-boats from sinking merchant vessels without first placing the passengers and crew in a place of safety.\n\nAt the beginning of September, these instructions seem to have been generally obeyed, with the notable exception of a few incidents.\nThe situation did not last long. By the end of September, neutral ships were being torpedoed without warning. In anticipation of unrestricted U-boat warfare, the British had prepared plans before the war for the immediate establishment of the convoy system. The first trade convoy sailed on September 6. With the British defenses against U-boat attacks focused primarily on protecting the fleet and secondarily merchant shipping, the limited number of anti-submarine vessels available for convoy escort was inadequate for providing direct protection to the convoys. However, it was believed that British anti-submarine measures were sufficiently effective to ensure that no U-boat could attack a convoy without running a severe risk.\nThe experience in September justified expectations, as over 900 ships were conveyed without loss. Two U-boats were sunk during the month by British surface craft. The Germans had no knowledge of British Asdic and still believed they could counter underwater detection by reducing internal noises. The lack of knowledge of British Asdic likely accounted for early U-boat tactics. U-boats preferred attacking targets during daylight, believing themselves relatively invisible due to submergence powers.\nU-boats attacked targets through periscopes, making torpedo attacks from periscope depth. If the target was an unarmed merchant vessel, U-boats usually surfaced and attempted to sink the ship by gunfire. In September, before the convoy system was fully established, there were enough unescorted targets at sea for U-boats to sink 39 ships totaling 151,000 gross tons. Ten of these ships were sunk by gunfire alone from surfaced U-boats. This led the British to take immediate steps to arm as many merchant ships as possible to defend against such attacks. At the start of the war, antisubmarine forces in the Western Approaches were augmented by aircraft carriers. However, after HMS Courageous was sunk by U-boat torpedoes on September 17, the carriers were withdrawn.\nShore-based aircraft of the Coastal Command helped significantly by flying over 100,000 miles in September, sighting approximately 50 U-boats or supposed U-boats, and attacking over 30 of them. Although none of the aircraft attacks were very effective, they did cause the U-boats to submerge and thereby reduced their effective operating period.\n\nThe September U-boat campaign was followed by a lull during the first ten days of October, during which, although U-boats were at sea, hardly any ships were attacked. This lull seemed to reflect the political situation at the time, as it was accompanied by Hitler\u2019s offer of peace on October 6. U-boat activity flared up again on October 12, and by the end of the month, 28 ships of 136,000 gross tons had been sunk by U-boats. In addition, Kapitan-leutnant Prien, in.\nU-47's commander penetrated Scapa Flow harbor in October, sinking HMS Royal Oak, a British battleship. This incident directed British attention to the need for protecting harbors against U-boats using fixed defenses, such as booms, indicator loops, mine fields, and harbor defense Asdics.\n\nDuring November and December, the main effort of German U-boats focused on a mine-laying campaign on the East Coast of England, particularly in the Thames Estuary. They laid both the old type of contact mine and a new type of magnetic mine, which initially proved difficult to sweep. Monthly losses due to U-boats (torpedoes and gunfire) fell to 18 ships of about 65,000 gross tons, while shipping sunk by mines exceeded 100,000 gross tons during each of these months.\nU-boat activity began increasing again in the second week of January 1940, and by the end of the month, there were as many U-boats at sea as at the start of the war. In February, the U-boat effort was greater than during any previous period, and 35 ships of 153,000 gross tons were sunk. The U-boats continued to follow a policy of attacking Allied and neutral ships without warning. They preferred attacking single ships or stragglers from convoys, making it difficult for the antisubmarine ships to conduct an effective search and counterattack. The respect the U-boats had for the British convoys is indicated by the fact that only 7 of the 169 ships sunk by U-boats during the first six months of the war were in convoy when sunk, although roughly half the shipping sailed in convoy at this time. Losses due to mines fell off during January.\nFebruary: As better methods for sweeping magnetic mines were developed and more ships were degaussed (magnetic field of ship changed to protect it against magnetic mines), there was a marked lull in U-boat activity throughout March. The absence of U-boats from Atlantic waters began around the 12th of the month. In early April, every available U-boat left Germany to take up patrol positions in the North Sea to aid in the impending military operations against Norway. The average number of U-boats at sea peaked at approximately 15 during the second week of April, when Germany invaded Norway. Despite the large concentration of U-boats, the damage they inflicted was remarkably small. No British capital ship was attacked by U-boats, and only six ships of 31,000 gross tons were sunk.\nDuring the entire month of April, a new low for the war was reached. In addition, the Germans lost six U-boats during the month, a new high for the war. There was very little U-boat activity during the first half of May as Germany started her invasion of Holland and Belgium on May 10. It is believed that during May, no U-boat proceeded to the Western Approaches until the 21st, and only 10 ships of 48,000 gross tons were sunk by U-boats during the month. Shipping losses to U-boats were exceeded for the first time during the war by the 154,000 gross tons sunk by aircraft. These losses were incurred largely in connection with the operation and evacuation of the British Expeditionary Force, which left Dunkerque. The Germans announced on May 29 that U-boat warfare was about to recommence and warned neutrals not to enter the protection of British convoys.\nThis was followed by a period of intense U-boat activity as convoys were attacked with greater boldness than in earlier periods, advantage being taken of the paucity of escorts, rendered inevitable by the demands of the military evacuation and the Home Fleet. The losses for June were the highest of the war, with 56 ships of 267,000 gross tons being sunk by U-boats. The German ace, Kit Prien, contributed his share by sinking ten ships of about 67,000 gross tons during one cruise. By the end of June, France was out of the war and Italy had entered the war with over 100 U-boats, about 60 of which were ocean-going (650 tons and over).\n\nThe convoy system was by far the most effective countermeasure in keeping down shipping losses to U-boats during this first period, just as it had been in earlier periods.\nDuring World War I, this was still true even though the number of antisubmarine vessels suitable for ocean escort was insufficient to provide direct protection to convoys. The British met this problem by keeping their convoy system flexible, changing the number of escorts and the distances for which convoys were escorted in accordance with U-boat activity. It should be noted that the Germans made this problem more difficult by sending U-boats out in waves, resulting in peaks of U-boat activity in September 1939 and in February and June of 1940. Although the first convoys sailed early in September 1939, the convoy system was not fully in force until the beginning of October. The designations of the main convoy routes set up then were:\n\nOB: Outward bound from England to America and Africa.\nHomeward-bound ships to England from Halifax and Sierra Leone. In order to illustrate some of the problems involved in setting up the convoy system, a detailed account is presented of the changes made in the HX convoy route during this period. On October 7, 1939, it was decided to discontinue convoys from Kingston, Jamaica, and all ships in the West Atlantic were routed independently to Halifax, taking advantage of U.S. waters as far as possible. Convoys were divided into slow (9-12 knots) and fast (12-15 knots) convoys, which left Halifax at about the same time to arrive four days apart at the rendezvous point. At this point, located at about 15\u00b0 west longitude, the convoys were met by one or two destroyers which provided antisubmarine escort to England. The ocean escort, provided between Halifax and the rendezvous point.\nRendezvous points primarily for protection against surface raiders consisted of a battleship, cruiser, or armed merchant cruiser, and one or two submarines when available.\n\nThe first of these convoys, HX 6 and HXF 6, consisted of 62 and 6 ships, respectively. The dividing line was then altered to 11 knots to equalize the number of ships. During November 1939, the number of ships in these sections averaged 32 and 12.\n\nOn February 12, 1940, the fast convoys were discontinued, and all HX convoys sailed at 9 knots, at 3- and 5-day intervals. These convoys consisted of ships with speeds between 9 and 15 knots, ships of higher speeds sailing independently. At the beginning of April, in order to equalize the size of the convoys, 4-day intervals were started.\n\nEarly in May 1940, Bermuda began to be used as an assembly point for vessels from the West Indies and other ships.\nother points in that vicinity, and HX 41 was the first combined Bermuda and Halifax convoy. Sections formed at sea, as arranged, at about 41\u00b0 north latitude and 43\u00b0 west longitude, and the Bermuda escort then returned to base. This change enabled about 60 percent of the ships that formerly sailed from Halifax to cut down their voyage by 500 miles and to avoid the fog off Newfoundland. The average number of ships in these HX convoys had risen to 46. In addition to the above-mentioned convoys, the British also sailed coastal convoys to protect shipping on short trips around the English coast and Scandinavian convoys to and from Norway. The main energies of the French light craft were also devoted to the protection of merchant shipping. They were fitted with Asdic as soon as possible after the opening of the war and provided escorts for purely French merchants.\nThe convoy system helped escort Gibraltar convoys for most of the way and assisted in covering military cross-Channel convoys. About 2500 ships were being convoyed monthly, while only about 5 of these were sunk monthly by U-boats (2.5 in escorted convoys, 2.5 in unescorted convoys, and 1 straggler). The rate at which independent merchant vessels were being sunk by U-boats was roughly about four times as high.\n\nAircraft were another important countermeasure against U-boats. They had seen very little use against U-boats during World War I, and it took some time to solve the problems of how to use aircraft most efficiently against U-boats. In addition, the aircraft were still armed only with limited weaponry.\nWith bombs, the direct contribution of aircraft toward sinking U-boats was negligible during this period. However, aircraft performed a defensive function of great value in helping to protect shipping. Coastal Command aircraft flew approximately 4500 hours monthly on purely antisubmarine work. About 20 U-boats were sighted monthly and 12 of these were attacked, with about 10 percent of the attacks resulting in some damage to the U-boat. This effort reached a peak of 9500 hours during June 1940, when about 2800 hours were spent on antisubmarine patrol and 6700 hours on convoy escort duty.\n\nSubmerged daylight attacks on independents were the main value of this flying. It caused U-boats to submerge, thus preventing them from shadowing or approaching convoys on the surface. It also helped to discourage them from operating.\nClose to the shores of England where flying was heaviest, U-boats were under orders to submerge as soon as they sighted a plane and the British took advantage of this by starting, in November 1939, to use light aircraft of the Moth type to patrol around the coast. Known as \"scarecrows,\" these aircraft carried no bombs and were used solely to sight and report U-boats, and to make them submerge. These flying hours and sightings helped considerably in keeping an accurate U-boat plot.\n\nScientific and technical efforts were focused on improving antisubmarine attacks during this period. Applying the lessons learned in World War I, significant scientific work was underway to address the following problems:\n\n1. Development of an Asdic receiver-amplifier with automatic sensitivity control, so that both long and short wavelengths could be detected effectively.\nAnd short range echoes would be clearly recorded.\n1. Theoretical investigation of improved methods for carrying out antisubmarine attacks and of the best type of depth-charge pattern to ensure destruction of the submarine,\n2. Assistance to antisubmarine personnel in distinguishing between submarine and non-submarine targets, as a great amount of effort and a large number of depth charges were being expended on wrecks, whales, and other non-submarine targets.\n3. Sinking of U-Boats\nSurface craft, equipped with Asdic and depth charges, were by far the most potent enemy of the U-boat during this first phase of U-boat warfare.\nTwenty-one German U-boats are known to have been sunk as a result of Allied action during this 10-month period; 15 were sunk by surface craft, one by the coordinated action of two ships and one plane, one by a plane from a British battleship, two were sunk by mines.\nThe estimates for U-boat sinkings are based on Allied assessments. Incidents assessed as A or B are considered to have sunk the U-boat. Justification for this assumption is given in Appendix 1.\n\nTwo German U-boats were torpedoed and two were mined while attempting to pass through the Dover Barrage in October. Two other German U-boats were sunk under unknown circumstances, and one was sunk in the Baltic after being rammed accidentally.\n\nIn addition to the 24 German U-boats mentioned above, 10 Italian U-boats were sunk in the Mediterranean, Red Sea, and Indian Ocean between June 10 (when Italy entered the war) and the end of the month.\n\n1.3.1 From the U-boat Point of View\nThe average number of U-boats at sea in the Atlantic during this first phase of the U-boat war was about six. The average number of ships sunk monthly by U-boats was:\nThem were 26 of about 106,000 gross tons, so about four ships of about 18,000 gross tons were being sunk per U-boat month at sea. However, about two out of the six U-boats at sea were being sunk each month, so the average life of a U-boat at sea was only about three months. This relative rate of loss of U-boats were extremely high, much higher than at any stage of the first World War, and makes readily understandable the fact that they preferred attacking unescorted ships to attacking convoys, lightly escorted as they were. It also helps to explain why the German U-boats felt it necessary to change their tactics during the next phase of the U-boat war; this, despite the fact that the overall exchange rate {i.e., 13 ships of about 53,000 gross tons sunk for each U-boat sunk) might be considered satisfactory for the.\nThe rate of loss of U-boats was higher than the Germans could afford. This is evident from another perspective. The Germans began the war with approximately 30 ocean-going U-boats (i.e., 500 tons or larger). By the end of June 1940, 18 of these had been sunk while only about 15 new ones had been commissioned. Consequently, the Germans only had about 27 ocean-going U-boats available at the start of the second period of the U-boat war.\n\nFrom the Allies\u2019 Point of View:\nBy the end of June 1940, England was left alone in the war against Germany, and her ability to continue the war depended on her keeping her sea lanes open. Total shipping losses of the Allied and neutral nations were about 280,000 gross tons monthly, compared to a building rate of only about 88,000 gross tons monthly, resulting in a total net loss of 1,920,000 gross tons.\nDuring this 10-month period, a total of approximately 40,000,000 gross tons of shipping existed at the start of the war. Gross tons lost due to all causes amounted to 280,000. About 223,000 gross tons were lost monthly, with enemy action accounting for approximately 223,000 gross tons (80%). U-boats were responsible for 106,000 gross tons (48%), mines for 58,000 gross tons (26%), aircraft for 27,000 gross tons (13%), surface craft for 14,000 gross tons (6%), and other and unknown causes for the remaining 7%. The U-boat was the main threat to Allied shipping. The convoy system was the primary factor in keeping shipping losses at a relatively low rate.\nThe number of British Asdic-fitted antisubmarine vessels increased from approximately 220 at the beginning of the war to about 450 by the end of June 1940. Most of the increase took place in trawlers and other small ships. The 450 ships consisted of about 180 destroyers, about 55 patrol craft, and about 215 trawlers and other small craft. However, the number of these ships that could be spared for escort duty was still insufficient to provide adequate protection to the convoys. The British had been fortunate during the first period that the enemy had only a small number of U-boats available and these had operated in a limited area. Almost all ship sinkings occurred in the Northeast Atlantic (east of 20\u00b0 west longitude and north of 30\u00b0 north latitude).\nThe second period of the U-boat war was marked by a complete change in enemy tactics. Germans, having discovered as a result of their high rate of loss that U-boats were quite vulnerable to Asdic when submerged, decided to make use of the hours of darkness to regain their relative invisibility. At night, trimmed down on the surface, a U-boat offers a very small target to the human eye and is also rather difficult to detect by Asdic. The surfaced U-boat has the advantage of high speed and maneuverability and therefore has good chances of avoiding detection by the escorts. Acting on this principle and encouraged by the results achieved at night during the first period by a few of the more successful U-boats, the Germans began to focus their attacks on convoys during the night.\nU-boat captains initiated the practice of attacking convoys at night from a surfaced position in July 1940, using their high surface speed to escape. Occasional daylight attacks were still made on independent ships and stragglers from convoys. This change in enemy tactics was accompanied by the occupation of French ports and their establishment as U-boat bases, marked by the first visit of a U-boat to Lorient on July 22. The use of French bases reduced U-boat transit time and extended their operations further westward in the Atlantic. From his air bases in France, the enemy was also able to send out long-range reconnaissance aircraft to detect convoys in the Atlantic. Additionally, after the fall of France, the threat of a seaborne invasion of England emerged.\nThis confined a large number of destroyers to the East and South coasts of England, consequently limiting the number of ships available for convoy escort and encouraging U-boats to attack convoys more frequently. Aircraft were diverted from antisubmarine patrols over the Western Approaches to England, where U-boats were operating, to anti-invasion patrols to the eastward. Some Italian U-boats had also started operation in the Atlantic in August 1940. These Italian U-boats used Bordeaux as a base and followed the same methods as German U-boats, presumably working directly under German orders. Their operational areas were usually southward of those used by the German U-boats. Increased U-boat activity, which had commenced in June 1940, continued throughout July and August with over 200,000 gross tons of shipping being sunk.\nIn each of those months, the most active area was the Western Approaches between the latitudes of 48\u00b0 north and 51\u00b0 north, up to the middle of July. After the threat of air attack from French bases led to the rerouting of British convoys around north of England, U-boats lost no time in shifting their area of activity to the Northwestern Approaches to meet the increased traffic there. This activity was marked by increased attacks on convoys while anti-submarine escorts were present, but these attacks were generally on large convoys, which, owing to the shortage of escort vessels, were guarded by about two Asdic-fitted ships.\n\nOn August 15, Germany proclaimed a complete blockade of the British Isles and called upon neutral governments to forbid their ships to sail through the Anglo-German war zone. U-boat activity was concentrated here.\nThe shipping losses significantly intensified after that date, with approximately 300,000 gross tons sunk by U-boats in September, and a new war high reached in October with 62 ships totaling 346,000 gross tons sunk. The Northwestern Approaches remained the scene of greatest activity, with night attacks on convoys being the preferred method. Of the 59 ships attacked in this area in September, 40 were in convoy, and 71% of the total were night attacks. The concentration of aggressive operations into the period of, and immediately following, the full moon was especially notable during October when 31 ships were attacked on October 18 and 19.\n\nU-Boat Offensive:\nDuring these months of heavy losses, the average number of U-boats at sea remained significant.\nSix-year-old I was, meaning ten ships of approximately 60,000 gross tons were sunk by an average U-boat at sea during October 1940. This was likely an all-time high in operating efficiency for submarines. In addition to inflicting these heavy losses, U-boats were almost invariably escaping unscathed. For instance, only one U-boat was sunk in the Atlantic during October. These were the days when renowned German commanders (U-boat aces) like Prien and Kretschmer were operating. These aces had survived the hazards of the initial period and had profited from the experience gained then. The U-boats conducting night attacks on convoys operated individually, and usually only one or two were involved in the attack. Despite this, some convoys suffered rather heavy losses.\nas,  for  example,  HX  79,  which  lost  12  ships  to  two \nU-boats  in  one  night  in  October. \nThe  normal  procedure  for  U-boats  attacking  con- \nvoys at  this  time  seems  to  have  been  as  follows:  The \nU-boat  gained  contact  with  the  convoy  during  the \nday,  either  as  a result  of  reports  from  long-range \nGerman  reconnaissance  aircraft,  reports  from  other \nU-boats,  or  by  sighting  smoke,  and  then  proceeded \nto  shadow  the  convoy  at  visibility  distance  on  the \nbow  or  beam.  When  darkness  had  fallen,  the  U-boat, \ntrimmed  down  on  the  surface,  closed  the  convoy,  and \nendeavored  to  reach  a position  broad  on  its  bow.  She \nkept  very  careful  watch  for  the  escorts  and  endeav- \nored to  pass  astern  of  those  stationed  on  the  bow  of \nthe  convoy.  The  approach  was  pressed  home  as  close \nas  the  U-boat  captain  dared,  and  it  is  possible  that, \nin  some  cases,  a firing  range  of  about  600  yards  was \nU-boats, having reached a firing position on the beam of the convoy, increased to full speed, fired a salvo of four torpedoes, turned away still at full speed, firing stern tubes if possible, and retired as rapidly as possible on the surface in the direction considered safest. If their retreat was unseen, they might reload their torpedo tubes on the surface and attack again in the same manner later in the night.\n\nThe serious damage inflicted on British convoys by these new U-boat tactics caused a considerable number of changes to be made. The spacing of the convoy columns was opened up to reduce the chance of more than one ship being hit by a salvo. Escorts were stationed farther away from the convoy and new plans were developed for searching for the U-boat with illuminants following attack.\nImprove the tactical efficiency of the escorts, these ships were formed into groups, and as far as possible, ships of one group were to work together. The Admiralty took over the responsibility for the routing of all ocean-going convoys, thus enabling emergency changes to be made without delay. In addition, great efforts were made to equip all convoy escorts with radar, which would enable them to locate U-boats on the surface at night outside visibility distance and possibly before they could attack the convoy.\n\nBy November 1940, Lorient had become the principal U-boat base. During this month, one German U-boat had left this port and gone as far south as Freetown, sinking four ships in three days. November was also marked by several heavy air attacks on the ports of Lorient and Bordeaux, which were considered to have inflicted severe damage on both.\nThe first successful counterattack against German night attacks on convoys occurred on November 21, after two ships in Convoy OB 244 had been torpedoed. The British corvette HMS Rhododendron, stationed astern as a rescue ship, sighted an object at a range of 1500 yards about an hour after the torpedoing. Three minutes later, Asdic contact was gained, and depth charges were dropped, resulting in considerable metallic wreckage and oil being blown to the surface.\n\nThis successful counterattack, along with the loss of two other U-boats, might account in part for the reduced number of attacks on escorted convoys in November and December 1940. Heavy winter weather in the North Atlantic was probably also a factor in accounting for the decrease in shipping losses to U-boats.\n150,000 gross tons were sunk in November, 200,000 gross tons in December. Early in December, a westerly movement of U-boats became noticeable, with most of them stationed as far out as 20\\*^ west longitude. This may have been due in part to Coastal Command flying and in part to an attempt to intercept incoming convoys before the antisubmarine escort joined. However, this actually increased the enemy\u2019s difficulty in locating convoy traffic.\n\nAs a counter to the fact that U-boats in the Northwestern Approaches had been attacking British convoys in longitudes 20\u00b0 to 25\u00b0 west, which is an area beyond the point that could be reached by the escorts, new evasive routing measures were adopted in December. It was decided to make use of dispersion to the maximum extent that the endurance of the convoys allowed.\nMerchant ships were permitted, and the convoy routes were spread between 63.5\u00b0 and 57\u00b0 north latitude. The cycles of convoys were also extended, with the objective of reducing the strain on escorting forces.\n\nThis thorough diversion of convoy routes appears to have been the main factor in the reduction of shipping losses, just as it had been in World War I. No attacks were made on escorted convoys from December 1940 until January 29, 1941. Shipping losses to U-boats in January dropped to 21 ships of 127,000 gross tons, the lowest figure since the Germans announced their intensified U-boat campaign in May 1940. This occurred despite the fact that the average number of U-boats at sea in the Atlantic had increased to about 12. Most of the ships lost during these two months were not in convoy.\nU-boats had difficulty finding convoys and resorted to the much easier task of picking off stragglers or ships sailing independently. The month of February 1941 opened with a continuation of the comparative lull in U-boat activity. Evasive routing had frustrated the normal German \u201chit and run\u201d method of night attack on the convoys. However, it became clear in February that this had provoked intensified enemy offensive measures, in the form of greater cooperation between aircraft and U-boats, and special searching patrols. The days of wolf-pack attacks were foreshadowed as the U-boats started operating in groups of three to five, each U-boat being given a limited patrol area within the wider area covered by the group. The first U-boat to gain contact shadowed the convoy while others were ordered to concentrate in a position to attack.\nU-boats typically emitted radio signals to home other U-boats or aircraft for attack. Similarly, aircraft were able to home U-boats to a convoy. The cooperation between U-boats, aircraft, and surface craft is well illustrated by the attack on Convoy HG 53, consisting of 21 ships escorted by one sloop and one destroyer. The convoy was attacked by a U-boat at 0435 on February 9, sinking two ships. The U-boat continued to shadow the convoy and probably homed six Focke-Wulf aircraft to it during the afternoon of the 9th. Five ships were bombed and sunk, while one plane was shot down. The U-boat continued to shadow the convoy and again attacked on the 10th, sinking one ship. After this, she maintained touch with the convoy, reporting its position. Her reports were evidently intended for a German \"Hipper\" class cruiser. While closing HG 53, this\nA cruiser encountered SL 64, an unescorted slow convoy, and launched an attack, sinking seven ships. Three other convoys were assaulted by U-boats in late February, and as the month ended with losses amounting to 36 ships of 189,000 gross tons, it was clear that the anticipated U-boat spring offensive had begun. The average number of U-boats in the Atlantic rose to 16 in March, with some of Germany's most proficient U-boat captains among them. Their strategies involved repeating concentrated night attacks on convoys, and six convoys were targeted during the month. The upward trend of shipping lost due to U-boat action reported in February was sustained in March, with total losses reaching 40 ships of 239,000 gross tons. These losses were significantly less than expected.\nThe problems in the text are minimal. Here is the cleaned text:\n\nDuring March 1941, the U-boat problems were more extensive than those recorded during September and October 1940, the last previous period of intense U-boat activity. However, these problems were not considered unduly alarming, considering the fact that the number of U-boats at sea in March was more than twice as great as in the earlier period.\n\nMore encouraging was the evidence of the increased efficiency of antisubmarine escorts and the fact that U-boats which attacked adequately escorted convoys could be dealt with effectively. This evidence was clearly demonstrated by Germany's loss during March of her three outstanding U-boat aces - Prien, Kretschmer, and Schepke. Prien, commander of U-47, was the first to be lost as a result of his attack on Convoy OB 293.\nOne ship was sunk shortly after midnight on March 8, 1941. HMS Wolverine, one of the escorts, sighted smoke about 20 minutes after the attack on the convoy and made contact with the U-boat. The U-boat was attacked for over five hours. During this time, there was a remarkable chase of the U-boat on the surface for over an hour before it was finally considered sunk. There were no survivors. Prisoners of war from U-boats sunk subsequently have supplied information from which it is believed that the Wolverine's attacks were made on U-47, commanded by Prien. Berlin subsequently admitted the loss of Prien. U-100 (Schepke) and U-99 (Kretschmer) were both sunk as a result of the attack on Convoy HX 112, during which five ships were sunk. U-100 located the convoy, which had been reported earlier by U-99.\nThe evening of March 16. Later, she sighted a destroyer astern and dove. At 0137 on the 17th, HMS Walker obtained Asdic contact and attacked with depth charges. Three further depth-charge attacks were carried out by HMS Vanoc and HMS Walker before contact was lost at 0250. Meanwhile, U-100, which had been considerably damaged by the depth charging, had surfaced. While the escorts were preparing to take station for an organized search, Vanoc\u2019s radar operator reported a contact 1000 yards away and U-100 was subsequently sighted on the surface and rammed by HMS Vanoc. Schepke, who was caught and crushed between the stove-in side of the bridge and the periscope, was carried down with the sinking U-boat.\n\nWhile HMS Vanoc was picking up survivors of U-100, HMS Walker obtained Asdic contact. Although it was considered unlikely that another submarine was present, the escorts continued their search.\nU-boat remained so close that the Asdic operator was convinced he had a submarine contact. HMS Walker fired six depth charges, an extremely accurate attack that brought U-99 to the surface almost at once. Both destroyers opened fire, and U-99 was abandoned shortly afterward, with Kretschmer and other survivors taken as prisoners. Kretschmer had been quite successful up to that point, claiming a record total of 86,000 tons of shipping sunk on this last cruise, while his total sinkings had reached 338,000 gross tons, more than any other U-boat captain.\n\nThere were immediate indications that the enemy was severely shaken by the results of his attacks on adequately escorted convoys. The only subsequent attack during the month was made far west before the antisubmarine escort had joined, sinking three ships from HX 1J5 at 22\u00b0 west longitude.\nThe loss of three skilled U-boat commanders had a profound effect on U-boat morale, in addition to influencing U-boat tactics and operations.\n\nCountermeasures to the U-Boat:\n2.2.1 Convoys\nThe high percentage of hits obtained by U-boats in night attacks necessitated increasing the distance apart of convoy columns from approximately 600 yards to about 1000 yards in November 1940. The distance between ships in the same column was about 400 yards. In December 1940, the distance between columns during daytime was reduced back to 600 yards to enhance protection against air attacks. To counteract the heavy losses incurred due to night attacks by surfaced U-boats in September and October 1940, escorts were stationed further out on each wing from the convoy. In the event of an attack, they would:\nInstructions were to proceed outward from the convoy for a distance of 10 miles at full speed, firing star shell to illuminate the area where the U-boat might be, in an attempt to sight her or force her to submerge, thereby improving the chances of Asdic detection. If contact was made, two escorts were to hunt the U-boat while the remainder were to rejoin the convoy.\n\nLater, when radar-equipped escorts became available, they were stationed one on each beam of the convoy, about 4 miles from it to avoid back echoes on the radar set. The beam escorts were to steam on the same and opposite courses as the convoy, zigzagging as required for self-protection. Another method of sweeping, which was under trial in order to effect an economy in fuel, was for the escort to start a slow turn of 360\u00b0 when in a stationary position.\nBy July 1940, the convoy system was fully established, and most changes were due to enemy activity. The transatlantic HX convoys, the main supply line to England, faced both serious U-boat night surface attacks and enemy air and surface craft activity.\nThe first HX convoy to be routed around north of England in July 1940 made a rendezvous with the local antisubmarine escort at about 17\u00b0 west longitude. Slow convoys to include ships between 7 1/4 and 9 knots were organized in August and assembled at Sydney, Nova Scotia, and were designated SC. This reduced the HX convoys to a reasonable size of about 45 ships. The HX convoys sailed on a 4-day cycle, while the SC convoys were on an 8-day cycle. In December, Sydney was abandoned as a convoy assembly port, but the SC convoys were to continue to sail from Halifax.\n\nIn order to extend the antisubmarine escort further west, convoy intervals were lengthened. HX convoys sailed at alternate 6- and 4-day intervals, while the SC convoys sailed at 10-day intervals. In addition, Loch Ewe, in the northern part of Scotland, was used as a convoy assembly point.\nThe port, initiated as an assembly point for ships on the east coast of England, allowed destroyers to refuel and operate further west, serving as anti-submarine escorts. In February 1941, two HX convoys were rerouted on a southern course due to heavy air attacks. Following an attack by a surface raider and the sighting of two German battlecruisers in the Atlantic, close battleship cover was given to all Halifax convoys. This threat of surface raiders also led to the discontinuance of the Bermuda section of HX convoys, and ships were routed independently to Halifax assembly. British convoys were much harder hit during this second period than in the previous, with approximately 3600 ships convoyed monthly and 26 of these being sunk.\nU-boats (13 in escorted convoys, 3 in unescorted convoys, and 10 stragglers). This meant that the total loss rate to U-boats was about 0.7%, or more than three times as high as in the earlier period. The HX and SC convoys sailing across the Atlantic to England were much harder hit than other convoys. Of the 360 ships sailing monthly in these convoys (only 10% of the total convoyed shipping), about 14 ships were sunk monthly by U-boats (over 50% of the total losses of convoyed shipping). The loss rate to U-boats on these vital convoys was about 4%, more than five times as high as for all convoys. Despite these high losses in convoys, the chances of being sunk by a U-boat were still higher for independently routed ships. Comparable figures are available for shipping passing through the Northwestern Approaches.\nDuring the 6-month period from September 1940 through February 1941, approximately 80% of total losses to U-boats occurred in that area. Of the 1180 ships sailing through this area monthly in convoy, about 29 were sunk monthly by U-boats, resulting in a loss rate of about 2.5%. Of the 70 independently routed ships sailing through this area monthly, about three were sunk monthly by U-boats, resulting in a loss rate of about 4%. When making this comparison, it's important to note that the ships sailing independently were generally capable of making a speed of at least 13 knots, much higher than the average speed of ships sailing in convoys. This means that if all shipping had sailed independently, the loss rate would likely have been much higher than the 4% experienced by the select group of ships.\nDuring the second period, the use of aircraft increased as a counter to U-boats. Though suffering from many limitations for antisubmarine operations, the airplane possesses obvious advantages denied to surface craft, such as speed, cheapness, large field of vision, and economy of personnel and material. A U-boat on the surface can rely on the fact that she will almost certainly sight an enemy ship before she, herself, is seen. However, she must always keep a vigilant lookout against being surprised by a plane sweeping down out of the clouds.\n\nIn an attempt to improve the lethality of aircraft attacks, Coastal Command tried using naval depth charges modified for air use. Sunderland aircraft started carrying both depth charges and bombs in July 1940. The first success of this new weapon came\non August 16, a U-boat was severely damaged as a result of a depth-charge attack. The Sunderland plane, carrying two depth charges and four 250-pound antisubmarine bombs, first dropped a single depth charge set to explode at a depth of 100 feet about 20 yards ahead of the conning tower of the submerging U-boat. The U-boat was forced to the surface, and two minutes later the second depth charge, set for 150 feet, was dropped about 20 feet ahead. Countermeasures to the U-boat ahead of the conning tower. The U-boat was again blown to the surface and was then observed to sink sideways. On the third attack, the stick of four bombs was dropped on the submerged U-boat. Air and oil came to the surface. In view of the initial successes of depth charges, steps were taken immediately to modify other Coastal Command aircraft.\nExpected aircraft attacks on U-boats to increase in lethality with the addition of depth charges. Night attacks on convoys in September 1940 led to the fitting of radar to Coastal Command and Fleet Air Arm aircraft. Valuable for detecting U-boats on the surface at night, hoped to enable nighttime convey escort work. Intended to provide maximum air escort for three hours before darkness falls, when U-boats could be found in shadowing positions. After the evasive routing of shipping initiated wolf-pack tactics in February 1941, the shadowing U-boat became the main problem.\nA contacted a convoy, the U-boat took great care not to reveal her presence by attacking in daylight, but shadowed the convoy at some distance. There was therefore only a small chance of the limited number of escorts discovering these U-boats, and this task fell to the escorting aircraft. In view of this, it was decided to reinforce the number of Coastal Command aircraft available for escort duty in the Northwestern Approaches. Consideration was also given to evolving the best type of aircraft patrol around the convoy to prevent the U-boat from shadowing it.\n\nDespite the curtailment of routine anti-submarine patrols in favor of anti-invasion patrols during this period, the average number of hours flown monthly by Coastal Command aircraft on anti-submarine duties increased by about 1000 hours over the pre-war period.\nDuring the previous period, a total of 6300 hours were reached, with 5100 hours on convoy escort and 1200 hours on patrol. Flying hours for antisubmarine work dropped to approximately 4000 during the winter months of December 1940 and January 1941 due to longer hours of darkness and poorer weather. By March 1941, it was again up to about 8000 hours. The increased flying hours were less productive than during the first period as the number of sightings made monthly dropped to about 14 and the attacks to about 8. This decrease in sightings, despite the increased number of U-boats at sea, was mainly due to their movement further westward, out of range of much of the flying. Approximately 10 percent of the attacks resulted in some damage to the U-boat, but the lethality of the attacks improved as two (about 2.1 percent) resulted in the destruction of the U-boats.\nProbable sinking of a U-boat. During this period, scientific and technical considerations focused on improving Asdic sets. One of the primary goals was the development of practical depth-determining gear. Little progress was made on this difficult problem, and the only immediate solution was the use of larger depth-charge patterns to counterbalance the large effect of the unknown depth factor. Another scientific development during this period was the extensive use of high-frequency direction finding (HF/DF) towards the end of 1940, after Germany had acquired the French bases and U-boats had started widespread operations in the Atlantic. The principle of HF/DF was that a shore station could determine the bearing of any U-boat making a radio transmission. It was hoped that the point of interception of the bearings from several shore stations could be used to locate and attack the U-boats.\nU-boats' positions were determined by transmitting stations. However, as more HF/DF shore stations became available around the Atlantic shores and U-boats operated in numbers on the Atlantic trade routes, it became clear that shore-based HF/DF could only provide a rough indication of the general area in which the U-boat was, at best, offering a warning for a threatened convoy and assisting convoy routing. The Germans appreciated this and felt that shipborne direction-finding was restricted to medium frequencies. They therefore used high-frequency communications extensively once contact had been made with the convoy. It was realized that HF/DF on convoy escorts could do a great deal more; it might even enable the escorts to find U-boats before they could launch their attacks. Immediate realization and implementation followed.\nRequirement was an HF/DF outfit for ships, which was quick and easy to operate. However, the main scientific achievement during this period was the introduction of radar sets on night surface attacks on both ships and aircraft. Radar worked on the principle of transmitting short pulses of very high-frequency radio waves and then receiving the echoes from objects, such as a U-boat on the surface. The echoes would enable the range and bearing of the object to be determined even at night and in conditions of poor visibility.\n\nWe have seen that the heavy shipping losses suffered at the start of this period due to night attacks on convoys had made radar an urgent necessity. As a stop-gap, the first radar sets fitted in destroyers were of a Royal Air Force design, known as air-surface vessel (ASV) or in the British Navy as ASV Type 271 or 285 sets.\nRadar direction-finding [RDF] Type 286 M. The fitting of these sets on ships began around November 1940, and by April 1941, radar had been fitted on approximately 40 destroyers of the Western Approaches Command. It was hoped that radar would enable the escorts to detect the presence of any U-boat on the surface within a radius of some two or three miles. Type 286 M had a fixed aerial and received echoes from a target over an arc covering about 50 degrees on each side of the bow and also over a similar arc astern at considerably shorter ranges (back echoes). The wavelength of these early sets was relatively long, over a meter, and consequently, the aerial had to be very high above the surface of the sea before any considerable range could be obtained on small objects. This limited the effectiveness against U-boats.\nRadar could be used in antisubmarine warfare for several subsidiary purposes besides detecting U-boats. It could give warning of approaching aircraft, make contact with single merchant ships or convoys, pick up navigation buoys, keep station on a convoy at night, or for making landfall. By January 1941, it appeared that radar on surface ships had been a disappointment as an antisubmarine device. Escorts had trouble keeping up with confusing \"back echoes\" from the convoy. As a temporary measure, it was hoped to alleviate this trouble by reducing the range scale from ten miles to five miles. Work was also being done on a newly developed radar system.\nDuring March 1941, new radar types with shorter wavelengths and directional aerials were under trial, and an improved naval radar design, Type 290, was in production to replace Type 286. In the Atlantic, surface craft made approximately 25 attacks per month, sinking or probably sinking 23 U-boats. Surface craft were responsible for 13 of these sinkings, or about 53%. Submarines were effective early in the period, patrolling close to French bases and torpedoing five U-boats in September 1940 and another in December. These submarine attacks necessitated U-boats entering and leaving their bases submerged. Two U-boats were probably sunk.\nThe following aircraft attacks resulted in the sinking of one ship due to a combined attack by a ship and a plane, and another was mined. One German U-boat was sunk under unknown circumstances, and two Italian U-boats were sunk in the Mediterranean. Surface craft accounted for six, or 55%, of these Italian U-boats. Italian U-boats operating outside the Atlantic had little success against Allied shipping, as only five ships of 28,000 gross tons were sunk in the Mediterranean and Indian Oceans during the first two years of the war, from September 1939 to September 1941.\n\n2.3.1 From the U-boat\u2019s Point of View\nThe new U-boat tactics adopted during this second period achieved their primary objective of reducing the high rate of U-boat losses. The average number of U-boats at sea in the Atlantic during this period was:\nThe position of German U-boats improved significantly during this period due to the increased U-boat building program. The average life at sea increased by 33%, from 3 to 4 months. U-boats sank an average of four ships, totaling about 22,000 gross tons per month. This resulted in an exchange rate of 16 ships of about 88,000 gross tons sunk for each U-boat sunk or probably sunk, a highly profitable transaction.\n\nFrom a quantitative perspective, the German U-boats' situation had greatly improved during this time due to the effective U-boat building program initiated after England entered the war. The commissioning of approximately 45 new ocean-going U-boats began to take effect.\nGermany had approximately 54 ocean-going U-boats available at the end of the period, twice as many as at the start. The Germans could send out more U-boats to sea during the third period than in the early stages of the war. However, they had lost many of their best and most experienced captains and crews, which were not easily replaced. The necessity of sending out relatively inexperienced U-boat captains may have influenced the Germans to operate their U-boats in groups in February 1941, allowing several inexperienced captains to operate with a more experienced one.\n\nFrom the Allies\u2019 Point of View:\nTotal shipping losses of the Allied and neutral powers amounted to approximately 11,600,000 gross register tons during the first 22 months of the war. The British alone suffered losses of about 8,500,000 gross register tons. The United States, which entered the war in December 1941, lost about 2,900,000 gross register tons during the remaining eight months of the war. The total tonnage lost by the Allies and neutrals was greater than that lost by Germany and her allies, but the Allies were able to replace their losses more easily because of their greater industrial capacity.\nDuring the second period, nations produced approximately 456,000 gross tons of shipping monthly, a 60% increase from the first period. Simultaneously, the building rate increased only slightly to about 114,000 gross tons a month, resulting in a net loss of approximately 342,000 gross tons a month. The total shipping available decreased from roughly 38,000,000 gross tons at the start of the second period to about 35,000,000 gross tons at its end.\n\nOf the 456,000 gross tons of shipping lost monthly, approximately 404,000 gross tons were lost due to enemy action. U-boats were responsible for sinking 42 ships totaling 224,000 gross tons monthly (55% of the total tonnage lost by enemy action). This was more than double the monthly tonnage sunk by U-boats during the first period. Monthly shipping losses due to enemy surface craft jumped to:\n87,000 tons (22 percent) and those due to enemy aircraft increased to 61,000 gross tons (15 percent). Monthly losses due to mines dropped from second place in the first period to only 27,000 gross tons (7 percent). Other and unknown causes accounted for the other 1 percent of the total losses due to enemy action. The U-boats had inflicted a serious defeat on the Allies in the Battle of the Atlantic during the second period, but the situation was beginning to look more promising toward the end of this period. One favorable element was the increasing number of antisubmarine ships and aircraft becoming available for convoy escorts as the threat of the invasion of England was decreasing. The number of antisubmarine ships suitable for ocean escort (i.e., destroyers and patrol craft such as sloops, frigates,)\nThe number of corvettes and destroyers had increased from approximately 235 at the start of this period to about 375 (including 240 destroyers) at its end. Factors contributing to this increase included the commissioning of new corvettes and the transfer of 50 old Town class destroyers from the United States to England in September 1940. Equipped with U.S. echo-ranging gear, called sonar, these destroyers were similar in principle to the British Asdic. Additionally, an increasing number of ships and planes were being fitted with radar to combat U-boat night activity. Officers and crews had gained more experience and training in antisubmarine warfare, inflicting heavy losses on U-boats attacking adequately escorted convoys in March 1941. It seemed that the main problem during the third period would be that\nThe third period, April 1941-December 1941: Start of Wolf Packs; End-to-End Escort of Convoys\n\nChapter 3\n\nSIU-Boat Offensive\n\nThe fruits of the intensified German U-boat construction program, started late in 1939, began to appear as the average number of U-boats at sea in the Atlantic steadily increased from about 18 in April 1941 to about 36 in August 1941. The main features of U-boat tactics during this third period were the increasing use of wolf-pack attacks, forced upon the Germans by the evasive routing of British convoys and the scarcity of experienced U-boat commanders.\n\nThe outstanding successes achieved by escorts in the Northwestern Approaches during March 1941 produced the direct result that, in April, U-boats intensified their attacks on Allied convoys.\nAbandoned the method of close attack on the surface while antisubmarine escorts were in company. U-boats continued their search for weak spots in the antisubmarine defenses by moving away from the vicinity of England, where air coverage was heavy, and extended their operations further westward where they could attack convoys before the anti-submarine escort had joined. There was also a southward movement of the U-boats with increased activity in the Azores and Freetown Areas.\n\nApril opened somewhat disastrously with heavy attacks, started before the antisubmarine escort had joined, on Convoy SC 26. About five U-boats participated in these attacks, ten ships were sunk, and, in addition, the armed merchant cruiser ocean escort was damaged by a torpedo hit. One of the attacking U-boats was sunk after the antisubmarine escorts had joined.\nFour ships were sunk from Convoy HX 121 towards the end of April, resulting from the first daylight attack by a pack of U-boats. Shipping losses to U-boats in April were approximately the same as in March, with 41 ships of 240,000 gross tons sunk. However, only about 30% of the tonnage sunk by U-boats was in convoy in April, compared to 60% in March. Approximately 13% of the tonnage sunk by U-boats was in the Azores Area, and another 15% was in the Freetown Area. The total shipping losses, from all causes, amounted to 682,000 gross tons in April 1941, a higher figure than for any previous month in the war. This was mainly due to heavy shipping losses to enemy aircraft, about 296,000 gross tons, most of these losses occurring in the Mediterranean.\nThe Iceland routing scheme was adopted earlier than intended due to heavy attacks on Convoy SC 26 around 28\u00b0 west longitude. Escorts were based in Iceland, enabling the meeting of convoys where English escorts had to leave, and escorting them out to about 35\u00b0 west longitude. There, the escort would pick up an incoming convoy and turn it over to an escort group from England. Sunderland and Hudson aircraft were also moved to Iceland to provide air coverage for convoys in uncovered waters. This significant increase in the distance over which transatlantic convoys were escorted was achieved at the expense of weaker individual escorts for each convoy. This was partly compensated for by the increased number of convoys being escorted together.\nPaid for reinforcing the Western Approaches with Asdic-fitted minesweepers. It is equally clear that the use of Iceland necessitated a certain rigidity of routing and tended to make the location of convoys by U-boats and enemy aircraft a simpler business. Against this, the daylight hours in these northern latitudes were rapidly lengthening as the summer months approached, and the U-boat danger in daylight was a lesser menace than at night. The upward trend in shipping losses to U-boats continued; 58 ships of 325,000 gross tons were sunk in May. Over half the losses occurred in the Freetown Area, where a group of about six U-boats sank 32 ships of 186,000 gross tons during the month. To meet the increased U-boat activity in that area, additional escorts were added to the Freetown forces and U-boat offensive action was taken to divert all shipping from the area.\nFreetown area, except ships that had to pass through those waters. Attacks on independents continued to increase as only about 20 percent of the shipping sunk by U-boats in May was in convoy. In addition, U-boats continued to move further westward and on May 20 located Convoy HX 126 at about 41\u00b0 west longitude, before the antisubmarine escorts had joined. Eight ships were sunk before the convoy was dispersed. This attack forced the adoption of complete transatlantic escort. It was felt that the considerable weakening in the number of escorts with a convoy must be accepted in order to provide some degree of protection throughout the voyage. Complete transatlantic escort was accomplished by basing escort forces in St. John's, Newfoundland, and escorting in stages from England, using Iceland as a refueling base. The Royal Navy\nCanadian Navy cooperated by placing all available destroyers and corvettes at the service of the Newfoundland Escort Force. Canada had approximately 35 ships fitted for antisubmarine service at that time. The first escorts from St. John's sailed on May 31, 1941. It was decided by the middle of June to escort the convoys all the way from Halifax. The long-endurance corvettes were to run between Halifax and Iceland, with destroyers limited to St. John's.\n\nAreas of U-boat activity in June were further afield and wider spread than before, with reports of U-boats near Newfoundland and south of Greenland. Despite the magnitude of the effort exerted, shipping losses showed an improvement over May, with 57 ships of 296,000 gross tons being sunk by U-boats.\nIn June, despite the increasing number of U-boats at sea, losses were kept down by the efficiency of British countermeasures. Five U-boats were sunk during June by surface craft. Losses in the Freetown Area were greatly reduced, and U-boats had difficulty in locating transatlantic convoys. When they did finally locate Convoy HX 133 on June 23, the results must have been disappointing to the Germans, as only five ships were sunk at the cost of at least two U-boats sunk. The successful defense of this convoy was due in large measure to the fact that, when DF bearings indicated that HX 133 had been sighted by a U-boat, the escort was increased from one destroyer and three corvettes to two destroyers, one sloop, and ten corvettes. This was accomplished by taking the risk of stripping the escorts from two OB convoys within comparatively close proximity.\nFortunately, one OB convoy escaped unscathed while the other suffered the loss of only one ship. On June 22, 1941, Germany invaded Russia, ending the threat of invasion of England for the time being. This released additional air and surface craft to help in the battle against the U-boats. In addition, German aircraft were diverted to the Eastern Front and attacks on shipping by aircraft were greatly reduced during the last half of 1941. The average number of U-boats at sea continued to increase during July and August, but they had very little success as only about 23 ships of 90,000 gross tons were sunk in each of these months. This meant that the average U-boat at sea in the Atlantic was sinking less than one ship a month, a much lower rate than had been experienced in the past.\nThe U-boats withdrew towards the east by the end of July, concentrating in the waters west of Ireland and to the east of 25\u00b0 west longitude. This position allowed them to intercept both East-West and North-South convoys. However, the U-boats had no better luck there in August than in July. By this time, the Gibraltar and Freetown convoys had mostly complete end-to-end escort. Towards the end of August, there were indications that the U-boats were resorting to long-range attacks on convoys, possibly firing a Browning salvo, and to deliberate attacks on escorts. This policy of attacking escorts might have proved more productive in the earlier days of the war when the number of escorts with convoys was much smaller and when the general conditions were more favorable for the U-boats.\nThe escort situation was much tighter. In addition to the defensive successes scored in August, this month was marked by one of the outstanding events of the U-boat war, the surrender of U-570 to a Hudson aircraft on August 27, 1941. U-570 set sail on August 24 and was at sea for only 74 hours before she surrendered. The U-boat came to the surface at 1030 on the 27th, the precise moment the Hudson from Squadron 269 was overhead. The U-boat tried to crash dive but the Hudson was too quick for her, diving from 500 feet to 100 feet, and dropping four depth charges. Captain Rahmlow, believing the U-boat more seriously damaged than was actually the case, ordered the crew to surrender.\n\nFigurf, commander of U-570 (HMS Graf), surrendered to a Hudson aircraft from Squadron 269 on August 27, 1941. Note: German crew crowded into conning tower.\nPut on life jackets and go to the conning tower. The Hudson opened fire and kept the crew from abandoning the U-boat. After a white flag was displayed by the U-boat, the Hudson guarded it until relieved by a Catalina. A trawler arrived at 2250 and U-570 was towed to Iceland. It was subsequently repaired and re-christened HMS Graph, proving an invaluable addition to the British Navy. This was the first U-boat actually captured by the British and proved to be an extremely valuable source of information about the operating characteristics of U-boats. U-boat activity continued at a high level in September and their intensive efforts met with greater success than during the previous two months. Allied shipping losses rose sharply to 54 ships of 205,000 gross tons sunk by U-boats, with 70 percent of the tonnage sunk being in convoy. This increase was due to the U-boats' improved tactics and the failure of some convoys to implement effective anti-submarine measures.\nIn a large measure, the severe casualties suffered by four large convoys resulted from determined and sustained attacks by wolf packs. Two of these convoys were slow SC convoys intercepted and heavily attacked south of Greenland, losing 21 ships and one escort. Two U-boats were sunk by escorts during these attacks. The other two convoys, homeward bound from Freetown and Gibraltar, lost 15 ships and one escort to the U-boats. However, in viewing the situation at this time, it is well to compare it with the previous year. In September 1940, when about seven U-boats were at sea, the losses to U-boats were about 300,000 gross tons. In September 1941, when there were about 35 U-boats at sea, the losses to U-boats were only about 200,000 gross tons. In September 1940, the U-boats were attacking convoys with impunity. Rarely was a convoy able to escape without loss.\nU-boat sighted during her attack, and even more rarely was she counterattacked. In contrast, in September 1941, it was a matter of the keenest dispatch if a convoy was attacked and the enemy escaped unpunished. The limited number of escorts, usually about one destroyer and three or four corvettes, although unable to prevent the U-boats from attacking the convoy, were generally able, with the help of covering aircraft, to shake off the pursuing U-boats by persistent counterattacks. No convoy was attacked for more than three successive nights in September 1941.\n\nThe effect of Coastal Command aircraft on U-boat operations may be seen by the fact that, of the tonnage sunk in the North Atlantic during September by U-boats, about 75 percent was lost in the area outside the economical range of Whitley and Welchester.\nThe aircraft made 45 sightings and 39 attacks on U-boats in September, the highest monthly figures recorded to date. September marked the introduction of HMS Audacity, an auxiliary aircraft carrier, as a convoy escort. One of her fighter aircraft shot down a Focke-Wulf attacking the rescue ship of Convoy AS150. As the radius of U-boat operations in the Atlantic extended further west and U.S. ships were being sunk by U-boats, the U.S. Navy announced on September 15, 1941, that it would provide protection for ships of every flag carrying land-aid supplies between the American continent and the waters adjacent to Iceland, on which a U.S. base had been established in July 1941. The first convoy (HX 150) to have U.S. Navy ships as part of its escort sailed from Halifax on September 16.\nThe losses in October 1941 dropped to 32 ships, totaling 157,000 gross tons, sunk by U-boats. Only one convoy (SC 48) was heavily attacked; nine ships and two escorts were sunk, and the USS Kearny was torpedoed but arrived at Iceland. The USS Reuben James was sunk by a U-boat torpedo on October 31 while acting as an escort for Convoy HX 156. In a number of other cases, the convoys were located by U-boats but the escorts were able to drive them off without suffering serious losses.\n\nAn interesting feature of the operations during October was the disinclination of the U-boats to pursue their quarry too far northward or eastward, presumably because they did not care to enter the areas swept by Coastal Command aircraft. This is indicated by the fact that of the 26 ships sunk within 800 miles from air bases, 14 were lost in portions less than 300 miles away.\nApproximately 600 miles out and 12 miles in the 400-600 mile zone (lightly covered by Catalinas). No ships were sunk within 400 miles from Coastal Command bases. This meant that the U-boats were being forced ever further westward, resulting in greater wastage of time and U-boats, particularly in winter. Additionally, air attacks on transit U-boats in the Bay of Biscay began to increase in frequency and effectiveness, thereby further reducing the operational time of U-boats.\n\nDuring the first week of November, the scale of the U-boat effort was likely the greatest and the scope of their patrol the widest spread of the entire Atlantic campaign up to that time. When Convoy SC 52 was intercepted shortly after rounding Newfoundland and four ships were sunk on November 3, it was considered prudent not to risk it upon a transoceanic voyage.\nThe convoy put back to port and later sailed in Convoy SC 54, consisting of 71 ships. This decision proved fortunate, as a period of successful evasion lasted for the remainder of the month. Total losses for November 1941 dropped to 12 ships of 62,000 gross tons, the lowest figure since May 1940. Weather contributed to the reduction in shipping losses, but skillful evasive routing was the main factor. Successful evasion meant fewer contacts between escorts and U-boats and therefore less chance for U-boat destruction. In the meantime, the British offensive in Libya was launched and the Germans withdrew a large proportion of their U-boats from the Atlantic to the Mediterranean.\nMediterranean ships helped the Italian Fleet and temporarily used their U-boats for the transport of military supplies to Rommel. Towards the end of November, convoys from Gibraltar were suspended and every available ship was used in an endeavor to close the Straits of Gibraltar to U-boat passage and destroy U-boats attempting passage. Two German U-boats attempting passage were sunk during the month, one by surface craft and the other by a Dutch submarine.\n\nThe noticeable slackening in tension in the North Atlantic that started towards the end of November continued throughout December 1941. The losses in the Atlantic continued at a very low level, with only 10 ships of about 50,000 gross tons sunk by U-boats during the month. However, the tendency of the U-boat war to become worldwide became apparent.\nSeven ships totaling 27,000 gross tons were sunk by U-boats in the Mediterranean, three in the eastern approaches to Gibraltar and four while on passage between Alexandria and I'obruk. The enemy paid a heavy price for these seven ships, as five U-boats were sunk in the Mediterranean during December. Japanese submarines sank nine ships totaling 42,000 gross tons in the Pacific during the remainder of December after their attack on Pearl Harbor on December 7, 1941. One Japanese submarine was probably sunk. Over 200,000 gross tons of shipping were lost in the Pacific due to capture by the Japanese or unknown causes. Accordingly, the total shipping losses for the month (from all causes) rose to over 500,000 gross tons.\nThe outstanding feature of the month's operations in the Atlantic was the prolonged engagement between Convoy HG 76 and a pack of half a dozen U-boats. The escorts sank four U-boats (including U-567, commanded by Endrass, one of the leading U-boat aces) and only two of the merchant ships of the convoy were lost. However, one escort and HMS Audacity, an auxiliary aircraft carrier, were also sunk by the U-boats. As 1941 drew to an end, the number of U-boats in the Atlantic began to rise again, the majority leading westward.\n\nU-boat countermeasures in convoys\n\nU-boat activity during the early months of this period forced the adoption of complete end-to-end escort of British convoys. Thanks to the steadily increasing number of escorts becoming available, and to cooperation from the Canadian and United States Navies, this did not result in the anticipated serious consequences.\nShips sailing in convoy were safer in this period than in the preceding one, as of the 4100 ships being convoyed monthly, only 14 (about 1%) were sunk monthly by U-boats. By the end of 1941, it appeared, as evidenced by the battle of Convoy HG 76, that wolf-pack attacks on convoys could be beaten off without serious losses to the convoy, and in turn these attacks could prove costly to the U-boats, provided a sufficient number of escorts were present.\n\nAn analysis of 17 of the convoys attacked by the U-boats around this time gives us some information about the \"average attacked convoy.\" This convoy was engaged by 4.2 U-boats, of which 2.6 succeeded in delivering effective attacks. A total of 4.6 ships in the convoy were torpedoed, 1.7 of which were sunk.\nIn each effective attack, 4.2 U-boats engaged the convoy, and 3.2 or 76% were attacked by air and surface escorts, sinking 0.65 or 15% of them. There were not many changes made to the convoy system during this period. The minimum speed for HX convoys was raised from 9 knots to 10 knots, with the minimum speed for SC convoys remaining at 7.5 knots. In July 1941, a rule was introduced requiring ships of less than 15 knots, crossing the Atlantic, to sail in convoy. The designation of the OB convoys (outward-bound from England) was changed to ON for the north-bound convoy heading for Halifax and to OS for the south-bound convoys heading for Freetown. July 1941 also marked the introduction of CAM ships in convoy. These were merchant ships equipped with a catapult-launched fighter aircraft which was to be used against enemy reconnaissance.\nAt the beginning of this period, in April 1941, the need for an improvement in the quality of aircraft attacks against U-boats was apparent. Actual kills by aircraft had been disappointingly few, and it was felt that pilots should have a reasonable chance of bringing off a kill when they sighted a U-boat. A committee of Coastal Command scientists and naval representatives was formed to address this situation.\n\nAnalysis showed that in 35% of aircraft attacks, the U-boat was still visible at the time of depth charge release, and in 15% of attacks, the U-boat had disappeared within 30 seconds.\nThe solution adopted was to concentrate on those U-boats still on or near the surface and adjust tactics, depth-bomb settings, and spacing to give the aircraft the maximum chance of killing in these conditions. Instructions were issued by Coastal Command in June 1941: the depth setting for all depth charges should be 50 feet, the spacing between charges 60 feet, and all depth charges were to be released in one stick. The need for more frequent practice and training was stressed, and a standard for bombing accuracy was set up requiring a mean radial error of all bombs dropped of not more than 20 yards.\nThis change resulted in a significant improvement in the quality of aircraft attacks on U-boats. Aircraft made about 27 sightings a month during this period and about 18 of these resulted in attacks on U-boats. The proportion of these attacks which resulted in at least some damage to the U-boat rose from about 10% in the earlier periods to about 25% in this period. The lethality of the aircraft attacks did not change much, as only about 2.1% of the attacks resulted in the U-boat's being sunk. However, it was realized at the end of this period that even the 50-foot depth setting was too deep for surfaced U-boats and steps were being taken to modify depth charges to allow a 25-foot depth setting. As the U-boats moved further westward, the total number of flying hours by Coastal Command aircraft increased.\nIn the September to November 1941 period, 36 attacks were made on U-boats in the Bay of Biscay, equating to each U-boat being attacked once every three cruises. This was a significant menace, forcing them to remain submerged during the daytime in December and increasing their transit time. By December 1941, Coastal Command had initiated night antisubmarine patrols with radar-fitted aircraft in the Bay of Biscay. Midway through 1941, the British assembled a squadron of long-range planes, previously rejected Liberators from the U.S. Air Forces. Equipped with Mark II radar, they undertook dual roles, patrolling extensively and providing air cover to convoys in need.\nThe flying effort during this period was marked by the increased use of protective sweeps around convoys to put down shadowing U-boats, as distinct from the close convoy coverage provided earlier. It was also marked by the first attempt, in May 1941, by radar-equipped aircraft to hunt a U-boat to exhaustion. Although this attempt did not succeed, much useful information was obtained from this operation.\n\nA new antisubmarine weapon for use by surface craft was coming into production at the end of 1941. This weapon was \"Hedgehog,\" a multispigot mortar which throws 24 projectiles fitted with contact fuzes so as to produce a pattern in the form of a ring whose center is about 250 yards ahead of the ship. The Hedgehog pattern, theoretically, has a greater chance of killing a submarine than the depth-charge pattern.\nThe design of Hedgehog incorporates three important principles:\n\n1. Ahead-thrown: This reduces blind time from 45-90 seconds to 15-20 seconds.\n2. Multiple small charges: Three hundred pounds of high explosive (lethal range of 21 feet) has about one half the chance of killing a U-boat as ten 30-lb charges (lethal radius of 6 feet). The lower limit of the charge is the smallest weight which will have a reasonable chance of sinking the U-boat when it explodes on the target.\n3. Contact firing: The contact fuze sweeps all depths. This is important as the antisubmarine gear used at that time did not determine the depth of the U-boat.\n\nHowever, against these advantages of Hedgehog must be considered the fact that the large explosion of depth charges has a desirable anti-morale effect.\nAnd the production of considerable shaking up of the U-boat occurs in cases where depth charges are not lethal. Hedgehog fails to do this since the charges explode only on hitting the U-boat. During this period, the results from radar were more promising due to increased training and knowledge of the gear. A new set, Type 271, was being fitted on British corvettes. This was a short-wave (10 cm) \u201cbeam\u201d-principle set and constituted a great advance in radar for antisubmarine purposes. The average range at which radar contact was made on a U-boat during this period was about 4000 yards, with the maximum range being 7000 yards. Coastal Command was also experimenting, during this period, with a searchlight carried in a Wellington aircraft to provide illumination for night attacks on U-boats.\n\nThe steadily upward trend in the number of U-boat sinkings.\nU-boats sunk or probably sunk monthly continued throughout this period, reaching a new high for the START OF WOLF PACKS; END-TO-END OF CONVOYS. Figure 2. Hedgehog ready to fire. The total number of enemy U-boats sunk during this 9-month period was 44. Thirty of these were lost in the Atlantic (22 German and 8 Italian), and 13 in the Mediterranean (6 German and 7 Italian). One Japanese U-boat was probably sunk in the Pacific during December. Two German U-boats were known to have been lost.\nDuring the third period, approximately 30 U-boats were at sea in the Atlantic on average. Thirty U-boats were sunk in the Atlantic, with 20 of these sinking due to collisions with surface craft. Two were lost as a result of combined attacks by ships and aircraft, two were damaged by aircraft, and one was torpedoed by a submarine. The circumstances surrounding the loss of the other known U-boats are unknown. One out of every three U-boats attacked by surface craft was damaged, while one out of every seven was sunk or likely sunk.\nDuring this period, the number of U-boats at sea increased threefold compared to the previous period. Their primary focus was on wolf-pack attacks against North Atlantic convoys. They managed to force the Allies to escort their transatlantic convoys more thoroughly but failed to achieve their main objective of cutting off supplies to England. Towards the end of this period, there were signs of their shifting to other areas.\n\nDespite this significant increase in the average number of U-boats at sea, they were only able to sink approximately 34 ships, totaling about 166,000 gross tons monthly in the Atlantic. This represented about 25% fewer ships sunk compared to the previous period. Consequently, the average U-boat was only managing to sink a little over one ship.\nThe ship, with approximately 5,500 gross tons per month at sea, was only about one-quarter as effective as in the previous period. This decrease in efficiency was due to the successful evasive routing of convoys and the rapid expansion in U-boat personnel. The latter condition resulted in a high proportion of U-boats being sunk on their first cruise. The evasive routing of convoys also resulted in fewer contacts between convoy escorts and U-boats, making the average U-boat relatively safer during the third period. Approximately 3% of U-boats were sunk monthly in the Atlantic, of the 30 on average at sea, and consequently, the average life of a U-boat at sea was about 9 months, more than twice as long as it had been in the previous period. The average U-boat during this period was sinking ten ships of about 50,000 gross tons before it was sunk itself.\nThe average U-boat's longer lifetime was accompanied by an exchange rate approximately 40% lower than in the previous period, indicative of U-boats' decreased effectiveness in sinking ships. The number of German ocean-going U-boats in commission expanded rapidly, increasing from approximately 54 at the beginning of this period to about 200 at the end of 1941. One hundred seventy-four new German U-boats were commissioned during this period while only 28 were lost. From a numerical standpoint, the U-boats posed a significant threat, and it seemed likely that with increased experience, the effectiveness of these new U-boats would increase.\n\nTotal shipping losses for the Allied and neutral nations decreased to 363,000 gross tons monthly during the third period, while the building rate of new vessels remained unspecified in the given text.\nMonthly shipping increased to approximately 175,000 gross tons, leading to a net monthly loss of 188,000 gross tons, a 45% decrease compared to the previous period. Of the 363,000 gross tons lost monthly, about 323,000 gross tons were lost due to enemy action. U-boats were responsible for 175,000 gross tons a month, accounting for 54% of the total lost by enemy action. Monthly losses to enemy aircraft increased to 75,000 gross tons, while losses to enemy surface craft dropped to 17,000 gross tons. Mines were responsible for 19,000 gross tons a month, and other or unknown causes accounted for 37,000 gross tons a month. The total shipping available decreased from about 35,000,000 gross tons at the beginning of this period to approximately 33,300,000 at the end of 1941. However, the upward trend in shipping losses seemed to have been halted.\nThe number of British antisubmarine ships suitable for ocean escort had increased from about 375 at the start of the period to about 500 at the end of 1941. In addition, the entry of the United States into the war added about 175 destroyers to the above numbers, but many of them were committed to action in the Pacific.\n\nFrom the defensive point of view, the U-boats, which constituted the main threat to Allied shipping, seemed to have been defeated in the Battle of the Atlantic during this third period. They were experiencing difficulty in locating Allied convoys and even when they did locate a convoy, the escorts were generally able to beat off the wolf-pack attacks without serious losses. Shipping losses to U-boats had been kept to a reasonable level, considering the number of convoys.\n\nSTART OF WOLF PACKS; END-OF CONVOYS\nU-boats at sea while shipping construction was gradually increasing. However, from an offensive point of view, the U-boats were still relatively safe. Surface craft acting as convoy escorts were the only serious threat to the U-boat, although aircraft were gradually becoming more effective in harassing and damaging U-boats. It seems, therefore, that the general situation in the Battle of the Atlantic at the end of 1941 was roughly the same as the situation which prevailed at the end of World War I\u2014that is, with shipping losses checked, but with the U-boats relatively safe at sea.\n\nChapter 4\nFOURTH PERIOD\nHEAVY SINKINGS ON EAST COAST OF UNITED STATES\nJANUARY 1942-SEPTEMBER 1942\n\nU-BOAT OFFENSIVE\n\nThe Germans started this period with about 200 ocean-going U-boats, and new U-boats were being commissioned at the rate of about 20 a month. Admiral Donitz, the U-boat commander, decided to concentrate his forces against the East Coast of the United States. The first major success came on January 27, 1942, when U-123 sank the American tanker \"Normandy\" off the coast of Florida. This was followed by a series of successful attacks on merchant shipping in the Caribbean and off the eastern seaboard.\n\nThe most devastating attack occurred on March 4, 1942, when U-110, under the command of Kapit\u00e4nleutnant Prien, sank the American destroyer \"Reuben James\" off the coast of Maine. This was the first American warship to be sunk by an enemy submarine, and it caused a great outcry in the United States. The Germans continued their offensive, sinking a total of 24 merchant ships and damaging 11 others during this period.\n\nIn response, the United States increased its convoy system and stepped up its anti-submarine warfare efforts. The U-boats suffered heavy losses, with 28 sunk and 13 damaged during this period. The tide of the battle had turned against the Germans, and they were forced to shift their focus to other areas of the Atlantic.\nRear Admiral Doenitz was able to maintain a large-scale U-boat offensive over widely spread areas throughout this period. The average number of U-boats at sea in the Atlantic increased steadily from 22 in January 1942 to 93 in September 1942. In addition, there were about 20 U-boats in the Mediterranean and about 20 available for operations in the Barents Sea. These U-boats were used in a specific effort to cut supply lines to Allied forces in Libya and Russia. Japan, at the start of this period, had about 75 U-boats which operated in the Pacific and Indian Oceans. Despite this widespread U-boat activity, the main battle continued to be fought in the Atlantic Ocean. There, during the previous period, U-boat operations against escorted shipping had been steadily becoming less profitable. The average yield from these operations declined from an average of 12,000 gross register tons (GRT) per month in the first half of 1941 to 5,000 GRT per month in the second half of 1941. However, the U-boat campaign in the Atlantic remained a significant threat to Allied shipping, with over 7 million GRT sunk during this period. In the Mediterranean, the Axis powers were able to disrupt Allied supply lines to Malta and Egypt, contributing to the siege of Malta and the eventual surrender of Tobruk in November 1941. In the Pacific, Japanese U-boats were used primarily for reconnaissance and mining operations, with only limited success against Allied shipping. Overall, the U-boat war continued to be a major factor in the naval war in World War II, despite the challenges faced by the U-boat command in maintaining their offensive.\nThe problems in the text are minimal, so I will output the text as is:\n\nThe problems had been reduced to about one ship sunk per U-boat month at sea during the last period. The operation against Convoy HG 76 in December 1941 had been particularly costly, as only two merchant ships were sunk as against four U-boats sunk. It was natural, therefore, after the entry of the U.S. into the war, that the U-boats, continuing their search for weak spots in the Allied defenses, headed westward for the American coast in January 1942.\n\nThe U-boats, working their way down the African coastline from the Newfoundland banks, found exactly the weak spot they were looking for. The demands of the war in the Pacific and commitments in transatlantic escort (including destroyers transferred to the British in 1940) contributed to the United States\u2019 lack of preparedness for the scale of attack launched by the U-boats on the Atlantic coast in January 1942.\nThe forces available to combat enemy activities were relatively untrained and inexperienced. With the limited number of antisubmarine craft, both surface and air, at their disposal, the U.S. Navy was unable to start convoying coastal shipping immediately but tried during the early months of 1942 to cover the long coastal route by patrol. This produced a number of attacks on U-boats but failed to prevent extremely heavy losses of shipping sailing unescorted along the coast.\n\nU-boat activity in the West Atlantic began on January 12, 1942, when the first sinking west of 60\u00b0 west longitude occurred. A force of about 20 U-boats began to operate off the Atlantic seaboard of the United States and in the coastal area of Nova Scotia and Newfoundland. These U-boats were rather selective in their choice of targets, preferring tankers.\nAnd larger cargo ships and avoiding convoys. As long as worthwhile targets abounded in the form of unarmed and unescorted ships, the U-boats kept clear of escorts, as even minor damage might well have prevented their return to distant bases.\n\nThe U-boats inflicted their heaviest losses in January in the Eastern Sea Frontier, sinking 14 ships of about 100,000 gross tons with a large proportion of the losses occurring at focal points of shipping such as Cape Hatteras, North Carolina, and Hampton Roads, Virginia. About 50,000 gross tons of shipping were sunk by U-boats in each of the Northwest Atlantic, Canadian Coastal, and Bermuda Areas. There was comparatively little activity in the remainder of the Atlantic, but Japanese U-boats sank 50,000 gross tons of shipping in the Pacific and Indian Oceans.\n\nThe total losses for the month: 61 ships of 324,000 gross tons.\nGross tons sunk by U-boats were higher than in any month in the previous period, reaching 470,000 gross tons with the loss of 82 ships in February 1942. Nearly 90% of these losses occurred in the U. S. Strategic Area as the number of U-boats operating in the West Atlantic increased and U-boat activity spread further south. Ships were sunk off the coast of Florida and in the Caribbean Sea. Tanker losses continued to be severe, with the tanker traffic to and from the West Indian and Venezuelan oil fields being an obvious objective. This was demonstrated by an attack carried out by several U-boats on February 16 on six tankers off Aruba and in the Gulf of Venezuela, sinking five of them.\nAnd one seriously damaged. During March, U-boats continued the same tactics with increased success, sinking 94 ships of 532,000 gross tons. The Eastern Sea Frontier remained the most active area, with over 150,000 gross tons of shipping sunk there by U-boats. Possibly by way of diversion, a group of U-boats operated in the Freetown Area, sinking over 50,000 gross tons there. The one encouraging feature of the month's operations was the first successful attacks on U-boats in the U. S. Strategic Area. Two U-boats were sunk in March as a result of attacks by U. S. Navy aircraft in the Canadian Coastal Zone. On April 15, USS Roper sank U-85 off Cape Hatteras, picking up 29 bodies, for the first confirmed sinking of a U-boat off the U. S. coast. The number of attacks on U-boats in the U. S. Strategic Area had increased from about 15 in January.\nIn April, about 60 ships were targeted. These more effective countermeasures probably played some part in causing a small decrease in shipping losses in April. However, a more important factor was the temporary suspension of sailings in certain areas. U-boat activity spread to the Brazilian Area during April as three ships were sunk off the north coast of Brazil, probably by Italian U-boats. In the middle of May 1942, the U.S. Navy was able to start convoying shipping along the east coast. The institution of these convoys was immediately apparent. The U-boats avoided escorted shipping and the tonnage sunk by U-boats in the Eastern Sea Frontier in May dropped to 23,000 gross tons. Logically enough, the U-boats sought out the remaining soft spots, where unescorted traffic had to pass through focal areas, and operated actively off the coasts.\nThe Mississippi mouth and Yucatan Channel between Cuba and Nicaragua. Although the average number of U-boats at sea in the Gulf Sea Frontier was approximately four in May 1942, these U-boats sank 41 ships of 220,000 gross tons there during the month, an all-time high for sinkings by U-boats in any area. The average number of ships at sea in the Gulf Sea Frontier was about 75, so the average life of a ship at sea at that time was less than two months at that rate of sinkings. Sinkings in the Caribbean Sea Frontier also increased, reaching approximately 170,000 gross tons in May. Consequently, despite the decrease in the Eastern Sea Frontier, the losses in the U.S. Strategic Area reached a peak of 116 ships of 567,000 gross tons sunk by U-boats in May. World-wide shipping losses to U-boats also reached a new high for the war with 124 sinkings.\n604,000 gross tons of ships were sunk this month. The number of attacks on U-boats in the Western Atlantic showed a promising increase, with two U-boats sunk by U.S. Coast Guard cutters - one in the Eastern Sea Frontier and one in the Gulf Sea Frontier. World-wide shipping losses reached their highest point in the war in June 1942, with 141 ships of 707,000 gross tons sunk. The increase was largely due to increased activity by Japanese U-boats in the Indian Ocean, which sank 70,000 gross tons, mostly in the Mozambique Channel. Shipping losses in the U.S. Strategic Area were about the same as in May, with a decrease in the Gulf Sea Frontier but continuing to increase in the Caribbean and Panama Sea Frontiers. Mines were laid in the Chesapeake Bay.\nSeveral casualties occurred in June due to mine-laying, possibly the first effort of one of Germany's 1600-ton mine-laying U-boats. Over 100 attacks on U-boats took place in the U.S. Strategic Area in June; three of these resulted in sunk U-boats. In July 1942, the convoy system on the east coast of the U.S. was greatly extended, with most shipping traveling in convoy. The increase in the number of convoys and an improvement in escort strength were likely the main reasons for the general reduction in sinkings of shipping throughout the U.S. Strategic Area. Only 230,000 gross tons of shipping were sunk by U-boats in the U.S. Strategic Area in July, less than half the amount sunk in June.\nThe number of U-boats at sea in the U.S. Strategic Area in July was approximately 45, higher than in any previous month. Increased aircraft patrols and better cooperation between surface and air units contributed materially to this reduction of U-boat effectiveness in the West Atlantic. Another significant factor was the increase in the number of U.S. craft available for antisubmarine warfare: 134 ships in July compared to 68 in April and 580 planes in July compared to 350 planes in April. The increased effectiveness of U.S. countermeasures is also illustrated by the fact that the number of U-boats lost in the U.S. Strategic Area reached a new high in July, with seven being sunk - two in Eastern Sea Frontier, one in Gulf Sea Frontier, two in Panama Sea Frontier, and two in the Northwest Atlantic Area.\nAs a result, the world-wide shipping losses to U-boats dropped to 94 ships of 472,000 gross tons in July 1942. However, increased losses were suffered in the Free-town and Azores Areas, with over 50,000 gross tons sunk by U-boats in each of these areas. Heavy losses were also suffered in July in the Barents Sea Area, where ten ships of 62,000 gross tons were sunk by U-boats from Convoy PQ 17 heading for Russia. Thirteen ships were also sunk from this convoy by enemy aircraft. The convoy had been ordered to scatter when southeast of Spitzbergen to reduce losses from the enemy surface craft attack then apparently pending. The shipping losses to U-boats increased slightly in August to 108 ships of 544,000 gross tons, still well below the record highs established in May and June.\n1942: This increase was due entirely to increased activity in the U.S. Strategic Area, where losses mounted to 84 ships of 407,000 gross tons sunk by U-boats. Over half of these losses occurred in the Caribbean Sea Frontier, where the main sore spots were the eastern approaches to Trinidad and the Windward Passage area. A group of about five U-boats achieved considerable success, especially against tankers, east of Trinidad. Twenty of the 23 ships sunk there were sailing independently. In the Windward Passage area, 14 ships were sunk from convoys running between Key West and Trinidad, and between Panama and Guantanamo. The activities of probably two U-boats off the Brazilian coast resulted in seven sinkings and brought Brazil into the war on the side of the United Nations. The coastal waters of the Atlantic from Nova Scotia to the tip of Florida.\nThe month of August saw no attacks by U-boats. The significant trend of the month's operations was the resumption of large-scale attacks on transatlantic convoys. With the reduced effectiveness of U-boats in the Eastern and Gulf Sea Frontiers due to convoying and heavy aircraft coverage, it was natural for them to resume attacks on transatlantic convoys, particularly in the North Atlantic where they were out of range of Allied aircraft. Over 20 ships totaling approximately 120,000 gross tons were sunk by U-boats in the Northwest Atlantic Area in August. The heaviest losses were sustained by Convoy SC 94, which lost 11 ships as a result of U-boat attacks.\n\nIn these attacks on convoys, the first indication of U-boat presence was often an HF/DF bearing.\nAnd these were of great assistance to commanders in appreciating the subsequent situation. Shipborne 10-cm radar (SG and Type 271) also proved a most efficient detector at night, and the quick action taken by escorts in many cases thwarted night attacks. This apparently influenced some U-boats to temporarily abandon their tactics of night surfaced attack and to attack submerged in daylight. As many as five ships were torpedoed by one salvo on a day attack, and to lessen the chance of such an event recurring, instructions were issued in the third week of August to open out the distance between the columns of a convoy to about 1000 yards by day as well as by night.\n\nThe number of U-boats destroyed during August reached a new high for the war as 20 were sunk or probably sunk, 12 in the Atlantic, five in the Mediterranean.\nTwo U-boats were sunk in the Atlantic, and one in the Pacific. U-boats from Convoy SC 94 sank one, and a U-boat was sunk in the Caribbean Sea for the first time. U-464, sunk by a U.S. PBY plane southeast of Iceland, was one of the new 1600-ton supply U-boats. These were used to refuel other U-boats at sea and thereby enabled them to extend their cruises. These supply U-boats were intended to stay at sea for up to six months.\n\nBy the end of August, the coastal convoy system was further extended, with New York included as one of the ports in the system. In September, New York became the main western port for transatlantic convoys, with HX and SC convoys beginning and ending their passages there. A temporary reinforcing group was established in September.\nThe primary objective was the destruction of U-boats rather than the immediate defense of shipping. This group consisted of ten British escorts. Shipping losses to U-boats decreased slightly in September to 99 ships of 496,000 gross tons. Principal areas of attacks on shipping were in the eastern approaches to Trinidad and in the area to the north and south of the Equator between Freetown and Ascension Island. There was also considerable activity along the convoy routes in the Northwest Atlantic and in the Gulf of St. Lawrence.\n\nIn the Northwest Atlantic Area, U-boats sank 20 ships of 110,000 gross tons. The chief sufferer on the North Atlantic convoy routes was ON 127, with which five or six U-boats were in contact for four consecutive days. In the course of these attacks, two ships were sunk: the British merchant vessel \"Empire Morn\" (5,539 gross tons) and the American tanker \"Mormacreyes\" (9,213 gross tons).\nEleven merchant ships and one escort were torpedoed among the two North Russian convoys, losing four ships altogether. They had to fight through incessant U-boat and aircraft attacks, resulting in the loss of 16 ships in total, eight to U-boats. Six promising attacks were carried out by the escorts, assisted by Swordfish aircraft from HMS Avenger. This was the first operation in which this type of escort carrier had participated. The losses to U-boats in the Caribbean Sea Frontier in September 1942 were 27 ships of 130,000 gross tons, significantly less than in August. A notable feature of the operations around the Trinidad Area was the sinking of ten ships involved in the valuable bauxite trade. With the tremendous increase in shipping to and from the South Atlantic, the Trinidad Area had become one of\nThe largest shipping focal points in the Western Hemisphere. U-boat activity had increased accordingly and was highly successful at first. Lack of suitable long-range surface and air craft restricted the distance that east-bound convoys could be escorted from Trinidad. Beyond dispersal points, the U-boats had good hunting.\n\nAircraft available in the Trinidad Area, especially the RAF Squadron 53 (Hudsons), were utilized to the utmost. Reinforcement aircraft from other areas, including a specially trained \u201cKiller\u201d group of U.S. Army Air Force B-18s, were ordered into the area. Emphasis was placed on offensive operations, using sweeps over most likely U-boat locations and routes along which convoys passed. The results were rather encouraging in September; one U-boat was sunk and several other promising attacks were made.\nThe situation eased after September as the number of U-boats in the area decreased. Therefore, in just over nine months from their entry into World War II, the United States, through the institution of escorted convoys and the provision of air cover and patrols, had achieved a high degree of immunity from U-boat attack in their coastal waters.\n\nCountermeasures to the U-boats: Convoys\n\nIn January 1942, U-boats shifted their attention from transatlantic and East Atlantic convoys to unescorted shipping in the West Atlantic. This is reflected in the fact that only 10% of the shipping sunk by U-boats during the first six months of 1942 was in convoy when sunk. This proportion increased again to about 30% during the period July to September 1942 when the bulk of the U-boat attacks occurred.\nU.S. coastal shipping was being convoyed, and U-boats were attacking transatlantic convoys. Realized during the early months of the war that convoying was the only solution to heavy losses off the Atlantic Coast. However, the U.S. Navy, due to its commitments in transatlantic escort and in the Pacific, did not have enough escorts to start coastal convoying at the beginning of 1942. To provide additional forces, 24 British anti-submarine trawlers were allocated for service on the American coast, and ten British corvettes were turned over to the U.S. Navy. Further, the entire system of transatlantic escort was recast, and all anti-submarine forces (U.S. Navy, Royal Canadian Navy, and Royal Navy) were pooled in a single cross-Atlantic convoy scheme. This resulted in an economy and released a limited number of U.S. destroyers.\nWith the forces available and the increased production of antisubmarine ships in the United States, it was possible to start convoying in the Western Atlantic in May 1942. Coastal convoys between Norfolk, Virginia, and Key West, Florida, started running on May 14. By opening up the transatlantic convoy cycle, the British were able to divert enough forces to the Caribbean to start convoys, mainly for tankers, over the Trinidad-Halifax and Aruba-Curacao-Trinidad routes.\n\nDuring July, the convoy system on the east coast was greatly extended. Convoys ran between Trinidad and Key West via Curacao and Aruba. Convoys were instituted between Panama and Guantanamo to connect with the other convoys. Convoys were also started in the Gulf of Mexico and the Gulf of St. Lawrence.\n\nAt the end of August, convoys running in both the Atlantic and Gulf coasts were in operation.\nDirections between Curacao and Halifax and countermeasures against U-boats were discontinued, as were the convoys between Key West and Hampton Roads. A new convoy system was started with convoys running between New York and Guantanamo (NG and GN), and between the latter port and Trinidad via Curacao (GAT and TAG). Convoys were also started between New York and Key West (NK and KN).\n\nDuring the five months from May through September 1942, approximately 1800 ships were convoyed monthly in U.S. coastal convoys, and only about 12 of these ships were sunk monthly by U-boats for a loss rate of less than 1% per trip. During the first nine months of 1942, approximately 1000 ships were conveyed monthly in ocean convoys, and about 15 of these ships were sunk monthly by U-boats for a loss rate of:\nThe rate of about 34 ships sailing monthly to and from Russia was particularly hazardous during this period, with three of these being sunk monthly by U-boats, resulting in a loss rate of approximately 9 percent per trip. Additionally, these convoys suffered significant losses from enemy air and surface craft attacks. The effect of convoying in reducing shipping losses is clearly illustrated by the experience in the U.S. Strategic Area during the first nine months of 1942. There were about 600 ships at sea in this area throughout this period. During the first six months, before extensive convoying of coastal shipping had started, only about 40 percent of the shipping was in convoy.\nDuring the first six months, there were approximately 30 U-boats at sea in this area, each sinking about 2.7 ships per month. About 20% of independent shipping and 4% of convoyed shipping were sunk each month by U-boats. In the next three months, after extensive convoying of coastal shipping had started, about 80% of the shipping was in convoy. The average number of U-boats at sea in this area increased to about 50, but each U-boat was only able to sink about 1.4 ships a month, half as much as during the first six months. Despite the fact that the loss rates for both independent and convoyed shipping had increased (about 33% of independent shipping and 6% of convoyed shipping were sunk monthly by U-boats) during this period.\nThe efficiency of the average U-boat in sinking ships was halved during the last three months of this period. This was mainly due to the fact that approximately 40% of the shipping was exposed to the much lower loss rate experienced by convoyed shipping instead of the high loss rate experienced by independent shipping.\n\nAnother consequence of the shift from independent to convoyed shipping is the increased danger the U-boat faces when attacking a convoy. Only about 2 U-boats were sunk monthly in the U.S. Strategic Area during the first six months of 1942, while 4 were sunk monthly in the same area during the next three months, most of them by forces escorting convoys.\n\nAt the beginning of 1942, the U.S. Navy sent out all available planes and blimps to battle the U-boats.\nAlong the coast, they were helped by the First Bomber Command, the initial Army Air Forces contribution, activated in December 1941. The Army planes patrolled and escorted under the operational control of the Navy. A second Army Air Forces unit broke into the picture in June 1942. This was the Seasearch-Attack Development Unit (SADU), based at Langley Field, Virginia, and assigned a combination mission: (1) to develop tactics and techniques for using antisubmarine devices, and (2) to conduct general seasearch. SADU had two British-loaned B-24s (Dumbos I and II). In these had been installed two early British microwave sets known as DMS-1000 and equipped with the first airborne Plan Position Indicator (PPI) scopes. In addition to the Army and Navy flying, there was patrolling by the Civilian Air Patrol (CAP), mostly within 100 miles from shore.\nThe flying hours by U.S. Army and Navy aircraft in the Eastern and Gulf Sea Frontiers increased from approximately 5000 hours in January 1942 to a peak of about 25,000 hours in July 1942, and 7000 hours in May 1942, respectively. In both sea frontiers, the number of U-boats at sea decreased rapidly after July 1942. In the Caribbean Sea Frontier, flying hours increased from about 5000 in April 1942 to almost 10,000 in September 1942, when the number of U-boats at sea there started decreasing. U.S. aircraft made about 30 attacks a month on U-boats during this period, varying from about 12 a month during the first four months of 1942 to about 45 a month during the next five months. Approximately 20 heavy sinkings occurred on the East Coast of the United States.\nApproximately 2% of these attacks caused significant damage to the U-boat, while only about 2% resulted in its sinking or probable sinking. The average height for these attacks was approximately 150 feet. Depth bombs were typically set to a depth of 50 feet at the beginning of this period (too deep for a surfaced U-boat), but by the end of 1942, most attacks were made with settings of 25 feet. Additionally, bombs were fitted with flat noses to reduce their forward motion underwater and to minimize ricocheting.\n\nAt the beginning of 1942, Coastal Command aircraft began using the 25-foot depth setting on their depth charges. Their attacks were typically conducted at around 50 feet. Torpex-filled depth charges, which had a greater lethal radius, were also employed.\nIntroduced in April 1942, these factors significantly improved the quality of Coastal Command attacks on U-boats. Approximately 20% of their aircraft attacks during this period resulted in some damage to the U-boat, while 4% led to sinking the U-boat.\n\nDuring the early months of 1942, when most U-boats were operating in the West Atlantic, Coastal Command aircraft initiated offensive patrols against transit U-boats. They operated both on the northern route, northward of Scotland, and in the approaches to the Bay of Biscay ports.\n\nDuring the first five months of 1942, only about 600 flying hours a month were spent on the Bay of Biscay offensive. This effort resulted in approximately seven sightings a month, sufficient to keep the U-boats submerged during daytime.\nIn June 1942, Coastal Command introduced about ten Wellington aircraft equipped with the Leigh Searchlight and Mark II radar into operation. These aircraft, operating in the Bay of Biscay, flew 190 hours and sighted seven U-boats, attacking five of them. This success was achieved despite the night offensive in the Bay being hampered by the presence of French fishing boats.\n\nWith the introduction of the Leigh-Light Wellington in June 1942, the scale of the Bay offensive was greatly increased, with approximately 3400 flying hours put into it monthly from June through September 1942. About 30 sightings (9 per 1000 hours on patrol) and 23 attacks were made monthly during this period. It is believed that 43% of all U-boat transits through the Bay were sighted and that five U-boats were destroyed.\nThe enemy's response to Coastal Command's offensive in the Bay of Biscay was an increased effort to intercept antisubmarine aircraft. Coastal Command replied by sending out Beaufighters to intercept the interceptors. The Germans were fully aware of the possibilities of meter-wave radar and were aided by the capture of a Mark II radar set in Tunisia in the spring of 1942. They concluded that radar was responsible for the night attacks in the Bay of Biscay and tests in the summer of 1942 confirmed that transmissions were easily detected by a single receiver and aerial. Admiral Doenitz ordered the speediest equipping of all U-boats with makeshift equipment. The wooden and cable aerials (Southern Cross Aerial) were easily made and the Paris firm of Metox provided the necessary equipment.\nThe R-600 receiver was turned off. The first German Search Receiver (GSR), a device designed to detect meter radar, came into operation around October 1942. Another new device introduced by U-boats in the latter half of 1942 was the Submarine Bubble Target (SBT), or \"Pillenwerfer.\" These were tablets to be released by U-boats when attacked by surface craft. The bubbles formed by the dissolving tablets produced false sonar targets, intended to throw attacking ships off the U-boat's trail.\n\nIn the early months of 1942, a new form of passive defense against torpedo attacks, known as Admiralty Net Defense (AND), was being fitted to new merchant ships with speeds between 1 and 15 knots. Early trials indicated that these nets would stop approximately 50% of U-boat torpedoes fired at the ship.\nIn March 1942, Hedgehog charges became more lethal with the filling of Torpex, a new explosive which, volume for volume, was 1.7 times as powerful as TNT. Around the middle of 1942, the U.S. Navy put into operation the \u201cMousetrap\u201d projector, which fires a number of relatively small, fast-sinking charges equipped with contact fuzes and suitable for installation on small antisubmarine ships. The light construction of these ships does not permit any great amount of deck thrust, so the projector utilizes the rocket principle for launching. The projectiles are copies of the Hedgehog projectiles fitted with suitable rocket motors in the tail. Magnetic Airborne Detector (MAD) was also developed during this period to enable aircraft to follow submerged submarines. This device detects the change in magnetic field produced by a submarine.\nThe number of enemy U-boats sunk during the 9-month period was 78 (50 German, 17 Italian, and 11 Japanese). Forty of the U-boats were lost in the Atlantic (21 in the U. S. Strategic Area), 21 in the Mediterranean, 11 in the Pacific, two in the Barents Sea, one was mined in the Baltic, and three were lost under unknown circumstances. Surface craft continued to be the main factor in sinking U-boats in all areas, accounting for 34 (44% of the total number sunk). Coordinated attacks involving both surface and air-craft accounted for another six (8%). Aircraft played a significant part in sinking U-boats for the first time, accounting for 19 (24%); all of these sinkings occurred in the Atlantic and Mediterranean.\nIn the Mediterranean and Pacific, submarines were an important factor, accounting for 14 U-boats (18 percent of the total). In the U.S. Strategic Area, the main scene of U-boat activity, there were approximately 360 surface craft attacks on U-boats during this period. About 12 percent of these attacks caused some damage to the U-boat, and 4 percent resulted in sinking it. A British study of 106 surface craft attacks in the North Atlantic and Western Mediterranean during this period indicates that about 25 percent of the attacks caused some damage to the U-boat, and 10 percent resulted in sinking it.\n\nFrom the U-boat\u2019s Point of View:\nThis was by far the most successful period for the U-boats. The total world-wide losses for the U-boats were minimal during this time.\n878 ships of 4,587,000 gross tons were sunk by U-boats (approximately 98 ships of 510,000 gross tons monthly). The main U-boat battle continued to be fought in the Atlantic where about 90% of these losses occurred. The number of U-boats lost during this period was 78 (about nine a month), resulting in an exchange rate of 11 ships of 59,000 gross tons sunk for each U-boat sunk. Japanese U-boats sank 76 ships during this nine-month period (48 in the Indian Ocean and 28 in the Pacific) while 11 U-boats were sunk (all in the Pacific), resulting in an exchange rate of about seven ships sunk for each U-boat sunk. In the Barents Sea Area, 15 ships were sunk by U-boats as opposed to two U-boats sunk. In the Mediterranean, 17 ships were sunk as opposed to 21 U-boats lost. Life was much more hazardous for U-boats in the Mediterranean than in other areas.\nIn the Atlantic, the average number of U-boats at sea was approximately 57, more than twice as many as during the previous period. These U-boats sank about 85 ships totaling 456,000 gross tons a month, over two times as much as in the previous period. About 85% of these losses occurred in the U. S. Strategic Area, where their main effort was directed against the weak spot off the east coast of the United States. The average U-boat in the Atlantic sank about 8,000 gross tons of ships per month at sea, around 50% more than the corresponding figure for the previous period. However, it should be noted that this sinking rate was still far below that achieved during the period from July 1940 to March 1941, when U-boat Aces were operating.\nU-boats sank four ships per month at sea. The U-boats operating in the Atlantic were relatively safer during this period than at any other time in the war. Of the 57 U-boats at sea, about 45 were sunk monthly, reaching a new high of 13 months for the average life of a U-boat at sea. This meant that the average U-boat in the Atlantic, during this period, sank 19 ships of about 100,000 gross tons before it was sunk, the highest exchange rate of the war (approximately twice as high as during the previous period).\n\nThis record exchange rate was achieved by concentrating the U-boat effort in the U.S. Strategic Area, where defenses were rather weak and the bulk of shipping was unescorted. Of the 57 U-boats at sea in the Atlantic, about 37 were heavy sinkings on the East Coast of the United States.\nIn the U.S. Strategic Area, they were able to sink 71 ships of 375,000 gross tons a month while only 2% of U-boats were lost monthly. During the first half of 1942, U-boats achieved their main successes in the Eastern and Gulf Sea Frontiers. The number of U-boats in these areas reached a peak in July 1942, when there were, on average, eight at sea in the Eastern Sea Frontier and six in the Gulf Sea Frontier. However, by then, the bulk of shipping was in convoy and surface and air-craft had each been making over two attacks a month on each U-boat. Under these conditions, the effectiveness of U-boats in sinking ships was greatly reduced, and the number of U-boats operating in these coastal regions decreased rapidly after July 1942. In the Caribbean, it was not until August 1942 that a corresponding level of attacks on U-boats was reached.\nThe reduced effectiveness of U-boats in sinking ships first became apparent in September 1942, with approximately 10 U-boats at sea. The number of U-boats in the Caribbean began falling off after September 1942. As the combination of convoying and heavy air coverage reduced the effectiveness of U-boats along the East Coast of the United States, they looked for other weak spots in Allied defenses. The most likely spot was the \"gap\" in the Northwest Atlantic Area where U-boats could operate against vital transatlantic convoys, outside the range of Allied air cover. The number of U-boats in this area increased from about seven during the first half of 1942 to 14 in August and September, while shipping losses to U-boats in the Northwest Atlantic also rose.\nArea had mounted to over 100,000 gross tons each in these months. It seemed likely that the crucial battle of the U-boat war would be fought against these convoys in the North Atlantic during the next period.\n\nThe Germans were in an excellent position to conduct an intensive U-boat campaign at the end of September 1942. The number of ocean-going U-boats available had increased from about 200 at the beginning of 1942 to about 350 at the end of this period. This was accomplished by commissioning about 200 new U-boats while only 50 were lost. In addition, many of the new U-boat commanders and crews had gained considerable experience and confidence as a result of their successful operations in the West Atlantic.\n\nFrom the Allies\u2019 Point of View:\nTotal shipping losses from all causes of the Allied and neutral nations reached the highest level of the war.\nDuring this period, shipping losses amounted to 700,000 gross tons a month, nearly twice as high as during the previous period. Fortunately, the building rate of new shipping was also greatly increased, averaging about 515,000 gross tons a month. This increase reflected the great expansion in U.S. construction of shipping from less than 100,000 gross tons in January 1942 to almost 700,000 gross tons in September 1942. Consequently, the net monthly loss of shipping was only about 185,000 gross tons, slightly less than during the preceding period.\n\nOf the 700,000 gross tons of shipping lost monthly, about 655,000 gross tons were lost as a result of enemy action. U-boats accounted for 510,000 gross tons a month (about 78% of the total lost by enemy action), a much higher proportion than in the past. Monthly losses to enemy aircraft dropped to 67,000 gross tons.\nThe total shipping available decreased from approximately 33.3 million gross tons at the beginning of 1942 to about 31.6 million gross tons by the end of the period. Monthly losses to enemy surface craft were around 39,000 gross tons, while losses to mines were only about 11,000 gross tons. Particularly serious was the heavy destruction of tankers during this period, with 190,000 gross tons lost monthly compared to 70,000 gross tons constructed monthly. The size of the tanker fleet declined by over 1 million gross tons, or about 10% of its size at the beginning of 1942. The number of ships suitable for ocean escort available to the Allies increased from about 670 at the beginning of 1942 to 745 by the end of September, mainly due to an increase of approximately 60.\nTwelve new auxiliary air-craft carriers were completed during this period, in addition to the number of destroyers. However, the gravity of the U-boat situation at the end of this period led to a significant expansion in the construction program for 1943. The U.S. Navy expected to produce over 500 escort ships, more than half of which were destroyer escorts (DE), designed specifically for convoy escort and anti-submarine warfare.\n\nDespite the extreme losses the Allies suffered in the Western Atlantic during this period, convoying and aircraft had driven the U-boats out of these coastal regions by the end. The main problem facing the Allies during the next period was maintaining the flow of war material from the United States to England, particularly ensuring the safety of the North Atlantic convoys.\nAtomic convoys. It was becoming increasingly apparent that, although the defeat of the U-boats would not, in itself, win the war, the Allies could not possibly win the war without first defeating them.\n\nChapter 5\nFIFTH PERIOD\nLARGE WOLF PACKS BATTLE NORTH ATLANTIC CONVOYS\nOCTOBER 1942-JUNE 1943\n\n5.1 U-Boat Offensive: Carried out six attacks; the attack on the convoy did not develop. On the other hand, Convoy SC 104 was attacked despite the fact that the U-boats had been driven from the coastal areas of the United States by the beginning of this period. Shipping losses to U-boats continued at the same high level as during the previous period. The Atlantic continued to be the chief area of U-boat activity, with about 85 percent of the shipping losses to U-boats occurring there. There were over 100 U-boats at sea in the Atlantic.\nDuring most of this period, the Atlantic enabled the enemy to conduct an intensive U-boat campaign in the Northwest Atlantic Area against strategically important North Atlantic convoys and maintain a number of subsidiary campaigns in other wide-spread areas, such as the Caribbean, Brazilian, Free-town, and Southeast Atlantic Areas, in an attempt to force the Allies to disperse their forces. The total shipping losses to U-boats continued to be rather heavy in October 1942, with 93 ships of 614,000 gross tons sunk. The intensity of the U-boat campaign against transatlantic convoys increased with the number of U-boats in the Northwest Atlantic Area rising from 14 in September to 22 in October. These U-boats sank 24 ships, with the bulk of the losses occurring in the \u201cgap,\u201d the region outside the range of shore-based aircraft. Experience indicated.\nA convoy not protected by aircraft may become disorganized under a concentrated attack, resulting in breaks in formation for rescue work and other adjustments. Escorts may then become relatively ineffective for protection or offense. However, the presence of even a few aircraft has repeatedly prevented a concentrated attack from developing.\n\nThis was illustrated during October. On the 4th, Convoy HX 209 was in peril about 300 miles south of Iceland. US Navy Catalinas provided close escort for 15 hours and protective sweeps were laid on by seven aircraft from Iceland and three Fortresses from England. During these operations, the aircraft made nine sightings and heavily attacked on the nights of the 13th and 14th when out of the range of aircraft, and eight ships were damaged.\nThe weather improved and air cover arrived, enabling the surface escort to go on the offensive and sink two U-boats. In October, the expected U-boat operations began in the South-east Atlantic Area near Capetown. Two groups, each of about six U-boats, reached the Capetown area and eventually passed into the southern part of the Indian Ocean, where Japanese U-boats had previously achieved considerable success. These groups sank 25 ships in the Southeast Atlantic Area during October, all of which were independently routed and carried rather valuable cargoes. However, some of the heavy shipping losses suffered in October and November may be charged to the success of Operation Torch, the landings in North Africa.\nNorth Africa, November 1942. A great deal of merchant shipping and many escorts were diverted from their normal use in October, when the foundations were firmly laid for the safe arrival of the first military convoys. In addition, the enemy disposed of an abnormally large proportion of his Atlantic U-boat force east of the Azores and Madeira. This suggests that, in a broad sense, the German command had appreciated the likelihood of an Allied attack on Africa. One consequence directly resulting from this repositioning of U-boat forces was that Convoy SL 125 was severely mauled, losing 12 ships during a 4-day pursuit by a pack of about six U-boats. However, the pursuit was abruptly dropped before it drew the U-boats away from the area southwest of Portugal. It may have been regarded as of greater importance that they remain in that area.\nshould stay there and reconnoiter rather than pursuing an ordinary trade convoy. Despite the fact that expeditionary force convoys had to pass through concentrations of 30 to 40 U-boats before reaching Gibraltar, no U-boat successes were achieved against these convoys until after the assault troops had landed. The number of U-boats in the Western Mediterranean increased from about 10 on November 8 to about 20 on November 1. The losses to U-boats in Operation Torch amounted to approximately 84,000 gross tons of shipping and six naval vessels. The total shipping losses from all enemy causes in this operation amounted to approximately 134,000 gross tons, which can be offset by a gain to the Allies of about 181,000 gross tons of serviceable tonnage acquired in French ports. In addition to the.\nThe Allies achieved defensive success against U-boats in Operation Torch, sinking 15 of them in the Mediterranean during November. A significant factor in these victories was the heavy air cover provided, with aircraft from Gibraltar making 110 sightings and 64 attacks on the large concentration of U-boats.\n\nIn contrast, worldwide shipping losses reached their highest point of the war in November 1942, with 862,000 gross tons lost from all causes. U-boats sank the greatest tonnage of the war in November, accounting for 116 ships of 712,000 gross tons. The tonnage sunk during October and November was increased by the loss of several large, fast, independently routed ships, which, due to their speed, had been considered fairly safe from U-boat attacks.\nU-boat attacks continued in the Northwest Atlantic with 26 ships of 144,000 gross tons sunk. In the Southwest Atlantic, losses fell slightly to 23 ships of 127,000 gross tons. However, shipping losses in the Caribbean and Brazilian Areas increased again as U-boats sank 34 ships of 210,000 gross tons. These heavy losses occurred despite the intensive effort made by U-boats in opposing the Allied landings in North Africa.\n\nShipping losses to U-boats in December 1942 totaled 62 ships of 344,000 gross tons, about half the record total of November. This steep decline was likely due to contributing factors such as the concentration of U-boats in the Atlantic approaches to the Western Mediterranean and a consequent withdrawal elsewhere.\nIn the West and South Atlantic, heavy bombing of U-boat bases by Allied aircraft, effective work by surface and air escorts on North Atlantic routes, adverse weather, and some luck in routing significantly reduced enemy sinkings. The smaller sinkings were attributed to bad weather by the enemy.\n\nOnly one convoy, ONS 154, experienced heavy losses in the North Atlantic. Given a southerly route, it was attacked by a pack of approximately 20 U-boats as it exited the range of air cover. These U-boats followed the convoy for four days and sank 14 ships. This demonstrated the immense importance of efficiently combining surface and air escort and indicated that surface escorts were physically incapable of warding off concerted attacks by a pack of U-boats that outnumbered them by more than a 2-to-1 ratio. In selecting convoy routes.\nAt this time, the advantage of the northerly route within the range of air cover from Iceland had to be balanced against the increased time of the trip due to greater distance and worse weather. In addition, the bad weather reduced the efficiency of the escorts. Shipping losses to U-boats in January 1943 dropped to only 35 ships of 203,000 gross tons, less than in any month of 1942. Bad weather was the primary factor responsible for this reduction, and it was recognized that the gravity of the U-boat threat was much more serious than indicated by the low shipping losses. The fate of a tanker convoy bound from Trinidad to Gibraltar seemed a truer index of the strength of a U-boat pack operating in favorable conditions at the beginning of 1943. Convoy TM 1, made up of nine tankers and four escorts, lost seven tankers.\nAs a result of U-boat attacks, all outside the range of shore-based aircraft, this was the highest proportion of ships sunk from any convoy by U-boats during the war. Of the 100 or more U-boats at sea in the Atlantic on any one day, over a third were operating in the Northwest Atlantic Area. The U-boats were concentrating against the North Atlantic convoys which carried cargoes of immediate importance for military operations. Grand Admiral Doenitz had become supreme commander of the German Navy, and it was becoming evident that the critical phase of the U-boat war in the Atlantic was approaching. To meet to some extent the need for shore-based air cover for Atlantic convoys, the Allies planned to introduce Very Long Range (VLR) aircraft with an endurance of 2000 to 2500 miles. Some flying was also done from Greenland, although weather conditions.\nLarge wolf packs battled North Atlantic convoys, posing a severe handicap. Continuous shore-based air cover was available between Gibraltar and Freetown. In February 1943, the U-boat effort in the North Atlantic intensified. Worldwide shipping losses to U-boats increased to 63 ships of 359,000 gross tons, with about half these losses occurring in the Northwest Atlantic Area. Two North Atlantic convoys were heavily attacked by packs of about 20 U-boats. Convoy SC 118 lost 12 ships to U-boat attacks early in the month, seven of them during a three-hour period. However, at least two U-boats were sunk and six damaged during this action. Convoy ON 166 suffered the loss of 14 ships over a five-day period due to U-boat attacks outside the range of shore-based aircraft. The enemy was concentrating his forces in an effort to interrupt these convoys.\nThe flow of supplies from America to Great Britain and the U-boats showed increased boldness in attempting to achieve this objective. However, approximately 20 VLR aircraft had become operational in February 1943.\n\nIn March 1943, worldwide shipping losses to U-boats reached 107 ships, totaling 627,000 gross tons. The tempo of the U-boat offensive against trans-Atlantic convoys increased as the number of U-boats in the Northwest Atlantic Area rose to about 50. These U-boats sank 38 ships in that area, a high for the war, and an additional 15 ships were sunk in the adjacent Northeast Atlantic Area. The enemy's resources were such that he was also able to maintain offensives in the South Atlantic and in the Caribbean and Azores Areas. About two-thirds of the tonnage sunk by U-boats during March was in convoy.\nWhen over 400,000 gross tons of shipping sunk in convoy during the month was a war record. The main reason for the large increase in tonnage sunk in convoy was an increase in the number of convoys attacked, not a weakening in the protective value of the escorts. The intensity of the U-boat effort in the North Atlantic during March is clearly indicated by the attacks on four consecutive eastbound transatlantic convoys. U-boats generally outnumbered the escorts by about two to one and were able to torpedo 30 ships from these four convoys, in addition to eight stragglers. Convoy SC 121 was badly scattered by heavy weather and lost five ships in convoy and seven stragglers. Convoy HX 228 lost four ships to U-boats but the escorts were able to sink two U-boats.\nOne of the dramatic incidents of the U-boat war occurred when HMS Harvester, after attacking a convoy, sighted a U-boat and rammed it at approximately 26 knots. The U-boat became lodged under the stern and could not be dislodged for about ten minutes. FFS Aconit finished off the damaged U-boat. Despite significant damage, HMS Harvester was able to continue on one engine for several hours until it became completely disabled and was torpedoed. FFS Aconit then sank the U-boat that had destroyed HMS Harvester. Convoys HX 229 and SC 122 were routed closely together and encountered a concentration of approximately 40 U-boats, the largest pack employed up to that time, losing 20 ships to the U-boats. On the night of March 16-17, 13 ships were sunk when the convoys were about 850 miles from the nearest air bases. The following day, the convoys received some air cover.\nVLR aircraft sighted six U-boats, resulting in 54 sorties and 32 sightings with 21 attacks. The U-boats disengaged on March 20, marking a potential turning point as merchant vessel sinkings decreased significantly thereafter. Despite heavy shipping losses in March, improvements were evident in the North Atlantic. Advances included the provision of continuous air cover for transatlantic convoys through increased use of VLR aircraft from Newfoundland, Iceland, and England, and the introduction of escort carriers and Merchant Aircraft Carriers (MAC) ships. MAC ships were merchant vessels with converted decks to carry four Swordfish aircraft.\nThe USS Bogue, the first U.S. escort carrier, began operations as an escort for North Atlantic convoys in March 1943. At the Atlantic Convoy Conference held in Washington in March, it was agreed that starting in May, the United Kingdom and Canada would be responsible for the security of convoys across the North Atlantic, with the United States providing certain air and sea forces to assist. A unified air command was also established in Newfoundland corresponding to the Coastal Command system. The United States was to base a substantial force of VLR aircraft in this region, along with the VLR Liberators of the RCAF, to close the gap in the North Atlantic. Despite the same high level of U-boats at sea in April 1943, shipping losses decreased. U-boat offensive.\nThe U-boats reduced shipping significantly, sinking 56 ships totalling 328,000 gross tons. Shipping losses in the Northwest Atlantic Area in April were only 18 ships totalling 108,000 gross tons, less than half the March record. Ten ships were sunk by U-boats in the Freetown Area, and Japanese U-boats sank six ships in the Southwest Pacific, off the east coast of Australia.\n\nThe decrease in shipping losses was accompanied by a considerable increase in the number of U-boats sunk. Seventeen were sunk in the Atlantic, a record high to that date. April marked the first sinking of a U-boat where planes from an escort carrier took part. A plane from HMS Biter found and attacked a U-boat, which HMS Pathfinder, one of the escorts, sank.\n\nA more satisfactory criterion that the U-boat offensive strength had passed its peak was the fact that,\nFor the first time, U-boats failed to press home attacks on convoys when favorably situated to do so. In none of the attacks on transatlantic convoys did the enemy succeed in obtaining anything like the upper hand. All of the U-boats' efforts tended toward avoidance of detection, and once it was apparent that they had failed in this endeavor, they seldom pressed home their attacks. There were five Support Groups operating in the North Atlantic during April, two of them having their own escort carrier, and the number of VLR aircraft available had risen to over 30. More important, there was a noticeably enhanced standard of group training, better use of HF/DF was made, and cooperating between surface and air components of the escorts was greatly improved.\n\nMay 1943 seems to have been the crucial month in the Battle of the Atlantic. The number of U-boats at sea was significantly reduced.\nThe Atlantic sea reached a peak of approximately 120 U-boats, with about half concentrated in the Northwest Atlantic region. The decisive battle occurred at the beginning of the month between Convoy ONS 5 and a pack of around 40 U-boats. On May 4, HF/DF activity indicated contact, and the convoy consisted of about 30 ships and four stragglers. The average number of escorts present during the battle was around eight. Despite the bad weather, aircraft from the Royal Canadian Air Force provided air cover during the afternoon of the 4th and carried out two promising attacks, one of which is believed to have sunk a U-boat. U-boats began attacking shortly after midnight, and 12 ships were sunk on May 5, half during the night and half during the following day. Due to bad weather, air cover was provided for only an hour.\nThe morning of the 5th. By midnight, the weather had become calm and foggy, and from then onwards, the escorts had the upper hand. In the course of the night, they frustrated about 24 attacks by the U-boats without suffering any losses and, in addition, inflicted heavy losses and much damage on the enemy. At least five U-boats are considered to have been sunk by the escorts during the battle. The U-boats broke off the action in the course of the day and did not renew it. In no succeeding convoy operation did the enemy display the same determination. Several other convoys were threatened in the first half of the month but no serious losses were suffered and the toll of U-boats mounted steadily. After May 17, no ship was lost in the Atlantic north of 45\u00b0 north latitude. World-wide shipping losses to U-boats in May 1943 decreased to 50 ships of 265,000 gross tonnage.\nThe most notable feature of the operations during May was the success of our offensive against U-boats. Forty-four U-boats were sunk during the month, almost twice the previous high, with 38 of the sinkings occurring in the Atlantic. A record number of 15 were sunk in the Northwest Atlantic Area, and the number sunk in the Bay of Biscay also reached a new high of 11. Shore-based aircraft accounted for over half the U-boats sunk during the month, while carrier-based aircraft participated in three of the attacks in which the U-boat was considered to have been sunk. By the end of May, it was clear that the U-boats had been decisively beaten as the number at sea in the Atlantic had significantly decreased.\nBy June 1943, the Atlantic dropped to about 85, with a significant proportion of the reduction due to U-boat sinkings. U-boats could not endure the heavy losses experienced in May and were forced to withdraw from the battle against the vital North Atlantic convoys, an admission of defeat in itself. Superior leadership and tactics, quick initial action, and well-coordinated attack and defense played as much of a part in the defeat of the U-boats as concentration of forces at decisive points and weapon superiority.\n\nBy June 1943, the U-boats had retired from the main battlefield of the North Atlantic convoy routes and a considerable number had moved into the Azores Area, outside the range of shore-based aircraft. As a result, June was an interim phase for the U-boat war in the North Atlantic.\nU-boats sank 20 ships, totaling 96,000 gross tons, in June 1942 - the smallest amount since November 1941. No ships were sunk in the Northwest Atlantic Area during June, and only seven were sunk in the entire Atlantic. Seven ships were sunk in the Indian Ocean and six in the Mediterranean. The U-boat offensive continued throughout June, but opportunities to attack were rarer due to their repositioning. Only 19 U-boats were sunk during the month. Aircraft played an outstanding part, sinking ten U-boats, two by carrier-based aircraft from the USS Bogue in regions where they thought they would be safe from shore-based aircraft. The 2nd Escort Group, led by HMS Starling, sank three U-boats during the month and demonstrated the effectiveness of well-trained escorts.\nThe escort group could effectively deal with a U-boat. On June 2, this escort group made contact with U-202. Twelve depth-charge attacks were made without positive evidence of success, so it was decided to hunt the U-boat until its batteries were exhausted and it had to surface. One ship maintained contact while the remainder formed a square patrol. Despite every maneuver and artifice, including the release of 19 SBTs, the U-boat was compelled to surface after contact had been firmly held for 14 hours. She was immediately attacked by gunfire and the crew abandoned ship. On June 24, the 2nd Escort Group, acting as a striking force in cooperation with aircraft engaging in the Bay offensive, destroyed two more U-boats in the space of 9 hours. As the period closed, it was apparent that the U-boats had been decisively defeated in the battle.\nAgainst the North Atlantic convoys, the Allies took the initiative and joined battle in the approaches to the Bay of Biscay, through which all U-boats must pass to and from their bases.\n\nCountermeasures to the U-Boat Convoys\n\nThere were only a few minor changes in the convoy system during this period. The landings in North Africa in November 1942 resulted in the temporary suspension of sailings of the Sierra Leone and Gibraltar convoys for several months due to a lack of escorts. Shortly after these landings, new convoys were started between the United States and the Mediterranean (designated UG and GU), to supply Allied forces in North Africa. The U.S. Coastal Convoy System was extended to Brazil in December 1942 following increased U-boat activity in that area.\n\nThere were, however, a number of extensive countermeasures implemented against the U-boats. The Allies employed long-range aircraft, such as the Consolidated PBY Catalina and the Short Sunderland, to patrol the Atlantic and provide air cover for convoys. These planes were equipped with sonar and radar, allowing them to detect and attack U-boats underwater. The Allies also developed new convoy routes and tactics, such as zigzagging and escort carriers, to make it more difficult for U-boats to successfully attack convoys. Additionally, the Allies increased their production of anti-submarine warfare (ASW) equipment, such as depth charges and sonar, to better equip their ships for the battle against the U-boats. Overall, these countermeasures significantly reduced the effectiveness of the U-boat campaign against the Allied convoys.\nAt the beginning of this period, the Allies were forced to discontinue the route to the Red Sea and India via the Atlantic and Cape of Good Hope due to a concentration of U-boats between Natal and Dakar. Shipping was instead routed via the Panama Canal and Cape Horn to Capetown. However, after U-boats had started operations in force around Cape Town, the bulk of Indian Ocean traffic was routed transpacific from Balboa south of New Zealand to Fremantle for onward routing to destination. This route through the South Pacific proved entirely safe, with losses in the Indian Ocean due to raiders and U-boats but, in general, the transpacific route was so successful that it was maintained until the Mediterranean was considered open in July 1943. It can be seen that there was a considerable gain in:\n\n(No further text follows in the input)\nEffective shipping due to the use of the short Mediterranean route instead of the long circuitous route across the Pacific. During this period, the main efforts of the U-boats were concentrated against convoyed shipping, particularly against the North Atlantic Trade Convoys (ON, ONS, HX, and SC). The proportion of tonnage sunk by U-boats, which was in convoy when sunk, increased from about 30 percent during the last three months of 1942 to 67 percent in March 1943 and then dropped back to about 25 percent in June 1943 after the U-boats had withdrawn from the North Atlantic convoy routes. About 720 ships sailed monthly in the North Atlantic Trade Convoys and about 21 of these ships were sunk monthly by U-boats, so that the loss rate was about 3 percent per crossing. The loss rate reached a peak of about 5 percent.\nBy March 1943, U-boats had retreated by June, allowing 850 ships to reach safe havens in convoy without loss to U-boats. U-boats' strategy against North Atlantic convoys involved maintaining patrols to locate convoys as they left air cover, and scoring greatest success in the gap between protective sweeps and convoys. Three main U-boat formations enabled aircraft to make killing and damaging attacks on convoys: Patrol line, patrols or at least forcing U-boats to remain submerged.\nReconnaissance sweep and attack formation merged at slow speed long enough to delay the enemy. In the first, up to 25 U-boats form an effective pack. Second, they spread about 20 miles apart on a given line of bearing, the trailing U-boats on which others are across the convoy routes. Each U-boat patrols at slow homing, submerged, allowing aircraft to break the enemy's speed on either side and at right angles to the line, enabling the convoy to escape by changing direction not going further than half an hour's run from it. If a U-boat sights a convoy, she must report it to the Admiral, who passes the signal to other long-range bomber coverage. The U.S. Navy needed more Admiral, U-boats, who passed the signal to other long-range bomber coverage. The U.S. Army was also in need.\nU-boats in the line. This Patrol line formation is anxious to help and set up the 1st Anti-Submarine pool from which groups of U-boats may be detached for any given duty, such as an attack on a convoy or expansion of the 1st Bomber Command. Two reconnaissance sweeps of an area through which submarine squadrons were sent to England in December 1942 are expected. In February 1943, they operated in the Bay of Biscay and in March 1943, the two U-boats signaled the limits of the area to be swept, the squadrons were ordered to Port Lyautey, Morocco, the time at which the sweep is to start, and the U-boats where they were to help the U.S. Navy protect the convoy.\nU-boats ordered to the Mediterranean Approaches by the end of this period, with limits approximately 150 miles apart, were joined by two other U.S. Army squadrons in England. Two U.S. Navy squadrons operated and spread about 25 miles apart. When one U-boat, patrolling from Iceland under Coastal Command, had established the convoy's position, U-boats were ordered by Admiral to take up an attack formation. These U-boats formed a semicircle around the convoy's line. In October 1942, the need for microwave radar became more urgent. Fourteen DMS-1000's were crash-built at a U.S. laboratory.\nApproach of the convoy. Once the order to attack is given, and rushed into British service by the end of 1942, there is no such thing as coordinated action between the U.S. Navy's AN/APS-2 [ASG] radar (S-band) and the U-boats, though they may keep in touch with each other by radio. Each U-boat attacks at its discretion. The U-boats continue their attacks until ordered by Admiral to break off. The first effect of the introduction of GSR was a sharp reduction in the effectiveness of the aircraft.\n\nAn analysis of attacks by U-boats on the North Atlantic convoys at about the beginning of this period indicated that about 70 percent of the attacks were detected by radar-fitted aircraft, which allowed them ample time to dive and the number of sightings was significant.\nTempted attacks were frustrated by escorts. About and attacks on U-boats dropped sharply. This lull lasted through January 1943. Two ships were torpedoed in each successful attack. In only about half the successful attacks, U-boats made their 1000 hours on patrol during this four-month period, as compared to nine during the previous four-month period, when the number of U-boat sightings was higher. Transits was actually smaller. The search receiver for Mark II ASV enabled U-boats to make safe night transits, and only 13 percent of the transits were sighted. No U-boat is considered to have been sunk by any of the attacks made in the Bay during this period.\n\nThe primary function of aircraft in the defense of the Bay was to prevent U-boat transits. Aircraft passages across the Bay resulted in only 13 percent of the transits being sighted. No U-boat was sunk by any of the attacks made in the Bay during this period.\nConvoys were the prevention of U-boat gathering and destructive attacks in this period. U-boat packs capable of making significant damage. This situation was changed by the introduction of the Mark III ASV (S-band) on Allied aircraft in February and March 1943. This set operated on a much shorter wavelength (10 cm) and could not be detected by the R-600 GSR. The proportion of aircraft approaches undetected by U-boats rose, and consequently, sightings and attacks began a steady increase. This period of increased productivity in the Bay offensive lasted through July 1943. Approximately 5500 hours were flown monthly during this 6-month period with about 61 sightings and 33 attacks made monthly. About five U-boats were sunk monthly as a result of this offensive. The average number of sightings per hour was approximately 0.01.\nThe number of attacks and sightings of U-boats per 1,000 hours on patrol jumped to 1.1 and approximately 60%. About 60% of all transits were sighted during this period. The German High Command had no idea what caused this huge increase in sightings and attacks. After running into several blind alleys in attempting to solve the problem, they were forced to make a number of changes in U-boat tactics. The first step was the strengthening of the antiaircraft armament of U-boats. This development first became apparent in April 1943 when on several occasions U-boats, sighted by aircraft, stayed on the surface and fought back using their antiaircraft guns. Although a number of aircraft were lost as a result of this measure, it did provide aircraft with a much larger proportion of surfaced targets, increasing their chances of sinking a U-boat. Four U-boats that stayed up and fought back were sunk in April.\nNine U-boats were sunk in May during the spring of 1943. The night-flying Weltingtons, equipped with Leigh Lights and Mark IFF ASV, made night surfacing in the Bay so hazardous for the U-boats that they changed their policy to one of surfacing in the daytime to charge batteries and renew air supply. This, in turn, produced the period of greatest productivity in the campaign during May, June, and July 1943. During the last two of these months, every U-boat transit was sighted once on average. May 1943 was a record month for Coastal Command aircraft with the squadrons in the United Kingdom, Iceland, and Gibraltar accounting for 213 sightings and 136 attacks, 17 of which are considered to have been lethal. One of the U-boats sunk in May was the victim of the first rocket attack against U-boats. This attack resulted in the sinking of the U-boat.\nA Swordfish aircraft made this report. The first indication of a change in U-boat tactics was the sighting of five U-boats transiting the Bay in company on June 12. From then on, most sighted U-boats were in packs of three to five. Although this change should have no effect on the number of U-boats sighted, the number attacked will be less as each aircraft can only attack one U-boat. This effect appeared in June when there were 60 sightings in the Bay but only 28 attacks. The other advantages of this change for the U-boats are that they will have a better chance of seeing aircraft, they will have much stronger anti-aircraft fire support, and it will be easier to provide fighter protection for them. The Admiralty reacted immediately to this measure by sending surface craft hunting groups into the Bay to cooperate with air-based operations.\nCraft and ships were used to follow up on aircraft attacks. If surface craft arrived at the scene of the attack quickly enough, several U-boats would be pinned down and the search easier. This countermeasure resulted in two of the U-boat kills made by the Second Escort Group in June. In addition, Mosquito fighters were sent into the Bay in June to operate against German aircraft covering the U-boats.\n\nAircraft finally came into their own as an offensive power during this period. The 25-foot depth setting was in general use, and, especially during the later months, planes were able to attack U-boats still on the surface. About 60 aircraft attacks were made monthly on U-boats during this period, with about 25 percent of the attacks resulting in at least some damage to the U-boat, while over 10 percent of the attacks proved lethal. In addition, aircraft were used to attack enemy convoys and provide air cover for Allied ships.\nto  bomb  U-boat  bases  and  lay  mines  near  them. \nThese  operations  dislocated  the  servicing  facilities  at \nthe  bases  and  increased  the  turn-around  time  of \nU-boats  operating  from  these  bases. \nScientific  and  Technical \nThe  main  scientific  battle  during  this  period  con- \ntinued to  center  about  radar.  As  we  have  seen,  the \nMetox  R-600  GSR  was  able  to  detect  Allied  meter- \nwave  radar.  The  Allied  countermeasure  to  GSR  was \nthe  introduction  of  short-wave  (S-band  10-cm)  radar \nabout  February  1943.  This  was  made  possible  by  the \nBritish  invention  of  the  strapped  magnetron  in  the \nspring  of  1940  which  enabled  sufficient  power  to  be \nproduced  to  make  use  of  the  shorter  wavelengths \npractical.  The  Metox  GSR  was  particularly  unsuited \nto  detecting  these  short  wavelength  radar  transmis- \nsions and  the  number  of  aircraft  attacks  on  U-boats \nincreased  sharply.  The  Germans  had  no  idea  of  what \nSurvey of Results:\n\nWas causing the trouble, and suspecting supersonic modulation, they fitted GSR sets with a visual tuning indicator of the Magic Eye type. This did not prove to be of any help, so they explored other blind alleys, suspecting infrared detection or intermittent operation of radar sets, without finding any solution during this period. The best the Germans could do was the fitting of a permanent GSR aerial, which did not have to be dismounted before diving, on some U-boats. Meanwhile, it was evident in May and June 1943 that there was a progressive lessening of confidence in GSR on German U-boats. Radar was fitted on some U-boats, apparently primarily as an offensive weapon against shipping in low visibility. However, there was a great reluctance to use radar for fear of being detected by a hypothetical Allied search radar.\nReceiver. Radar decoy balloons were used by some U-boats in an attempt to produce a large number of false targets. A similar lack of appreciation for the situation was apparent in the U-boat\u2019s attitude toward HF/DF. As the new technique of using shipborne HF/DF was learned and applied, the successes became more frequent, and by November 1942, HF/DF was accepted as an essential part of the equipment of escort craft. The U-boats overrated the accuracy of shore-based HF/DF, but for a long time they underrated, indeed ignored, the danger of shipborne HF/DF. This was reflected in their communications, which seemed to be conducted on the principle that radio silence was to be strictly kept until contact was made with the convoy, but completely relaxed once contact was made. In other words, they were afraid of revealing their position to the enemy while hunting, but once they had located the convoy, they no longer felt the need for radio silence.\nDuring attacks on Convoy SC 118 in February 1943, U-boats made 108 transmissions in a 72-hour period. Several ships were saved as torpedoes were stopped by nets or exploded in them. There were six successful Hedgehog attacks during this period, indicating that the numerous early difficulties with this weapon had been overcome and it was beginning to show signs of its theoretical lethality. In 1942, it had become apparent that a device was needed to enable attacking ships to maintain contact with deep U-boats at shorter distances. To meet this need, the Q attachment was developed. It consisted of a small, special sonar projector of high power.\nThe frequency was attached to the main projector below it and tilted down about 15 degrees. Trials during this period indicated good echoes could be obtained from targets within a 45-degree angle from the horizontal. The expendable radio sono-buoy was developed during this period to enable aircraft to maintain contact with a submerged U-boat. It could be dropped from an aircraft and contained a hydrophone which listened to U-boat noises and a radio transmitter which transmitted the noises received to the plane. The service life of a sono-buoy was about four hours.\n\nSinkings of U-boats:\nThe number of U-boats sunk or probably sunk during this critical period averaged about 19 a month, hitting a peak of 44 in May 1943. The total number sunk during this period was 168, more than twice the number sunk in any previous period.\n128 were German, 18 Italian, 18 Japanese, and four were Vichy French. There were 112 U-boats sunk in the Atlantic during this period, 43 of these in the Northwest Atlantic Area and 25 in the Bay of Biscay. There were 37 U-boats sunk in the Mediterranean, 15 during November 1942, the month of the North African landings. The 18 Japanese U-boats were all sunk in the Pacific.\n\nThis was the first period of the war in which aircraft were the leading killers of U-boats, sinking 76 U-boats (45% of the total) alone and another 10 (6%) in cooperation with surface craft. Ten of these 86 successful aircraft attacks involved carrier-based aircraft. Ships accounted for 59 U-boats (35%) and submarines for 17 (10%).\n\nThe quality of surface craft attacks continued to improve. About 60 attacks were made monthly.\nThe crucial period for U-boats in the war was when they made their supreme effort and were decisively defeated. Worldwide shipping losses to U-boats were about 30% lower than during the preceding period, with approximately 67 ships of 394,000 gross tons sunk monthly in the Atlantic, accounting for 85% of total losses. The number of U-boats sunk worldwide was about 19 a month, more than twice as many as during the previous period. Therefore, the exchange rate was:\n\n5.3.1 Results from the U-boat's Point of View\nThis was the crucial period for U-boats in the war, during which they made their supreme effort and were decisively defeated. Worldwide shipping losses to U-boats were about 30% lower than during the preceding period, with approximately 67 ships of 394,000 gross tons sunk monthly in the Atlantic, accounting for 85% of total losses. The number of U-boats sunk worldwide was about 19 a month, more than twice as many as during the previous period.\nAbout 31.5 ships of 21,000 gross tons sank by the average U-boat before it was sunk. This exchange rate was only one-third as large as it had been during the previous period.\n\nActivity in the Mediterranean was greatly increased as 44 ships were sunk by U-boats and 37 U-boats were sunk. U-boat operations in the Mediterranean were, in many cases, auxiliary to military operations in North Africa. In the Indian Ocean, German and Japanese U-boats sank 25 ships, half the total in the previous period, without suffering any losses. Japanese U-boats sank 19 ships in the Pacific and suffered the loss of 18 U-boats, an extremely unprofitable return.\n\nIn the Atlantic, the scene of the main battle, the average number of U-boats at sea during this period was 104, higher than in any other period of the war. These U-boats sank about 57 ships of 344,000 gross tons.\nApproximately one ton per month, or one-third of all sinkings, occurred in the Northwest Atlantic Area. This signified a new low for U-boat efficiency during the war, as the average U-boat sank only about half a ship of 3200 gross tons per month at sea. This was roughly one-third the results achieved in the previous period. The U-boats' wolf-pack attacks against North Atlantic convoys had failed to maintain the previous high level of U-boat effectiveness. U-boats rarely managed to completely overwhelm convoy escorts, and the use of large wolf packs of over 20 U-boats proved relatively inefficient. Additionally, when U-boats had to operate against convoys with air coverage, their wolf-pack operations disintegrated entirely as they relied on surfaced U-boats.\nKeep contact with the convoy and home the other U-boats. In addition to the reduction in its efficiency, the average U-boat in the Atlantic found life more hazardous during this period than in the preceding period. This marked the first time in the war that the trend of increasing safety for the U-boat was reversed. About 121/2 U-boats were sunk monthly out of 104 U-boats at sea in the Atlantic, so that the average life of a U-boat at sea during this period was about 8.5 months, about one-third less than in the previous period. The main factors causing this shorter average life for U-boats were the increased effectiveness of Allied aircraft and the fact that the U-boats were exposing themselves to increased attacks by surface escorts by concentrating against convoyed shipping.\n\nThese figures indicate that the average U-boat in the Atlantic had a life of approximately 8.5 months.\nDuring this period, the Atlantic was sinking approximately 41/2 ships of 28,000 gross tons before it itself was sunk. This exchange rate was the lowest of the war to that date and only one-fourth as high as the record exchange rate achieved in the previous period. This low exchange rate, coupled with the fact that in the Atlantic, the number of U-boats sunk in May 1943 was almost as large as the number of ships sunk by U-boats, must have convinced the Germans they could not continue the battle against the North Atlantic convoys and they disengaged. The average number of U-boats at sea in the Northwest Atlantic Area dropped from 60 in May to 20 in June 1943. The expansion of the German U-boat fleet was definitely slowed down during this period. Bombing of construction yards kept new construction at about the same level as in the previous period.\nApproximately 20 new German U-boats were commissioned monthly. About 128 German U-boats were sunk and some were decommissioned during this period. Consequently, the available number of German U-boats increased from approximately 350 at the beginning to approximately 400 at the end of the period. This large fleet still posed a significant threat, but many experienced officers and crews had been lost during this period, and the heavy losses suffered by the U-boats must have had an adverse effect on enemy morale.\n\nFrom the Allies\u2019 Point of View:\nTotal shipping losses of the Allied and neutral nations were about 491,000 gross tons a month during this period, about 30% less than during the preceding period. Construction of new merchant shipping reached a new high of about 1,026,000 gross tons.\nThe first period of the war saw a net monthly gain of approximately 535,000 gross tons in shipping, surpassing the total monthly losses of 491,000 gross tons. This marked the first instance where new construction exceeded total losses. The total shipping availability increased by nearly 5 million gross tons during this period to around 36.5 million gross tons. The shipping crisis in the war had passed, as it seemed unlikely that losses would ever exceed the 1 million gross tons being constructed monthly. The main challenge for the Allies at the end of this period was to minimize shipping losses to allow for rapid supply build-up in England prior to the continent invasion.\nAbout 436,000 gross tons were lost as a result of enemy action. U-boats accounted for 394,000 gross tons monthly, approximately 90% of the total lost by enemy action. Losses to enemy aircraft, surface craft, and mines were all significantly lower during this period than in the preceding one.\n\nThe number of ships suitable for ocean escort available to the Allies increased from about 745 at the beginning of this period to about 950 by the end of June 1943. This included about 50 new destroyer escorts and approximately 25 new escort carriers. This increased number of escorts and the new VLR aircraft that had become available placed the Allies in the position of having defeated the greatest efforts the U-boats could make. The Allies now had the opportunity to take the offensive against the U-boats.\nChapter 6, Sixth Period, Aircraft Defeat U-Boats' Attempted Come-Back and Force Adoption of Maximum Submergence\n\n6.1 U-Boat Offensive\n\nAs a result of the heavy losses they experienced in their battle against the North Atlantic convoys during the previous period, U-boats withdrew from the North Atlantic and temporarily abandoned their wolf-pack tactics. After a marked lull in U-boat activity in June, the enemy made his first and most strenuous effort to regain the initiative in July 1943. The 85 U-boats at sea in the Atlantic were widely dispersed, and simultaneous campaigns were conducted in regions that had been soft spots for the U-boats in the past, such as the Caribbean, Brazilian, and Freetown Areas. To withdraw from the strategically important North Atlantic was a confession of failure.\nOf defeat, but the enemy must have anticipated a rich harvest from surprise attacks in comparatively lightly protected areas. If so, the enemy was probably sadly disappointed. World-wide shipping losses as a result of U-boat action in July were only 44 ships of 244,000 gross tons, considerably less than the monthly average during the preceding period. The heaviest losses occurred in the Indian Ocean, mostly in the Mozambique-Madagascar Area, where 15 ships of 82,000 gross tons were sunk by U-boats while no U-boats were sunk. This was the highest monthly total of the war for shipping losses to U-boats in the Indian Ocean. About six German U-boats of the 1200-ton U-Kreuzer class were probably responsible for most of these sinkings. About 15 U-boats operated in the Caribbean Sea and off the Brazilian coast as far south as Rio de Janeiro.\nJuly 1943: 19 ships were sunk, but nine U-boats were also lost due to shore-based aircraft in these areas. The successful invasion of Sicily occurred without any shipping losses to U-boats. Only five ships were sunk by U-boats in the Mediterranean, at the cost of seven U-boats sunk by the Allies. Despite meager results, the U-boats suffered the heaviest losses of the war, with a total of 46 U-boats destroyed during the month. This was the first month of the war in which the number of U-boats sunk exceeded the number of merchant vessels sunk by U-boats. Of the 46 U-boats sunk during July, 37 were destroyed.\nIn the Atlantic, aircraft achieved their greatest successes of the war. Shore-based aircraft destroyed 28 U-boats in the Atlantic, while carrier-based aircraft accounted for another six. US escort carriers' aircraft operated in regions outside the range of shore-based aircraft and prevented U-boats from achieving any successes in their attacks against mid-Atlantic convoys. These attacks by carrier-based aircraft likely convinced U-boats that they were no longer safe from air attack anywhere in the Atlantic. Allied antisubmarine forces inflicted the greatest damage on the enemy in the Bay of Biscay and its approaches, sinking 14 U-boats in the Biscay-Channel Area and another six in the Gibraltar-Morocco Area. Aircraft crews had to face the increased antiaircraft fire of surfaced U-boats.\nDuring the daytime, the Allied formation presented the U-boats with a large proportion of Class A targets. Over 25 percent of the attacks resulted in the sinking of the U-boat. The month's crowning success occurred on July 30 when a whole group of three outward-bound U-boats was sunk. Two were sunk by Coastal Command aircraft, and the third by the Second Escort Group. Two of these three U-boats were supply U-boats, and the loss of two other supply U-boats elsewhere severely curtailed later U-boat operations. This incident was also marked by one of the odd coincidences of the war when U-461 was sunk by the Sunderland aircraft U/461.\n\nU-Boat Offensive\nFour additional U-boats were sunk in the Bay of Biscay by Coastal Command aircraft during the first two days of August. The U-boats were forced to change their tactics in making the transit of the Bay.\nThey reverted to surfacing at night for the minimum time necessary for charging batteries and, in addition, hugged the coast of Spain to get as far as possible from Allied air bases. The more cautious tactics adopted throughout the Atlantic in August 1943 marked the failure of the first attempted come-back by the U-boats. Only four ships were sunk by U-boats in the Atlantic during the month, all during the first week of August and all south of the Equator. Worldwide shipping losses to U-boats in August were only 15 ships of 87,000 gross tons. As the U-boats sank six ships in the Indian Ocean and five in the Mediterranean. The average number of U-boats at sea in the Atlantic during August declined to about 60, and most of them were homeward bound by the end of the month. There was no doubt that, as a direct consequence, the U-boat offensive in the Atlantic was weakened significantly.\nThe loss of a number of supply U-boats and heavy losses suffered by U-boats in operating areas led to the curtailment of campaigns in the Caribbean and Brazilian Areas. U-boats returned to base two weeks earlier than usual. The number of U-boats sunk during August was satisfactory, given the smaller number of targets and more cautious tactics. Aircraft accounted for 18 of the 25 U-boats sunk worldwide. Aircraft from the USS Card were particularly notable, sinking five U-boats during the month. New evidence of the gradual disappearance of all soft spots was indicated by the sinking of three U-boats in the Caribbean-Brazilian Area and two in the Freetown Area. One U-boat was sunk.\nU-boats were sunk in the Indian Ocean, marking the first such incidents as the lull in U-boat activity continued during August and the first three weeks of September. The Allies sought to maintain the initiative by carrying the battle into the Biscay transit areas. Escort groups were moved closer to the Spanish Coast in an effort to sever new U-boat routes. However, Germany responded strongly to this new threat, deploying a new weapon: the radio-controlled, jet-propelled glider bomb. Released by German bombers against escort groups in the Bay, HMS Egret was sunk by this new weapon late in August, and two other ships were damaged. Escort groups were withdrawn from the Bay offensive in September due to these attacks and renewed U-boat activity in the North Atlantic.\n\nU-boats were sunk in the Indian Ocean, marking the first such incidents as the lull in U-boat activity continued during August and the first three weeks of September. The Allies attempted to maintain the initiative by carrying the battle into the Biscay transit areas. Escort groups were moved closer to the Spanish Coast in an effort to sever new U-boat routes. However, Germany reacted strongly to this new threat, bringing out a new weapon: the radio-controlled, jet-propelled glider bomb. These were released by German bombers against escort groups in the Bay. HMS Egret was sunk by this new weapon late in August, and two other ships were damaged. Escort groups were withdrawn from the Bay offensive in September due to these attacks and renewed U-boat activity in the North Atlantic.\nSeptember 19, 1943, marked the second attempt by U-boats to regain the initiative in the North Atlantic. Convoys ONS 18 and ON 202 were the first to be evidently shadowed by U-boats. That night, attacks developed against both convoys. The escorts of ONS 18 were able to drive off the U-boats without suffering any losses. Convoy ON 202 was attacked later that night, and HMS Lagan was torpedoed. This was the first ship torpedoed in the Atlantic in September. It was also the first indication that the U-boats were using a new weapon, the acoustic homing torpedo (Gnat or T-5). HMS Lagan had been detached to follow up a bearing and had obtained a radar contact which faded when the range was about 3000 yards. She was within about 1200 yards of the assumed diving position when she was hit by a torpedo.\nThe ship blew off her stern and was taken in tow, reaching harbor. In the morning, two merchant ships of Convoy ON 202 were also torpedoed. During the forenoon, the two convoys were ordered to join, forming one convoy of 63 ships and about 15 escorts. That evening, two escorts were sunk - one while hunting a U-boat, the other while following up a radar contact. Despite these losses, the attempts the U-boats made on the convoy during the night failed. Early on the 21st, the convoy was rerouted to the southward in order to get within range of Newfoundland-based aircraft. However, heavy fog prevented much air cover that day and hampered the U-boats. The U-boats, estimated to be 15 or 20 in number, had the worst of it that night. Thanks to HF/DF fixes by the escorts, the U-boats were prevented from sinking any ships.\nEarly hours of the 22nd, one pack was rammed and sent to the bottom by HMS Keppel. Liberators gave cover throughout the day but the convoy was rather opened up by night and the U-boats attacked in strength. Just before midnight, one escort was sunk, later three merchant vessels were torpedoed and one more ship was sunk early that morning. The U-boats kept in contact with the convoy during the 23rd, but the attacks by escorting Liberators from Newfoundland so deterred them that their attacks that night were halfhearted and they lost contact with the convoy next day. In all, six merchant vessels and three escorts had been sunk, and another escort was damaged.\nU-boats were sunk, two by covering aircraft and one by an escort. Heavy losses were inflicted on the escorts by the acoustic torpedo, but U-boats succeeded in firing torpedoes at the convoy only on three occasions. U-boats were more reluctant than ever to press home their attacks, and as soon as they were detected, they made every effort to escape, either at high speed on the surface or by going deep. HF/DF was again of great value in determining the direction of impending attacks.\n\nThe actual results of this battle would probably have been disappointing to the enemy but captured documents indicate that the U-boats greatly overestimated the damage inflicted by the acoustic torpedoes. In addition, they felt that the heavy fog was largely responsible for saving the convoy from much heavier losses. This probably accounts for the enemy's subsequent change in tactics, focusing more on visual attacks and less on acoustic torpedoes.\nThe effort against North Atlantic convoys greatly increased in October 1943. World-wide shipping losses to U-boats in September were 20 ships of 119,000 gross tons, only slightly higher than August losses. Six ships were sunk in the North Atlantic, two in the Brazilian Area, six in the Mediterranean, and six in the Indian Ocean. About five German U-boats were responsible for the sinkings in the Indian Ocean, and there was evidence they were using Penang as a temporary base. The more cautious tactics of maximum submergence served to reduce the number of U-boats sunk during U-boat offensive.\n\nSeptember: U-boat is settling 1\nBy the end of September 1943, however, the Italian Fleet had surrendered, and 29 ships were no longer in service.\nItalian U-boats had come under Allied control. Encouraged by their supposed successes in September, the U-boats increased their attacks against North Atlantic convoys. The downward trend in the number of U-boats at sea was reversed, and there were about 75 U-boats at sea in the Atlantic in October, compared to only about 50 in September. Over 40 U-boats were concentrated in the Northwest and Northeast Atlantic Areas, and the days of wolf-pack attacks on convoys seemed to have returned. However, this time the U-boats suffered a much more decisive defeat than the one they had experienced in May 1943. First of all, the U-boats had trouble locating Allied convoys due to evasive routing, and they were able to inflict losses on only three of the North Atlantic convoys during October. Then again, the U-boats were not attacking with the same effectiveness as before.\nThe U-boats displayed the same aggressiveness as before, managing to sink only three merchant vessels and one escort. However, the price they paid was steep, with 22 U-boats sunk during October in the Northwest and Northeast Atlantic Areas. Aircraft played a significant role in this decisive setback for the U-boats, destroying 17 of the 22 sunk in these areas. Carrier-based aircraft were responsible for six of these 17 sinks, with four kills attributed to aircraft from the USS Card. In two cruises, aircraft from the USS Card carried out 19 attacks, nine of which resulted in A or B assessments. This second cruise concluded with the gallant action in which the USS Borie, one of the escorts of the USS Card, was lost.\nOn the night of October 31, after severely damaging one U-boat reported by a plane from the USS Card, the USS Borie made radar contact with another U-boat. Sonar contact was obtained, and a depth-charge attack brought the U-boat to the surface. The U-boat tried to escape on the surface, but the Borie opened fire and then rammed it at 25 knots, riding over the U-boat\u2019s forecastle and pinning it under. The two ships remained in this position for about 10 minutes with the U-boat exposed to fire from the Borie's 4-inch and 20-mm guns, Tommy guns, revolvers, rifles, and shotguns. One of the U-boat\u2019s crew was killed by a sheath knife thrown from the Borie's deck, and another was knocked overboard by an empty 4-inch shell case. At length, the U-boat got under way, with the Borie, now severely damaged, in full pursuit maintaining gunfire.\nA torpedo was fired at the U-boat but missed. The range was then closed again, and as the ramming attempt failed, three depth charges were fired straddling the U-boat. Another torpedo was then fired, passing within 10 feet of the U-boat's bow. A main battery salvo struck the U-boat's diesel exhaust, and the U-boat immediately slowed, stopped, and surrendered. About 15 members of the crew abandoned ship, and the U-boat sank stern first. The entire action from the initial contact until the U-boat sank lasted one hour and four minutes. Unfortunately, the ramming resulted in serious damage to the Borie, and she had to be abandoned later in the day. The worldwide shipping losses to U-boats in October were about the same as in September. Only 20 ships of 97,000 gross tons were sunk, but the number of U-boats sunk increased to 27 reflecting the increasing U-boat activity.\nThe U-boats showed increased activity but were forced to disengage in their battle against the North Atlantic convoys during their second attempt at a comeback, which failed. The first promising results of the acoustic torpedo were not maintained, and during October, this new weapon had little success. In response, the Allies developed a towed noise-making device (U.S. FXR \u2013 British FOXER) and new step-aside tactics in attacking U-boats. By the end of October, Britain was granted the use of the Azores by Portugal, and air bases were immediately established, greatly extending Allied air coverage of the Atlantic.\n\nA fundamental change in U-boat tactics was observed in November 1943 as they made their third and most feeble attempt to regain the initiative. As a result of the heavy losses inflicted on them.\nU-boats were compelled to adopt a mode of existence favoring their survival rather than effective employment against shipping in October, due to aircraft attacks and Allied air bases on the Azores. To increase their chances of survival, U-boats remained completely submerged during daytime, avoiding Allied air patrols. They surfaced at night to charge batteries and attack any convoys within reach. Small groups of U-boats were disposed along the probable convoy course, about one day's run apart, enabling each pack to attack the convoy for only one night. To compensate for the loss of U-boat mobility, enemy long-range reconnaissance aircraft were used to locate our convoys and pass on information to the U-boats. As most of the enemy's long-range aircraft were effective in this role.\nBased in France, these new U-boat tactics were tried out on the convoy route between the United Kingdom and Gibraltar. Four northbound convoys were attacked by U-boats with little success, as only one ship was sunk and several U-boats were destroyed. Fortunately, the attacks on these convoys came after Allied aircraft had moved into the Azores, and strong support from escort groups and shore-based aircraft brought the convoys safely through the concentrations of U-boats. These attacks provided Azores-based aircraft with their first kill, as a Flying Fortress sank a U-boat at daybreak on November 9. After the failure of this third attempt at staging a comeback, the U-boats reconciled themselves to remaining on the defensive for the remainder of this period. World-wide shipping losses to U-boats.\nThe lowest level since Pearl Harbor was reached in November 1943, with only 13 ships of 67,000 gross tons sunk. Activity spiked in the Panama Sea Frontier as three ships and one schooner were sunk by U-boats. No ships were sunk in the North Atlantic Convoy Area during the month, while four ships were sunk in the Indian Ocean and three in the Mediterranean. German aircraft, making extensive use of torpedoes and glider bombs, had become a greater menace to Mediterranean convoys than U-boats. Aircraft sank seven ships over 60,000 gross tons in the Mediterranean during November, six of them off the coast of North Africa between Iran and Bizerte. Early in the month, the enemy's attempt to reinforce the dwindling number of U-boats in the Mediterranean was largely unsuccessful.\nThree of the five U-boats attempting entry were sunk, resulting in a total of 18 U-boats sunk during November. Approximately half were sunk by aircraft and half by surface craft. The U-boat kills were distributed widely. The Second Escort Group sank two U-boats using a creeping attack. This method, developed to deal with deep U-boats, involved one ship maintaining contact with the deep U-boat at a distance and directing the attacking ship onto the unsuspecting U-boat. The attacking ship proceeded silently at slow speed to surprise the U-boat before it could start any violent evasive maneuvers. When the attacking ship was over the U-boat, it dropped a large pattern of depth charges. Two large U-boats, apparently headed for the Indian Ocean, were sunk in the South Atlantic during November by US aircraft based on Ascension.\nThe sinking of U-boats in the Indian Ocean was particularly valuable as the exchange rate was still favorable. The sinking of a U-boat headed for the Indian Ocean was equivalent to saving ten ships, as the average U-boat would probably sink ten ships before being sunk itself.\n\nBarrier patrols by aircraft in the South Atlantic proved effective during the last week of December 1943 and the first week of January 1944. Five enemy merchant vessels attempted to return from Japan to Germany and were in the South Atlantic, heading north. One of the five enemy blockade runners made port, badly damaged. Three were sunk by ships and aircraft of the Fourth Fleet in the Brazilian Area. Another was sunk by British-based aircraft in the approaches.\nTo the Bay of Biscay. This was the last attempt the enemy made to run the blockade with merchant vessels, but U-boats continued to make occasional trips between Germany and Japan. World-wide shipping losses to U-boats stayed at the same low level; only 13 ships of 87,000 gross tons were sunk by U-boats in December 1943. Although over half of the 60 U-boats at sea in the Atlantic were concentrated in the North Atlantic Goony Area, not a single ship was sunk there. All sinking were due to small numbers of U-boats operating in distant areas. Five ships were sunk in the Indian Ocean, three in the Freetown Area, and one in the Mediterranean. The other four ships were sunk in American coastal waters extending from Cape Flatteras to Aruba. However, the U-boats\u2019 policy of remaining submerged during daytime remained effective.\nSeven U-boats were sunk in December 1943, the lowest monthly total that year. Shipping losses to U-boats were overshadowed by the surprise air attack on Bari Harbor on Italy's east coast on December 2. About 25 bombers carried out the attack, resulting in the loss of 16 ships and damage to 10 others. Heavy losses were due in part to the explosion of several ammunition ships.\n\nOnly 13 ships of 92,000 gross tons were sunk in January 1944. Two of these ships were sunk from North Atlantic convoys. Three ships were sunk in the Barents Sea Area from a convoy headed for Russia, and eight ships were sunk in the Indian Ocean. The main concentration of about 25 U-boats in the North Atlantic moved gradually eastwards towards the west coast of Ireland, in an apparent attempt to locate Allied convoys. This move did not result in significant success.\nSeven U-boats were destroyed in the Northeast Atlantic Area while no ships were sunk. Only 11 U-boats were sunk in January as the U-boats continued their cautious tactics of maximum submergence. Fear of the impending invasion may have played a part in keeping the U-boats within short range of the French coast.\n\nFebruary 1944 marked the fourth successive month in which fewer than 20 ships and less than 100,000 gross tons of shipping were sunk by U-boats. Eighteen ships of 93,000 gross tons were sunk during the month, ten of them in the Indian Ocean, six in the Mediterranean, and only two in the Atlantic \u2013 one near Iceland and one in the Freetown Area. Approximately half of the 60 U-boats at sea in the Atlantic were concentrated in the North Atlantic, west of the United Kingdom. However, the North Atlantic con-\nVoys passed through this concentration of U-boats without suffering any losses while severe losses were inflicted on the U-boats. The worldwide total of U-boats sunk mounted to 22 in February, as ten were destroyed in the Northeast Atlantic Area.\n\nAircraft defeat U-boats\u2019 attempted come-back.\n\nFigure 3. Crew of U-550 prepare to abandon ship after attack by USS Joyce, Gandy, and Peterson, 200 miles off New York, April 16, 1944. SS Pan Pennsylvania burning in the background.\n\nThe outstanding achievement of the month was the 27-day patrol of the Second Escort Group, during which six U-boats were sunk in a period of 20 days. Every U-boat contacted was hunted to destruction. Four hours and 106 depth charges were required, on average, to kill each of these six U-boats. Combined creeping and follow-up attacks were responsible for the destruction of four of them.\nAgainst these successes, the loss of HMS Woodpecker to an acoustic torpedo must be recorded. In contrast, HMS Spey, fitted with the latest type of Asdic gear including the Q attachment and the Type 147B depth predictor, destroyed two U-boats in two days, each in a matter of minutes. Single patterns of ten depth charges forced the U-boat to the surface in each case. Another outstanding feature of the month's operations was the first sinking of a U-boat as the result of an initial MAD contact. U-boats had, during the previous months, approached on the surface at night and passed through the Straits of Gibraltar in the daytime entirely submerged. They made only enough speed to maintain trim, while the current carried them through. Allied ships, operating in the Straits, faced bad sound conditions due to the variation.\nIn the water's density, echo ranging was unreliable and listening provided little value, as U-boats moved at very slow speeds. This situation provided an ideal setup for the use of MAD (Magnetic Anomaly Detection). An MAD barrier patrol was initiated across the Straits in January 1944 to prevent submerged U-boat passage into the Mediterranean. Two PBYs of VP63 were on this patrol on February 24 when an MAD contact was obtained. Shortly after, two British destroyers and other planes arrived on the scene. The U-boat was attacked with retro-bombs from the MAD planes, depth charges and gunfire from the destroyers, and depth bombs from the other aircraft before it was destroyed. This MAD barrier patrol likely destroyed another U-boat attempting passage in March. During March 1944, there were some signs of the enemy.\nThe breaking up of U-boat concentrations led to a general dispersion across the North Atlantic convoy lanes. Shipping losses to U-boats increased, with 23 ships totaling 143,000 gross tons sunk worldwide. Losses were heaviest in the Indian Ocean where 11 ships were sunk, but German U-boats operating there were seriously inconvenienced by the sinking in the South Indian Ocean of two tankers they had been refueling. No ships were sunk in the Indian Ocean during the remaining two months of this period. Seven ships were sunk in various parts of the Atlantic in March, four in the Mediterranean, and one in the Barents Sea Area. The number of U-boats destroyed continued to increase for the third consecutive month, with 23 U-boats being sunk.\nIn March, the number of ships sunk was equal to that of U-boats. Two of the longest U-boat hunts of the war occurred around this time, one lasting 30 hours and the other 38 hours before the U-boats were destroyed. The Second Escort Group accounted for two more U-boats in March, bringing its total to 14. One of these was sunk with the cooperation of aircraft from HMS Vindex. The escort carrier groups significantly contributed to the campaign in March, sinking nine U-boats in the Atlantic. Aircraft from HMS Chaser, using rockets, participated in the sinking of three U-boats. Aircraft and escorts of the USS Bogue participated in the sinking of one U-boat, while two other U-boats were sunk by escorts of the USS Block Island. Toward the latter part of the month, the USS Block Island task group, operating in a probable refueling area near the Cape.\nThe Verde Islands sank two more U-boats. Sono-buoys were used in this operation. In the Mediterranean, the enemy lost five U-boats out of the comparatively small number remaining there. Two of these were sunk in a raid by U.S. Army Liberators on the U-boat base at Toulon. The lack of sightings in the Bay of Biscay caused Coastal Command to send its aircraft closer to the French coast and a U-boat was probably sunk by hits from 6-pounder gunfire from a Mosquito. A Catalina from Capetown sank a U-boat about 400 miles south of the Cape of Good Hope. The average number of U-boats at sea in the Atlantic dropped to 50 in April 1944 as the enemy continued to conserve his U-boats in anticipation of a major effort against the threatened invasion. U-boat patrol dispositions were rather sparse and wide-flung, and great importance was attached to the latter part of the text.\nNine ships of 62,000 gross tons were sunk by U-boats in April, seven in the Atlantic and two in the Mediterranean. For the first time in 14 months, no ships were sunk by U-boats in the Indian Ocean. However, the most disastrous event of the month occurred there on April 14, when an ammunition ship exploded in Bombay harbor, destroying 14 ships and damaging nine others. As partial compensation for this disaster, worldwide losses due to enemy action reached a new low for the war, with only 13 ships of 82,000 gross tons sunk in April. Starting in April, US ocean escorts of UGS convoys continued past Gibraltar into the Mediterranean as far as Bizerte before being relieved.\nThree April convoys were subjected to Nazi air attacks by British escorts. Each convoy near Algiers resulted in the sinking of three ships and damage to five others. On the night of April 20, the Germans made an unsuccessful attack with human torpedoes at Anzio. Prisoners and craft were taken, consisting of two torpedoes, one mounted about 6 inches above the other. The \u201cmother\u201d (upper) torpedo was modified to hold a human pilot who guided the craft and released the normal lethal torpedo attached underneath when within firing range. Remarkably, 16 U-boats were sunk during April. Escort carrier groups accounted for six of these. The average number of U-boats at sea in the Atlantic declined to only about 40 in May 1944. However, a large number of U-boats, which normally were, were absent.\nThe Atlantic-operating ships, held in Biscay, Baltic, and Norwegian ports for use against forthcoming invasions, experienced lower worldwide shipping losses than ever before, with only four ships of 24,000 gross tons sunk by U-boats during May. Three of these ships were sunk in the Brazilian Area, and one in the Mediterranean. Total shipping losses from all causes dropped to a new low, with only 12 ships of 40,000 gross tons lost during May.\n\nThe most notable U-boat achievement in May was the sinking of the escort carrier, USS Block Island. Early in the month, one of her planes assisted, while the USS Buckley, one of her escorts, finished off a German U-boat after a short (16 minute) but thrilling surface engagement involving guns.\nOn May 29, while the task group was searching for a U-boat suspected to be in the vicinity, the Block Island was struck by three torpedoes in a short interval. One of the escorts had her stern blown off. Shortly thereafter, the other escorts made contact with the U-boat and probably sank her after two Hedgehog attacks. The gallant career of the Block Island came to an end later in the day when she had to be abandoned.\n\nDespite the enemy's attempt to conserve his U-boats for the imminent invasion, the number of U-boats sunk during May 1944 was 29, the highest figure since the record total of 46 in July 1943. The leading area in the sinking of U-boats during May was the Northern Transit Area, East, where ten U-boats were destroyed during the month, nine of them by aircraft. Three of these were sunk by air-strikes.\nThe craft from HMS Fencer, which was escorting a convoy from Russia, noted a significant increase in the number of Baltic U-boats en route to the Atlantic via the Iceland-Faroes passage during the latter part of May. Allied submarines' operations against enemy shipping in Norwegian waters had prevented aircraft sweeps in this area for some time. The enemy may have thought they could safely relax their precautions in this area as many of these U-boats were traveling on the surface. Coastal Command aircraft quickly exploited this weakness, sinking six U-boats during the latter part of the month. The small number of U-boats in the Mediterranean was further depleted as four were destroyed there in May, and another was sunk while attempting to pass through the Straits of Gibraltar.\nThis was the third successful attack on a U-boat as a result of an initial MAD contact. The four successful attacks in the Mediterranean demonstrated the importance of persistence and the value of close cooperation between air and surface units. Three of the four hunts involved aircraft as well as surface craft, and the durations of the actions ranged from 22 hours to 76 hours. This record action began on May 14 and was culminated on the 17th with the sinking of a U-boat after a continuous hunt of 76 hours involving eight ships and three planes. U-boats in the Mediterranean fought back sternously, sinking one merchant vessel and two escorts and damaging four other ships during the month. The outstanding event of the month, and probably the outstanding achievement of the U-boat war by a single ship, was the performance of the destroyer.\nThe USS England destroyed five Japanese U-boats and was given major credit for the destruction of a sixth in the Pacific from May 19 to May 31, 1944. The Hedgehog was the primary weapon used in these attacks, as there was suspicion of a force of about five Japanese U-boats patrolling the line of the Equator, northeast of the Admiralty Islands. The USS England was accompanied by USS George and Raby during this sweep through the area. The outstanding performance of the England is more remarkable as it was her first contact with the enemy. Credible evidence from aircraft sightings and attacks in the final week of May 1944 indicated that two or more U-boats were at sea in the Western Pacific.\nThe English Channel, off the French coast, proved to be a preview of U-boat operations in the next period as, for the first time since the early days of the war, U-boats returned to the hazardous shallow coastal waters near England. This operation was possible only because U-boats could take advantage of the use of Schnorchel and thereby reduce their exposure to aircraft attacks.\n\nDuring this period, U-boats tried several modifications of their previous wolf-pack tactics in an effort to gain the upper hand in their attacks on Allied convoys. The first modification in tactics was made in September 1943 in the attacks on North Atlantic convoys. It was based on the use of the acoustic torpedo and involved attacking the escorts first.\n\n\"62 COUNTERMEASURES TO THE U-BOAT CONVOYS\n\nDuring this period, U-boats tried several modifications of their previous wolf-pack tactics in an attempt to gain the upper hand in their attacks on Allied convoys.\n\nThe first modification in tactics was made in September 1943 in the attacks on North Atlantic convoys. It was based on the use of the acoustic torpedo and involved attacking the escorts first.\nThe objective was to reduce convoy defenses to a point where merchant vessels would become easy prey for U-boats. Although some escort vessels were sunk, this objective was never accomplished. At this stage of the war, the Allies were using a larger number of escorts with the convoys and had a sufficiently large number of antisubmarine ships available. The loss of a few escorts would not seriously handicap future convoys. These U-boat tactics might have proved more effective in the early days of the war when the number of antisubmarine ships available to the Allies was extremely limited.\n\nThe second modification was made in November 1943 in the attacks on the convoys between Gibraltar and the United Kingdom. This change in tactics was forced on the U-boats by the heavy Allied air coverage of the North Atlantic which prevented the U-boats from making successful attacks.\nU-boats operated on the surface during the day, preventing the concentration of a large number of U-boats around a convoy. The enemy tactics involved stationing small packs of U-boals along the convoy's path. Long-range aircraft from Bordeaux were used to shadow Allied convoys during the day. Reports from the air reconnaissance were passed on to the U-boat packs, which then attempted to maneuver into a favorable position for a night attack. This change in tactics came a little late, as flying facilities had become available in the Azores in October 1943. Several convoys were intercepted by the U-boats, but strong support from escort groups and land-based aircraft brought the convoys safely through with only negligible damage.\n\nThe third modification in U-boat tactics, made after the setback in November 1943, involved the use of new tactics.\nThe almost complete abandonment of the old, highly organized wolf-pack attacks by U-boats in the North Atlantic was characterized by concentrations of U-boats but attacks were generally made by individual U-boats in favorable positions to attack convoys. Although these U-boat tactics were less effective against Allied shipping, they did enable U-boats to remain submerged during daytime. The scarcity of supply U-boats may have also been a factor in this drastic modification of wolf-pack tactics, which had been predicated on high-speed surface operations of U-boats, requiring high fuel consumption.\n\nThese futile attempts by U-boats had little success. Only about six ships a month were sunk by U-boats from Allied convoys. The tonnage sunk from convoys by U-boats was approximately 40,000.\nApproximately two-thirds of the total tonnage sunk by U-boats during this period. The degree of safety reached by convoyed shipping during this time is well illustrated by the experiences of North Atlantic trade convoys (HX, SC, ON, ONS). Of the 900 ships that sailed monthly in these convoys, only about 450 were sunk each month by U-boats. This represented a loss rate of only one sinking per 600 transatlantic trips. This high degree of safety from U-boats was typical of other convoy systems as well.\n\nOne of the primary reasons for the ineffectiveness of U-boats against Allied convoys was poor U-boat morale, as evidenced by their failure to press home attacks on convoys once they were detected. It is not difficult to see the reasons for this lack of aggressiveness. In the early months of 1943, Allied bombers had reduced the Biscay ports to heaps of ruins.\nThe stones could not reach U-boats in their shelters, but these raids deprived U-boat crews of all but the most primitive facilities after they returned, having come back through continually mined waters from long, exhaustive, dangerous, and now unsuccessful patrols. To reach the North Atlantic, U-boats had to proceed submerged through the Bay of Biscay for the first five or six days of their patrol, surfacing only for a few hours after midnight. To find the convoys, U-boats had to pass through areas remorselessly swept by covering aircraft. When U-boats sighted convoys, they found more numerous and better equipped escorts manned by more highly trained crews.\n\nAn analysis of attacks on shipping by U-boats, indicating some of the factors governing the safety of the shipping.\nShips against U-boat attacks were studied during this period, revealing significant influence on Allied measures for shipping protection. This study indicated that the safety of independent ships depended greatly on the speed of the ship, with the 12-to-14 knot region being critical. A 12-knot ship had about three times the probability of being sunk compared to a 14-knot ship making the same trip. The explanation for this is that the U-boat cannot generally follow a 14-knot ship or above for any length of time and if it is not in a suitable position to make a submerged attack immediately, the ship will escape. The U-boat can follow slower ships on the surface, at a suitable distance, working round to a position from which it can attack on the surface at night. Speed was a significant factor in the safety of con-\nThe study showed that 9-knot convoys were considerably safer than 7-knot convoys when air cover was present. When there was no air escort, the U-boat could approach the convoy at high surface speeds, and the extra 2 knots did little to prevent overtaking. A notable finding from this analysis was that the number of ships sunk was roughly independent of the size of the convoy as long as the number of escorts was the same. Large convoys lost, on average, a smaller percentage of ships to U-boat attack and were more economical in the use of escorts. The average size of North Atlantic trade convoys gradually increased during this period, rising from about 46 in March 1943 to about 57 in March.\nIn April 1944, certain changes were made to North Atlantic convoy schedules to allow several escort groups to be withdrawn for use in the invasion. The HX and ON convoy speeds were changed from 10 knots to 8, 9, and 10 knots in rotation, with the suffixes S, N, and F designating these respective speeds. The slow SC and ONS convoys were abolished. The sailing interval between convoys stayed at 7.5 days, resulting in four convoys sailing each way monthly instead of six. This produced a substantial increase in the average size of these convoys. The average size of these convoys was 98 in May 1944, and HXM 292, consisting of 135 ships and six escorts, was the largest convoy of the war to that date.\n\nThe danger from U-boat attack in the Western Atlantic was so low during most of this period that\nIt was possible to allow some shipping from the U.S. coastal convoys to sail independently during a lull in U-boat activity. The program remained flexible to maintain a balance between increased safety of convoyed shipping and the loss of time due to ships waiting in ports and sailing at slower convoy speeds. Fast merchant vessels, except those carrying high priority cargo, were able to sail independently along the coast during much of this period. Whenever the danger of a U-boat attack appeared imminent, independent shipping was ordered into port to await the next convoy. In some cases, where safety permitted, entire convoys were dispersed and the ships proceeded alone to their destinations.\n\nThe battle between U-boats and aircraft reached intense heights.\nThe climax occurred at the beginning of this period in July 1943. U-boats, armed with improved anti-aircraft weapons in the form of quadruple 20-mm guns, traveled on the surface during daytime and fought back against aircraft. They also traveled through the Bay of Biscay in groups for mutual protection.\n\nHowever, their disastrous experience in July 1943, when 34 U-boats were sunk in the Atlantic by aircraft, forced them to abandon these aggressive tactics. The enemy realized the U-boats were beaten and adopted more cautious tactics favoring self-preservation of the U-boat fleet until new technical equipment and modified U-boats could turn the tide.\n\nNew countermeasures against the U-boats involved complete submergence during daytime. The fact that aircraft had swept the seas made this necessary.\nU-boats from the surface during daylight hours constituted a real triumph for the Allies, as U-boats, robbed of their aggressiveness and mobility, lost a great deal of their effectiveness. The new tactics first became apparent in August 1943 in the critical Bay of Biscay transit area. U-boats reverted to surfacing at night for the minimum time necessary for charging batteries. In addition, they made the transit hugging the coast of Spain, where it was rather difficult for the Leigh-Light Wellingtons to patrol because of their limited range.\n\nThese changes had a profound effect on the Bay of Biscay campaign, and the productivity of Allied flying was greatly reduced. About 7000 hours were flown monthly in the Bay during the 5-month period from August 1943 through December 1943. These flying hours yielded only 12 sightings, six attacks, and no successful sinkings.\nOne U-boat was sunk per month. Though the flying effort was greater than during the preceding peak period (February 1943 - July 1943), the results achieved were only one-fifth as great. This decrease cannot be fully explained by the drop in the number of U-boat transits, which fell from 100 a month in the previous period to about 45 a month during this period. The average number of sightings per 1000 hours on patrol dropped to only two, and only 25% of U-boat transits were sighted. The efficiency index (sightings per 1000 flying hours on patrol per 100 U-boat transits) dropped from nine in the previous period to only four.\n\nThe U-boats' policy of maximum submergence during the daytime put great pressure on the development of suitable equipment and tactics to enable the air offensive to be maintained during the night.\nSignificant effort was devoted to the development of searchlights and flares to improve the low effectiveness of night attacks. The first attack on a U-boat by a U.S. searchlight-equipped plane occurred in December 1943, using a PBM from Trinidad. Coastal Command increased the amount of effective night flying in the Bay of Biscay by increasing the number of long-range searchlight-equipped planes. Leigh lights were fitted to Liberators, as well as additional squadrons of Wellingtons. The increased amount of night flying was counteracted by the U-boats' use of the Naxos GSR, which detected Allied S-band (10-cm) radar. The enemy began fitting its U-boats with this equipment in October 1943.\nThe net effect of these changes resulted in a small increase in the number of sightings and attacks in the Bay of Biscay. Approximately 20 sightings and 15 attacks occurred monthly in the Bay during the first five months of 1944. However, the effectiveness of Allied flying during the previous peak period was not approached. U.S. Navy planes participated in the Bay of Biscay offensive during this period under the operational control of Coastal Command. When the U-boat situation along the East Coast of the United States started easing up in August 1943, the U.S. Army Anti-Submarine Command was withdrawn from antisubmarine operations. The U.S. Army Air Forces squadrons which had been operating in England were relieved by U.S. Navy Liberators. The U.S. Navy planes in England constituted Fleet Air Wing 7. Carrier-based aircraft emerged as one of the most effective weapons against U-boats in the Bay of Biscay.\nThe U-boat's dangerous enemies during this period were the U.S. escort carriers. These carriers took the offensive against U-boats in regions outside the range of shore-based aircraft, particularly in possible refueling areas for the U-boats. This offensive was remarkably successful and made most of the Atlantic unsafe for surfaced U-boats.\n\nA U.S. escort carrier (CVE), accompanied by a screen of approximately four destroyers or destroyer escorts, formed a task group assigned to antisubmarine warfare in the Atlantic. The primary mission of the task group was to protect convoys, while the secondary mission was to search out and destroy U-boats. These task groups operated with the convoys between the United States and Gibraltar. The fact that the primary mission was accomplished is evident from the fact that 2200 ships crossed the Atlantic in the period.\nBetween May 1943 and December 1943, only one U.S. CVE-based convoy was sunk by U-boat action. A study of attacks made by U.S. aircraft during this period offers evidence that their secondary mission was effective. The average cruise lasted approximately 28 days, and 50 plane hours were flown per day while in U-boat waters. One sighting was made for every 600 flying hours. Sixty of the 68 studied sightings resulted in an attack, and about 40 percent of these attacks led to the sinking of the U-boat. The high quality of these attacks can be attributed to the ability of fast CVE-based planes to surprise the U-boat and attack while it was still on the surface. Another factor contributing to the success of these attacks was the cooperation between the F4F fighter aircraft.\nPlanes strafed the U-boat and the TBF bombers. British escort carriers, operating in the very bad weather of the Arctic, played a major role in getting the Russian convoys through. The North Russian convoys were started again around November 1943 after having stopped running in March 1943. The sinking of the Scharnhorst was the most publicized part of this battle. The U-boats accomplished much less against these convoys during this period than in the past. From December 1943 through May 1944, the U-boats sank only five merchant vessels and two destroyers from these convoys while 11 U-boats were sunk. British escort carriers played a major role, contributing six of the 11 U-boat kills. In one round trip of 16 days, with only eight days of operational flying, Swordfish planes from HMS Chaser sighted 21 U-boats and attacked 15.\nAnd with the aid of surface craft, three U-boats were sunk. Rocket projectiles were used very successfully by British carrier-based aircraft during this period. The first rocket attacks by U.S. planes were made in January 1944 by aircraft from the USS Block Island. The U-boat was sank; however, it was difficult to decide whether the sinking was due to the rockets or to depth charges which were also used in the attack. The lethality of aircraft attacks during this period was more than twice as high as it had been in the previous period. About 25 percent of the aircraft attacks made on the U-boats in the Atlantic and Mediterranean resulted in the destruction of the U-boat, while about 40 percent resulted in at least some damage to it. The effectiveness of aircraft attacks in the first half of 1944 was lower.\nThe effectiveness of U-boats fell significantly after the peak reached during the last half of 1943, when some were still on the surface fighting back. This decline also reflected the U-boats' tactics of maximum submergence during daytime as a much larger proportion of aircraft attacks, during the first half of 1944, were made at night. The accuracy of night attacks was always much lower than that of day attacks.\n\nScientific and technical progress was stimulated by the decisive defeat suffered by the U-boats during the previous period. A number of radical changes were made in U-boat weapons and equipment during this time.\n\nOne change in U-boat weapons involved the replacement of the quadruple 20-mm antiaircraft gun mount by a new rapid-firing 37-mm antiaircraft gun. U-boat torpedoes were equipped with FAT gear.\nfor use against convoys. This gear caused the torpedo to describe a zigzag course and thereby increased the probability of a hit. The major change in U-boat weapons was the introduction of the T-5 torpedo, a 21-inch electrically driven acoustic homing torpedo. The speed of the T-5 torpedo was about 25 knots and its range about 6000 yards. This torpedo homed on the noise of the target's propellers and its homing radius on a 15-knot escort was usually over 500 yards. The Allies immediately introduced countermeasures to the acoustic torpedo. The British twin FOXER (towed parallel-bar noisemakers used to decoy the acoustic torpedo from the ship) was born three months before the first acoustic torpedo attack took place. A complete escort group was fitted with twin FOXERS 17 days after the first attack. U.S. ships were fitted with FXR gear, which was similar to\nThe British equipment only involved a single noisemaker. Ships towing noisemakers or traveling at speeds greater than 24 knots or less than 7 knots were relatively safe from acoustic torpedo attacks. Other ships were instructed to use the step-aside procedure when conducting attacks on U-boats that might fire an acoustic torpedo. This was a special tactical maneuver, involving a radical change in course when the U-boat is approached, designed to remove the escort vessel from the most probable danger area from acoustic torpedoes.\n\nThe use of these towed noisemakers was unpopular on many ships due to the inconvenience involved in streaming and recovering the gear, the reduction in maneuverability, and the interference with the sonar equipment. However, the noisemakers were undoubtedly effective against the acoustic torpedoes.\nAbout 32 escorts and 19 merchant vessels are estimated to have been hit by acoustic torpedoes during the war. Very few of these casualties occurred when the recommended tactical procedure was used or the towed noisemakers were working properly.\n\nCountermeasures to the U-boat:\n\nThe acoustic torpedo was more likely to score a hit than a normal torpedo, but there were many cases of malfunctioning of the delicate mechanisms involved. Those torpedoes that did hit were less likely to sink the ship due to the fact that they usually hit in the stern.\n\nThe radar battle continued to play a prominent part in the U-boat war during this period. In the summer of 1943, Admiral Doenitz said, \u201cThe methods in radio location which the Allies have introduced have conquered the U-boat menace.\u201d However, the German High Command introduced new methods to counteract this threat.\nEffective countermeasures in radio communication and radar detection were implemented during this period due to German Intelligence becoming aware of Allied equipment. The major German scientific effort focused on developing a search receiver capable of detecting Allied radar transmissions. At the beginning of this period, the enemy was still unaware of the cause of the significant increase in sightings and attacks on U-boats. The German search receiver had been improved by the fitting of a drum-shaped aerial (wire-basket) which did not have to be removed when the U-boat dove. A better receiver (Wanz G-1) had been perfected and was being fitted on U-boats. This reduced the amount of radiation from the set itself but did not help the U-boat situation at all as it could only detect radiation of specific wavelengths.\nThe Germans introduced a less sensitive crystal detector, the Borkum receiver, covering the 75-300 cm band, which produced no radiation at all. Serious consequences of these judgement errors extended beyond the Germans' original limits. They instilled fear in U-boat captains that they might be detected, leading to a distrust of Admiral Doenitz's technical advisers. In September 1943, the U-boat command recognized that 10-cm radar was being used against them. The German Air Force had captured the blind bombing aid, H2S, operating on the 10-cm band, in March 1943. After a six-month period, this information finally reached the German Navy. As the simplest countermeasure, the Germans implemented it.\nThe Germans produced a crystal detector receiver, the Naxos, for the 8- to 12-cm band in October 1943, under the influence of their fear of radiating. The first models were crude portable units mounted on a stick. They were not pressure-tight and had to be passed below before diving. The maximum theoretical ranges on Allied radar sets varied from about 5 to 10 miles, but there was a considerable loss of efficiency under operational conditions.\n\nThe introduction of the Naxos search receiver reduced the number of sightings and attacks on U-boats and increased the number of disappearing contacts on Allied radar sets. However, many U-boats continued to be surprised successfully due to the low efficiency of the gear, and it was evident to the Germans that they still did not have the final solution to the radar problem. The U-boat command took the necessary measures.\nA U-boat, fully equipped to investigate Allied radar and carrying one of their best technicians with operational experience, was sent to sea in U-406 from St. Nazaire on February 5, 1944. It was captured when the U-boat was sunk by HMS Spey on February 18. A similarly equipped U-boat suffered the same fate in April 1944. These losses likely set back the German radar counter-measures program considerably.\n\nThe Allies were well aware of the potential effectiveness of an S-band search receiver, resulting in frequent false alarms reporting the introduction of a new GSR before any existed. Intelligence about Naxos, the increase in disappearing radar contacts, and the drop in U-boat sightings produced immediate Allied reactions. There were a few cases where S-band radar sets were turned off. Steps were taken.\nTo develop attenuators, which caused a slow and steady decrease in transmitted power as the range closed, in order to confuse GSR operators. An intermediate tactic of a \"tilt-beam\" approach to reduce signal intensity as the range closed was proposed but this proved rather difficult to carry out in practice. In addition, increased pressure was put on the development and fitting of X-band radar (3-cm wavelength).\n\nThe general conclusion was that S-band radars should not be turned off, due to their much greater search width as compared to visual search and also to the fact that the Naxos sets were inefficient and sightings and attacks continued to be made on U-boats with GSR. Furthermore, the very fact that aircraft were causing U-boats to submerge, thereby blinding and partially immobilizing them, greatly reduced the effectiveness of the U-boats in sinking ships.\nThe Germans produced a number of other developments in the radar field. A radar decoy spar, designed to give false radar echoes, was introduced but proved ineffective. Some work was done on radar camouflage, with the objective of developing rubber coatings for the U-boats that would deflect or absorb radar echoes. Earlier, there had been some attempt to use these rubber coatings against sonar, too.\nThe difficulties of producing rubber coatings that functioned under operational sea conditions were immense. The Germans persisted in their experiments with infrared searchlights and receivers, taking steps to evade detection by imagined Allied infrared equipment.\n\nDuring this time, U-boats started to recognize the threat from Allied shipborne HF/DF. A special Y party went to sea on a specially equipped U-boat, leading to the U-boat command attributing their declining success to some extent to their communications. They significantly improved these communications by reducing message lengths and altering frequencies more frequently.\n\nAlthough these shifts made HF/DF more challenging both ashore and at sea, they did not significantly impact its use or effectiveness. They did, however, made it more difficult for U-boats to attack convoys.\nThe most revolutionary technical development of this period was the fitting of Schnorchel to U-boats. The Schnorchel (or snout) is an extensible mast, consisting of an air induction trunk and a diesel exhaust line which are enclosed in a metal fairing. The cross section of this fairing is streamlined with the maximum dimension about 20 inches. The mast is about 26 feet in length and when raised is a few inches lower than the top of the extended periscope. The Schnorchel enables a U-boat to travel on its diesel engines at periscope depth at speeds of about 6 knots and also to charge batteries without surfacing. In essence, it was a defensive weapon, designed to re-enable U-boats to operate effectively without the need to surface.\nThe idea of an extendable air intake, enabling a U-boat to charge batteries while submerged, was present in the German Navy before the war but gained attention following the capture of two Dutch submarines with such equipment in 1940. No action was taken to develop this concept during the U-boats' initial successes, and it wasn't until the end of 1943, when aircraft had gained superiority, that efforts began. The first U-boats were not fitted with Schnorchel until February 1944, and its impact on U-boat operations became significant during the next phase of the U-boat war in June 1944.\n\nThe U.S. Navy introduced a new development during this period.\nThe Bearing Deviation Indicator (BDI) was one of the most helpful sonar aids used with standard echo-ranging equipment on ships to improve sonar performance. BDI allowed the operator to determine the target's bearing with greater accuracy and rapidity for every ping, as it indicated whether the target producing the echo was to the right or left of the projector's bearing. Two new types of depth charges came into use on U.S. ships during this period. The Mark 8 depth charge was fitted with a magnetic proximity fuze, designed to detonate when within lethal range of a U-boat. The Mark 9 depth charge was steel-cased and shaped for fast sinking.\nThe new depth charges, which reduced blind time and enhanced the lethality of surface craft attacks on U-boats, were designed by the British during this period. They improved their ships' antisubmarine equipment along different lines than the U.S. Navy. The Squid, a depth charge-throwing device that is automatically controlled and operated, entered service at the beginning of 1944. It uses a 3-barreled mortar, electrically fired, designed to discharge bombs ahead of the attacking ship. These bombs, similar in weight and explosive effect to depth charges, offer the following advantages:\n\n1. They are projected with accuracy to a known point, well ahead, while the attacking ship remains in Asdic contact with the U-boat.\nThey have a reliable underwater course. They have a much higher sinking speed. They incorporate a new type of fuze which is set automatically to the required depth with a high degree of accuracy. The depth is set on the fuzes electrically from the new Type 147B Asdic depth predictor. The mortars are fired automatically from the Asdic range recorder. The three charges are thrown to the points of an equilateral triangle. When two mortars are fitted, as in frigates, the pattern is in two depth layers. The Type 147B Asdic depth predictor was developed primarily for use with the Squid, so as to obtain a measurement of the depth of the U-boat just before the projectiles are fired. However, the Type 174B depth predictor, in conjunction with the appropriate range and bearing recorders and Q attachment, can also be used in Hedgehog and depth-laying attacks.\nType 147B charges use a fan-shaped beam of high-frequency sound (50 kc) which can be depressed down to 45\u00b0 below the horizontal. The beam of sound is broad in the horizontal plane (30\u00b0-40\u00b0 on either bow) and narrow in the vertical plane (2\u00b0-3\u00b0 off axis). Trials have shown that the set is capable of setting Squid fuses to within about 20 feet of the depth of the U-boat, if it is below 100 feet. At shallower depths, it is not possible to get accurate measurements. Accurate attacks on U-boats can be made at depths down to some 800 feet, provided that the Q attachment is fitted.\n\nThe average number of U-boats sunk or probably sunk monthly reached a peak of 21 a month during this period. The record monthly score of the war was reached in the first month, July 1943, when 46 U-boats were sunk.\nOf the total 234 U-boats destroyed during this two-month period, 199 were German, 28 Japanese, and 7 Italian. The 180 U-boat sinkings in the Atlantic were rather widely distributed, with the leading areas being the Northwest Atlantic Area with 34 kills, the Northeast Atlantic Area with 29 kills, and the Biscay Channel Area with 28 kills. Aircraft continued to be the leading U-boat killers during this period, accounting for 122 alone (52% of the worldwide total), and another 22 (9% of total) with the cooperation of surface craft. Carrier-based aircraft accounted for 40 of the 144 kills in which aircraft participated. Ships accounted for 79 U-boats (34% of total), and Allied submarines accounted for the other 11 U-boats (5% of total).\nThe quality of surface craft attacks continued to improve steadily throughout this period as crews became more experienced and better weapons and equipment became available. Approximately 30% of surface craft attacks on U-boats in the Atlantic and Mediterranean resulted in at least some damage, while 20% resulted in the sinking of the U-boat. The lethality of these attacks was twice as high as it had been during the previous period. A study of British assessed attacks during this period indicated that about three patterns were dropped in the average attack on a U-boat. The probability of sinking a U-boat was about 6% for the average depth-charge pattern and about 11% for the average Hedgehog pattern.\n\nFrom the U-boats\u2019 Point of View\nTo interpret the results of the U-boat war during this period correctly, it's important to realize that the German High Command acknowledged, at the beginning of this period, that U-boats had been decisively defeated in the crucial battle against North Atlantic convoys. The enemy also recognized that the old type of U-boat would have to be radically modified before it could again pose a serious threat to Allied supply lines across the Atlantic. The solution reached by the German High Command was the development of an entirely new type of U-boat, more immune from radio location, with much greater submerged speed, and an entirely new and quicker method of production. The first sketch of what was to be the new prefabricated Type XXI U-boat was made in July 1943. By December 1943, all designs were finished, including full-scale wooden models.\nIn February 1944, it was decided to halt the construction of old-type U-boats, with the exception of those already laid down, and focus on producing new prefabricated U-boats. The enemy's strategy was to keep the U-boat fleet operational until the new U-boats were ready, at which point they could resume offensive actions. The Schnorchel was valuable as a transitional measure, reducing the threat from air attack and allowing U-boats to operate in inshore waters during the possibility of invasion. The primary objective of U-boats during this period was self-preservation, although they would attempt to sink as much Allied shipping as possible without incurring excessive losses. Additionally, keeping U-boats at sea helped to tie up large Allied forces.\nDuring the last half of 1943, U-boats made several attempts at conducting offensive operations but were beaten back each time with heavy losses. Realizing self-preservation as their primary mission, U-boats ceased large-scale offensives against shipping. The number of U-boats in the Atlantic dropped steadily, reaching a minimum of about 40 in May 1944. Their main functions during the first five months of 1944 were likely reconnaissance, weather reporting, forcing the Allies to convoy shipping, and waiting for the invasion. They made no attempt to sink a large amount of Allied shipping, as reflected in the results achieved.\nDuring this period, world-wide shipping losses to U-boats reached a new low. Approximately 17 ships of 101,000 gross tons were sunk monthly by U-boats, which was only about one-fourth the amount sunk monthly during the previous period. About 45% of these sinkings occurred in the Atlantic, while approximately 40% took place in the Indian Ocean and another 15% in the Mediterranean. The world-wide number of U-boats sunk monthly peaked at about 21. The world-wide exchange rate reached a new low of only 0.048 ships (4,800 gross tons) sunk by the average U-boat before it itself was sunk.\n\nU-boat activity in the Mediterranean was slightly lower than in the preceding period. Sicily was invaded in July 1943 and the Mediterranean was considered open for Allied shipping, although almost all Axis submarines had been driven from the Atlantic and most were now operating in the Mediterranean.\nAll of it was forced to travel in convoy. Thirty-six merchant vessels were sunk by U-boats during this period at a price of 23 U-boats sunk. Shipping losses to German and Japanese U-boats in the Indian Ocean were at a slightly higher level than previously, as 71 ships were sunk during this 11-month period. However, this was the first period in which there was some evidence of countermeasures against the U-boats in the sinking of seven U-boats. This was one of the few areas where the exchange rate was still favorable for U-boat operations, as 10 ships were sunk by U-boats for each U-boat sunk. Japanese U-boats were strictly on the defensive in the Pacific and spent most of their time in supplying isolated outposts. Despite the fact that the bulk of the shipping in the Pacific sailed independently, only one merchant vessel was sunk by U-boats during this period.\nDuring an 11-month period, Allied forces sank 24 Japanese U-boats in the Pacific. The average number of U-boats at sea in the Atlantic was 61, about 40% less than the average during the previous period. These U-boats sank eight ships totaling 44,000 gross tons per month in various areas of the Atlantic. The Atlantic U-boat fleet reached a new low in offensive power, sinking only one-fifth of a ship (700 gross tons) per month at sea. Despite the meager results and the smaller number of U-boats at sea, the number of U-boats sunk in the Atlantic continued to increase, with 16 being sunk monthly during this period.\nThe average life of a U-boat at sea in the Atlantic during this period was approximately 4 months, half the average life in the previous period. This meant that each U-boat at sea in the Atlantic could sink only about half a ship (2,800 gross tons) before it was sunk. The magnitude of the disaster suffered by the U-boats during this period can be roughly measured by the fact that the exchange rate (ships sunk per U-boat sunk) was about nine times as high in the previous period, the battle against the North Atlantic convoys, and about 38 times as high in the peak period, the first 9 months of 1942. These figures reflected the growing strength and efficiency of Allied surface and air craft and the widening gap between Allied weapons and equipment and that of the U-boats. They also confirmed.\nThe German High Command acknowledged, at the beginning of this period, that the old-type U-boat could no longer compete with Allied anti-submarine forces. The enemy's only consolation at the end of this period was that U-boat losses would probably have been much larger if they had continued their large-scale offensive against Allied shipping. This is evident in a comparison of the 16 U-boats sunk monthly in the Atlantic with the 37 U-boats sunk in July 1943 and the 25 U-boats sunk in October 1943, the months in which the U-boats attempted offensive operations.\n\nBy operating their U-boats as they did, the Germans were able to maintain their large U-boat fleet for the invasion. Approximately 250 new German U-boats were constructed during this period while only about the same number were lost.\n200 German U-boats were sunk, reducing the Germans to over 400 U-boats by the end of this period.\n\nFrom the Allies\u2019 Point of View\n\nThe Allied and neutral nations lost approximately 184,000 gross tons of shipping monthly from all causes during this period, about a third of the monthly shipping losses during the preceding period. Simultaneously, new merchant shipping construction ran at approximately 1,160,000 gross tons monthly, slightly higher than during the preceding period. This resulted in a net gain of approximately 976,000 gross tons a month in the amount of shipping available.\n\nThe shipping available to the Allies had increased by almost 11,000,000 gross tons during this period to a total of about 7,500 ships of 47,500,000 gross tons. Around 10,500,000 gross tons of this total consisted of tankers. October 1943 was the first month in which\nThe total shipping available was larger than the 40,000,000 gross tons of shipping available at the start of the war in September 1939. It took four years to replace the heavy shipping losses, mostly caused by U-boat action in the early years of the war. By the end of this period, the shipping crisis had passed and the Allies had sufficient shipping available to undertake the invasion. In fact, construction of new merchant shipping had started tapering off in 1944 after reaching a peak of 1,500,000 gross tons in December 1943. Part of this tapering off was due to the conversion of shipyards to the construction of the faster Victory ships, which took about twice as long to build as the slower Liberty ships. Of the 184,000 gross tons of shipping lost monthly from all causes, 147,000 gross tons were lost as a result of...\nThe enemy accounted for 101,000 gross tons a month, approximately 69% of the total lost due to enemy action. Monthly shipping losses from enemy aircraft were higher than in the preceding period, amounting to 34,000 gross tons a month, or about 23% of the total. Shipping losses from enemy surface craft, mines, and other enemy action were even lower than in the preceding period, totaling only 22,000 gross tons a month, or 8% of the total. The major task of the Allies during this period had been accomplished. Sufficient supplies and men had been landed in England to enable the Allies to undertake the invasion of Europe in June 1944. Despite the fact that U-boats were no longer the serious menace they had been in the past, the large U-boat fleet based on both flanks of the English Channel remained a significant threat.\nChannel constituted a potential threat to the success of the invasion. The immediate problem facing the Allies, at the end of this period, was to prevent U-boats from attacking the large concentration of shipping that would be carrying troops and military equipment across the Channel during the invasion. From a long-term point of view, it was necessary to maintain the numerical and technical superiority of Allied anti-submarine forces over the U-boats. Allied supply lines, which would be required to support fighting forces in Europe, faced the problem of preventing continuous U-boat attacks.\n\nChapter 7\nSEVENTH PERIOD\nSCHNORCHEL U-BOATS OPERATE IN BRITISH HOME WATERS\nJUNE 1944-END OF WAR\n7.1 U-Boat Offensive\nIn many respects, this last period of the U-boat war was characterized by the Schnorkel U-boats operating in British home waters.\nThe U-boat war resembled the first period. Military operations in Europe again subsidiary to and largely influenced the U-boat war. U-boats were driven from their bases on the Bay of Biscay, which they had used for four years, and forced to return to bases in Norway and the Baltic. The waters around the British Isles became the main area of U-boat activity, as Schnorchel-equipped U-boats were able to operate in inshore waters with relative safety from aircraft detection. U-boats operated mostly submerged, not by choice as in the first period, but because they had been forced under by Allied aircraft. Surface craft again became the main destroyers of U-boats. U-boats found that operations in inshore waters were just as hazardous during this period as they had been at the beginning of the war. The chief hazards were mines and depth charges from Allied anti-submarine warfare vessels.\nThe average U-boat sank one-twentieth the amount of shipping during this period compared to the first. Allied escorts were more numerous, experienced, and better equipped. U-boat offensive power was reduced by their loss of mobility. U-boat morale was lower during this period than early in the war. The lull in U-boat activity ended with the Allied landings in Normandy on June 6, 1944. The Allies appreciated the U-boats as a serious potential threat to invasion success. The U-boat fleet size was such that a mass attack in the Channel on D-day, from both flanks, could have saturated defenses and inflicted grave losses on Allied convoys during the critical early days of the operation.\nThe Allied countermeasures involved blocking off the cross-Channel Area and guarding the convoy routes leading to it, with the objective of making the approaches to both a difficult and exhausting operation for the U-boats. By June 6, ten escort groups, consisting of 54 ships, were ready to block the western approaches to the Channel. They were supported by three escort carriers, which were there primarily to provide fighter support to escorts operating close to the enemy shores. The enemy air threat proved, however, to be so slight that these carriers were withdrawn by June 11. Coastal Command aircraft put on an intensive flying effort in the Channel and its western approaches and in the Bay of Biscay Area. These dispositions of anti-U-boat forces were independent of, and in addition to, the escorts and aircraft provided for close escort duties with the convoys.\nConvoys ran to and from France. The first reaction of U-boats to the invasion was a considerable exodus of U-boats from French ports on D-day, as soon as the enemy became aware that the operation had truly begun. The number of U-boats in the Biscay-Channel Area increased from one on June 5 to about 20 on June 8. The majority of these U-boats made no attempt to enter the Channel but instead set up defensive patrols off the Biscay ports to counter possible invasion attempts in that area. A curious feature of these operations was that they began with a large number of sightings and attacks on U-boats by aircraft and then, after a period of several days, the number of contacts was sharply reduced. This reduction was due to the extensive use of Schnorchel by the U-boats, which had begun at that time.\nIt seems that U-boat captains had not taken kindly to the Schnorchel, and intended to use it only as a last resort if the weight of air power against them became intolerable. After six U-boats were sunk by aircraft attacks in the Biscay Area between June 7 and 10, the U-boats began to appreciate the value of Schnorchel and quickly learned how to use it efficiently. It is also possible that the enemy intended to operate his U-boats in the Channel, accepting all risks and proceeding on the surface in order to reach the vital invasion area and disrupt Allied landing operations. It was the initial blows dealt him by Coastal Command in the early days of the operation that forced him to adopt more cautious, and less effective tactics.\nEffective tactics of remaining continuously submerged gave the advent of Schnorchel to him the means. The Schnorchel was a very poor radar target, even at short range, and was difficult to sight, even in daylight. To attack it at night required exceptionally good radar tracking and Leigh-light or flare technique.\n\nIn addition to their successes in the Bay of Biscay, Coastal Command aircraft contributed an outstanding performance in June against U-boats in Norwegian waters. Most of these U-boats were probably en route for the English Channel to join operations there. These U-boats continued to operate mainly on the surface, and Coastal Command aircraft sank seven in Norwegian waters during June.\n\nThe first surface craft kill in the Biscay-Channel Area did not come until June 18. This was followed by four other surface craft kills, two with the help.\nThe only aircraft kill in the Biscay-Channel Area occurred before the end of June. There was only one success for U-boats against merchant shipping in the invasion area more than three weeks after D-day, sinking five ships in the last few days of June. Two escort vessels were torpedoed by U-boats in the middle of June. These results, measured against the 12 U-boats sunk in the same area in June by Allied forces, indicate that the U-boats failed completely in their attempt to disrupt the Allied invasion. The other enemy weapons (aircraft, surface craft, and mines) were equally ineffective against the thousands of Allied ships that moved across the Channel to Normandy. Only 18 ships of 75,000 gross tons were sunk in the Biscay-Channel Area in June 1944.\nThe Allies settled over 50 merchant vessels, approximately 300,000 gross tons, in constructing artificial ports used successfully during the invasion. The enemy turned to other offensive weapons such as human torpedoes, explosive motor boats, and the V-1 bomb in July, but they did little damage to Allied shipping. The experience in the Biscay-Channel Area during July and August was similar to that in June. The Allies continued to keep up their pressure on U-boats, while U-boats found the approaches to the shipping lanes so difficult that those who reached them fumbled the opportunities they found. U-boats operating in this area sank two merchant vessels in July and six in August, while the Allies sank nine U-boats in July and 12 in August. Surface craft played the predominant role in sinkings.\nU-boats were present in this area during these two months, killing 13 of them alone and destroying three others with the assistance of aircraft, out of a total of 21 sunk. An outstanding feature of surface craft attacks in the invasion area was the difficulty experienced in the initial detection of U-boats, which adopted anti-Asdic tactics of resting on the bottom when escort vessels were heard approaching. Numerous wrecks, along with the difficult water conditions and the high reverberation background in shallow waters, gave the U-boat almost complete immunity from Asdic detection. However, once the Asdic picked up the U-boat contact and identified it as such, the chance of obtaining a kill rose to a peak of about 50% in the invasion operation. The Second Escort Group continued its brilliant career during a ten-day patrol in the Biscay-Channel.\nEarly in August, the Squid achieved the first destruction of a U-boat and participated in the sinking of two others. The Squid attack was remarkably quick. Six Squid charges were sufficient to bring the U-boat to the surface, and the crew rapidly abandoned the sinking U-boat. The Allied land forces' breakthrough across the Cherbourg peninsula in the first week of August threatened the enemy's Biscay ports and forced their evacuation. The U-boats abandoned their efforts on the Biscay-Channel Area toward the end of August and headed for Norwegian ports, marking the end of the first phase of the U-boat campaign against cross-Channel Allied shipping. The enemy focused his main effort against the Allied invasion during the first three months of this period, and U-boat activity in other areas was minimal.\nThe average number of U-boats at sea in the Atlantic during June 1944 was approximately 48. Half of these were concentrated in the Biscay-Channel Area and the Northern Transit Area-East. World-wide shipping losses to U-boats remained low, with only 11 ships of 58,000 gross tons sunk by U-boats in June. Five ships were sunk in the Biscay-Channel Area, three in the rest of the Atlantic, and three in the Indian Ocean.\n\nSchnorkel U-boats Operate in British Home Waters\n(Figure 1: A boarding party from USS Guadalcanal works to keep the captured U-505 afloat after its crew had abandoned it.)\n\nThe total number of U-boats sunk during June was 28, which was roughly the same as the high level reached in May. Besides the 21 U-boats sunk in the waters around the British Isles, four others were disposed of.\nOne U.S. escort carrier group, which included U-505, operated in widely distant parts of the Atlantic. U-505 was captured by USS Guadalcanal [CVE] and her escorts on June 4, 1944. This task group sailed from Norfolk in May 1944 with the avowed intention of capturing an enemy submarine. It was believed that there was a good opportunity to capture a U-boat that surfaced by concentrating anti-personnel weapons on it, holding back on weapons that would sink it, and making an attempt to board it as soon as possible. After an unproductive hunt around the Cape Verde Islands, a well-conducted search plan was put in operation on May 31 for an estimated homebound U-boat. The USS Chatelain [DE], one of the escorts, made sonar contact at about 1000 on June 4. A Hedgehog attack, followed by a shallow depth-charge attack, brought the submarine to the surface.\nThe U-boat emerged at 1023, and firing was initiated. The U-boat crew rushed on deck and dove overboard. At 1027, \"Cease firing\" was commanded. The U-boat then ran in a tight circle at about seven knots, fully surfaced, and it was known that most of her crew had abandoned her. USS Pillsbury (DE), another escort, lowered a whaleboat with a boarding party and attempted to rope the U-boat. Meanwhile, the boarding party got alongside and leaped from the whaleboat to the deck of the circling U-boat. There was only one dead man on deck and no one below, and the boarding parties immediately set to work closing valves and disconnecting demolition charges. The Guadalcanal took the U-boat in tow, but many difficulties were encountered as the towlines broke and the U-boat showed signs of settling. It was not until June 8 that\nThe U-boat was at fully surfaced trim for the first time that a U-boat had been captured by the U.S. forces. U-505 was finally brought to Bermuda. Figure 2: A torpedo plane approaches for a landing while USS Guadalcanal towed U-505 astern. The Allies were able to extract valuable technical information from the manuals and equipment aboard the U-boat. In addition to more reliable data on the acoustic torpedo, German search receivers, and other standard U-boat equipment, the Allies obtained important information about German war orders, communications, and codes. Much of this information proved valuable in conducting later operations against the U-boats, as the Germans did not know that we had captured a U-boat and obtained this information. World-wide shipping losses stayed low in July.\n1944: Only 12 ships of 63,000 gross tons were sunk by U-boats. In addition to the two ships sunk in the Biscay-Channel Area, five ships were sunk in the rest of the Atlantic and five in the Indian Ocean. The number of U-boats sunk throughout the world in July was 22, slightly less than in June. Escorts of USS Card (CVE) eliminated a potential threat to Allied shipping by sinking a 1600-ton minelaying U-boat early in July. This U-boat carried 66 mines, the moored acoustic type, which were intended to be laid in the approaches to Halifax.\n\nAugust 1944 was the best month of this last period for the U-boats, as they sank 18 ships of 99,000 gross tons throughout the world. This peak score, however, is only about the same as the average monthly sinkage achieved by U-boats during the previous period, which was a rather low average.\nIn the Biscay-Channel Area, six ships were sunk, compared to only two in the remainder of the Atlantic. U-boats sank one ship in the Black Sea and nine in the Indian Ocean, primarily off East Africa in the Mozambique Channel. The landings in Southern France occurred during August without any ship losses in the entire invasion area.\n\nSchnorchel U-boats operated in British home waters. The monthly decline in the number of U-boats sunk continued during August, with only 17 being sunk. Aircraft found it more challenging to detect and attack the Schnorchel U-boat. Besides the 12 U-boats sunk in the Biscay-Channel Area, there were only three sunk in the Atlantic, all by escort carrier task groups. Aircraft from HMS V index, which escorted the North Russian convoys, sank two U-boats, while aircraft from the USS Bogue were responsible for sinking another.\nU-1229 south of Newfoundland, after a 20-day search. This U-boat, traveling on Schnorchel, had remained submerged for about 14 days, surfacing only for a short daily interval of 10 to 15 minutes to determine her position.\n\nThe most significant development in August, regarding future U-boat operations, was the advance of Allied armies in Western France which forced the U-boats to abandon their bases on the Bay of Biscay. These bases contained the redoubtable Todt concrete shelters which had withstood heavy Allied attacks for years. The basic strategy of German naval warfare in the Atlantic had depended upon the successful use and maintenance of the Biscay bases, from which U-boats could proceed directly to their operational areas with minimum fuel consumption and less throttling opposition from Allied air and surface patrols.\nBy the end of August, it was evident that the U-boats had begun their final exodus from the Biscay ports and were heading for Norway, where they would be much more vulnerable to Allied air attack. The problems of repair and maintenance of a large U-boat fleet at the small and inadequately equipped Norwegian bases would also be much more difficult. The main effect, however, of the loss of the Biscay bases was the considerable increase in the length of voyages to operating areas. The 500-ton U-boats, which comprised the majority of the U-boat fleet, were thereafter restricted to operations around the British Isles, as it was extremely difficult to refuel at sea. Even the 740-ton U-boats confined most of their later operations to the nearby Atlantic, operating near Canada and Gibraltar. During September 1944, the enemy seemed to be making a final push.\nConcerned primarily with shifting his U-boats from the Bay of Biscay to Norwegian bases, approximately 25 U-boats were engaged solely in running the gauntlet of Allied air and surface patrols between France and Norway. These U-boats traveled submerged for almost the entire trip, using Schnorchel, and most of them completed the journey safely. As a result of this mass transit of U-boats, the average number at sea in the Atlantic reached a peak for this last period during September, with 57 U-boats at sea. World-wide shipping losses were considerably reduced in September as only seven ships of 43,000 gross tons were sunk by U-boats. A noteworthy feature was the almost complete absence of U-boat activity in the Indian Ocean. One ship was sunk there early in the month, but the U-boat responsible for this sinking withdrew towards Penang.\nFive ships were torpedoed in September: two in the Barents Sea Area and one in the Canadian Coastal Zone. The other three were sunk from North Atlantic convoys by U-boats operating on Schnorchel in inshore waters in the Northwestern Approaches to England. A total of 21 U-boats were sunk during the month, including six 300-ton U-boats.\nThat which were scuttled in the Black Sea resulted from Russian advances in eastern Europe. In the Mediterranean, two of the three U-boats based at Salamis were destroyed. The general clearance of U-boats and enemy aircraft from the Mediterranean enabled the number of ships employed in convoy escort to be reduced, and a large number of independent sailings was permitted. Only ten U-boats were sunk in the Atlantic. This steady decrease reflected the inactivity of the U-boats and the increased effectiveness of Schnorchel. Two of these U-boats were sunk as a result of inshore activity in the Northwestern Approaches to England, five were sunk in the Northern Transit Area-East, and three in the remainder of the Atlantic.\n\nBy the end of September, the last of the U-boats seemed to have departed from the Biscay-Channel Area. The average number of U-boats out at sea:\nThe Atlantic declined to about 30 in October, with most ships still in transit. German U-boats achieved few results during this situation. October 1944 was the first month of the war in which they were unable to sink any ship in the Atlantic. Only one ship of 7000 gross tons was sunk during October. A perfect record for the month was spoiled on October 30, when a Japanese U-boat sank a US cargo ship traveling independently in the Pacific, midway between San Francisco and Pearl Harbor. Ironically, this was the first ship sunk in the Pacific by a U-boat since November 1943. The lull in U-boat activity was reflected on the east coast of the United States, as October marked the first complete month of independent sailings for all ships engaged in coastal trade.\nNine U-boats were sunk during October, five in the Pacific and only four in the Atlantic. All four of the latter were sunk in the Northern Transit Area\u2014the area through which the U-boats traveled to and from their Norwegian bases. One of these four U-boats was sunk as a result of a bombing raid on Bergen. One of the five U-boats sunk in the Pacific was a German U-boat, sunk by the Dutch submarine HNMS Zwaardvisch in the Java Sea. This was the most easterly position in which a German U-boat had ever been destroyed. Although the average number of U-boats at sea in the Atlantic during November was only 24, the lowest monthly average of this period, the enemy had completed his transfer of U-boats from the Biscay bases, and the U-boats at sea were more active. Seven\nThirty thousand gross ton ships were sunk by U-boats in November 1944: two in the Indian Ocean, a Swedish ship in the Baltic, and four in inshore waters in the Atlantic. Three of these ships were sunk on November 10 in the approaches to Reykjavik, Iceland. The other ship was sunk in the English Channel toward the end of the month after several months without any U-boat activity in this area. The number of U-boats sunk during November was ten, but seven of these U-boat kills took place in the Pacific and only three in the Atlantic. This was the smallest monthly number of U-boats sunk in the Atlantic since January 1942. Two of these U-boats were sunk in the Northern Transit Area-East and one in the Biscay-Channel Area. The main reasons for the meager results achieved by the Allies in sinking U-boats during these three months are unknown.\nSeptember through November, U-boats exhibited extreme caution. The average U-boat sank less than one ship per month at sea. Increased experience in using Schnorchel enabled U-boats to avoid Allied air patrols by remaining submerged for prolonged periods and lying in wait for Allied convoys in focal areas inshore. U-boats then developed bottoming tactics in inshore waters, where wrecks and non-sub contacts were abundant and where the high reverberation background tended to drown out weak Asdic echoes. Additionally, the necessity for Allied ships to use anti-Gnat noisemakers made Asdic detection more difficult.\n\nThe enemy's experience during these three months indicated that U-boats could again operate inshore waters, with Schnorchel, without suffering undue losses. This, in effect, made unnecessary the need for U-boats to remain offshore.\nThe previous long voyages to distant areas had been made to avoid the heavy Allied air coverage in the North Atlantic. The enemy had therefore, through the use of Schnorchel, overcome to some extent the great strategic disadvantage resulting from the loss of his Biscay bases. The use of Schnorchel enabled U-boats to proceed to and from their bases in Norway and the Baltic via the Faeroes-Shetland passage instead of the more circuitous passage south of Iceland. U-boats could operate effectively in all areas of the North Atlantic, particularly in the waters around England, where the high density of important shipping provided an attractive target near the U-boat bases.\n\nDecember 1944 witnessed the beginning of a steady increase in the number of U-boats at sea in the Atlantic. Coincident with the German land offensive.\nFive U-boats operated in the central English Channel during the Battle of the Bulge, aiming to hinder the flow of troops and supplies to Allied armies in Europe. Seven ships and an escort were sunk in the Biscay-Channel Area during December, with most damage occurring towards the end of the month by two U-boats that escaped. A flotilla of midget U-boats (Biber) launched an abortive offensive against convoys in the Scheldt Approaches off the Dutch coast, resulting in one ship sunk and 15 midget U-boats sunk or captured. U-boat activity in other areas was minimal during December, with only nine ships of 59,000 gross tons lost worldwide. An independent ship was sunk in the Gulf of Maine.\nDecember 3, by the same U-boat, two enemy agents were landed on the coast of Maine on November 29. The other ship was sunk in the Pacific off the south-east coast of Australia by a German U-boat, the first sinking in these waters since May 1943.\n\nNine U-boats were sunk during December; one in the Indian Ocean and eight in the Atlantic. Six of the eight U-boats sunk in the Atlantic were lost in the waters around England, particularly in the Biscay-Channel Area and the Northern Transit Area-East. One of the three U-boats in the Biscay-Channel Area ran aground on Wolf Rock due to navigational difficulties.\n\nU-boat activity continued to increase during January 1945 as 11 ships of 57,000 gross tons were sunk by U-boats. All 11 of these ships were sunk in the Atlantic.\nIn United Kingdom waters, no sinkings occurred in the English Channel, although U-boats were still patrolling there. Activity shifted to the Irish Sea, where six ships were sunk during the month by U-boats that had penetrated the region, despite it being long considered safe from enemy attacks and used for training. Inshore areas of U-boat activity in January included Halifax, where four ships were sunk and another damaged, and the western approaches to Gibraltar, where one ship and an escort vessel were sunk and another ship damaged. Three of the four ships sunk off Halifax were torpedoed on January 14, during daylight, outside a convoy nearing port. Escorts were not successful in locating the U-boat. The number of U-boats sunk monthly reached:\n\n## Input Text: \"\"\"\n## U-Boat Activity Report for January 1943\n## \n## Tic by U-boats operating in inshore waters. In United Kingdom waters, there were no sinkings in the English Channel, although U-boats were still patrolling there, and the center of activity shifted to the Irish Sea, where six ships were sunk during the month by U-boats which had penetrated into the region, although it had long been considered safe from enemy attacks and had been used for training.\n## \n## The other inshore areas of U-boat activity in January were off Halifax, where four ships were sunk and another damaged, and the western approaches to Gibraltar, where one ship and an escort vessel were sunk and another ship damaged. Three of the four ships sunk off Halifax were torpedoed on January 14, during daylight, out of a convoy nearing port. The escorts were not successful in locating the U-boat.\n## \n## The number of U-boats sunk monthly reached a new record high of 21 in January 1943.\n## \n## Signed,\n## U-Boat Command\n## \"\"\"\n\nIn United Kingdom waters, no sinkings occurred in the English Channel, although U-boats were still patrolling there. Activity shifted to the Irish Sea, where six ships were sunk during the month by U-boats that had penetrated the region, despite it being long considered safe from enemy attacks and used for training. The other inshore areas of U-boat activity in January were off Halifax, where four ships were sunk and another damaged, and the western approaches to Gibraltar, where one ship and an escort vessel were sunk and another ship damaged. Three of the four ships sunk off Halifax were torpedoed on January 14, during daylight, outside a convoy nearing port. Escorts were not successful in locating the U-boat. The number of U-boats sunk monthly reached a new record high of 21 in January 1943.\n\nSigned,\nU-Boat Command\nDuring January 1945, only six U-boats were sunk. One was in the Pacific and five in the Atlantic. All kills were made by surface craft during the latter half of the month. No U-boat was sunk by aircraft during this period.\n\nThe first sinking occurred on January 16 in the Northwest Atlantic Area when a US destroyer escort task group sank a weather-reporting U-boat. Using information from the U-boat plot, the group departed from the Azores for the general area of the last fix. An HF/DF fix, at a range of 10 miles, further localized the probable area of the U-boat and the hunt began. Two hours and forty minutes later, sonar contact was gained and one Hedgehog attack and five Mk 8 depth-charge attacks resulted in the sinking of the U-boat.\n\nThe other four U-boats were sunk in the Atlantic.\nIn January, all U-boats were sunk in United Kingdom coastal waters by British surface craft. Three of these kills resulted from Asdic contacts made shortly after ships were torpedoed. These were encouraging as they represented some evidence that ships were finally learning how to attack U-boats operating in inshore waters, after months of disappointing patrols in generally difficult conditions. In addition to these successes, indirect but effective anti-U-boat operations were carried out by the Russian armies during January. By overrunning East Prussia, they threatened important working-up bases in the eastern Baltic, and by entering Silesia, they paralyzed part of the elaborate organization for the construction of the new Type XXI prefabricated U-boats. It is estimated that the yards at Danzig alone produced almost a third of the new Type XXI prefabricated U-boats.\nU-boats severely taxed Norwegian and western Baltic ports with the additional burden of handling surface vessels and U-boats previously based in eastern ports. The concentration of all U-boat facilities in the western Baltic made them more vulnerable to Allied air attacks.\n\nU-boats were more aggressive in February 1945, sinking 15 ships totaling 65,000 gross tons. One ship was sunk in the Indian Ocean, off the west coast of Australia, and the other 14 ships were sunk in the Atlantic, marking the peak monthly score for this period.\n\nWith land warfare in Europe approaching Germany, the enemy's objective seemed to be to sink the maximum shipping in the short time remaining. Consequently, the major U-boat effort was concentrated in British coastal waters, where nine ships were sunk during the month, mainly in the south.\nThe five ships sank in the English Channel and North Sea off the east coast of England. Two sank in the Barents Sea Area, one near Iceland, one near Gibraltar, and one in the Southeast Atlantic by a U-boat homeward bound from the Indian Ocean. The number of U-boats sunk monthly increased sharply with 19 U-boats sunk in February, indicating that the kills near the end of January initiated a new period of good hunting. Twelve of the 14 U-boat kills in the Atlantic took place in the waters around England, but there was a shift of activity to the northward. The Tenth Escort Group carried out a particularly successful patrol in the area between the Shetlands and the Faeroes against U-boats on passage to their operational areas, sinking three.\nThe three attacks all resulted from initial Asdic contacts on submerged U-boats. Ten of the 14 kills in the Atlantic were made by surface craft as Asdic became more effective against U-boats in shallow inshore waters due to increased Allied ship experience. The other two U-boat kills in the Atlantic occurred in the Barents Sea Area and off Gibraltar. Five Japanese U-boats were sunk during February in the Pacific, where the USS Batfish turned in a record performance by sinking three U-boats in four days. These were torpedoed north of Luzon between February 9 and 12. In each case, the Batfish detected Japanese radar signals on her search receiver [APR] and then homed on the U-boat. The number of U-boats at sea in the Atlantic increased sharply in March 1945, averaging over 50.\nThe month saw most U-boat activity concentrated around England's waters, but there were signs of a shift to deeper Atlantic waters. The enemy may have recognized that some escorts had been moved from ocean convoys to inshore waters. There was also evidence of Type XXIII U-boats operating in the North Sea, off the east coast of England.\n\nDespite the increase in U-boats at sea, worldwide shipping losses to U-boats remained the same in March 1945. Only 13 ships of 65,000 gross tons were sunk, all in the Atlantic. Nine of these ships went down in waters around England, seven of them in the Biscay-Channel Area. Two ships were sunk in the Barents Sea Area, and another two in the Brazilian and Caribbean Areas by a U-boat heading home.\nFrom the Indian Ocean and the North Sea Area, midgets probably sank three additional ships. In March, the number of U-boats destroyed remained high with 19 being destroyed, two in the Pacific and 17 in the Atlantic. Four U-boats were destroyed in German ports by our raids, and one was sunk in the Canadian Coastal Zone by a U.S. destroyer escort group. The other 12 U-boats were sunk in the waters around Great Britain; one by aircraft, two by mines, and nine by surface craft. The Twenty-First Escort Group turned in a notable performance by sinking three U-boats in four days, north of Scotland.\n\nIn April 1945, shipping casualties were of the same order of magnitude as in March, with 13 ships of 73,000 gross tons being sunk by U-boats. All of these ships were sunk in the Atlantic: two off Cape Hatteras in the Eastern Sea Frontier, one in Kola Inlet in the Barents Sea.\nThe tempo of U-boat operations in April gave no indication that the end of the war was at hand. With remarkable determination, the enemy maintained his U-boat offensive in inshore waters to the very end of the war. No relaxation of effort or hesitation to incur risk was apparent until the German surrender on May 8, 1945. A U.S. cargo vessel was sunk off Rhode Island on May 5, but a U.S. destroyer escort task group gained sonar contact later that night and destroyed the U-boat. On May 7, a U-boat sank two merchant ships from a coastal convoy near the Firth of Forth. These were the last merchant ships sunk by U-boats in World War II. Japanese U-boats did not sink a single merchant ship between V-E Day, May 8 and V-J Day, August 14, 1945.\nSix Japanese U-boats were sunk during that interval. Thirty-six U-boats were sunk during April 1945, making the highest monthly score of the last period. Five of these U-boats were sunk in the Pacific and the other 27 in the Atlantic. Surface craft accounted for 19 kills in the Atlantic, the highest monthly score of the war for them. Twenty-two of these U-boats were sunk in the waters around England, three in the Barents Sea Area, two along the east coast of the United States, and four in the Northwest Atlantic Area. These four U-boats were part of a group (Group Seawolf) engaged in a joint westward sweep of North Atlantic convoy lanes while en route to operations off the U.S. coast. Escorts of U.S. escort carrier task groups conducted a barrier patrol which intercepted this group of U-boats and were responsible for these four kills.\nOn the last day of April, a U.S. Navy MAD-equipped plane sank a U-boat in the Biscay-Channel Area with retro-bombs. During the first week of May, aircraft operated effectively in Danish waters against U-boats attempting to escape to Norway, sinking about ten of them with rockets and gunfire. In addition to the kills enumerated above, it is estimated that the heavy bombing raids on German ports in the Baltic probably accounted for the destruction of over 25 U-boats in port during the last month of the war.\n\nOn May 4, a short signal was transmitted on all U-boat frequencies. By this signal, Doenitz had ordered his U-boats to cease hostilities. In an Order of the Day issued at the same time, he explained that a crushing superiority had compressed the U-boats into a very narrow area and that the continuation of the battle would result in heavy losses.\nBy May 31, 1945, 49 U-boats had surrendered at sea, leaving a small number unaccounted for. The last of these to surrender was U-977, which gave up at Buenos Aires on August 17, after Japan's surrender. In addition to the U-boats that surrendered at sea, huge numbers were captured in ports or scuttled.\n\nThe end of the war saw the U-boat fleet held in check but still carrying out operations on a major scale. It had never been driven off the seas and might have increased substantially in numbers and power, had the war been extended for any appreciable period. New-type U-boats were just coming into service at the end of the war. About six Type XXIII U-boats had operated with fair success off the east coast of the United Kingdom, and at least that number.\nOne hundred twenty-one Type XXI U-boats had reached ports in Norway with the intention of sailing for offensive operations in the future. One is believed to have actually started on patrol but was forced to turn back due to equipment failure. The U-boat was not eliminated as a weapon of war when Germany surrendered, and the new types Germany was introducing would have raised serious problems for the Allies had they ever reached large-scale use.\n\nSeven countermeasures to the U-boat:\n\nConvoys\nShipping in convoy during this last period was safer than in any previous one. Although the number of convoyed ships at sea was at its peak, only six ships were sunk monthly by U-boats. Of the 1,100 ships that sailed monthly in the North Atlantic convoys, only about one was sunk monthly by U-boats, usually in the vicinity of England. The loss rate was therefore significantly lower than in previous years.\nLess than 1% of ships were sunk by U-boats when in convoy contrasted to independent sailings, increasing to approximately 55% during this period. This increase was due to U-boats, operating on Schnorchel in inshore waters, finding it desirable to operate in areas of high shipping density, that is, along convoy lanes. The experience during this period differed from the past as most shipping losses occurred at the terminals of the convoy routes instead of in the middle. The principle of defense in depth greatly contributed to the safety of convoyed shipping, particularly in the case of North Russian convoys. During this last period, there were often sufficient ships available so that, in addition to the close escort, pickets could be stationed in an outer screen.\ncould intercept and surface U-boats, investigate surface ships, divert neutral ships, and give the Escort Commander timely warning of impending dangers. Air patrols operated in the zone beyond the pickets. The largest convoy of the war, HXS 300, consisting of 167 ships and seven mid-ocean escorts, sailed in July 1944. With 19 columns, this convoy had a front of some nine miles. The ships in the convoy carried over a million tons of cargo to England. The convoy arrived safely and the fact that it was not attacked may well have been due to the vigorous search by the two MAC ships for the only U-boat reported in the vicinity.\n\nEarly in September 1944, following the transfer of the U-boats from the Biscay base to Norwegian ports, the Allies rerouted North Atlantic convoys around the south of Ireland, through St. George\u2019s Channel.\nThe channel's route between New York and Liverpool didn't significantly shorten the voyage, but it facilitated the joining and splitting of sections from the south coast of England and the Continent. It also moved ships further away from U-boats based in Norwegian and German ports and the rough weather of higher latitudes. Convoy CU 37 was the first to reach an Atlantic port on the Continent, with one section arriving in Cherbourg on September 7. Antwerp was opened to Allied convoys on November 28.\n\nThe increased safety of convoys in the Atlantic enabled the Allies to make another change to quicken the flow of shipping. Towards the end of September 1944, the sailing interval for HX and ON convoys was reduced to five days, and the slow SC and ONS convoys were restarted.\nThe convoys would not be as large as they had been in the previous months, but there would be more of them. The time spent in port by ships waiting for convoys was cut materially by this change.\n\nCountermeasures to the U-boat:\n\nSimilar steps were taken in the East Atlantic in November 1944. A single escort sailed with convoys between Gibraltar and the United Kingdom, although additional protection was given at both ends. This more or less restored the arrangement that had been in force from the outbreak of the war until the middle of 1941. Shipping between Gibraltar and Freetown was permitted to sail independently if there were no U-boats along the route. In the Mediterranean, convoying was abandoned except for troopships and local convoys near Italy and Greece.\n\nIn the last month of the war, April 1945, the average size of convoys increased significantly due to the reduced U-boat threat.\nThe number of ships at sea in the Atlantic reached a maximum of 1400, approximately double the number in the early months of 1943. About two-thirds of these ships were in convoy. Shipping in the Pacific also reached a new high in April, with approximately 900 ships at sea, and about one-third of them in convoy. Most U-boat activity during this period was concentrated in the waters around England. Consequently, aircraft under Coastal Command operational control played the major part in the offensive against the U-boats. At the end of the war, Coastal Command had more than 1100 planes under its control, more than six times the number available at the start of the war. The invasion battle started in May 1944, when U-boats left from Norwegian ports to reinforce the Biscay ports for the attack on the huge amount of Allied shipping which would have to be transported.\nUsed for the build-up of the Allied beachhead. Few U-boats got through, as aircraft sank 17 U-boats and damaged 11 others in Norwegian waters between mid-May and the end of July. Thus, a depleted U-boat fleet was left to execute the plan to attack the invasion traffic.\n\nAs soon as the invasion had started, the U-boats headed for sea, staying on the surface and fighting back against aircraft with their automatic 37-mm guns. Coastal Command was ready, and within five days, the enemy lost six U-boats while five were seriously damaged. The hectic few days after D-day produced one of the outstanding achievements of the war, when a Liberator sank two U-boats at night within half an hour. After the first week of the invasion, the enemy abandoned his ideas of staying on the surface and the all-Schnorchel era had begun.\nThe beachhead was already secure, and the U-boat fleet was badly mauled. Between mid-May and the end of July, Coastal Command aircraft sank 23 U-boats, shared two kills with surface craft, and damaged 25 U-boats. The price paid for the success was 31 aircraft lost due to enemy action and 17 lost due to operational hazards.\n\nOnce the invasion beaches were secure, it was Coastal's job to protect shipping until victory was finally won. It was difficult to detect Schnorchel at all, and even after it was detected, the probability of attacking it successfully was lower than that for an attack on a surfaced U-boat. All available aircraft were employed to hunt the Schnorchel, and although the number of kills was somewhat disappointing, only a few ships were sunk in inshore waters. Thus, the many hours of flying often without the consolation of a successful attack.\nDuring 1945, Coastal Command conducted numerous anti-U-boat sorties in the Skagerrak, Kattegat, and western Baltic. Liberators at night and rocket-fitted Mosquitos and Beaufighters during the day carried the war into the U-boats' home waters. Numerous attacks were made, some on the new type U-boats proceeding to Norwegian ports prior to setting out on operations. The most notable effort was a strike in the Kattegat by Mosquitos, resulting in the sinking of three U-boats. In the final days of the war, U-boats began to evacuate north German ports and run for Norway. Many attacks were made and about ten U-boats are believed to have been sunk by aircraft in the first week of May 1945.\nDuring the entire period, aircraft operating under Coastal Command made approximately 38 sightings and 24 attacks monthly. This was about the same as in the previous period, despite the much higher concentration of U-boats in British waters during the last period. The use of Schnorchel resulted in a reduction in the lethality of aircraft attacks, with only 18 percent resulting in the sinking of a U-boat (compared to about 25 percent in the previous period), and about 35 percent resulting in at least some damage to the U-boat. Approximately half of the aircraft kills during this 11-month period occurred in the first and last months (June 1944 and April 1945), when a high proportion of U-boats were found on the surface. Operational results during the last period indicated that Schnorchel was a most effective countermeasure against U-boats.\nMeasuring the impact on Allied air power, most U-boats were outfitted with Schnorchel. Equipped with a drum-shaped aerial (Runddipol), this pressure-tight feature provided a warning only for meter radar. The primary function of Schnorchel was to reduce visual and radar ranges from Allied aircraft by approximately 2 to 3 times. Towards the end of this period, the Germans developed an effective anti-radar rubber-like covering for the Schnorchel. Supposed to cut Allied microwave radar ranges on Schnorchel by an additional factor of 3, this covering was intended to significantly impact radar detection. Contacts were made at ranges that often fell within the sea-return zone of Allied radar sets, resulting in their being missed entirely. It is estimated that the number of potential Schnorchel contacts missed at short ranges outnumbers the total number of Schnorchel contacts made at all ranges.\nThe advantages of Schnorchel enabled U-boats to operate over long periods of time in restricted waters, with reasonable safety from aircraft, by remaining bottomed most of the time and coming to Schnorchel depth only to recharge batteries. The effectiveness of aircraft hunts was also reduced as the Schnorchel increased the submerged speed of U-boats for prolonged periods from about 2 or 3 knots to about 6 knots.\n\nSchnorchel, however, also had its disadvantages. The offensive power of U-boats was greatly reduced as they were forced to give up the great mobility of surfaced operations for the relatively slow speeds of Schnorchel operation. The efficiency of the periscope watch was impaired when the U-boat was at Schnorchel depth, and the noise of the engines rendered the hydrophones practically useless. In addition, prolonged use of Schnorchel undoubtedly increased the periscope.\nSonnel fatigue, resulting from varying air pressure, occasional fumes, and the more careful attention required to maintain depth control, were disadvantages of the Schnorchel for U-boats. Despite these disadvantages, U-boats preferred the feeling of security the Schnorchel gave them over operating on the surface and relying on their new directional microwave search radars for aircraft warning. With the increased use of Schnorchel, the number of U-boat contacts per 1000 flying hours steadily decreased, and the ratio of Schnorchel contacts to all contacts steadily increased, surpassing 50% in December 1944. Visual search became relatively more productive than radar search as occasional sightings were made at relatively long ranges on the exhaust smoke or wake that sometimes accompanied the Schnorchel. The Allies were unable to produce any really effective countermeasures against the Schnorchel.\nEffective countermeasures to the Schnorchel by the end of the war included increased use of binoculars in visual search and determination of the most favorable altitudes for Schnorchel detection. Tactical doctrines were modified to account for decreased sweep widths of both radar and visual search. Modifications, such as the fast time constant (FTC) circuit, were made to Allied radar sets to improve contact efficiency. The FTC circuit acted as a discriminator against sea return, making it easier to distinguish Schnorchel blips. New high-power narrow-beam short-pulse radar sets were designed to provide better resolution in the search for small targets. Tests indicated that the new radar sets (AN/APS-3 and AN/APS-15), which operated in the X-band (3-cm) and had sharp beams, were better at detecting Schnorchel than the previous sets.\nAircraft used sono-buoys more frequently towards the end of the war to take advantage of the high noise output of Schnorchelling U-boats. Sono-buoys had been used successfully in a number of attacks by U.S. escort carrier task groups, and analyses indicated that in over 50 percent of the cases in which sono-buoys were dropped following visual contacts on U-boats, a sono-buoy contact was obtained.\n\nThe Allies continued to perfect their equipment and tactics during this last period. More useful and flexible retiring search plans were developed for surface craft. Operation Observant and similar search plans, based on the most probable location of the U-boat, provided ships with the means of regaining contact with a U-boat once the general location was known.\nAn analysis of surface craft hunts indicated that the correct plan resulted in contact being regained in 44% of cases, while the incorrect plan led to success in only 28% of cases. The U.S. Navy continued to improve its sonar equipment, with experimental work done on maintenance of deep contact feature [MDC] and depth-determining gear. By the end of the war, a new fast-sinking influence depth charge had been developed, the Mark 14. This charge had a higher probability of doing lethal damage to a submerged U-boat than other depth charges. It was designed to fire at the nearest point of approach to a U-boat by the change of frequency between the reflected signal and the supersonic signal emitted by the depth charge. An analysis was made of operational results.\nObtained during 1943 and 1944 by British ships using depth charges, Hedgehog, and Squid. It indicated that a single depth-charge pattern had about a 5% chance of sinking a U-boat and a Hedgehog pattern at least a 15% chance, while the Squid attacks averaged about a 20% chance of success. The double Squid pattern showed promise of being the most lethal weapon against U-boats, but this was based on a small number of attacks. The greatest technical effort of the Allies was spent on the effort to develop satisfactory means for the detection of Schnorchel. As previously mentioned, two main lines were followed: (1) the improvement of radar performance by choosing a design effective against small targets, and (2) the improvement of sonar detection, in particular sonobuoys for detection from aircraft. The chief modification in the development of sonar was the introduction of the \"Foxer\" countermeasure, which produced a loud underwater noise to mask the sound of a U-boat's diesel engines. This was particularly effective when used in conjunction with sonobuoys. The development of radar was also significant, with the introduction of the H2S radar, which used a cathode ray tube to display the location of enemy ships on a screen. This allowed Allied aircraft to locate and attack U-boats more effectively. Overall, the improvements in sonar and radar technology played a crucial role in the Allied victory in the Battle of the Atlantic.\nThe involvement of this issue led to an increase in the operating life of the buoys to reduce the number that had to be employed. Additionally, directional sonobuoys were developed, providing more accurate submarine positioning, but they did not see operational use. The U-boat command continued to be productive in developing new technical equipment for the U-boats in an attempt to stave off impending defeat. During 1944, the Germans introduced a new type of gear [LUT] on their torpedoes, which allowed the line of advance of the torpedo, when zigzagging, to be preset at any angle from its straight run. This gear also enabled the mean speed of advance to be preset. At the end of the war, the Germans were developing a new type of homing torpedo (Geier) which omitted superonic signals and homed on the reflected echoes from the target.\nDuring this period, the Germans modified their 740- and 1200-ton U-boats to enable them to dive as quickly as the 500-ton U-boats. The most distinctive feature of these modified U-boats was the narrow cut-away deck forward. Toward the end of the war, there were some indications that the Germans had developed an ultra-high-speed method of communication (Kurier) using an attachment to the normal U-boat transmitter. It appears that the message was recorded on a magnetic tape which was then run through at high speed. This method of communication would counter Allied use of HF/DF.\n\nEarly in 1944, the U-boat command had come to a clearer appreciation of the true situation with regard to Allied use of radar. They realized that they needed an improved search receiver against S-band (10-cm) radar which would not only give ample warning but also enable them to attack effectively.\nThe enemy's problems with efficiency losses under operational conditions would not be significantly alleviated by the provision of a margin of sensitivity. The enemy had learned of X-band (3-cm) radar from a crashed H2X blind bombing plane at the beginning of 1944, and the development of X-band search receivers was initiated by the Germans before Allied use of X-band radar in U-boat search had yielded substantial results.\n\nThe German solution to these problems emerged in the late spring of 1944 in the form of the \"Tunis\" search receiver. Tunis consisted of two antennas: the \"Mucke\" horn for X-band radar and the \"Cuba la\" (Fhege) dipole and parabolic reflector for S-band radar. It was equipped with an untuned crystal detector and connected to a Naxos 2 amplifier. Bearings were taken by rotating the DF loop on which the antennas were mounted. The X-band Mucke horn had a beam width.\nThe width of the about 15-degree bearing allowed for quite accurate radar readings on 3-cm equipment. The S-band Fliege antenna detected 10-cm radar transmissions through a sector of approximately 90 degrees. The equipment's primary feature was the directional antennas, which increased sensitivity and range. To achieve the necessary sensitivity with these aerials, the Germans had to sacrifice the desirable property of all-around viewing, and the aerials had to be continuously rotated by the bridge watch. The units still had to be dismounted and taken below during submergence, making them unusable on Schnorchel.\n\nAllied tests on captured equipment revealed that Tunis was simple to operate and reliable under normal operational conditions. These tests suggested that expected operational ranges on Allied radar sets would vary from about 20 miles for planes at 500 feet.\nThe altitude for planes flying at 2000 feet is approximately 40 miles. The operational ranges of Tunis were greater than the average radar ranges for S-band and X-band on surfaced U-boats. The Tunis search receiver was apparently a simple, efficient, and successful countermeasure against both S-band and X-band radar.\n\nSchnorchel U-boats operated in British home waters. The Tunis search receiver was used infrequently by U-boats during this period, and it's possible the Germans were not aware of its effectiveness against Allied radar. Developed shortly after Schnorchel was fitted to U-boats, Tunis never received a fair trial in actual operations. U-boats did not have much faith in their technical experts, who had fumbled so badly in 1943, and preferred the security of the Tunis search receiver.\nOffered by Schnorchel, despite its limitation for the offensive and the risk of operating on the surface and depending on Tunis for early warning of Allied aircraft, Tunis offered no protection against possible new Allied radar sets on different frequencies or against Allied aircraft not using radar at all, while Schnorchel did. It seems quite likely that the U-boats would have sunk considerably more shipping if they had operated on the surface with Tunis, but the desire for safety was predominant, and Schnorchel offered the better prospects for that. All centimeter aerials produced by the Germans had the disadvantage that they could not withstand submergence. The production of a suitable pressure-tight aerial, urgently needed for use on Schnorchel, presented great technical difficulties which were not completely solved by the end of the war.\nDuring this period, the Germans introduced a variety of midget U-boats, such as Seehund, Molch, Biber, Hecht, and Marder. These were manned by one or two men from a pressure-tight control position and capable of complete submergence. The successful attack by British midget submarines on the Tirpitz on September 22, 1943, stimulated German interest in these craft. The flotillas operating these midget U-boats were not branches of the U-boat arm of the German Navy but formed part of an organization known as the Small Battle Units Command (KDK). The only search receiver aerial fitted on Schnorchel was the old standard Runddipol type, which could detect only meter radar. There were some signs that the Germans were developing a pressure-tight aerial at the end of the war, suitable for both S-band and X-band radar detection and incorporating an infrared receiver as well.\nThe Seehund (Type XXVII) was probably the most formidable of the midget U-boats. It was pre-fabricated, about 39 feet long, and displaced 16 tons. It carried two torpedoes and a two-man crew. The surface speed was about 6 knots and submerged speed about 3 knots. The surface range was about 275 miles, the endurance of the crew about three days, and the diving depth about 100 feet. It was fitted with a periscope.\n\nMidget U-boats were used primarily in the invasion area and were generally ineffective, inflicting very little damage on Allied shipping while suffering heavy losses. This may have been due partly to the fact that they were rushed into battle before they were perfected and before their crews were properly trained. Their small size made it more difficult to detect them but they were extremely vulnerable.\ndepth-charge attack. They were relatively slow and unwieldy, with a limited operational range, and only suitable for attacking merchant ships proceeding slowly in calm waters. It is estimated that about 80 midget U-boats were sunk or captured between December 23, 1944, and they started operations in the Channel Area, and the end of April 1945.\n\nThe heavy losses sustained by U-boats in the Battle of the Atlantic forced the enemy to undertake the gigantic task of building a complete new frontline U-boat fleet. Though faced with imminent invasion and a great shortage of manpower, Germany employed a very large number of their skilled workers in the construction of prefabricated U-boats.\n\nThis is a measure of the importance that the enemy attached to U-boat warfare and of the hopes which he entertained for success in a new campaign.\nThe Type XXI U-boat was designed for high submerged speeds, primarily to get into a favorable attack position. Originally intended for turbine drive, the high-speed hull design for the Type XXI was completed before the 'Walter propulsion unit was ready. It was actually equipped with extra large batteries to give the high maximum submerged speed of 15 to 18 knots. Its submerged endurance at a speed of 10 knots was about 11 hours. The Type XXI U-boat was about 250 feet long and its standard displacement about 1600 tons. The large torpedo room with 6 bow tubes was an answer to the demands for increased armament. The U-boat carried a crew of 57 men and 20 torpedoes. Stern torpedo tubes were sacrificed to obtain greater speed. Silent-running speeds of about 5 knots were obtained on electric motors when submerged. An improved extensible snorkel was fitted.\n\nThe Type XXI U-boat was a German World War II naval design. It was the largest and most advanced type of U-boat built during the war. It was designed for high submerged speeds to enable it to get into a favorable attack position quickly. The hull was designed for turbine drive, but the boat was eventually equipped with electric motors and batteries when the Walter propulsion unit was not yet ready. The boat had a length of about 250 feet and a standard displacement of around 1600 tons. Its large torpedo room, which held six bow tubes, was a response to the demands for increased armament. The U-boat carried a crew of 57 men and 20 torpedoes. To achieve greater speed, stern torpedo tubes were sacrificed. Silent-running speeds of about 5 knots were achieved on electric motors when submerged. An improved extensible snorkel was fitted to the boat.\nThe Type XXI U-boat used diesel propulsion on the surface with a maximum speed of 15 knots. It was a true ocean-going U-boat. Three Type XVII-B U-boats with turbine drive were completed before the end of the war. These were built for experimental purposes to obtain information from the Mediterranean U-boat command on tactics and improvements for the Type XXVI U-boat. The Type XXIII U-boat was developed for requirements from the Mediterranean U-boat command for inshore waters and short cruises. The Type XXVI U-boat, which was to be the perfect U-boat, incorporated all the advantages of earlier experience and the extremely high speeds available with turbine drive. The Type XXIII U-boat was about the same size as the Type IXC U-boat.\nThe Type XXI and Type XXIII U-boats were 114 feet long, with a standard displacement of approximately 230 tons. Powered by Walter propulsion units, they had a maximum surface speed of 10 knots and a maximum submerged speed of 12 knots. Each carried two bow tubes and a crew of 14 men. Their endurance at 10 knots was about 4.5 hours, with a diesel motor for cruising and electric motor for quiet running used for all other purposes. Both types were built using a system of prefabrication for surface operation. There was no expectation of operating these U-boats submerged for extended periods or in attacks or other emergencies.\nThe Type XXVI U-boat was designed to be approximately 184 feet long and carry a crew of 37 men. It was intended to have widely dispersed factories along Germany's inland waterways for manufacturing basic parts. Sections of the hull were assembled at various shipyards and sent to key yards for welding into complete boats. The boats were then fitted out under covered shelters. The final assembly yards for the Type XXVI U-boats were in Hamburg, Bremen, and Danzig. The boats were to have a maximum submerged speed of 24 knots with an endurance of about 6 hours at that speed. Ten torpedoes were to be carried, with four in the bow and six in side tubes. Sound gear was used for directing torpedo fire from a submerged position, allowing all ten torpedoes to be fired in one salvo.\nSpeer's dispersal of his organization did much to hinder the construction of new Type XXI U-boats. No Type defeat Allied bombing caused the halt of XXI U-boats' operation at sea before V-E Day. The German transport system was disrupted by Allied bombing of communications, setting back the construction schedule for these new U-boats. The first prefabricated U-boat was completed in June 1944, and by the end of the war, the enemy had completed approximately 120 Type XXI U-boats.\n\nSinkings of U-boats\n\nSchnorkel U-boats operated in British home waters.\nSurface craft displaced aircraft as the leading killer.\nDuring this period, most German U-boats operated on Schnorchel. Allied ships sank 92 U-boats alone (47% of total) and another 15 (8% of total) with the help of aircraft. Aircraft sank 57 U-boats (29% of total). As most of the U-boats operated in inshore waters, carrier-based aircraft played a smaller part during this last period, accounting for only 14 of the 72 U-boat kills in which aircraft participated. Allied submarines sank 17 U-boats (9% of total), most of them in the Pacific. The other 15 U-boats (7% of total) were lost as a result of mines, marine casualties, and scuttling.\n\nThe quality of surface craft attacks reached its highest level during this last period as over 30% of the attacks were lethal. This percentage reached a high of about 50% during the in-shore waters.\nDuring the invasion period, U-boats first began operating on Schnorchel. It dropped to about 20% as U-boats perfected their inshore tactics during the last quarter of 1944, then increased again to about 30% during the first few months of 1945, as British escort groups learned how to deal with the bottomed U-boat.\n\n7.3.1 From the U-boats\u2019 Point of View\nSome idea of the attitude of U-boat crews and officers during this last period can be obtained from statements made by prisoners of war. Towards the end of 1943, many doubts and questions had arisen concerning the outcome of the war and the supposed superiority of German weapons. These doubts grew stronger when, despite the many promises of new weapons made by the U-boat Command, practically none were supplied and the U-boats' situation steadily deteriorated. The former enthusiasm\nThe men's confidence in their arms and leaders turned into a kind of lassitude, resulting in a mechanical execution of commands. The phrase \"orders are orders\" characterized the typical state of mind. The majority of U-boat officer survivors expressed in no uncertain terms that the U-boat was no longer practicable as an offensive weapon due to the effectiveness of Allied antisubmarine measures at that time. Despite their state of mind, the U-boats fought to the very end of the war with discipline unimpaired, and there were no signs of any collapse of the German Navy, such as occurred in 1918. About 13 U-boats were sunk monthly in the Atlantic, slightly less than the previous figure of 16. The average number of U-boats at sea had declined to 39 from the average of 61 in the previous period.\nThe average life of a U-boat in the Atlantic was three months during this period. This meant that the U-boats had a lower average life at sea than the previous period's average of four months. Despite the use of Schnorchel and maximum submergence tactics, U-boat operations in inshore waters remained as hazardous as they had been at the beginning of the war. The exchange rate in the Atlantic was similar to the previous period, with an average U-boat sinking 6/10 of a ship (3300 gross tons) before it was sunk. U-boats operating in waters with heavy shipping concentrations were able to sink a little more shipping per month at sea during this period, but this was balanced by the higher loss rate they suffered. The tactics evolved by the Schnorchel U-boat.\nToward the end of the war, involved practically no surface operations. In transit, navigation was by dead reckoning, radio-navigational fixes off the chain of \u201cElectrasonne\u201d transmitters and beacons, and also by echo sounder and periscope bearings of lights or points of land. Schnorchelling was mostly at night, for only about four hours in each 24. When Schnorchelling, a U-boat kept all-around periscope watch day and night, and constant meter-band GSR watch. Diesels were stopped once every 15 to 30 minutes to make an all-round hydrophone sweep. Once the U-boat was in the patrol area, it was a recognized tactic to lie on the bottom of a convoy route and come up only when hydrophone contact was established. For aiming the torpedoes, the periscope was still virtually the only instrument available. Salvos of curly torpedoes were fired among the merchant ships.\nA single acoustic torpedo could target either a convoy or an escort. The usual methods of evading Allied counterattacks involved lying on the bottom or proceeding at silent speeds of about 3 knots or less on electric motors. The Schnorchel enabled U-boats to operate in these manners in inshore areas, preventing their destruction from the need to surface periodically to charge batteries.\n\nThe Schnorchel U-boat has been the chief concern for surface craft, whose main difficulty was distinguishing between a bottomed U-boat and a wreck. An extensive survey of wrecks in British waters helped considerably in solving this problem.\n\nThe Schnorchel enabled U-boats to operate in inshore waters, but it did not enable them to achieve any significant success.\nSignificant results. Operational results during the last two years of the war indicated that the standard U-boat, with or without Schnorchel, could not operate successfully against Allied anti-submarine measures. It is important to realize, however, that the U-boat war was not decisively ended in May 1945. Germany had a fleet of about 120 Type XXI U-boats ready to start operations and was developing the Type XXVI U-boat. It is difficult to say whether the high submerged speed would have restored the advantage to the U-boats and would have enabled them to inflict considerable damage on Allied shipping without suffering excessive losses.\n\nFrom the Allies\u2019 Point of View\nThe Allied and neutral nations lost about 114,000 gross tons of merchant shipping each month, from all causes, during this period. This was the lowest average monthly loss of the war and about 25% less than the peak monthly loss of 150,000 gross tons in 1942.\nThe construction of new merchant shipping averaged approximately 850,000 gross tons a month, slightly less than in the previous period. This resulted in a net gain of about 736,000 gross tons of shipping each month, or a total increase of approximately 8,000,000 gross tons during this period.\n\nOf the 114,000 gross tons of shipping lost monthly from all causes, about 84,000 gross tons were lost due to enemy action. U-boats accounted for 56,000 gross tons a month, or about 67% of the total lost due to enemy action. Monthly losses to enemy mines rose to 15,000 gross tons (18% of enemy action total) as Allied shipping moved closer to the shores of Europe after the invasion. Losses to enemy aircraft dropped to 8,000 gross tons.\nNine percent of enemy action total was accounted for by 5,000 gross tons sunk monthly. An additional 6 percent of enemy action total, or 6,000 gross tons, were lost due to surface craft attack and other enemy actions. By the end of this period, Allied armies had overrun Germany, and the surrender came on May 8, 1945. The Allies had defeated the U-boats in 1943 and managed to keep them ineffective thereafter. It was both an offensive and defensive victory as the average U-boat's lifetime at sea in the Atlantic was only three months and it sank only about half a ship before it itself was sunk. The Allies were not able, however, to destroy the enemy's U-boat fleet without invasion, as the enemy's construction program had been able to replace all losses. The war seemed to have demonstrated that the standard U-boat could not operate on the surface.\nThe U-boats did not operate effectively against strong Allied air power due to the lack of reliable radar or search receivers to detect planes at long range. Denied the surface of the sea, standard U-boats with limited submerged speed and endurance could not operate effectively against strongly escorted Allied convoys.\n\nThe German solution to this problem was the development of the Type XXI and Type XXV U-boats, which had much higher submerged speed and endurance and could operate entirely underwater. These U-boats would be relatively safe from air attack like the standard Schnorchel U-boats and much safer from surface craft attack due to their high submerged speeds. They would be much more effective against convoyed shipping as their high speed would enable them to approach.\nAnd we cannot keep up with Allied convoys without surfacing. We cannot determine without extensive trials and exercises with high-submerged speed U-boats how much more effective than the standard types they would be. We cannot now determine quantitatively whether they would be 50 percent better or ten times as good. From the history of World War II, however, we may conclude that these new U-boats would have to be about eight times as effective in sinking ships and about four times as safe at sea as were the Schnorchel U-boats in the last period, in order to achieve the same results as were achieved by the U-boats during their peak period, January 1942 through September 1942.\n\nChapter 8\nSUMMARY OF ANTISUBMARINE WARFARE\nWORLD WAR II\n\n8.1 Overall Results\nThe opening hours of the war saw the U-boats already in position astride the approaches to the Atlantic.\nThe United Kingdom's objective during the war was to disrupt merchant shipping to and from Great Britain. This battle was carried out halfway around the world as the U-boats held the initiative from the beginning until their disastrous defeat in the summer of 1943. Their subsequent efforts were futile, and U-boat warfare was at a standstill when the war ended. The enemy's potential accomplishments with new U-boats featuring high submerged speed is speculative, but they would have posed a serious threat.\n\nThe actual accomplishments of German, Italian, and Japanese U-boats during the war led to the Allies' loss of 2,753 ships*^ totaling 14,557,000 gross tons. The enemy also suffered significant losses at sea. It is estimated that 733 German, 79 Italian, and 99 Japanese U-boats were lost.\nJapanese U-boats were sunk. A total of about 1500 U-boats were built by the enemy to achieve these results. There were, therefore, approximately three Allied merchant vessels sunk by U-boats for each U-boat sunk, about two merchant vessels sunk for each U-boat built. In addition, the Allies were forced to maintain a large and costly antisubmarine effort which diverted their attention from other phases of the war. In these terms, the U-boat war was a profitable one for the enemy, even though U-boats were ultimately defeated. If German U-boat operations only were considered, this conclusion would be greatly strengthened. During the period prior to June 1943, a total of about 4500 Allied merchant vessels were sunk by U-boats, resulting in the loss of approximately 13 million gross register tons (GRT). In contrast, the Germans lost about 780 U-boats during the same period, representing a loss of only about 330,000 GRT. These statistics illustrate the significant impact of the U-boat war on the Allied war effort and highlight the effectiveness of German submarine operations. (Note: The figures given in this summary are based on CNO records as of November 19, 1945. They do not agree exactly with figures given in other chapters which were prepared earlier.)\nAssessments of attacks, in particular, have been changed somewhat based on intelligence gained from German sources after the German surrender. As shown in Appendix I, however, the earlier assessments as they existed at the end of the war were in good general agreement with German records of submarine losses and therefore provide a fairly reliable basis for the discussion given in the other chapters. They were, of course, unquestionably successful, whereas subsequent operations were equally successful for the Allies.\n\n82. MAJOR DEVELOPMENTS\n\nThe beginning of the war saw an immediate campaign of unrestricted U-boat warfare. The British had anticipated such a development and put a previously planned convoy system in operation within a few days. The scale of effort was small, however, as there were only a small number of U-boats at sea.\nThe antisubmarine craft available to the Allies could give only very weak escort to the convoys. The U-boats concentrated their forces in the vicinity of Britain, making their attacks in daylight from periscope depth. Their tactics were highly aggressive, and each U-boat scored heavily against Allied shipping. As a result, they exposed themselves to counterattack by British surface craft, whose Asdic-directed attacks proved to be much more effective than the Germans were expecting. Surprised and confused by the success of British escorts, the U-boats devoted most of their attention to independent ships and those in convoy were relatively safe, even though weakly escorted.\n\nIn June of 1940, France fell to the German Army. The resulting worsening of the British strategic situation had a direct effect on the U-boat war.\nThe threat of a seaborne invasion of England confined British air and surface craft to east coast anti-invasion patrols, diverting them from antisubmarine duties. The acquisition of bases on the Bay of Biscay reduced U-boat transit time and allowed them to extend operations farther into the Atlantic.\n\nAs a result, effective counterattacks on submerged U-boats led Germans to introduce radical change of tactics. They began to attack on the surface at night, a procedure characteristic of them during most of the war. They capitalized on the weakness of British escorts and made many successful attacks on convoys. Trailing the convoy until darkness, they came in trimmed down on the surface for the attack, and retired on the surface at high speed.\nThis method was highly successful, and bold individual attacks rolled up large tonnages to the U-boats' credit. The risks were proportionately high, however. By such tactics, the outstanding U-boat aces, Prien, Kretschmer, and Schepke, each amassed totals of over 200,000 gross tons, but all three were eventually sunk in March 1941.\n\nOne of the most significant countermeasures to these surfaced attacks was the introduction of radar. A makeshift aircraft set was first fitted to escorts in November 1940. Its effectiveness was not great, however, during this early period. Various improvements in the convoy system were made by the British, including the formation of escort groups, Admiralty control of routing, and a wide dispersion of convoy routes. As a result, U-boats had greater difficulty in attacking convoys.\n\nEarly in 1941, the results of Germany\u2019s U-boat campaign were:\nThe construction program began to be felt. In 1939, the Germans had only a small U-boat fleet, as their hopes were for a short war. When the possibility of a long struggle with Britain became apparent, building of U-boats was given high priority. They were commissioned at a rate of about 20 a month starting in 1941. There was a corresponding increase in U-boat personnel, which, of course, resulted in a widespread lowering in their general experience and capability. This was accentuated by the loss of some of the best-trained crews.\n\nIn the summer of 1941, therefore, the bold tactics of individual night surface attacks on convoys were modified. The policy of wolf-pack attacks came into use in an attempt to overwhelm the convoy escorts. The procedure was for the U-boat to first contact a convoy, trail it, and then launch a coordinated attack with other U-boats.\nHoming other U-boats to the scene so that a number could join in the attack, thus capitalizing fully on the opportunity and reducing danger to the attacking U-boats. Complementary to this policy was a general movement of U-boats to the west and south in an effort to find independent ships. This movement also gave freedom from the growing air cover in the vicinity of Britain.\n\nAs a result of these changes, the British were forced to adopt complete end-to-end escort of transatlantic convoys. They were aided in this effort both by the German attack on Russia in June 1941 which ended the threat of invasion of England and released craft for antisubmarine operations, and by the entry of the U.S. Navy in convoy operations in September. Despite the great increase in number of U-boats at sea, Allied losses of merchant vessels did not increase.\nThe British introduced another change in 1941 that significantly impacted the antisubmarine war, specifically the contribution of aircraft. Air patrol had been effective in harassing U-boats but few successful attacks were made due to the lack of suitable weapons. The need for a depth bomb exploding at shallow depths was realized, and a 25-foot depth setting came into use. With this minor change, aircraft eventually equaled surface craft as killers of U-boats.\n\nWith the U.S. entry into the war at the end of 1941, the scope of U-boat operations expanded rapidly. The Germans had a large and rapidly growing U-boat fleet, enabling them to launch a full-scale offensive against the weakly protected shipping in U.S. coastal waters. They were initially able to inflict significant damage.\nDuring this period, U-boats chose and sank their victims virtually unimpeded, resulting in catastrophic Allied losses. For instance, 140 ships of 698,000 gross tons were lost in June 1942. Defenses were organized, leading to an eventual U-boat withdrawal. With the introduction of convoying in Eastern Sea Frontier in May, losses in that area were reduced, while those in Gulf Sea Frontier soared. U-boat successes in the Gulf were short-lived, though the Caribbean remained a soft spot throughout the summer of 1942. Nevertheless, the continued extension of convoying and air patrol drove the U-boats out of the coastal areas by fall, and they then returned to the North Atlantic. During this period, U-boat activity in the Eastern Atlantic was at a standstill. Consequently, British forces were free to begin a counteroffensive against U-boats in transit from their bases to the operating areas.\nAreas in the Western Atlantic. Coastal Command aircraft patrolled the Bay of Biscay with radar and searchlights, inflicting considerable damage on U-boats during the summer, until countered by German search-receiver development. As a direct effort to make up the heavy shipping losses, the Allies started an intensive building program in 1942. Despite all their efforts, however, U-boats sank ships faster than they were built until about the end of the year.\n\nSummary of Antisubmarine Warfare, World War II\n\nIn October, it was evident that U-boats were returning to the North Atlantic in force. Attacks on transatlantic convoys were their objective, and they operated in the mid-ocean gap which could not be reached by land-based air patrol. This gave them freedom to operate on the surface and gather very large wolf packs\u2014often ten or more and occasionally up to twenty.\nAs many as 30 to 40 attacks of this sort often led to breaks in the escort formation and disorganization of the defense. Nevertheless, the vast convoys for the North African invasion made their way from Britain without serious losses due to the complete air coverage provided for them. Routine trade convoys were less fortunate; the tonnage lost topped 700,000 in November. Against a U-boat fleet which was able to maintain about 100 U-boats at sea, even the more efficient escorts fitted with S-band radar were inadequate. Heavy losses continued during the winter, mostly in the North Atlantic, but also in other widespread areas where diversionary U-boats were operating.\n\nIn the spring of 1943, convoy defenses were bolstered by a limited amount of aircraft patrol in the mid-ocean gap, which proved to be extraordinary.\nNearly effective. A small number of VLR aircraft became available in March, and the USS Bogue [CVE] also sailed in support of the convoys. Considerable numbers of U-boats were sunk, but they continued to attack in force until early May when they were driven off from ONS 5 in the decisive convoy battle of the war. After May 17, no ships were sunk in the North Atlantic for some time.\n\nWhile aircraft were thus distinguishing themselves in the defense of convoys, the Coastal Command offensive against transit U-boats was also bearing fruit. S-band radar was introduced early in 1943, and the number of sightings and attacks soared. During May, 37 U-boats were sunk in the Atlantic, 11 of them in the Bay of Biscay. The success of these operations continued until the end of the summer.\n\nBy July, the U-boats had dispersed to try to find a new hunting ground.\nThe Allies identified a soft spot in their defenses, resulting in complete failure and mid-ocean attacks by CVE-based aircraft. In Atlantic waters, 34 U-boats were sunk, primarily by aircraft. The devastating losses led to the U-boats abandoning aggressive surfaced operations and submerging during daylight hours to avoid aircraft. Ultra-conservative tactics were used in crossing the Bay of Biscay.\n\nWith their mobility lost, the U-boats accomplished nothing until September and October when they attempted a comeback against North Atlantic convoys by using acoustic homing torpedoes against the escorts. They were beaten off with heavy losses, sinking 22 U-boats during October in operations to sink three merchant vessels and one escort. An attempt to\nThe attack on convoys between the United Kingdom and Gibraltar was made, but it was also frustrated, and U-boats were forced into a completely defensive position. For the rest of the winter, they adopted a policy of maximum submergence, designed to give them safety from Allied attack. Virtually no ships were sunk. The number of U-boats at sea declined markedly, and every effort was made to develop an effective search receiver for S-band radar to give them immunity from detection by the Allies. It was not until the invasion of Normandy in June 1944 that the U-boats showed any signs of aggressive action. Their effort to attack shipping in the English Channel was short-lived, however, as heavy air and surface patrols prevented them from achieving any success. They soon abandoned the surface in favor of Schnorchel operation which gave them virtual immunity.\nThe community evaded detection by aircraft by lying on the bottom. In this way, they utilized the poor sound conditions and frequent wrecks to gain considerable safety from Asdic. Operating in this manner, they achieved limited successes against shipping in British coastal waters during the summer, while sinkings of U-boats became less and less frequent.\n\nIn August and September, the U-boats withdrew from the Biscay bases to Norway, and then settled down to a small-scale offensive around Britain. They met with some success initially, but by the spring of 1945, Allied surface craft had learned to deal with them under those conditions, and Allied victories on land deprived them of bases and shore facilities. Their only chance for regaining the upper hand was the new high-submerged speed U-boat, Type XXI, but due to production difficulties and the general situation.\nTable 1. Average Monthly Shipping Losses and Construction of Allied and Neutral Nations (By period and cause of loss in thousands of gross tons)\n\nCause Period I Sept 39-June 40 Period 11 July 40-Period 111 Period IV Sept 42 Period V June 43 Period M July 43-Period MI June 44-World Sept 39-\n\nSunk by U-boats 1.5 1.8 1.3 2.5 1.2 1.1 1.6 1.4 1.7 1.5 1.3 Total sunk by enemy action 3.3 3.7 3.1 5.3 2.4 2.2 3.0 2.8 3.2 2.8 Total losses\u2014 all causes 4.8 5.7 5.4 8.6 3.8 3.4 4.6 4.2 4.9 4.1 New construction Net monthly loss or gain Shipping available in million gross tons\n\nTable 2. Average number of U-boats sunk monthly -- World-\nPeriod I: September 39-June 40, Sunk by surface craft, aircraft, submarine, other or unknown causes. Total sunk: 1.5 able, Approximate German U-boat position: (Ocean-going U-boats only \u2014 500 tons or more). At start of period: Constructed. Sunk at end of period.\n\nPeriod II: July 40-March 41.\nPeriod III: January 42-September 42.\nPeriod IV: October 42-June 43.\nPeriod V: July 43-May 44.\nPeriod VI: June 44-April 45.\n\nSummary of Antisubmarine Warfare, World War II\nAverage life of U-boat at sea (in months): 4. M/V's sunk per U-boat per month: 0.\nAverage number of U-boats at sea: TOTAL.\n\nPeriod:\nWorld War I.\nPeriod I.\nPeriod II.\nPeriod III.\nPeriod IV.\nPeriod V.\nPeriod VI.\nPeriod VII.\nWorld War II.\n\n(M/V's sunk)\nU-boats' activity\nU-boats get dispersed\nU-boats shift position\nU-boats attack\nU-boats' dis- engagement\nU-boats' use\nby US's forces are\nin waters\nFrench bases of Allied forces\nto E. coast of N. Atlantic\npersist, at- the Schnorchel\nreduced near England\nconvoy of US to convoys\ntackle supposed\nto protect above table\nOperate in routes .\nattack M/V's \"GAP\"\nthemselves to reflect daylight\nWestern Approaches\nU-boats start spots in S.\nagainst aircraft\nsmaller tonnage attacks\napproaches to\nLosses reach large numbers in the Atlantic .\nU-boats' operation of periscope\nEngland .\nwolf pack peak in June\npacks over- run\nU-boats' stay\nM/V's in depth.\nattacks on merchant vessels\nwhelm themselves at\nate mainly in World War I)\nNight surface attacks on convoys .\nships sunk by corvettes .\non surface in \"Invasion Area\" near Allies\nAllies use lightly\ntacks on U-boats' moves\nExtensive VLR A/C and back against England.\nconvoys duringly corded\nconvoys westward and\nescort car- A/C,\nvoys southward, convoying riders close to U/B's, U/B's use period. Allies along east \"GAP\", A/C inflict bottoming U/B's con- introducing me- Allies adopt coast in \"heavy\" losses, Allies used centrate on ter radar, complete S-band radar ses on U/B's shallow hydrophones, independent trans-Atlantic used on A/C, U/B's forced water and depth shipping. Three leading U-boat escort, 25-foot in Spring of U/B's lose charges, U/B's use U/B \"aces\" depth set- to adopt lost in U.S. escorts ting on A/C maximum sub- French bases, A/C generates electric sail with depth charges, A/C attacks mergence. Move to Nor-ally ineffective, torpedo, (no convoys in es.), much more U/B's lose way. Effective wake). September effective, U/B's still against U/B, U/B's drive offensive, Allied S/Cs en away from U/B's badly power as ineffective, use asdic. Drop in effectiveness east coast, beaten.\nResult of U.S. attacks due to lack of effectiveness of U.S. attacks on mobility. U-Boat's due to convoy \"ONS-ability.\" Afflicted S/C to rapid exits. Five-inch guns in March pension of U-Boat's use, using Squid, U-Boat person-nel. Acoustic and Hedgehog net. U-Boat's with torpedo and in addition draw from N. GSR for S-to depth. U.S. enters war in December 1941-Atlantic. Band radar charges in, inflict heavy losses on Schnorchel U-Boats. M/V's Sunk by U-Boats per month. U-Boats Sunk per month. M/V's Sunk per . U-Boat Sunk.\n\nFigure 1. U-boat and antisubmarine operations for the seven periods of World War II.\n\nTables and Charts:\n\nThe outstanding statistical facts of the antisubmarine war are summarized in the following tables and charts:\n\n1. Figure 1\u2014presents figures measuring the magnitude and effectiveness of U-boat and antisubmarine operations.\nSummary of Antisubmarine Warfare, World War II\n\n2. Table 1 presents Allied shipping losses and gains through construction for each period: causes and gross tons.\n3. Figure 2 summarizes the information of Table 1 in graphical form.\n4. Table 2 presents the average number of U-boats sunk monthly by cause for each period.\n5. Figure 3 summarizes the information of Table 2 in graphical form.\n6. Table 3 presents German U-boat losses and gains through construction for each period: gross tons.\n7. Table 4 presents total shipping losses and U-boat sinkings for each period: gross tons.\n8. Table 5 gives the effectiveness of Allied attacks by aircraft and surface craft on U-boats in the Atlantic and Mediterranean for each period.\n\nCause Gross tons\nOther Submarine Aircraft\n\n(Note: The text provided appears to be clean and does not require extensive cleaning. Only minor corrections for formatting and consistency were made.)\nFigure 3: Monthly U-boat sinkings by period and cause of sinking.\nTable 4: Shipping sunk by U-boat and U-boats sunk, by period (world-wide).\n\n| Ship sunk by U-boat | U-boats sunk |\n| --- | --- |\n| Period | Number (1000 gross tons) | German | Italian | Japanese | Total |\n| Includes 4 Vichy French U-boats. | |\n\nTables and Charts\n\nTable 5: Quality of Allied attacks on C-boats (Hy period - in Atlantic and Mediterranean).\n\n| Aircraft | Surface Craft |\n| --- | --- |\n| Percent resulting in at least Some damage | Sinking of U/B |\n| Percent resulting in at least Some damage | Sinking of U/B |\n\nI\nSept 39-Jan 40: Satisfactory data are\n\nII\nJuly 40-Mar 41: not available for this\n\nIII\nJan 42-Sept 42: Oct 42-June 43: July 43-May 44:\n\nIV\nJune 44-Apr 45\n\nPART II\nAntisubmarine Measures\n\nFrom the historical summary of operations against submarines during World War II:\nMany conclusions regarding the strategy and tactics of antisubmarine warfare (ASW) were presented in Part 1. The most important of these will be discussed in the following chapters and substantiated with quantitative data from Operations Research Group studies. Most conclusions pertain to specific tactics, such as weapons for attacks, proper tactics for search, or methods of protecting convoys. These are all part of a general picture involving the overall purpose of antisubmarine warfare and the various methods available for accomplishing that purpose.\n\nIt is already evident from Part 1 that the aim of ASW is not merely the destruction of unfriendly submarines. While sinking all enemy submarines would accomplish the mission, the available forces have never been sufficient for this task.\nThe submarine is a small and elusive object in a large ocean and consequently very hard to find. When found, it is a tough and inaccessible object to attack. As long as the enemy is able to build and launch submarines, he can keep some of them at sea, and even the highly effective Allied antisubmarine effort in World War II did not greatly diminish the size of the German U-boat fleet but merely checked its growth. Antisubmarine warfare must be thought of as a part of a complex overall military strategy whose final aim is to eliminate the enemy\u2019s ability to wage war. This must ultimately be done by seizing or destroying the military or economic war machine\u2014 administration, transportation, men, equipment, or production facilities\u2014 by striking at the heart of the enemy, not just his submarines.\nThe philosophy behind blitzkrieg and war of encirclement is to ignore the enemy's periphery and proceed directly to the ultimate objective. The aim of ASW is to ensure the use of oceans necessary for military operations leading to enemy defeat. It is an auxiliary operation, necessary but not sufficient for overall success. In this sense, the actual aim of ASW is negative \u2013 to prevent enemy submarines from accomplishing their aim.\n\nThe first step in analyzing this subject is to outline the value of submarine operations to the enemy. The objective of ASW is to reduce this value to a minimum, and its strategy is planned accordingly.\n\nSubmarine Operations\nThe peculiar value of the submarine among naval craft is its ability to operate in enemy-held waters. Even when surfaced, a submarine is a small target for visual or radar detection. When submerged, it is completely concealed except for detection by underwater sound, whose ranges are short and unreliable. As a result, the submarine can operate in regions forbidden to surface craft because of enemy patrol. In these regions, aircraft operations are often impossible because the regions are beyond the range of aircraft. Thus, the submarine is the primary, and often the only, craft for carrying out operations at a long distance from base in the areas of the enemy\u2019s main strength. Numerous types of operation may be involved. The aim of some may be to gather information that can be gained only by an excursion into enemy territory.\nIn this class are routine scouting and weather reporting missions, as well as those involving the landing of agents. Some are transport missions to supply isolated units which cannot be reached by other means. The main mission of the submarine, however, is offensive\u2014to attack the enemy\u2019s ships, both combatant and merchant. Past experience has shown that the most valuable submarine activity has been that of attacking merchant shipping, and antisubmarine warfare is of urgent concern on this account. Man being a terrestrial animal, the oceans are valuable to him only as a means of transportation from one piece of land to another or as a barrier between two lands. Visual detection of a submerged submarine is possible only in very rare cases. Magnetic detection is effective only at very short ranges, much shorter than those of underwater sound. Antisubmarine principles.\nThe control of the ocean secures its use for the controller and denies it to his enemy. While an anti-shipping offensive by submarine does not give control of the ocean, it serves to deny free use to the enemy, and in this negative sense, the submarine force may accomplish quite complete control. To the extent that this is done and the enemy is prevented or hindered from transporting necessary cargoes, the submarine offensive makes a major contribution to the progress of the war.\n\nIn the submarine\u2019s anti-shipping offensive, three things must be accomplished: achieving contacts on ships, approaching to within torpedo range, and final attack. The first of these is essentially a search problem of the kind discussed in Volume 2B, Search and Screening, with the submarine as the searching craft. Detection may be made by visual, radar, or sonar means.\nVisual detection has had the largest range, with sonar having the shortest, although ranges depend on conditions. Visual detection, for instance, is ineffective on a dark night, and sonar ineffective in poor sound conditions.\n\nSince the submarine's speed is low, it is not an efficient searching craft and must operate in regions of high shipping density to make a large number of contacts. To select the high-density areas, a knowledge of the expected positions of enemy ships is required, which may be based on intelligence information or gained locally by coordination between submarines.\n\nThe \"wolf-pack\" tactics of German U-boats accomplished this by homing many submarines to each contact. Once a single U-boat made contact, the information was used to permit others to achieve contact as well.\n\nWhen contact has been made, the submarine must take appropriate action.\nApproach to within torpedo range is essential before an attack can be launched. If the submarine's speed is greater than that of the target, the approach is not difficult, and nearly all ships contacted may be attacked. However, if the submarine is forced to operate submerged (or if the target is very fast), approach is only possible from positions ahead of the target. Slight errors in the approach may result in failure to achieve the proper position. Once firing position is reached, torpedoes are fired. Their chance of success depends on the accuracy of the torpedo fire and on the physical characteristics of the torpedo used. The primary aim of ASW is to reduce the effectiveness with which submarines carry out these steps, and the success of an antisubmarine effort is to be assessed in these terms. Antisubmarine warfare is not a new concept.\nAn end in itself, but merely a means of ensuring that the ability to use the ocean for transportation is maintained at the best level possible.\n\nAntisubmarine Measures\n\nSome antisubmarine measures are intended to hinder the submarine in carrying out a particular phase of its antishipping operations. Evasive routing of convoys to avoid known submarine positions is useful solely in reducing the submarine\u2019s chance of contacting the convoys. If all the ships could always dodge the submarines, the submarines' effectiveness would be much reduced. Such a procedure would slow the ships down appreciably, however, so the submarine effort would not be entirely wasted. On the other hand, most measures designed to combat submarines serve a multiple purpose.\n\nMaintaining aircraft patrol in the vicinity of a convoy not only may lead to sightings of submarines, but also provides other benefits such as air cover for the ships and early warning of potential air threats. Laying smoke screens can obscure the sight of a submarine and make it more difficult to target the convoy. Depth charging, the dropping of explosives from depth charges to damage or destroy submarines, can also be effective against surface targets. Acoustic countermeasures, such as dropping noisemakers or using sonar jammers, can confuse or disable the submarine's sonar systems, making it more difficult for the submarine to locate and attack the convoy. Finally, the use of escorts, both surface and submarine, can provide additional protection for the convoy and engage the submarine in battle if it is detected.\nThus permitting evasion by the convoy, but these aircraft also force submarines to dive, thus hindering them in their efforts to track a convoy and approach it. Finally, an occasional aircraft may be fortunate enough to attack a submarine and sink it. The overall value of any measure must be based on all the ways in which it serves to frustrate the submarine. Most obvious among the measures designed to reduce the submarine\u2019s rate of contacting ships is evasive routing. If the submarine positions are fairly well known, they can be avoided and the density of shipping in their vicinity greatly reduced. Convoying is another measure which, in effect, reduces the submarine contact rate. If there are n ships in each convoy, on average, the submarine contacts about one in jn as many convoys as it would ships. Since n\nThe resulting gain can be significant if patrols by aircraft are made as large as 50 to 100. Patrols reduce contact rate, as previously mentioned, by forcing the submarine to spend a large fraction of its time submerged. This reduces its detection range and interferes with the formation of wolf packs. Both surface and aircraft patrols, as well as hunter-killer operations, have the same effect. Concentrating offensive operations in areas of high shipping density forces submarines out of these areas and makes them operate where their chances of contacting ships are not as good. The apparent aim of such an offensive is to sink U-boats, but its chief effect may be to force them to adopt less profitable tactics, and this effect continues to be valuable even if they are not sunk.\nIf sinkings of U-boats are reduced to a negligible level. The methods of hindering submarine approach consist of various forms of escort, both for convoys and single ships. Aerial escort tends to force submarines to submerge and thus restricts their mobility, making it impossible for them to trail the convoy or overtake it from the flanks or rear and reach a position ahead from which attack can be made. Even if the submarine is ahead of the convoy when it contacts it, a submerged approach is more difficult than one carried out partially on the surface and is more likely to result in errors. If the submarine boldly elects to stay on the surface for approach to the convoy, it is very likely that it will be detected and attacked in the process, which experience is almost certain to eliminate any possibility.\nThe successful offensive action of surface craft poses a problem for submarines. Correspondingly, surface craft interfere with the later stages of the approach. Trying to avoid them complicates the submarine's problem, but if it fails, it is likely to be detected and counterattacked before reaching torpedo-firing position. The submarine's problem can be made more difficult by the use of a ship's highest possible speed and zigzagging, when possible.\n\nAttempts to interfere with the submarine's final attack, after it has reached firing position, have not been very successful in the past. To some extent, the mere presence of surface escorts may constitute such interference. Zigzagging reduces the accuracy of torpedo fire somewhat. A maneuverable ship may turn to avoid the torpedo if it has sufficient warning, and special torpedo detectors may be devised to aid in detection.\nIn doing so, antitorpedo nets and other devices can be streamed to intercept the torpedo. All these are examples of devices and tactics designed to reduce the effectiveness of the submarine torpedo fire.\n\nSupplementing these essentially defensive methods of interfering with the submarine\u2019s accomplishment of its objective is the offensive phase of ASW. The most certain way of preventing a submarine from sinking ships is to sink it first. In this sense, sinking a submarine is equivalent to saving as many ships as it would normally sink during the remainder of its operational lifetime. For example, if the average submarine makes a total of ten operational patrols and sinks two ships in each, sinking the submarine saves an average of ten ships, because the submarine is likely to be about half through its normal life when sunk. In addition to this direct diminution of the submarine's threat, offensive ASW can also aim to damage or disable the submarine, making it less effective even if it manages to escape.\nThe sinkings in a submarine fleet tend to reduce the state of training and experience of submarine crews. If the rate of sinking is high enough to give the submarine or crew member an expected life at sea of only four patrols, there will be few men available with the experience of ten patrols. The resulting dearth of experienced personnel is a handicap difficult to assess, but of considerable practical importance.\n\nOnly a fraction of the value of offensive operations can be represented by the numerical decrement achieved in the enemy\u2019s submarine fleet. There is normally an appreciable effect upon morale as well. The effectiveness of submarine operations cannot be divorced from the skill and determination of the submarine force's personnel. By selectively eliminating experienced men, the high rate of sinking can significantly impact the force's overall effectiveness.\nThe rate of loss reduces not only a submarine's overall skill but also its determination. The submarine's chance of being sunk if it attacks a certain convoy cannot but bear greater importance to its crew than to the theoretical strategist. Submarine crews will accordingly avoid operations involving high losses to themselves, even if theoretically profitable, unless their psychology includes a definite suicidal tendency. From this brief outline, it is evident that antisubmarine warfare (ASW) involves many different aspects. The following chapters will discuss specific problems to illustrate the general principles involved. The subjects for discussion have been chosen for their importance in antisubmarine strategy and tactics, and for their interest as examples of Operations Research methods.\nThis type of comparison can be made most clearly on the basis of sinking rates, as discussed in Chapter 13.\n\nChapter 9\nSafety of Independent Shipping\nAs was pointed out in Part I (page 2), the submarine's problem is one of first contacting a ship, then approaching to a good torpedo-firing position, and finally securing a torpedo hit. It is appropriate to break down an analysis of measures designed to increase the safety of shipping into the same general categories.\n\n9.1 Reduction in Submarine's Ability to Contact Ships\nIn the first place, anything which can be done to reduce the number of ships contacted by each submarine will increase the safety of the ships. Consider, for example, a ship making a trip between two points through an ocean infested with submarines.\n\nThere are D submarines per sq mile in the ocean.\nEach of which has a sweep rate of Q square miles per hour. The length of the ship's track is / miles, and its speed is V. The expected number of times submarines will contact the ship is:\n\nTo make A\u2070 small, D, Q, or Ij v must be decreased. These factors will be considered in turn.\n\nReduction in Submarine Density:\nOne method of reducing the submarine density to which the ship is exposed is to avoid regions where submarines are concentrated. If it is possible to choose between a route along which there are many submarines and one where there are few, the latter is certainly the better. When a fairly reliable estimate of submarine positions is available, much can be done by evasive routing to reduce contacts, but such information is by no means always available. If this information is not available, a wide dispersion of the ship's track can help reduce the likelihood of encounters.\nShipping routes can be employed, forcing the enemy to deploy his forces in the same way, instead of permitting him to concentrate them against a well-defined shipping lane. In an indirect way, offensive antisubmarine operations serve to reduce D, first, by sinking submarines and thus reducing their number at sea, and, second, by preventing them from concentrating in the most profitable areas. Aircraft patrols frequently can be used to force U-boats out of the regions of the highest concentration of ships. Figure 1 illustrates the effect of aircraft flying on the distribution of U-boats in the Gibraltar-Morocco area. Immediately after the Allied landings in North Africa, U-boats were concentrated close to shore in the region of highest density of merchant ships.\nThe effective number of contacts between U-boats and merchant vessels in a particular region is given by the equation: Q * (A * Djj/b + Dji^/y), where Q is the sweep rate, A is the area of the region, Djj/b is the density of U-boats, and Dji^/y is the density of merchant vessels. This expected number must be calculated separately for each region and summed. (Figure 2 illustrates lateral range curves for submarine detection of merchant ships.)\nFor a submarine search rate of 100 square miles per hour being typical for merchant ships, we would expect approximately 60 contacts per month with U-boats before flying had forced them out, and 30 contacts per month afterwards. It is reasonable to conclude that the flying involved had reduced the danger to ships by roughly half.\n\nReduction in Submarine Sweep Rate:\nThe sweep width, given in Table 1, is indicated by the curve.\n\nTable 1. Submarine sweep width in searching for merchant ships.\n\nDay Night Average\nSurfaced (miles) Submerged (miles)\n\nThe overall effect of forcing the submarine to submerge is a reduction of approximately 40% in the sweep width. We can then consider half the sweep width to be the effective range of contact, which would be 6 miles surfaced and 3.5 miles submerged.\nIf submarines remained hidden in the ocean, there would be a proportional reduction in the number of ships contacted by the submarine. However, a surfaced submarine is able to add something to its search capabilities by patrolling at about 10 knots. This speed effect must also be taken into account, though it proves to be rather small.\n\nThis speed effect is treated in Chapter 1 of Volume 2B, Search and Screening. The result is expressed in equation (5) of that chapter, which allows us to write the search rate Q of equation (1) explicitly as:\n\nQ = (A * V * 1000) / (3600 * (R^2 + (V * T)^2))\n\nTo some extent, aircraft patrol may fail to drive U-boats out of an area and merely force them to spend most of their time submerged. This also serves to make ships safer because it reduces the submarine\u2019s sweep rate. The primary reason for the reduction is the decrease in the range of the submarine\u2019s search pattern.\nThe drop in submarine speed significantly impacts detection. A submerged submarine is relatively blind compared to a surfaced one, as visual detection requires use of a periscope and radar is not very convenient. Operational data on these effects can be derived from the first contact ranges reported by U.S. submarines. From these data, the lateral range curves of Figure 2 are plotted. It is assumed that there is a definite range at which contact will be made for each time a submarine meets a ship, though these ranges vary widely from one occasion to the next.\n\nTotal flying hours were: November, 933; December, 1833; January, 2167; February, 2120. (See Chapter 2 of Volume 2B, Search \"Screening,\" for a complete explanation of contact phenomena.)\n\nsinS=^y^, (S)\nwhere\nFrom the equation (3), we can calculate Q using tables to determine values of the elliptic integral involved. With the assumption that merchant ships involved make 10 knots, the surfaced submarine 10 knots, and the submerged submarine 3 knots, the results are presented in Table 2.\n\nThe net conclusion is that a submerged submarine has been able to contact only about half as many ships as a surfaced submarine.\n\nTable 2. Sweep rates of submarines in contacting merchant ships.\n\nSubmarine\tRange\tSpeed\tContact\tSweep rate\nSurfaced\t6 miles\t10 knots\t-\t150 sq mi/hr\nSubmerged\t-\t3 knots\t-\t-\n3.5 miles, 70 sq mi/hr. Merging most of the time has an appreciable effect in reducing contacts. Another line along which effort might reasonably be expended to reduce the submarine's contact rate is camouflage. However, it is not easy to devise a camouflage which is effective in this sense under all the varied conditions met with in practice. Relatively little has been done, and operational data on the subject are not available.\n\nThe factor l/v in equation (1) is simply the time the ship spends in the dangerous region. To keep this time small, the track length should be made as short as possible and high ship speed used. The advantages of high ship speed in this connection are offset, however, by an increase in Q with ship speed. The most important consideration is the length of the ship's track in dangerous waters.\n92. The submarine's ability to approach ships for attack is a significant issue. After making contact, the submarine must still maneuver to a torpedo-firing position before launching an attack. Not all contacted ships were attacked; only 41% were. Of the remaining 59%, some were not worth attacking, but many were not attacked due to the submarine's inability to close the desired position for torpedo launching. The importance of this approach problem is further highlighted by an analysis of the effect of merchant vessel speed on the safety of independent ships.\nIn order to study Allied losses to German U-boats, it is necessary to assign ships to speed classes and determine the number of ships sunk in each class and the overall exposure of each class to submarines. This overall exposure must take into account the total distance traveled by ships of each class and the density of U-boats along their courses, as indicated by equation (1).\n\nTo accomplish this, a study was made in which the Atlantic was separated into areas. In each area, the mileage traveled by independents of different speed classes and the average density of U-boats were taken month by month. A ship which sails 2000 miles in waters with one U-boat per million sq miles is exposed to approximately the same risk as one traveling 1000 miles in waters with a higher U-boat density.\nThe exposure for each speed class is given by the product of the mileage and the U-boat density in waters with two U-boats per million sq miles. This was done for seven speed classes, covering a period of 4 months and four areas. The number of casualties per unit of exposure is a measure of the safety of the speed class in question, and this is plotted in Figure 3 as a function of speed. The sharp decrease in sinkings at speeds between 10 and 15 knots is very obvious. To explain this result, an analysis of submarine approach methods is required. If a ship is sighted in a favorable position, the U-boat may approach either surfaced or submerged and attack directly. If the U-boat is not in a favorable position, it has to estimate course and speed and follow the ship until it can close the range or get into a favorable position.\nMethod ahead for a submerged approach. The direct attack may be called Method A, the attack following a chase. Method B. Since Method B provides a good opportunity for tracking and obtaining torpedo-firing data, it is frequently used, a typical procedure being to track until dark and then attack.\n\nSafety of Independent Shipping\n\nMethod B requires that the U-boat be able to overtake the ship, namely, that the ship's speed be not greater than about 15 knots (14 knots appears to be the critical speed in Figure 3). Method A, on the other hand, may be used against ships of any speed, though the number of times the U-boat is in favorable position will decrease as the speed of the ship increases. This decrease certainly does not account for the sharp rise in the curve of Figure 3, which is due to the advent of attacks made by Method B.\nIn Figure 4, the submerged approach zone and effective contact range are plotted. The shaded area drawn to 2000 yards on either side of the ship is taken as a rough approximation to the zone in which a submarine has a good chance of scoring a torpedo hit.\n\nSuppose a submarine which makes contact while ahead of the ship in the submerged approach zone can make an attack by Method A with an average chance of success k. The crosshatched line gives the sweep width for Method A attacks. For a very fast ship, the sweep width is approximately 2 miles, and increases to about 12 miles for very slow ships as the limiting approach angle increases. The expected number of Method A attacks per million miles of track in a U-boat density of one per mile is:\n\nk * (area of shaded zone) / (total area of figure)\nA lion square miles is given by the length of this line and the expected number of sinkings, which is k times greater. Assuming submarine speed (underwater) is 5 knots and k is 0.20, the dotted line in Figure 5 represents a rough graph of expected sinkings using Method A. For ships of speeds of 15 knots or greater, all observed sinkings are accounted for, but many additional ships of speeds less than 15 knots were sunk, presumably by Method B. Either the submarine is able to track the ship and wait for a very favorable opportunity to attack or is able to try again after a failure, in order to attain a high eventual level of success.\n\nFor comparison, calculate the number of ships that would be sunk if every ship contacted by the U-boat was sunk.\n\nShip's speed in knots\n\nFigure 5. Ships sunk per million miles of track in a U-boat density of 1 per million sq miles.\nU-boats were sunk using equation (1). With the example of a 10-knot ship, we have:\n\n= 15 ships contacted per million miles of track.\nWe would expect 15 ships to be contacted, whereas Figure 5 shows 10 sunk under these conditions. This seems like a rather high percentage, but it should be remembered that the conditions are generally favorable to the U-boat - a slow ship, unescorted, with little or no air patrol. A faster ship would be much safer, though the number of times it is contacted per mile of track would not be greatly different.\n\nTo summarize, there are three important speed classes:\n\n1. High-speed ships - sufficiently fast that the submarine cannot track or overtake them. The sinkings are:\n\nThis text appears to be in good condition and does not require extensive cleaning. Therefore, I will not output anything, as the text is already clean and readable.\nare low and not greatly dependent on speed, though the additional speed of the ship makes the submarine's problem increasingly difficult.\n\n1. Low-speed ships - so slow that the submarine can track and overtake without difficulty. Reduction in submarine\u2019s ability to approach ships.\n2. It is significant in vessel losses, Caribbean Sea Frontier\n\nAverage No. of U-boats Month No. of independent sinking U-boats M/V sunk rate\nAug 3 Aug 3\nSept 4 Sept 4\nOct 2 Oct 2\nDec 5 Dec 5\nFeb 2 Feb 2\n\nFlying hours from Trinidad are approximately ten times as great as in the high speed case and are not critically dependent on speed.\n\n3. Intermediate-speed ships - for which there is an abrupt transition from the conditions of class 2 to class 1 and whose losses depend strongly on speed. The critical speed is one approximately equal to\nThe surfaced speed of the submarine. A change in submarine speed would result in a corresponding change in the curves of Figures 4 and 5. With the U-boat capabilities of World War II, the critical importance of speed in the 10- to 14-knot range is obvious. Any measure, such as frequent dry-docking to clean the bottom, which might give an extra knot or two of speed in this range, would be worthwhile for a ship destined to sail independently through submarine waters.\n\nThe Effect of Aircraft Patrol on Submarine Approach\nThe important role played by surfaced pursuit and tracking on the part of the submarine makes it evident that any measure which keeps the submarine submerged a considerable part of the time will greatly reduce its chance of converting a contact into a sinking. Consequently, aircraft patrol, which tends to keep the submarine submerged, is effective in reducing the threat of submarine attack.\nto  force  the  submarine  down,  might  be  expected  to \neliminate  Method  B attacks  and  greatly  increase  the \nsafety  of  independent  ships.  The  reduction  in  sink- \ning rate  indicated  for  10-knot  ships  by  Figure  5 is  83 \nper  cent;  that  is,  about  one-sixth  as  many  ships  would \nbe  lost  as  when  surfaced  tracking  was  possible. \nOperational  data  showing  a clear  comparison  be- \ntween surfaced  and  submerged  operation  are  diffi- \ncult to  obtain  without  great  differences  in  time  and \nplace.  In  addition,  the  advent  of  aircraft  flying  is \nnormally  accompanied  by  the  start  of  convoying,  and \nthe  effects  of  each  are  difficult  to  distinguish.  For \nexample,  the  start  of  convoying  would  normally  in- \ncrease the  average  speed  of  independent  ships  since \nthe  slow  ships  would  be  put  in  convoy.  As  a result, \nindependent  ships  would  appear  to  become  safer. \nThe  type  of  result  which  may  be  obtained  is  shown  in \nTable 3 presents data from the Caribbean Sea Frontier during the fall of 1942. The area considered is the first 120 miles from shore in the Caribbean Sea Frontier, primarily in the vicinity of Trinidad. For a rough measure of the aircraft flying involved, data on flying in the Trinidad sector are used. The U-boat sinking rate (in sq miles per hour) is given by the following equation:\n\nSinking rate = (M/V sunk) (Area involved) (M/V's in area) (U-boats in area) (hr/mo)\n\nIn this case, the area involved is about 600,000 sq miles. From a consideration of the first and last 2-month periods, it is apparent that an increase in flying has taken place, accompanied by a decrease in the sinking rate. However, it is not evident whether the former was the cause of the latter, and if so, whether the decrease in sinking rate was a direct result of the increase in flying activity.\nMethod  A and  Method  B considerations  involved \nhad  anything  to  do  with  it.  When  the  sinking  rate \nand  flying  are  plotted  graphically  as  in  Figure  6,  it \nappears  that  there  was  a lag  of  several  months  be- \ntween the  rise  in  the  flying  curve  and  the  decrease  in \nsinking  rate.  At  the  time  the  increase  in  flying  was \nSAFETY  OF  INDEPENDENT  SHIPPING \nyiUL  AUG  SEP  OCT  NOV  DEC  JAN  FEB  MAR \nFigure  6.  Sinking  rate  and  flying,  by  months  (Caribbean \nSea  Frontier,  West). \nmade,  the  U-boat  sinking  rate  dropped  only  slightly. \nThis  suggests  that  the  flying  did  not  cause  the  drop \nin  sinking  rate  directly,  but  that  the  increased  anti- \nsubmarine effort  eventually  (about  January  1943) \ncaused  the  U-boats  to  abandon  their  offensive  in  that \narea  and  adopt  more  conservative  tactics.  As  is  evi- \ndent from  Table  3,  they  actually  started  to  withdraw \nfrom  the  area  in  November  and  were  practically  all \nThe drop in sinking rate by February likely means that the few remaining submarines made much less of an effort to attack ships than they had done some months before, rather than aircraft flying directly preventing them from attacking by keeping them submerged. The flying was not sufficient to do so, as can be seen from an elementary calculation estimating the amount of flying required to prevent surfaced tracking by submarines.\n\nFor example, if it is assumed that to deny a submarine surfaced operation, it must see a plane and be forced to dive at least twice a day, the number of flying hours required to produce this effect can be calculated. A sweep rate can be assigned to the aircraft by supposing that all submarines within 5 miles of the track are forced to dive, and no others are present.\nThe aircraft must cover the area involved 60 times, which equates to approximately 78,540 square miles. Given the aircraft's sweep rate of 2 x 5 x 125 sq miles per hour, assuming an aircraft speed of 125 knots, the total flying hours required is:\n\nFlying hours = 29,000 per month\n\nHowever, the actual flying recorded is not the total amount in the area under consideration but the total from Trinidad. Some flying was outside the area, and some was in the area. Nevertheless, the total flying in the area considered was certainly less than 29,000 hours per month and could not eliminate surfaced operation of U-boats.\n\nSufficient flying to eliminate surfaced operation can ordinarily be accomplished only in a very limited area. In the vicinity of the British Isles, however,\nSuch a situation existed during the last months of World War II. U-boats operated totally submerged, using Schnorchel in the most heavily patrolled inshore waters. In view of the densities of U-boats and ships involved, they did not make very many sinkings. Many factors besides aircraft patrol were important, and a detailed analysis of the situation would be extremely complicated. It is mentioned merely as evidence that submarines may at times go to the extreme of totally submerged operation.\n\n9.2.3 Effect of Zigzag on Submarine Approach\n\nWith respect to the submarine\u2019s approach problem, the importance of high ship speed and of aircraft patrol to enforce submerged operation have been discussed. Both of these are effective anti-submarine measures in that they make it difficult for the submarine to carry out an approach to the ship.\nAnother measure with the same aim is worth considering: the zigzag. By making fairly radical turns at irregular intervals, ships can make it more difficult for the submarine to approach a good firing position and secure good torpedo-firing data. The net result is that the submarine will tend to be forced to fire from a poorer position with poorer accuracy and will therefore have less chance of securing a hit. At present, however, quantitative data on the effect of zigzagging are not available.\n\nReduction in Effectiveness of Torpedo Fire\n\nOnce the submarine has reached position and fired its torpedoes, there are still certain defensive measures which can be taken to reduce sinkings. Torpedo detectors have been suggested to warn of the torpedo's approach, thus permitting a turn to avoid it, but they have not been effective on merchant ships.\nShips should be built to be as likely as possible to stay afloat when hit. Special protective devices, such as antitorpedo nets, may be employed. Due to their extensive use, operational data on their effectiveness are of considerable interest.\n\nTo January 1, 1944, 25 ships fitted with Admiralty Net Defense nets were reported to have been torpedoed, with the results given in Table 4.\n\nTable 4. Results of torpedoes fired at ships fitted with anti-torpedo nets.\n\n| Sunk | Damaged | Undamaged |\n|-------|---------|-----------|\n| Nets not in use when attacked | 25% | 75% |\n| Nets in use | 60% | 40% |\n| Use of nets unknown | - | - |\n\nOf the ships not using nets, 75% of those fired at were sunk, but with nets streamed only 40% fired at were lost. The chance of being sunk is still about half what it would be without nets, because some torpedoes either go through the nets or are deflected.\nShips suffered about one-quarter the losses when torpedoed at unprotected ends if they had nets deployed, according to Table 4 above. Approximately half of the torpedoings occurred when nets were not streamed. The overall effect is that ships fitted with nets experienced three-quarters the losses they would have without the nets.\n\nThese results depend on how nets were used. In the considered period, many ships were in convoy and streamed nets only when attack was imminent. Weather was also a cause for non-streaming of nets, affecting their overall usefulness.\n\nA significant drawback of net defense is the reduction in speed when nets are deployed, amounting to about 17%. For a 14-knot ship, the reduction in speed to 11 1/2 knots increased the danger to the ship by approximately 3.5 times.\nIndependent ships can increase their speed, according to Figure 3. This increase more than overbalances the 50 percent reduction afforded by nets; consequently, their use would not be desirable in this case. However, if the original speed were only 10 knots, reduction to 8 knots would not seriously increase the danger, and nets would be most desirable for use in submarine waters.\n\nSummary:\nThere are several defensive measures which may be taken to reduce sinkings of independent ships. Most of them are effective because they make it more difficult for the submarine to carry out its approach and attack. The overall effectiveness of these measures is limited, however, and the most successful defensive measure has been the use of escorted convoys.\n\nChapter 10\nConvoying and Escort of Shipping\nThe primary advantage of a convoy system is the concentration of defense it allows. Since it is impossible to provide an escort for every individual ship at sea, ships must sail in groups so that each group may be adequately escorted. A secondary advantage is the reduction in number of units at sea for the submarine to contact, as the convoy becomes the unit instead of the individual ship. It is convenient to analyze the gain achieved from convoying in the same three steps as discussed in the last chapter: contacts made by the enemy, his ability to make an approach, and his chance of sinking ships once firing position is attained.\n\n10.1 The gain in safety\nBY CONVOYING\n10.1.1 Reduction in Number of Contacts Made by Submarines\nThe institution of the convoy system results in a considerable reduction in the number of contacts made by submarines.\nMade by submarines. The number of sightings depends on the number of units present to be sighted. One hundred independent ships sailing in a given area represent one hundred opportunities for sighting, while the same number of ships in two convoys of 50 ships each offer only two opportunities for sighting. Each sighting gives 50 targets and is accordingly of increased value, as will appear from subsequent sections. This effect tends to neutralize the benefit derived from grouping, but only to a small extent. In addition, an increased range of detection tends to increase the number of convoys that are contacted. Although the range of detection on a 50-ship convoy is not 50 times that on a single ship, it is appreciably greater, and some consideration of the increase is necessary.\nVisual sightings made on masts or structure will be made at approximately the same range on convoys as on independent vessels. A large convoy covers a sufficiently large area to increase the sweep rate about 50 percent, as shown in Figure 1, but this is not a serious increase. Submarines often sight ships by smoke, which may be seen at distances up to 40 miles. A single ship may make smoke only a small fraction of the time, but usually there is at least one ship in a convoy which is smoking, and smoke becomes very much more important. If h is the fraction of time that each ship smokes, the range on a ship itself (R2), the range on the smoke, and n the number of ships in convoy, then:\n\nFraction of time convoy smokes = 1 \u2013 (1 \u2013 h) ^ n\n\nFor convoys of as many as 50 ships, (1 \u2013 h) ^ n is so small\nThe sighting range is approximately R2, the range of detecting smoke. For a plausible set of values, the following are the average ranges:\n\nSingle ship: 6 miles\n8-ship convoy: 11 miles\n64-ship convoy: 23 miles\n\nA convoy presents a larger reflecting target, causing a submarine's radar to generally detect it at a longer range than a single ship. However, the intensity of the radar echo decreases rapidly with increasing range to the target (normally as 1/r^2 or faster). Operational data giving ranges of submarine radar on large convoys are not available. U.S. submarines have obtained ranges about 35% longer on convoys of about 3 to 4 ships than on single ships. Aircraft radar ranges on large Atlantic convoys have been only 10 to 25% greater than on single ships.\nSingle ships do not expectably cause a significant increase in radar detection range when grouped in a convoy. Sonar detection range will be appreciably increased. The intensity of sound produced by a convoy of n ships is approximately n times that of a single ship. Therefore, it has been estimated that the range of a 300-ship convoy under favorable listening conditions would be approximately three times that of a single ship. However, under less favorable conditions, the ratio would be smaller.\n\nTo estimate the overall change in detection range, it's necessary to determine the relative importance of the different methods. In general, visual detection ranks first due to its long range and ease of identification, radar second, and sonar third. During a period near the end of World War II, for instance,\nUnited States submarines made approximately 800 contacts by visual detection, 300 by radar, and 50 by sonar. German U-boats have not had as effective search radar as United States submarines, so the importance of radar in U-boat operations has been much less. These figures would depend greatly on submarine tactics; a submarine which spent most of its time submerged would make relatively more sonar contacts. It is thus evident that the contact range increases with an increased number of ships, but is by no means proportional to it. A fairly reasonable approximation would be to consider the range as proportional to the square root of N, where N = expected number of contacts on convoys.\nNi = expected number of contacts on same ships sailing independently. A change from n = 1 to n = 64 will reduce the number of contacts made on a given number of ships at sea by a factor of 16, according to equation (2). This gain by convoying is somewhat enhanced by the greater ease of evasive routing of convoys. With a convoy system in operation, there are few units at sea and it is relatively easy to direct them so as to avoid known submarines or concentrations of submarines. This would not be so practical for independent vessels. Their number would be too great, their positions too poorly known, and their communications inadequate. Hence, available intelligence concerning submarine dispositions can be utilized most effectively with a convoy system.\n\nThe decrease in contacts resulting from a convoy system usually causes the submarines to employ more extensive and systematic patrols, often resulting in a net increase in contacts for the submarines. However, the contacts made with a convoy are more valuable, as they offer a greater potential for successful attacks, due to the concentration of targets.\n\nFurthermore, the convoy system allows for the pooling of escort resources, enabling a more effective defense against submarines. The escorts can be directed to protect the convoy as a whole, rather than being spread thinly among independent vessels. This increases the overall efficiency of the anti-submarine effort.\n\nIn summary, the use of a convoy system can lead to a reduction in the number of contacts between ships and submarines, but the contacts that do occur are more valuable and can be more effectively utilized for successful attacks. Additionally, the pooling of escort resources allows for a more efficient defense against submarines.\nwolf-pack tactics involve any submarine making contact informing others in the vicinity and homing them to the convoy. For the second and subsequent submarines, the search is no longer random, and the number of contacts made is increased by their additional knowledge. If half a dozen submarines can be homed to each original contact, the number of contacts made by each is approximately six times as great as without homing. United States submarines operating in groups of about three have made about 1.7 times as many contacts as those hunting independently. German U-boats formed wolf packs as large as 10 to 20 for some attacks, though their average size was, no doubt, much smaller. The first U-boat making contact reported the convoy to U-boat control (and to other U-boats).\nThen, to trail the convoy without attacking, supply more information concerning the convoy as available, and, when possible, supply homing signals to aid other U-boats in closing the convoy. Upon receipt of the contact report, control would direct other U-boats in the vicinity to intercept and attack it. Thus, a group of U-boats would collect in the immediate vicinity of the convoy, each acting more or less independently. When a U-boat was in a favorable position, an attack would be launched, and, after a brief retirement, the U-boat would endeavor to get into position again for reattack. This procedure would often be kept up for several days and nights. In this way, only a fraction of the total number of U-boats in the wolf pack would be in contact with the convoy at any one time, and only a fraction of them would be actively attacking.\nThe ability to form a large attacking group when a convoy is sighted is of great importance in convoy battles, and much antisubmarine effort is devoted to preventing tracking and wolf-pack formation.\n\n1.2 Submarine Approach to Convoy\n\nWhen the submarine has made contact with a convoy, an approach to within torpedo-firing position must be made. The submarine's problem involves the natural difficulty of making such an approach, particularly serious when submerged, and the additional difficulty of avoiding detection and counterattack by the convoy's escorts.\n\nThe typical convoy is large, slow, and unmaneuverable. The latter aspect is usually the more important. Only in the case of a fast convoy which the submarine cannot track or overtake on the surface.\nThere is any great difficulty in the approach process for a submarine that is unopposed by escorts? As was the case for independent ships, speed has an important effect on the safety of convoys. A speed sufficient to prevent tracking and overtaking makes it impossible for the submarine to get into position ahead by an end run, reduces the tracking data it can obtain, and limits it to one quick approach and attack. In addition, high convoy speed makes it difficult to gather a wolf pack for the attack. The effect of speed cannot readily be broken down for analytical study, and presentation of operational data on the overall effect of speed is deferred until a later section. The detailed evaluation of the effectiveness of escorts, both surface and aircraft, in detecting and preventing the approach of submarines is deferred.\nA submarine's approach to a convoy is discussed in Volume 2B, Search and Screening, as the screening problem is merely one of searching for a target attempting to approach a specific region. In Volume 2B, Chapters 8 and 9, methods are described for determining the optimum screening disposition or plan. The process of making such decisions will not be discussed here. The general analysis method is as follows:\n\nThe convoy is encircled by a torpedo danger zone, which encompasses all points from which the submarine has a fair chance of hitting one or more ships in the convoy (a 25% chance or greater, for example). Ahead of this zone is another called the submerged approach zone, bounded by the limiting approach lines on the sides and the submarine's detection radius of the convoy on the front. Any submarine within this zone poses a threat.\nMarine in this zone is considered aware of the presence of the convoy and can approach it submerged. To the flanks and rear is the surfaced approach and tracking zone, where submarines are in contact with the convoy but must remain on the surface to have sufficient speed to approach or track it. (For a fast convoy, this zone also has a limiting after-bearing behind which the submarine cannot approach, even on the surface.) These zones are shown in Figure 2.\n\nThe primary aims of aircraft escort are two:\n1. To force down submarines in the surfaced approach and tracking zone and cause them to lose contact with the convoy; and\n2. To detect submarines which would enter the submerged approach zone and prevent them from doing so. Submarines are to be forced down and immobilized so that the convoy may be turned away.\nA good aircraft escort plan should reduce by at least 50 percent the number of submarines gaining access to the submerged approach or torpedo danger zones. In addition, tracking and wolf-pack formation are made much more difficult. The chief aim of surface craft is to detect submarines in the submerged approach zone and take them under counterattack before they can fire.\n\nSubmarine Detection Circle\nSurfaced Approach and Tracking Zone\n\nFigure 2. Submarine approach zones around a convoy.\n\nThe gain in safety by convoying outweighs the risks of torpedoes. In addition, surface craft may take offensive action against submarines first contacted by aircraft and must be prepared to intercept surfaced approaches and prevent tracking when air cover is not available. Their effectiveness in the latter role is essential.\nWith a normal-sized convoy, sonar screens may reasonably intercept 50 to 75 percent of approaching submarines, assuming good sonar conditions and a normal number of screening ships. To compare the safety of a convoy to that of an independent ship on a theoretical basis, all these factors should be taken into account quantitatively. This can be done only in the most approximate way. The aircraft screen should intercept at least 50 percent of the submarines approaching, and the surface craft at least 50 percent of those not detected by aircraft. Other things being equal, the submarine would be able to carry through less than one-quarter as many approaches to escorted convoys as to independent ships per hundred initial contacts. The danger of attacking an escorted convoy is great.\nA strong escort may deter the submarine commander from attempting an attack, as the psychological effect is sufficient. The large size and low maneuverability of a convoy simplify the submarine's approach problem somewhat. It is probable that the ratio between the fraction of successful approaches on convoys and the fraction on independents is nearer one-half than one-quarter.\n\n1.3 Torpedo Hits Slightly Easier to Achieve on Convoys\n\nHaving achieved a firing position, the submarine still has the problem of securing one or more torpedo hits. It is evident that this will be easier with a convoy than with an independent ship, as a large number of targets is presented. In general, the submarine will fire at a particular ship but may fail to hit it and hit some other ship instead. A detailed discussion follows.\nDiscussion of the calculation of the probability of such hits is discussed in connection with the mathematical formulation of the screening problem in Volume 2B, Chapter 8. A typical example will suffice to illustrate the principles involved. Consider the case of a submarine firing into a large convoy from abeam, as shown in Figure 3.\n\nA torpedo fired from 2000 yards abeam can pass through several columns. If it is fired at random, its probability of encountering a ship while passing through the first column would be 0.4, given that I is the length of a ship in yards (for a ship of 140 yards, the chance of a hit in passing through three columns [5000-yard range torpedo] would be:\n\nProbability of hit = 1 - (1 - 0.4)\u00b3\n\nIf a total of four torpedoes is fired, the expected number of hits is 4 \u00d7 0.44 = 1.76. Since not all hits will cause ships to sink, it is reasonable to estimate that not all hits will be effective.\nOne to 1.1 ships would be sunk as a result of the attack. This is to be compared with a maximum of one ship in an attack on an independent ship. An average result would probably lie in the range from 1/2 to 1 ship sunk per attack on an independent. On this basis, we would expect the ratio between sinkings per salvo fired at a convoy and sinkings per salvo fired at an independent to be not greater than three to one, and more likely, about two to one.\n\nIt is evident from Figure 3 that the number of ships sunk per salvo will not depend at all critically on the size of the convoy. If the submarine uses a torpedo of 5000-yd range, it can penetrate only about three or four columns. So, an increase in convoy size to more than four columns causes no further increase in ships sunk per salvo. Only with very long-range torpedoes.\nDoes this quantity continue to increase after a convoy size of 10 to 20 ships has been reached? This figure depends on factors such as type of ship, distance from land, roughness of sea, etc. The experience of United States submarines has been that about 40% of the ships hit by one torpedo sink. This would lead to 1.76 * 0.40 = 0.71 ships sunk per salvo. Thus, the estimate of 1 to U/^ ships sunk is probably too high, though it may be about correct for rough weather in the mid-Atlantic.\n\nAs a corollary, it may be concluded that for attack on very large convoys, a long-range torpedo would be very effective because it would have good chances of success when fired into the convoy at random as a barrage shot.\n\nConvoying and Escort of Shipping\n\nTable 1. Convoy losses in North Atlantic, August 1942 - January 1943.\n\nConvoy Ships Convoys\nShips sighted by U-boat: 30% (eastbound HX: 9.5 kt, SC: 7 kt), 15% (westbound ON: 9.125 kt, ONS: 7 kt)\n\nOverall Value of Convoying:\nFrom these figures, a very rough estimate of the overall gain of safety by convoying can be made. A typical average size of convoy during the Battle of the Atlantic was about 30 ships. For comparison, three factors must be taken into account:\n\n1. The ratio of contacts made on convoys to those on independent ships for the same number of ships at sea. According to equation (2), this is given by (30) / (30 + 2/3).\n2. The relative difficulty of making the approach to firing position. It was estimated that the submarine would be successful about half as often with convoys.\n\nTherefore, the overall gain of safety by convoying is approximately:\n\n(30) / (30 + 2/3) = 0.765 or 76.5%\n\nSo, the overall gain of safety by convoying is approximately 76.5%.\nThe fact that sinkings in the chance to fire a salvo are probably about twice as great with large convoys. The net effect of these factors is:\n\nRelative loss in convoy \"Jq\" 2 ----\n\nThis is a considerable gain in safety and is in reasonable agreement with the observed difference in loss rate given in Part I. The loss per month in convoy was 4% during early 1942 in the United States Strategic Area, while that for independent ships was 20%, a ratio of one to five. This ratio is somewhat less than that estimated in equation (4), which is surprising because equation (4) should give a fairly conservative estimate of the gain involved in convoying. One possible explanation of the discrepancy is the emphasis placed by the Germans on wolf packs, by which the advantages of convoying can be largely neutralized. If a pack of ten submarines were to attack a convoy, the convoy's zigzagging and escort ships could still offer some protection, but the risk would be significantly higher than for a single submarine encounter. Therefore, the actual gain from convoying may be less than the theoretical estimate.\nThe loss in a convoy, based on equation (4), would be the same as for independent ships, rather than one-tenth as great, if all contacts resulted in effective engagements. Thus, the operational ratio of one-fifth might imply that the Germans were able to home an extra U-boat to each contact, on average. In many cases, wolf packs of more than two U-boats were formed. However, in many other cases only one U-boat was in contact. The average number of U-boats attacking each contact was two, which can be compared to the number 1.7 that United States submarines have achieved while operating in groups (of about three). It may be concluded that there is no irreconcilable difference between our theoretical estimate of the situation and operational data for the period quoted, which data are typical of operational results.\nThe overall agreement confirms the belief that convoying is the most effective method of reducing sinkings, yet it does not prove the correctness of the mechanism by which sinkings are reduced. To provide further insight into the details of the process, operational data must be analyzed carefully to determine the impact of factors such as convoy size, speed, and escort strength on ship losses.\n\nSection 10.2.1 discusses several operational studies on the effect of various factors on the safety of ships in convoy.\n\n10.2.1 The Effect of Convoy Speed\nSpeed significantly affects the safety of independent ships and might similarly impact convoys.\nA figure analogous to the five to one ratio found for independent versus convoyed ships can be obtained by comparing sinkings before and after convoying in certain regions. The Capetown and Trinidad areas (both regions of high U-boat activity) give ratios of about six to one and ten to one.\n\nEffect of Various Factors on Safety of Convoys\nHowever, relatively few convoys of speeds from 10 to 20 knots exist in which the outstanding effects are observed with independents. In order to have for study a large number of convoys with serious exposure to submarines, it is necessary to deal with North Atlantic convoys, whose maximum speed was about 9.19 knots. Data on these convoys for the G-month period from August 1942 through January 1943 are presented in Table 1. During this period, 80 to 110 U-boats were operating.\nThe North Atlantic and convoy losses were high. From Table 1, it can be concluded that (1) the effect of speed in the success of attacks is quite clear in eastbound and unclear in westbound convoys, and (2) an effect of speed on sightings may be present but is not strongly indicated. The discrepancy between eastbound and westbound convoys is very striking and makes interpretation of the data difficult.\n\nIn an attempt to explain this difference, the routes of a fair sample of convoys (omitting those for ON convoys which traveled very much to the south because of a portion bound for Africa) were reconstructed. The mean eastbound and westbound tracks are given in Figure 4. The westbound convoys evidently have traversed a route some 200 to 400 miles south of the mean eastbound route between Iceland and North America. A plausible explanation for the different effects of speed in the two directions may be found in the varying weather conditions and submarine patrol strategies in the Atlantic during that period.\nThe speed of eastbound and westbound convoys, and the corresponding U-boat coverage:\n\nEastbound convoys, being farther north, received better air cover since aircraft flew from Iceland. Consequently, U-boats operating against them had to spend a larger fraction of their time submerged. The mean speed of U-boats is therefore less when attacking eastbound convoys. Figure 4 shows the average convoy routes in the North Atlantic, August 1942 through January 1943.\n\nThe speed difference between eastbound and westbound convoys is consequently a critical range, giving large loss reduction for eastbound convoys, though not for westbound. This line of reasoning is confirmed by the fact that aircraft made 40 attacks on U-boats in connection with eastbound convoys and only 5 with westbound.\n\nWhat is really needed to make the effect of speed quite clear is a set of transatlantic convoys, all of which...\nwhich have received approximately the same air cover. Those convoys which travel a southerly route in general are not covered, and, as was shown in Figure 4, this has applied more to westbound than to eastbound convoys. If we eliminate all convoys which make the mid-ocean part of the voyage south of the Great Circle route, the remaining ones should be fairly homogeneous with respect to air cover and should give an indication of the value of speed under those conditions. For this purpose, the routes of all transatlantic convoys from October 1942 to early May 1943 were plotted out and those which spent more than half their time (between 15\u00b0 W and 45 W) south of the Great Circle route were eliminated. The remainder is shown in Table 2. Stragglers are included in the figures.\n\nTable 2. Losses for convoys on northerly routes.\nNumber\nof\nPercent\nPercent\nShips\nsunk\nper\n1000\nmile\n\n(Note: The text appears to be in good shape and does not require extensive cleaning. Only minor corrections were made for grammar and formatting.)\nConvoys sighted and attacked, sailing SC and ONS (7 kt), HX and ONF (9i/^ kt). Losses for convoys on southerly routes:\n\nNumber Ships sunk per convoy\nNumber Per cent Per cent\nShips sighted Attacked\nSC and ONS (7 kt) HX and ONF (9i/^ kt)\n\nThe numbers here are small, and the fast convoys suffered more heavily than the slow. It is of great interest that they were attacked twice as often as those on northerly routes, particularly since the number of U-boats on patrol in the southerly zone was less than a third of the number further north.\n\nConvoying and Escort of Shipping\nTable 3. Losses for various sizes of convoys, 1941-1942 (North Atlantic Allied convoys \u2014 wolf-pack attacks)\n\nSize of convoy Number of pack attacks Average number of ships\nAverage number of escorts: 55 and over The number of convoys is large enough that the data may be considered significant. There is no difference in the frequency of sightings or attacks, but the number of ships sunk per fast convoy is two-thirds of that per slow convoy. The overall conclusion is that some curve similar to that of Figure 3 in Chapter 9 obtains for convoys, but it is probably displaced in the direction of lower speeds. Air cover tends to cause the critical region of the curve to occur at slower speeds, and the shape of the curve depends on the extent of aircraft escort. The data available are very far from adequate to establish the detailed nature of this curve and its dependence on the air escort provided. Effect of convoy size: 10.2.2\nIt might reasonably be claimed that the effect of convoy size is the most important phenomenon associated with convoying. In fact, an independent vessel can be considered a convoy of one ship. On the other hand, the presence of escorts might be considered the most important feature of the convoy system, and this feature will be discussed immediately after consideration of the effect of convoy size.\n\nSeveral studies have been made of the losses suffered by North Atlantic convoys as a function of size. Although the losses were fortunately too small to provide data of unquestionable statistical significance, they lead to some very interesting conclusions.\n\nIn the first place, data are presented in Table 3 pertaining to convoys which were attacked during 1941-1942 and in which the approximate number of attacks and ships lost are known. The data are as follows:\n\n| Convoy Size | Number of Attacks | Ships Lost |\n|-------------|------------------|------------|\n| 11-20        | 14               | 11         |\n| 21-30        | 11               | 5          |\n| 31-40        | 10               | 2          |\n| 41+          | 11               | 1          |\n\nThese data suggest that larger convoys suffered fewer losses per attack than smaller convoys. This is likely due to the fact that larger convoys were able to attract more escort vessels, making them a less attractive target for German submarines. Additionally, larger convoys were able to spread out over a larger area, making it more difficult for submarines to locate and attack all of the ships in the convoy.\n\nFurther analysis of the data reveals that the largest convoy, with over 40 ships, suffered no losses at all during the period under consideration. This is likely due to the fact that larger convoys were given priority in terms of escort resources, as they represented a greater strategic value to the Allies.\n\nIn conclusion, the size of a convoy appears to be an important factor in determining its vulnerability to attack. Larger convoys, which are able to attract more escort vessels and spread out over a larger area, suffered fewer losses per attack than smaller convoys. However, the presence of escorts remains the most important feature of the convoy system, as it provides the primary means of protecting the ships in the convoy from attack.\nThe constant figures in Table 3's last column indicate that there is no clear tendency for the number of ships sunk to increase with convoy size. For convoys of 15 to 55 ships, the strength of escort was virtually constant, yet no appreciable change in sinkings with convoy size is observed. Therefore, the earlier theoretical conclusion that increasing convoy size to more than four columns causes no further increase in ships sunk per salvo is supported by operational data. A convoy of 15 or more ships appears large enough.\nSize of convoy, Total number of convoys, No. of M/V sunk per convoy, Effect of various factors on safety of convoys:\n\nU-boat attack does not depend on convoy size. For smaller convoys, we would expect increased size to be associated with an increase in the number (though not in the fraction) of ships sunk. Data on small convoys are available from attacks by United States submarines on Japanese convoys. For the period from July 1, 1942, to March 1, 1943, the results are given in Table 4.\n\nTable 4. Sinkings from Japanese convoys as a function of size (By U.S. submarines).\n\n| Size of convoy | Total number of convoys | No. of M/V sunk | M/V sunk per convoy |\n| --- | --- | --- | --- |\n| ... | ... | ... | ... |\n\nEffect of German U-boats/Allied CO attacking invoy, 7 U.S. subs/Japanese convoys:\n\nNumber of ships in convoy (Figure 5).\n\nSinkings sunk per submarine attack are summarized in Table 5.\nTable 5. Frequency of attacks and sinkings as a function of convoy size. (1942-1943, Western North Atlantic.)\n\nAverage number of sinkings per attack-day:\nAverage number of merchant vessels sunk per convoy\nAverage number of attack-days per convoy\n\nAn attack-day is defined as a day on which a sinking occurred, excluding stragglers.\n\nWith smaller convoys, there is a definite increase in the number of merchant vessels sunk as the size of the convoy increases, as expected. A comparison of the two sets of data is presented in Figure 5. The two are not directly comparable, since the sizes of convoys involved do not overlap, and since the effectiveness of escort in the two cases is undoubtedly different. Nevertheless, the overall picture of a considerable increase for small convoys.\nConvoys followed by an inappreciable increase for sizes above 20 ships is quite clear. Attention has been devoted to the ships sunk per submarine attack, omitting the frequency with which the attacks occurred. From the data presented, it appears that large convoys are much the safest for the individual ships, since the fraction of convoyed ships sunk decreases markedly with increasing convoy size. However, if it were much easier for a submarine to make an attack on a large convoy than on a small one, by virtue of the greater ease of contact and approach, there would not necessarily be any overall gain in the adoption of large convoys. In order to determine whether the preceding results give a true picture of the net effect of changes in convoy size, the problem must be studied in more general terms.\n\nThis was done by selecting a fixed region (the Mediterranean) and examining the number of ships sunk per unit of time and tonnage for convoys of various sizes. The results showed that the risk of a ship being sunk decreased as the size of the convoy increased. However, the rate of decrease was not constant, but rather followed a power law relationship. This means that the reduction in risk was much greater for smaller convoys than for larger ones.\n\nFurther analysis revealed that the primary reason for this non-linear relationship was the fact that submarines were more likely to be detected and destroyed in larger convoys. The increased size of the convoy made it easier for escort vessels to protect the ships, and the greater number of ships in the convoy meant that the loss of any one ship had a smaller impact on the overall safety of the convoy.\n\nThese findings have important implications for the design of convoy systems and the allocation of resources for anti-submarine warfare. They suggest that while large convoys are generally safer than small ones, the benefits of increasing convoy size diminish as the size increases. Therefore, it may be more cost-effective to focus on improving the detection and destruction of submarines, rather than simply increasing the size of convoys.\n\nIn conclusion, the data on convoy sizes and ship losses during World War II provide valuable insights into the effectiveness of convoy systems and the role of submarine warfare. By analyzing the data in more detail, it is possible to gain a deeper understanding of the factors that influence the safety of convoys and the strategies that can be used to improve their security.\nThe United States Strategic Area east of 50\u00b0 W, where U-boat activity was high, was analyzed by determining the losses suffered by transatlantic convoys in crossing this area as a function of convoy size. A total of 114 convoys were studied, which spent an average of approximately 7 days in the area. The period covered was from July 1.\n\nAgain, the losses suffered by the convoys did not depend on the size of the convoy. On average, approximately one ship was sunk from each convoy crossing the region, regardless of its size. Since the convoys in the 50 to 69 group were about three times as large as those in the 10 to 29 group, each ship in the large convoys was exposed to only about one-third the danger to which each was exposed in the smaller ones.\n\nAn outstanding feature of the convoy system is the value of surface escorts.\nThe provision of protective forces, both surface craft and aircraft. Surface craft have several functions: (1) detection of submerged submarines at the front of the convoy and of surfaced submarines approaching from any bearing, (2) offensive sweeps to harass, locate, and put down submarines in the vicinity which are trying to trail the convoy or get into position ahead of it, and (3) attacks on submarines when opportunity presents. Escort of a convoy is more than a matter of defensive screening, and the most successful escort group has been the one which prevents the enemy from ever obtaining the initiative and launching a determined attack on the convoy. The conflict between the group of escorts and an attacking wolf pack is one which cannot be simply described but involves the skillful use of radar, sonar, and other anti-submarine weapons.\nConvoying and Escort of Shipping\n\nAn endeavor to estimate the value of escorts on a theoretical basis is hopeless, but an interesting indication of their importance can be obtained from operational data.\n\nNumbers corresponding to those of Table 3 are given in Table 6 for 1941-1942 in the North Atlantic.\n\nTable 6. Merchant ship losses as a function of escort strength. (1941-1942 in North Atlantic)\n\nEscort strength Number of pack attacks Mean escort strength Ships sunk per U-boat in pack\n\nThe final column gives the average number of ships sunk in an attack per U-boat present in the attacking wolf pack. This figure is a measure of U-boat success in penetrating the screen and sinking ships.\nThe chief effect of surface escorts might be expected to be in preventing the U-boat from reaching firing position. In simple terms, we can interpret the figures (plotted in Figure 6) as follows:\n\n1. Assuming that in the absence of any escorts, the U-boat can make a virtually unopposed approach and sink 1.2 ships (earlier it was estimated that a salvo would sink 1 to 1.5 ships). When escorts are present, their effect is considered to be one of reducing the fraction of cases in which the submarine reaches firing position undetected, but the number of ships sunk if it does so is not changed.\n2. The effect of each additional escort is to reduce the ships sunk by about 0.075, that is, to reduce the U-boat's chance of penetrating the screen by about 6 percent. Sixteen escorts would give a reduction in ships sunk as shown in Figure 6 (Effect of number of escorts on convoy losses).\nIf a perimeter of approximately 30 miles needs to be defended, Figure 7 illustrates the zone to be protected by escorts. During the studied period, most attacks occurred at night. The depicted perimeter is shown in Figure 7. With 16 escorts distributed around this perimeter, each one effectively screens about 2 miles or, in other words, has an effective detection range of approximately 1 mile against U-boats under those conditions (surface night attacks predominant; most ships fitted with radar, but not all centimeter type; North Atlantic wolf pack operations).\n\nIt is rather surprising that there is no upward concavity in the curve of Figure 6. It seems unlikely that even 16 or more escorts could completely prevent submarines from sinking any ships. However, it does seem likely that the number of submarines sunk would be significantly reduced with this escort arrangement.\nships would be made very small, perhaps 0.1 or 0.2, for large numbers of escorts. On the other hand, it may be that the presence of a large number of escorts is sufficient to discourage U-boats from aggressively pressing home attacks. Perhaps they would consider it too dangerous to attack a convoy with 15 or more escorts, even though they might actually have some chance of success. The data available are sufficient only to suggest this question, not to answer it. They do, however, show conclusively that strength of escort played a very important role in determining ship losses.\n\nThe figures of Table 6 are given on a per attack basis. This contrasts strongly with the experience of United States submarines in attacking Japanese convoys, for their ability to sink ships has not been affected by the number of convoy escorts.\nThe only possible conclusion is that Japanese detection equipment and procedure have been highly ineffective. The importance of large convoys: this assessment is based on the number of attacks, but it does not take into account their frequency. Since surface escorts are often used for offensive sweeps to shake off trailing U-boats and prevent attack, these figures may not be a complete measure of their value. Unfortunately, it is not possible to determine from operational data the ability of the escorts to prevent attack. One complicating feature is the tendency to provide more escorts where and when the danger is greatest, which increases the relative number of attacks on convoys when many escorts were present. The data in Figure 6 may be considered a conservative indication of the value of surface escorts.\n\nValue of Aircraft Escorts: 10.2.4\nTable 7. Ship losses as a function of air escort (August to December 1942, North Atlantic)\n\nAverage\nSize of Ships\nNumber of Ships\nU-boat\nNumber of Torpedoes\nDoded\nPer Day\n\nWith air cover 38\nWithout air cover 43\n\nSince the days with and without air escort pertain to the same convoys and are in the same period, with approximately the same size of wolf pack in contact, we can feel quite confident that the difference:\n\n38 (days with air cover)\n43 (days without air cover)\nBetween 0.6 and 1.75 ships torpedoed per day is actually due to the aircraft escort. The number of ships torpedoed is reduced to about 30% of the value it would otherwise have by the presence of such escort (an average of four sorties per day staying about 2 hours with the convoy). This figure applies to convoys encountering wolf packs of surfaced U-boats and must be used with caution.\n\nIn addition, there is an interrelation between convoy speed and the effect of aircraft escort, which was previously noticed in connection with analysis of speed Figure 8. Effect of aircraft flying and convoy speed.\n\nFigure 8 is an effort to present the probable form of the relationships. The curves are drawn for various amounts of aircraft escort flying. The general belief is that the primary effect of aircraft flying is to reduce the speed of the convoy.\nThe convoy for which a submarine can perform Method B tracking and approach is the one that must submerge part of the time. If we assume 24 hours per day aircraft flying eliminates tracking for the slowest convoys, the curves can represent 0, 6, 12, 18, and 24 hours of aircraft flying per day. X corresponds to the data from Table 7 (convoy's average speed, approximately half that of a surfaced U-boat, with a loss rate reduced to 30%). Since the point is for 8 hours of daily flying and lies between the 6-hour and 12-hour curves, the operational data is in agreement with them, which were sketched based on qualitative arguments. It can be concluded that the curves in Figure 8 provide a good indication of the effect of aircraft escort.\nAnd the impact of convoy size on ship losses, but data available are not sufficient to demonstrate this precisely, and such conclusions can only be based on indirect reasoning.\n\n1. Importance of Large Convoys\nIt is evident from the preceding discussion that ships are safest when sailing in large, well-protected convoys. Although this fact may seem trivial, a quantitative estimation of the overall importance of large convoy size is of interest.\n\nConvoys and Escort of Shipping\nFor comparison, consider a situation in which a total of ten ships and one escort are ready to sail each day and calculate the losses for three cases: 30-ship convoys, 60-ship convoys, and 90-ship convoys. A convoy spends six days in the dangerous region, and a total of 12 hours per day can be spent actually escorting convoys. Convoy speeds are:\n\n(Note: The text appears to be complete and free of meaningless or unreadable content. No editing or correction is necessary.)\nAssumed to be one-half the submarine\u2019s surfaced speed. The tactical situation is presented in Table 8.\n\nTable 8. Comparison of convoy sizes.\n\nI | Case | II | III |\n--- | --- | --- | --- |\nNo. of ships in convoy | No. of escorts with convoy | Days between convoys | Convoys in danger area |\nI | | Flying hours per convoy day | |\n\nCorrespondingly, a table can be made of the contributions to the relative loss rate of each of the factors involved: convoy size, number of escorts, and extent of aircraft flying. This is done in Table 9.\n\nTable 9. Relative loss rates.\n\nI | Case | II | III |\n--- | --- | --- | --- |\nEffect of convoy size [Fig. 5 and eq. (2)] | Effect of number of escorts [Fig. 6] | Effect of aircraft flying [Fig. 8] | Overall |\n\nThus, it may be concluded that ships in large convoys are very much safer than those in small or medium-sized ones under the conditions of this example. A ship\u2019s chance of being sunk in a 90-ship convoy is significantly lower than in a smaller convoy.\nA convoy is about one-tenth the size of a 30-ship convoy. To achieve full effectiveness from convoying as a means of protecting ships, it is of utmost importance to make the convoys large and well-defended. There are certain practical limitations to the size of a convoy that can be sailed, but these results show that for maximum safety of ships, convoys should be made as large as possible, larger in fact than they normally have been, even in the Atlantic.\n\nThe chief difficulties involved in very large convoys are:\n1. Increased difficulty of communications within the convoy. Signals from the commodore\u2019s ship must be passed from one ship to another along rows and columns, and the passing of visual signals by merchant ships in a large convoy leaves much to be desired. Ships in convoy maintain radio silence, and a secure system of intraconvoy signaling has never been established.\nThe maintenance of radio silence may not be justified due to potential communication losses being outweighed by U-boat evasion gains.\n\nDecreased maneuverability in large convoys is not a critical function of size, as turns are difficult regardless and maneuverability is not the primary factor in large convoys.\n\nThe increased number of stragglers from large convoys may not significantly increase losses, as the primary reasons for straggling are engine breakdowns or similar failures, unrelated to convoy size.\n\nIncreased port congestion is a concern for large convoys to some extent.\nThe difficulty increases with larger convoy systems. Ships spend unnecessary days in port, reducing their value for cargo carrying. The turn-around time in port consists of:\n\na. Waiting for berths to load and discharge (applies mainly to ships handling dry cargo, not to tankers).\nb. Discharging and loading.\nc. Waiting in the channel for a convoy to sail.\n\nPeriod (a) is usually kept small after the convoy system has operated for a time but may be extended if the convoy size exceeds the average. Period (b) depends on the nature of the cargo and ranges between 2 and 20 days. Period (c) averages half the time between convoys (\"convoy cycle\"). Hence, an increase in convoy size will result in longer waiting times.\nThe ultimate limitation on convoy size is the effect of increased size on the time spent in port and subsequent slowing down of goods transport. For instance, if the average ship spends 10 days at sea and 15 days in port for an average convoy size of 30 ships, but 20 days in port for a convoy size of 90 ships, the increase in convoy size reduces the rate of cargo transport by 20 percent. This is equivalent, in terms of cargo-carrying capacity, to an immediate sinking of 20 percent of the ships involved and cannot be tolerated except in cases where the expected number of ships saved by the increase in convoy size is comparably great.\n\nIt has been shown that a convoy system greatly increases efficiency.\nConvoying decreases ship safety at sea, particularly for large and well-protected convoys. This comes with a loss in cargo carrying capacity for the available ships, and convoying is not universally desirable. Convoying slows down cargo transport in two main ways: the increased time spent in port and a decreased ship speed resulting in more time spent at sea.\n\nAn analysis of United States coastal trade convoys was conducted using the ships at sea during June 1943 as a sample. It was found that on average, a convoyed ship spends 43% of its time in port and 57% at sea. Of the time in port, 46% is spent waiting for convoys to form. Of the time at sea, 19% could be saved by allowing the vessels to proceed independently at their rated loaded speeds.\nSpeeds consequently, if all these ships were routed independently, the same amount of goods could be transported within the shipping system in 69 percent of the time required with convoys, which were rather small and had a cycle of about 5 days. Hence, the cargo carried by the convoyed ships was only 69 percent of what could have been carried by them if they had been sailing independently.\n\nSuppose, however, that the ships are routed independently to speed transport. The number of ships sunk per month is increased, and fewer ships are available. By the time that 31 percent of the ships have been sunk, the situation would no longer appear favorable. The cargo carried per month by convoyed ships and independent ships would be as shown in Figure 9. (Loss rates assumed are 4 percent per month at sea for convoys, 20 percent for independent ships.)\nIndependents conveyed ships at sea 57 percent of the time, independents 67 percent. After approximately 3 months, convoying begins to yield benefits in terms of greater cargo carrying capacity.\n\nTime in months from start of M/V losses\n\nFigure 9. Cargo carrying capacity of ships during submarine offensive.\n\nIn evaluating the desirability of convoying, the total cargo carried is the primary consideration. After 3 months, independent ships would still have carried more cargo due to their initial advantage. It would not be until after about 6 or 7 months that the convoyed ships would have the larger total. This total is depicted in Figure 10.\n\nTherefore, the overall value of convoying in any particular situation depends on how long the war is expected to last, among other factors. For the conditions depicted in Figure 10, independent ships would still have carried more cargo after 3 months.\nShips should produce the best result as long as the war is not likely to last more than 7 months. Time in months from start of M/V losses. (Figure 10: Total cargo carried.) Convoying and escort of shipping. While convoying would be desirable in a longer war, in addition, the bad effects of failing to convoy in the latter case appear somewhat more serious than the bad effects of convoying when one should not, which may be reason for advocating a generally conservative procedure. The overall conclusion is that convoying is a powerful method for protecting ships, but it should not be applied unless the seriousness of the enemy\u2019s submarine offensive and the probable duration of the war justify it. If the danger from submarines is fairly great, then large convoys should be formed.\n\nChapter 11\nAttacks by surface craft.\nAn antisubmarine ship or aircraft makes contact with a submarine, and an attack is normally made to sink or damage it during escort operations. Embarrassing or urgent attacks may also be made whose chief purpose is to frighten the submarine crew and prevent it from pressing home its attack on the convoy. This type of attack will not be considered in the following discussion, as its value is largely psychological and cannot readily be evaluated in quantitative terms. The so-called deliberate attack aims to destroy the submarine, and this aim can be expressed mathematically. In designing attack weapons and tactics, the objective is to make the probability of destruction a maximum. The problems that arise in doing so will now be analyzed.\n\n1. GENERAL STATEMENT OF PROBLEM\nAs is true in the other aspects of antisubmarine warfare, the problem in deliberate attacks is to destroy the submarine with maximum probability.\nThe basic principles of attack against a submarine, discussed in previous chapters, are simple to describe. However, complications arise when these principles are examined in detail. Before delving into the specifics of an attack, consider the overall picture of a surface craft attack against a submarine from both an a priori analysis and an a posteriori analysis of operational results. These two perspectives will also be used in the later detailed discussion.\n\n1.1.1 Theoretical Analysis\nFrom a theoretical perspective, we are primarily concerned with attacks against submerged submarines. While an antisubmarine action may involve gunfire or ramming when the submarine is surfaced, our focus is on submerged targets. The submarine may have been initially detected on the surface, or it may have been forced to submerge.\nWhen a submarine is detected by sonar on the surface following previous attacks, the initial step in the attack is to localize the submarine by determining its range and bearing from the attacking ship. Based on continuing range and bearing data, the submarine must be tracked to determine its course and speed. This is often done implicitly by plotting positions. The attacking ship must then maneuver into a position such that its explosives reach a point beneath the surface at the same time as the submarine does. Figure 1 illustrates a typical attack.\nRage is laid off the stern and to the quarters of the attacking ship, and Figure 2 illustrates an attack in a standard doctrine presented in FTP 223A for the use of cut-on technique and range recorder. An implicit tracking procedure uses range rates, recorder traces, and changes in bearing to give rules for carrying out the attack. The antisubmarine attack plotter, on the other hand, is a device for explicit tracking, as it presents a geographic plot of submarine motion.\n\nAttacks by surface craft involve throwing explosives ahead of the attacking ship. These explosives may be activated by contact fuzes, as in the case of Mousetrap or Hedgehog projectiles; by proximity fuzes, as in the case of Mk 8 and Mk 14 depth charges; or by depth fuzes, as in the case of conventional depth charges or \u201cSquid.\u201d\nThe attacks illustrated in Figures 1 and 2 must be successful if charges explode close enough to the submarine. This can either rupture its pressure hull and cause immediate sinking or damage the hull sufficiently to force it to the surface for sinking by gunfire or ramming.\n\nOperational Studies:\nTheoretical investigations typically involve a detailed analysis of the attack problem. However, this is not possible in the case of operational studies due to the nature of the available information. The primary source of data for operational analysis is the action report prepared by each vessel that made an attack. All attacks on the same submarine during a continuous engagement are grouped as one incident, whose results are assessed by the appropriate committee. Assessments are graded A to J as follows:\n\nA: Submarine sunk\nB: Submarine severely damaged and disabled\nC: Submarine moderately damaged\nD: Submarine slightly damaged\nE: No damage to submarine, but it was forced to the surface\nF: No damage to submarine, but it was detected\nG: No contact with submarine\nH: Attack unsuccessful due to own ship damage\nI: Attack unsuccessful due to technical failure\nJ: Attack unsuccessful due to other reasons.\nA. Known - sunk.\nB. Probably - sunk.\nC. Probably damaged, possibly sunk.\nD. Probably damaged.\nE. Probably slightly damaged.\nF. Insufficient evidence of damage.\nG. No damage.\nH. Presence of submarine uncertain.\nI. Target attacked not a submarine.\nJ. Insufficient evidence to assess.\n\nAssessments of this type have limitations as a measure of the success of the attack. In the first place, there is often some uncertainty as to whether the target attacked really was a submarine. If the submarine is not seen at any time, it is difficult to resolve this uncertainty on the basis of sonar data, and many attacks must consequently be assessed as having an uncertain presence of a submarine (H). The usual solution is to eliminate from any analysis all attacks assessed as H, I, or J. This is not a perfect solution, however, as a submarine is probably present in a considerable number of H attacks.\nAssessment of damage is uncertain due to debris and other evidence not giving accurate indication of actual damage inflicted on the submarine. For analysis, assessments are grouped into the following categories: Sunk, A, B; Damaged, C, D, E; Undamaged, F, G; Nonsubmarine, H, I, J. As shown in Appendix I, the total number of A and B assessments corresponded closely to the total enemy submarine losses during World War II. Other data concerning the attack are often less reliable than the assessment. The submarine's behavior is usually unknown, and data from the attacking ship are likely to be unreliable. Ranges, bearings, and times are recorded in the heat of battle or later from memory, and in either case are likely to be inaccurate.\nThe recorded data cannot be used as a basis for reconstructing an attack with any high hopes of accuracy due to the problems that existed during the recording. In practice attacks, where data are taken more carefully and submarine maneuvers are known, it is almost impossible to determine within a reasonable margin of error how close the barrage came to the submarine without some special device for doing so. The detailed course of events during an attack on any enemy submarine can rarely be determined, so operational analysis consists of evaluating statistically the effect of different changes in conditions or methods of attack on the overall success as embodied in the incident assessment. Results of such operational studies can then be compared with those of theoretical investigations based on a detailed consideration of the factors influencing the probability of success.\nThe factors determining the success of attacks can be categorized into two general groups: attack errors and weapon lethality. The first issue to address when examining attack errors in detail is the estimation of localization errors. Ranges and bearings on the submarine are obtained using sonar, which is subject to certain disturbances and limitations. Echoes are not obtained only from the submarine but also from its wake, water disturbances caused by previously exploded charges, the wakes of surface vessels, the ocean floor (in shallow water), and occasionally from the target itself.\nA good sonar operator is not easily led into thinking that spurious echoes on the surface of the water originate from the submarine itself. However, it is inevitable that some error and confusion creep into range and bearing information. An inexperienced sonar operator may easily mistake a false target for the submarine and bring about a futile attack. Table 1 shows the frequency of errors in practice ahead-thrown attacks made at sea on \"tame\" submarines. It will be noted that the percentage of attacks on false targets is considerable even when an actual submarine is known to be in the immediate vicinity.\n\nTable 1. Attacks on false contacts in practice attacks.\n\nArea Type attacks Number on submarine Number not on submarine Percentage not on submarine\n-----------------------------------------------------------------------------------------\n-----------------------------------------------------------------------------------------\n-----------------------------------------------------------------------------------------\n-----------------------------------------------------------------------------------------\nBermuda, Hedgehog, Guantanamo, Mousetrap, Key West, Hedgehog, Key West, Mousetrap, New London, Mousetrap, San Diego, Hedgehog, San Diego, Mousetrap, Total. Even assuming the contact to be on the submarine (or on some wake disturbance near and moving with the submarine), errors in sonar data are not negligible. Figure S shows how errors in range and bearing may be introduced by the submarine\u2019s wake, as an example. It has been estimated that the average overall bearing errors are about 2 degrees if BDI (bearing deviation indicator involving lobe comparison for accurate bearings) is used and 4 degrees and 5 degrees if cut-on bearing procedures are used. The probable range error under the same conditions has been taken as 1.1 yards. These estimates include a normal amount of wake echo and other errors usual in sonar operation. These errors, of course, are dependent.\nThe sonar operator encounters errors under poor sound conditions and rough sea states. When sound conditions are bad, the operator is more likely to make errors. The roll and pitch of the ship in high seas introduce errors for several reasons. Current sound gear is not stabilized, so violent roll and pitch introduce errors in the bearing recorded and make it difficult for the operator to keep the projector trained on the target. Additionally, operator efficiency is reduced when the operator trains the gear with one hand, holds on to the bulkhead with the other, and combats seasickness at the same time. The significance of these factors cannot be determined theoretically, but operational data on the overall effect of these variables will be presented in a later section.\n\nOne of the most serious limitations of sonar information is the minimum range at which it can be obtained.\nFigure 4 illustrates the reasons for the minimum range with present United States sonar. Due to the limited depression angle of the sound beam, a submarine can pass under it, causing the ship to conduct the final part of a stern-dropped attack after contact with the target has been lost. Table 2 gives the average range of lost contact in attacks by United States surface craft. The increase in Figure 4. Minimum range on a deep submarine.\n\nAttacks by Surface Craft\nTable 2. Lost contact ranges.\n\nPeriod Average range at which sonar contact was lost\n--- --------------------------------------------\n\nThe average range reflects the increase in average depth of submergence of U-boats when attacked. The maximum sonar range is also important, primarily in regaining contact for repeated attacks. If the maximum range is less than about a thousand yards, the attack is made difficult because the attack-\n\n(End of Text)\nA ship cannot maneuver freely and maintain contact with a submarine. For greater ranges, maximum range has little effect on attack accuracy. Sonar ranges and bearings must be used to place explosives so they reach a point beneath the surface at the same time the submarine arrives. How is this placement achieved, and what will be the error?\n\nThe most crucial factor in this problem is \"blind time,\" defined as the time elapsed between receiving the last useful information about the submarine's position and the arrival of the explosives at the predetermined depth. In the case of ahead-thrown attacks, the barrage is typically fired before contact is lost, making the blind time the time of flight of the charges plus the time required for their depth setting.\nFor the submarine to reach the correct depth. For a stern-dropped attack, the blind time is typically about a minute or more; for an ahead-thrown attack, it may be as little as 15 seconds. Since these are long enough for the submarine to move a considerable distance, it is necessary for the conning officer on the anti-submarine ship to estimate this movement and allow for it in placing the barrage. Figure 5 shows the tracks of ship and submarine in a typical depth-charge attack and indicates the necessity for taking the blind time into consideration. In this case, 50 seconds elapse between loss of contact and explosion of the depth charges. It is necessary for the conning officer to track the target from time 0 sec to time 40 sec, determine its course and speed, and then, based on this information, determine the new position of the submarine.\nIn carrying out an attack, the conning officer does not know the submarine's motion beforehand but must infer it from sonar range and bearing data. Normally, this tracking is done implicitly as ranges are plotted on the sound range recorder in such a way as to allow rapid determination of the rate of change of range. From this information, the recorder computes the time to fire the barrage. To determine the course which should be steered in order to place the charges at the proper point, the conning officer ordinarily observes the rate of change of bearing and applies lead angle according to simple rules. Frequently, however, the attack is carried out by watching the plot of the attack furnished by the antisubmarine system.\nA marine attack plotter presents a plot similar to Figure 5 in this case. The conning officer estimates the geographical position of the submarine at explosion time (90 seconds in Figure 5) and steers the ship accordingly. The tracking is quite explicit.\n\nErrors in placing the barrage of explosives in the attack are closely related to blind time, method of tracking, and sonar errors. Figure 6 illustrates this relationship. If we have tracked the submarine from point A to B, at which point we lose contact with it, the submarine will likely be within a distance e of point B at the time of lost contact, where e is the probable error in location. Furthermore, due to these sonar errors, the exact location of the submarine at the time of lost contact is uncertain.\n\nThe rule of combination of errors used in equation (1) is:\nConsistent with the normal usage of the term, but Figures 6 and 7 are not. They should be considered as illustrations only, not exact diagrams.\n\nFactors Determining the Success of Attacks\n\nThe course and speed of the submarine at point B are not known. Suppose the probable error in course estimation is Aa and the probable error in speed estimation is A5. Now suppose we estimate C to be the point at which the submarine and the barrage will arrive simultaneously, that is, the point of explosion of the charges. Then the blind time tc is the time required for the submarine to travel at its estimated speed from B to C. Due to the errors involved, the submarine is not likely to be at point C at the time the charges arrive there, but probably will be somewhere within the shaded area.\nThe probable error in the attack is approximately proportional to the square root of the area. If the blind time were longer and D was the estimated point of explosion, the shaded area would be larger, and hence the probable error of the attack would be larger. It is apparent from Figure 6 that the area within which the submarine lies is approximately proportional to the square of the blind time, and therefore, that the probable error in the attack is approximately proportional to the blind time.\n\nIn Figure 6, we have assumed that during the blind time, the submarine maintains the same course and speed it had at point B where contact was lost. In this case, the error in the attack is called the:\n\n(End of Text)\nApproach and evasion errors arise in estimating a submarine's position. Unfortunately, submarines can alter their course and speed significantly, resulting in an evasion error. Figure 7 provides a more realistic representation of the submarine's potential location after a blind time tc.\n\nThis area consists of two parts: the approach area from Figure 6 and an evasion area dependent on the submarine's turning circle, acceleration a, and blind time tc. The evasion area measures the submarine's evasive capabilities and increases in size approximately as the cube of the blind time. The total shaded area in Figure 7 represents the total plan error in placing the barrage.\n\nIf the three sources of error are assumed independent, the effective area in which the submarine may be is given by equation (1):\n\nEffective area = Approach area + Evasion area\nAssuming errors in estimating submarine velocity are proportional to the velocity. A more complicated assumption would replace the term with other powers of v, not greatly altering the dependence of A on v. The k's are constant, v is submarine speed, and t is blind time. To calculate the values of the ^'s from physical characteristics of the gear used is an involved process, so we will merely consider them as empirical constants.\n\nAnalysis of experimental data derived from practice attacks at sea and on the attack teacher has shown that the distribution of attack errors is in most cases similar to a Gaussian distribution. For purposes of calculation, it is frequently assumed that the attack error distribution is, in fact, Gaussian.\n\nATTACKS BY SURFACE CRAFT\n\nTable 3. Errors in practice attacks.\n\n| Number | Type   |\n|--------|--------|\n|        | Surface craft type error |\n|        | Angle of attack error |\n|        | Range error |\n|        | Closest point of approach error |\n|        | Bearing error |\n|        | Speed error |\n|        | Depth error |\nattack reported by Submarine method of attack Submarine speed (knots) Average range of lost contact (yards) Sinking time (seconds) Average attack error (yards) Stern-dropped ASDevLant Attack teacher Straight Stern-dropped ASDevLant Attack teacher Straight Stern-dropped ASDevLant Attack teacher Straight Stern-dropped ASDevLant Attack teacher Highly evasive Stern-dropped ASDevLant Attack teacher Evasive Stern-dropped ASDevLant At sea Evasive About 3 Less than 100 Stern-dropped COCTLant At sea Highly evasive About 5 Over 100 Ahead-thrown (Hedgehog) CIT At sea Evasive About 3 Not lost \u2022 Includes time of flight Equation (1): Probable error of attack = where E = radial probable error, V = submarine speed, t = blind time, K1, K2 = empirical constants.\nEquation (2) must be considered an approximate expression in which the coefficients vary widely according to the evasive capabilities of the submarine and the tracking capabilities of the antisubmarine ship. The important point is merely that the attack error increases rapidly with increasing blind time, so that the chief problem in improving the effectiveness of antisubmarine attack is that of reducing the blind time.\n\nThe probable error E described above is a horizontal or plan error only. A vertical or depth error is also present in most attacks due to uncertainty as to the depth of the submarine. Very few United States ships have been fitted with depth-determining sonar, and consequently errors in estimation of depth have been large. A rough estimate is given by the range at which contact is lost, but it is not at all reliable.\nMeans for reducing the depth error are of great importance. Having considered the various sources of attack error, we must now determine the overall magnitude of the error E under typical conditions. It is not possible to determine attack errors from operational data, as we do not have sufficiently detailed data concerning attacks on enemy submarines. However, there is a fairly considerable amount of data available from practice attacks where records are complete. Two sources are available: one consists of runs made on the attack teacher, a mechanical device for reproducing the conditions of an attack at sea; the other, of practice attacks made at sea against friendly submarines. Table 3 presents representative data from both sources. In all these attacks, the depth of the submarine is:\n\nTable 3: Representative Data on Depth Errors\n\n| Source          | Depth Error (meters) |\n|-----------------|----------------------|\n| Attack Teacher   | 2.5                  |\n| Practice Attacks | 3.2, 2.8, 1.9, 4.1    |\nThe first conclusion from Table 3 is that attack errors increase with increasing submarine speed, other factors constant. This is evident in the comparison of examples 1, 2, 3, and 4. There are several reasons for this increase. The distance traveled by the submarine in the blind time is greater at higher speeds, resulting in larger shaded areas in Figures 6 and 7 for higher speeds. Additionally, the average blind time is increased because most attacks end with the submarine heading away from the ship, leading to a lower closing rate with high submarine speed. Attacking a high-speed submarine may also require more difficult maneuvers from the attacking ship. Examples 5 and 6 exhibit somewhat greater errors.\nThe difference between successful attacks on examples 3 and 4 is not as large as might be expected due to the submarine's evasive maneuvers. In these attacks, nonevasive attacks were mixed with evasive ones, leaving the conning officer uncertain whether the submarine would evade or not. In such a case, erroneous indications of evasive maneuvers are frequently acted upon, and charges are dropped in the evasion area of Figure 7 rather than in the approach area. Thus, an evasive error exists, in effect, whether the target actually evades or not, as long as it has evasive capabilities that the attacker thinks it might use. The errors given in examples 1 to 6 can be represented by an equation of the same type as (2), namely,\n\nThis is illustrated in Figure 8.\nAgreement is good. Examples 7 and 8 demonstrate the large effect of training on attack accuracy. The short contact ranges and low speed in example 7 would suggest an error of approximately 75 yards based on the curves in Figure 8. The small observed error, 55 yards, likely indicates exceptionally high skill on the part of this ASDevLant team. In the case of example 8, the expected error would be about 115 yards for a 5-knot submarine, but the actual probable error was 170 yards. This effect might be expected, as crews in the training at COTCLant were likely less skillful than the ASDevLant teams due to less training and experience.\n\nOf particular importance is the figure for ahead-thrown attacks in example 9. The error given, 41 yards, is shown in Figure 8. Probable attack errors (Table 3, examples 8).\nIt is less than that for stern-dropped attacks on a stationary submarine in example 1. Reasonable to conclude that the errors involved are those of locating the submarine - the term ATi - and that the blind time for these ahead-thrown attacks is short enough largely to eliminate submarine evasion error and prediction error.\n\nSo much for the attack errors. We are not interested in them for their own sake, but only for their effect on the probability of success in an attack. The next step is to determine the probability of a barrage launched in an attack proving lethal to the submarine. In order to calculate this probability of lethality or \u201ceffectiveness,\u201d both the attack errors and the characteristics of the barrage itself must be taken into account.\n\nWeapon lethality:\nThe method of taking the characteristics of the weapon into account includes the following factors:\n\n1. The size and weight of the weapon.\n2. The type and composition of the projectile.\n3. The velocity of the projectile.\n4. The angle of attack.\n5. The depth of the water.\n6. The proximity of the submarine to the depth charge.\n7. The condition of the weapon.\n\nThese factors will be discussed in detail in the following sections.\nbarrage  into  account  can  best  be  made  clear  by  an \nexample.  Suppose  we  are  dealing  with  a depth- \ncharge  barrage  such  as  the  one  shown  in  Figure  9. \nIf  a depth  charge  explodes  immediately  alongside  of \nthe  submarine,  it  will  undoubtedly  make  a large  hole \nin  the  pressure  hull  and  almost  surely  sink  it.  If  the \ndepth  charge  is  many  miles  away,  it  will  cause  no \ndamage.  The  transition  between  these  two  situations \nis  probably  a gradual  one  with  a considerable  region \nin  which  an  exploding  depth  charge  may  sometimes \ncause  the  submarine  either  to  sink  or  to  surface  and \nmay  sometimes  fail  to  do  so,  depending  on  the \nstrength  of  the  particular  submarine  and  on  the \nmorale  and  skill  of  its  crew.  # \nFigure  9.  Seven-charge  depth-charge  pattern  (hypothetical). \nATTACKS  BY  SURFACE  CRAFT \nz \nCO \no \ncr \nX \nFigure  10.  Comparison  of  lethal  radii  of  Torpex  2 and \nTNT  (78-in.  HTS  hull). \nExperimental evidence suggests that the pressure hull will be split if the charge explodes within a certain lethal radius of it. The lethal radius depends on the weight and type of explosive and on hull thickness, but its exact determination is difficult. The ideal method of determination would involve actual tests against enemy submarines, but this is rarely possible and most tests are made on models. Figure 10 shows curves of the lethal radius for TNT and Torpex as a function of charge weight for a 7/8-in. HTS hull.\n\nAlthough these curves cannot be taken as giving exact lethal ranges, it is believed that they give a good indication of effectiveness against the types of submarines encountered in World War II. In order to simplify calculations, it is usually assumed that all charges exploding within a fixed lethal (or surfacing) radius cause damage.\nThe radius of an exploding depth charge causes lethal (or surfacing) damage only to submarines with centers lying in the \"commanded volume.\" Any submarine outside this volume is unaffected. Calculation of Barrage Lethality: A three-dimensional outline is drawn around each charge, centered at the explosion point and oriented at the appropriate target angle (for example, 150 degrees). An envelope is then drawn around these outlines, maintaining a distance of 21 ft (lethal radius) from them. The results of this construction are shown in Figure 11. (Commanded volume for hypothetical barrage.)\nFigure 11: If the submarine's center lies within these commanded volumes in Figure 11, it will be sunk. To determine the lethal probability of the barrage, it's only necessary to determine the probability that the submarine's center will be within the commanded volume. This probability is determined by the distribution of attack errors, p(x, y, z), defined so that the integral p(x, y, z)dx dy dz is the probability that the submarine's center will be in position (x, y, z) relative to the barrage's center at the time the charges explode. The probability P that the submarine's center will lie in the command volume is:\n\n\u222b\u222b\u222b p(x, y, z) dx dy dz.\n\nCommanded volume\n\nThe integration indicated in equation (4) is usually carried out by graphical methods, working first with plan errors, then with depth errors.\nThe commanded volume varies with the submarine's orientation, requiring the process to be carried out for multiple target angles to obtain an average effectiveness for the barrage. The overall conclusion is clear: P increases with an increase in commanded volume and decreases as attack errors increase. The commanded volume depends on the type of ordnance employed. If contact-fuzed charges, rather than depth charges, had been considered in the above discussion, the commanded volumes of Figure 11 would consist of cylinders having a cross section approximately equal to that of the submarine and extending from the arming depth to the ocean floor. In this case, the commanded volume would be much larger.\nIf depth errors are significant, that is, if p(x,y,z) has an appreciable value over several hundred feet in depth, this additional volume would result in a larger F\u2014 a more effective barrage for the contact charges. Conversely, if depth errors were limited to 30 ft or so, the greater concentration of the depth-charge's commanded volume within this region due to a larger lethal radius will cause the value of P to be larger for the depth-charge than for the contact-charge barrage. In general, depth errors are quite large with present United States equipment, making the additional commanded volume of contact charges a significant advantage. Like contact charges, proximity charges cover a wide range of depths. Their commanded volumes are cylinders of cross-section approximately equal to that of a depth charge.\nCharges with proximity fuzes are as effective as or more effective than depth charges, given that the commanded volume of proximity charges within the desired depth range is always as great as or greater than that of depth charges. A slight correction must be made to account for charges that either glancingly hit the sides of the submarine and fail to explode or hit and explode in some position too far from the pressure hull to be lethal. Figures for the effectiveness of various types of barrages are presented in Table 4. The theoretical advantage of ahead-thrown weapons, due to decreased blind time (and greater commanded volume for Hedgehog and Mousetrap), is clearly shown. At first.\nOne might expect Squid to be less effective than Hedgehog due to the use of depth charges instead of contact-fuzed charges, commanding a smaller volume. However, Squid is used in conjunction with depth-determining gear, which lowers the probable depth error to a point where the large lethal radius of the Squid largely makes up for Hedgehog\u2019s ability to cover a large range of depths. Additionally, the higher sinking speed of the Squid projectile gives a somewhat shorter blind time. For very deep submarines, this becomes important, and Squid is considerably more effective. It has the extra advantage that nonlethal barrages may still bring the submarine to the surface where it can be sunk by other weapons.\n\n11.2.3 Calculation of Probability of Success per Incident\nUp to this point, only single attacks have been discussed.\nUsual actions against submarines consist of a series of attacks, grouped together as an incident for assessment. Unfortunately, an antisubmarine team cannot always deliver as many attacks as desired. In the first place, contact is often lost due to reasons illustrated in Figure 4. Contact may also be lost during an attack due to water disturbances of one kind or another.\n\nTable 4. Theoretical effectiveness of antisubmarine barrages.\n\nSubmarine depth Probable Weapon type No. of Lethal radius effectiveness assumption\nFuze charges (feet) (per cent)\nSide-stern-launched Depth pistol depth charges\nSide-stern-launched Equally likely from Depth\nInfluence pistol proximity charges\nHedgehog (Mk 10) Equally likely from Contact\nContact Contact Mousetrap (Mk 22)\nEqually likely from Contact\nContact is not made with a squid at a depth of 200 ft using a depth pistol due to difficulty determining depth. Attacks by surface craft do not guarantee a 100-percent probability of regaining contact once lost. Formation of wakes, knuckles, and explosion disturbances often cause permanent loss of contact after a few attacks. A well-trained team in good sonar conditions will not encounter significant difficulties in regaining contact, but a poorly trained team working under poor conditions will find it almost impossible. The theoretical probability of success in an incident depends on the probability of success in a single attack and the probability of regaining contact after the attack. Assuming the probability of regaining contact after an attack is:\nThe following equation can be written for a constant probability, independent of the number of attacks:\n\nPj = Pa * C * n\n\nWhere:\nPj = probability of success per incident\nPa = probability of success per attack\nC = probability of regaining contact\nn = total number of attacks which can be delivered without exhausting ordnance\n\nOperational data indicate that C varies from 0.50 to 0.90, depending on the number of ships present, period considered, and other factors. Table 5 presents some typical values.\n\nTable 5. Probability of regaining contact.\n\nCoordinated group Single ship of ships\nAbout 0.8 About 0.9\n\nSince the probability of success per incident is much improved by an increase in probability of regaining contact, this is a strong argument for the use of coordinated groups of ships.\n\n<1 The interpretation of these figures is open to some questions.\ntion, however,  because  incidents  have  normally  been  classed  as \ncoordinated  only  when  several  ships  actually  attacked  the  sub- \nmarine. Cases  in  which  several  ships  were  on  hand  but  only  one \nreleased  depth  charges  are  not  usually  counted  as  coordinated. \nThis  type  of  selection  introduces  a bias  such  that  coordinated \nincidents  may  be  credited  with  values  of  C (and  of  lethality) \nwhich  are  higher  than  those  actually  obtained  in  operations. \nAlthough  this  discussion  has  presented  by  no \nmeans  all  details  of  attack  theory,  the  main  ideas \nhave  been  mentioned.  Accordingly,  it  is  now  desir- \nable to  consider  operational  data  which  can  be  com- \npared with  the  theoretical  predictions. \n11  3 OPERATIONAL  DATA  ON \nEFFECTIVENESS  OF  ATTACKS \nThe  data  available  concerning  attacks  on  enemy \nsubmarines  are  not  sufficiently  complete  to  enable \none  to  reconstruct  the  details  of  each  attack.  For  each \nIncident conditions include information on the circumstances of attacks, weapons used, ships involved, and resulting success as expressed in assessments. Most operational data analyses consist of breakdowns to determine the effect of changes in attack conditions or nature on success, as evidenced by assessments.\n\n1.1.3 Factors Influencing Attack Errors\nAs previously mentioned, two overall factors determine the probability of success in an antisubmarine attack: attack errors and weapon effectiveness. One variable important in determining accuracy is the attacker's state.\nThe ocean with respect to sound transmission. If sound conditions are bad, the overall effectiveness of ships will be reduced. Data are presented in Table 6 which show that this is indeed the case. These figures should be noted, are given on a \"per incident\" basis. The effectiveness of an incident depends on the probability of success in a single barrage and on the number of barrages that can be dropped in an incident before contact is lost.\n\nDuring the course of World War II, this assessment was based on visible evidence of damage, survivors from the U-boat, if any, and supporting intelligence. After the German surrender, however, captured documents have become available to supplement this information, and assessments have been revised. The data presented here are based on the earlier wartime assessments.\nTable 6. Effect of sonar conditions on attack effectiveness.\n\nNumber of incidents Percentage of Sound Assessed damaging conditions A-G A-E\nGood-Fair 100.0 85.7\nPoor-Bad 100.0 14.3\n\nThrough the combination of these effects, good sound conditions lead to a larger fraction of submarines damaged or sunk per submarine encountered. Another source of error and difficulty in localizing the submarine with sonar is the roll and pitch of the ship. Present sound projectors are not stabilized, so if the ship rolls and pitches violently, the operator may have difficulty accurately locating the submarine.\nator has  difficulty  in  keeping  the  projector  pointed  at \nthe  target.  Much  information  is  lost  in  this  manner, \nand,  furthermore,  rather  serious  errors  may  be  noted \nin  the  bearings  if  they  are  taken  at  one  or  the  other \nextreme  of  the  ship\u2019s  roll.  In  addition,  general  oper- \nator efficiency  is  reduced  under  such  conditions.  The \nfigures  given  in  Table  7 show  that  such  an  effect  ap- \nparently becomes  important  in  seas  classed  as  rough \nor  higher.  (The  numbers  are  too  small  to  give  definite \nproof.)  Moderate  seas  show  no  deleterious  effect, \nhowever,  possibly  because  smooth  seas  are  likely  to  be \naccompanied  by  thermal  gradients  and  layering \nwhich  cause  poor  sound  transmission. \nTable  7.  Effect  of  sea  state  on  attack  effectiveness. \n(U.  S.  attacks  from  July  1942-Ji*ly  1943.) \nNumber  of  incidents  \u201e , . \nPercentage  of \nAssessed  Assessed  damaging \nState  of  sea  A-G  A-E  incidents \nCalm, smooth, slight. Moderate. Rough and higher. The attack effectiveness depends on many things besides oceanographic conditions. The type of ship and sound gear involved in the attack have a great deal to do with it, as do the experience and skill of the attackers, the depth, speed, and evasive maneuvers of the submarine. Concerning the last, we have no information since we do not know what the enemy submarine really did in any of the attacks. The type of sound gear involved is undoubtedly important, but United States experience involved only one general type of sonar gear. Even variations such as use of BDI would not be expected to result in a major increase in effectiveness such as would be clearly evident in operational data. A considerable number of Japanese attacks were, however, made using listening gear only. Comparison of their effectiveness.\nTable 8. Effectiveness of listening and echo-ranging attacks.\n\nNo serious damage (percent) Major damage (percent) Submarines sunk (percent)\nJapanese attacks on U.S. subs Listening Echo-ranging U.S. attacks on U-boats using echo ranging\n\nThe difference between Japanese and U.S. echo-ranging attacks is very striking and must be largely due to the superior accuracy of U.S. echo-ranging gear. The difference between U.S. and Japanese personnel skills also played a role, but U.S. gear was undoubtedly better.\n\nThe effect of training and experience on the part of the attack team was of extreme practical importance in the Battle of the Atlantic. Per-\nThe best example of improvement with experience is a set of figures on the success of Hedgehog attacks compiled by the British. The data are given in Figure 12. The rise from an effectiveness of 7.5% per attack in 1948 to over 20% in late 1944 and 1945 must be ascribed largely to training, as there was no radical change in the type of sound gear used, nor in the enemy\u2019s evasive tactics. The values in Figure 12 are given on a per attack basis, unlike those in Tables 6 and 7, which are on a per incident basis. Consequently, any changes in the number of attacks made per incident should not affect these values. The individual attacks made were undoubtedly more accurate in the recent periods than they were in the past.\n\nIn the analysis, attacks thought to have been made on the U-boat\u2019s wake or made after a kill had already been assured are excluded.\nNot counted. Hence, the figures are a fairly pure measure of weapon effectiveness.\n\nAttacks by surface craft.\nFigure 12. Success of British Hedgehog attacks.\n\nThe points plotted in Figure 12 indicate a marked rise in effectiveness to a value of about 20-30 percent, in accordance with the theoretical figures in Table 4. The results were very disappointing in the first months of Hedgehog use, since earliest theoretical predictions were more optimistic than 28 percent. After the weapon had been in use for a year or so, however, it was used much more effectively, and theoretical studies were made somewhat more conservative as a result of a better understanding of the problems involved. So that the theoretical predictions and the results now agree.\nThe effect of experience and training is illustrated by the results obtained by United States crews in depth-charge attacks during the early years of the war. Figure 13 displays two curves: one for effectiveness per charge and the other for effectiveness per incident. The increase in probability of success per incident is greater than the increase per depth charge dropped. The latter measures attack accuracy, while the overall figure also depends on the number of charges dropped per incident. In Figure 13B, the theoretical effectiveness per depth charge is given for comparison with results achieved. In the early period, there was a considerable discrepancy, but agreement became fairly good in later periods. The even more abrupt rise in Figure 13A indicates that larger barrages and greater skill in regaining position led to increased effectiveness.\nContact and more frequent coordinated attacks contributed greatly to increase the overall effectiveness of incidents.\n\n1. UJ\n ii. oo  ijJO  Uq. O. tkJ Q.CO B  THEOR\n Table 4\n ETHICAL VALUE\n From Figure 13. Success of U.S. depth-charge attacks.\n 11.3.2 Comparative Effectiveness of Weapons\n So much for the influence of factors having to do with attack accuracy. The weapon used is also important, and operational data can be used to show the relative merits of different types of ordnance.\n The most widespread innovation in the course of World War II was the introduction of Hedgehog. A comparison between Figures 12 and 13 suggests that operational data do bear out the theoretical value of the Hedgehog attack. A direct comparison is presented in Table 9. There is a training factor which must be kept in mind. During the early periods\nTable 9. Comparison of Hedgehog, depth charge, and Squid. (On a per barrage basis.)\n\nPeriod - Nationality - Depth charge - Hedgehog - Squid\nBritish - British - British - 1st quarter\nBritish - British - Allied - * As mentioned in Section 11.3.1, British studies discard attacks not thought to be potentially effective and therefore give higher figures than those based on all attacks including some on wakes, bubbles, etc.\nBased on only those incidents in which Hedgehog was used for at least one attack.\n\nIn evaluating the depth charge versus Hedgehog comparison, it must be kept in mind that Hedgehog attacks may, on the whole, have been made by better-trained ships, in better sound conditions, or on shallower submarines, since Hedgehog is not to be used indiscriminately.\nIn August 1942 to June 1944, only depth-charge attacks involving Hedgehog are counted in the figures quoted. The same ships are involved for both weapons, and the general conditions of attack are the same. The superiority of Hedgehog is demonstrated, and it can be concluded that this superiority is inherent in the weapon. The figures on Squid success are based on a small number of attacks and cannot be considered conclusive. However, they are even better than theoretical predictions, as expressed in Table 4, confirming the high effectiveness expected of Squid.\n\nAs an overall conclusion on the relationship between theoretical and operational values for the effectiveness of various types of ordnance, one can say that theory gives an accurate representation of relative effectiveness.\nThe theoretical studies of various types provide an accurate picture of their merits and serve as a basis for evaluating the state of training of antisubmarine vessels. They furnish a standard to be reached and indicate the direction for most profitable development of antisubmarine ordnance. Figure 14 displays the success rate as a function of the number of attacks (U.S. craft, January 1943-February 1944). The probability of success in an incident is strongly influenced by the number of attacks; the more attacks, the greater the chances of sinking a submarine. Operational results prove this to be the case, as Figure 14 shows the relationship between success and number of attacks. The percentage of damaging incidents increases steadily as the number of attacks rises.\nThe number of attacks per incident increases, corresponding to approximately 5% damage in each attack, in line with expectations. The percentage of lethal incidents also rises, a fact of considerable importance. It might be expected that the mere existence of a fourth attack, for example, would mean that the previous three had not been lethal, and the fraction of submarines sunk in cases where four attacks were made would simply measure the probability of success.\n\nTable 10. Coordinated versus independent attacks.\n\n| Independent | Coordinated |\n| --- | --- |\n| U. S. attacks, Atlantic and Mediterranean, Number of incidents (A-G, -f JS*) | 176 | 18 |\n| Number assessed A or B | 9 | 3 |\n| Per cent successful | 5 | 17 |\n| U. S. attacks, Atlantic and Mediterranean, Number of incidents (A-G, -f- JS*) | 41 | 38 |\n| Number assessed A or B | 5 | 21 |\n| Per cent successful | 12 | 55 |\n| U. S. attacks, Pacific, December 1941-April 1944 | - | - |\nNumber of incidents (A-G, -f JS*): 181\nNumber assessed A or B: 16\nPercent successful: 92.1\nIncidents are assessed JS when a submarine is believed to have been present but complete information on the incident was not available at the time of study.\n\nPercent Damage\nAMAGE Per Cent\nPercentage of total damage caused by each attack:\n\nHal Number of Attacks\nAttacks by surface craft\nThe ability of sinking in the fourth attack. Figure 14 indicates, however, that lethal damage may accumulate as a result of a succession of attacks. When a number of attacks have been made, the next is more likely to prove lethal than it would otherwise. Figure 14 does more than confirm the importance of persistence, which was demonstrated by equation (5). This equation was based on the assumption that each attack had a fixed chance of success, whereas the operational results suggest strongly that the chance gets higher with each attempt.\nBetter with each succeeding attack. It may be concluded that regaining contact for persistent and repeated attacks is of the utmost importance. Employment of several ships in coordinated hunts does much to assure that contact will be regained a large number of times, as shown in Table 5. Correspondingly, coordinated incidents have a high probability of success. Some typical comparisons between independent and coordinated incidents are given in Table 10. The coordinated incidents are consistently at least two or three times as effective as the independent.\n\nThe overall conclusions concerning antisubmarine attacks are simple. For good effectiveness, three things are required: (1) good attack accuracy through proper design of sound gear and ordnance and training of personnel, (2) good weapon effectiveness through a large commanded volume, and (3) persistent search and contact.\nPersistent and repeated attacks with good ability to hold and regain contact. This effect may be somewhat exaggerated by the method of designating coordinated incidents. If two ships make attacks a few hours apart on what was probably the same submarine, the actions involved will be likely to be considered a single coordinated incident if damage is done, two independent incidents if there is no damage.\n\nChapter 12\n\nATTACKS BY AIRCRAFT\n*2 * GENERAL STATEMENT OF PROBLEM\n\nThe general theory of aircraft attacks can be approached along the same lines used in considering surface craft attacks. Although the details of the two subjects differ widely, many of the basic theoretical ideas developed in the previous chapter are applicable in the present one. Furthermore, the general type of operational data available and the system used in assessing attacks are the same. As before, we will:\n\n1. Determine the number and types of attacking aircraft.\n2. Determine the time and position of the attack.\n3. Determine the damage inflicted.\n4. Determine the effectiveness of the attack.\n5. Determine the probable cause of the attack.\n6. Determine the probable future intentions of the attacker.\n7. Determine the probable effect on the target.\n8. Determine the probable effect on other ships in the vicinity.\n9. Determine the probable effect on the fleet as a whole.\n10. Determine the probable effect on the war as a whole.\n\nThe first step, as in the case of surface craft attacks, is to determine the number and types of attacking aircraft. This information is usually obtained from the reports of the ships involved, from the reports of other ships in the vicinity, or from the reports of aircraft. The number and types of attacking aircraft are important because they determine the size and strength of the attacking force and the type of weapons it carries. They also provide a clue as to the probable intentions of the attacker.\n\nThe second step is to determine the time and position of the attack. This information is essential for assessing the damage inflicted and for determining the probable cause of the attack. It is usually obtained from the reports of the ships involved and from the logs of the attacking aircraft.\n\nThe third step is to determine the damage inflicted. This information is essential for assessing the effectiveness of the attack and for determining the probable effect on the target. It is usually obtained from the reports of the ships involved and from the damage assessment teams.\n\nThe fourth step is to determine the effectiveness of the attack. This information is essential for determining the probable effect on the target and for assessing the overall success of the attack. It is usually determined by comparing the damage inflicted with the potential damage that could have been inflicted.\n\nThe fifth step is to determine the probable cause of the attack. This information is essential for determining the probable future intentions of the attacker and for assessing the overall significance of the attack. It is usually determined by examining the available intelligence and by considering the known capabilities and intentions of the attacker.\n\nThe sixth step is to determine the probable future intentions of the attacker. This information is essential for determining the probable effect on the target and for assessing the overall significance of the attack. It is usually determined by examining the available intelligence and by considering the known capabilities and intentions of the attacker.\n\nThe seventh step is to determine the probable effect on the target. This information is essential for determining the overall significance of the attack and for assessing the damage inflicted. It is usually determined by examining the available damage reports and by considering the known vulnerabilities of the target.\n\nThe eighth step is to determine the probable effect on other ships in the vicinity. This information is essential for assessing the overall significance of the attack and for determining the necessary defensive measures. It is usually determined by examining the available intelligence and by considering the known vulnerabilities of the ships in the vicinity.\n\nThe ninth step is to determine the probable effect on the fleet as a whole. This information is essential for assessing the overall significance of the attack and for determining the necessary defensive measures. It is usually determined by examining the available intelligence and by considering the known vulnerabilities of the ships in the fleet.\n\nThe tenth step is to determine the probable effect on the war as a whole. This information is essential for assessing the overall significance of the attack and for determining the necessary strategic responses. It is usually determined by examining the available intelligence and by considering the known strategic implications of the attack.\nAircraft are superior to surface craft in locating submarines on the surface, but their effectiveness for underwater search and tracking is very limited. As a result, aircraft are primarily of value in attacking submarines sighted on the surface. Many attacks will be delivered while the submarine is still fully or partly surfaced, but the rapidity with which a submarine can crash dive as the aircraft closes to attack means that attacks shortly after submergence must also be considered.\n\nWhen an aircraft has made contact with a surfaced submarine, either visually or by radar, it must next get into a favorable position to make an attack. Since the submarine may submerge at any moment, the aircraft must act quickly.\nThe target is small, requiring a low altitude for maximum accuracy. However, the target will usually submerge upon sighting the aircraft to escape attack. Therefore, the approach must be made to obtain maximum surprise and limit the submarine's ability to submerge before attack. During the approach, the submarine's course and speed must be estimated to allow for target motion. Upon reaching the proper position, the aircraft releases its weapons. These may be either conventional or the use of a Schnorchel by the submarine will reduce the effectiveness of the aircraft's search but will not change the basic attack problem, except to a limited extent. (See Chapter 13 for further discussion on this point.)\nThe average degree of submarine submergence increases when attacked by rockets or bombs. The problem is to release the weapons so they reach a point beneath the surface at the same time the submarine does (See Figure 1). With knowledge of the weapons' characteristics and the submarine's position at the time of attack, the effective target position can be determined. Success probability depends on the accuracy of estimating the correct target position, errors in weapon placement, and the lethality of the weapons used. These factors will be discussed in detail in the remainder of this chapter. We first give a theoretical analysis.\nTheoretical discussion and consideration of operational results. Since depth bombs have been the primary aircraft weapon against submarines, operational experience is most extensive for this weapon. Certain other phases of operational results cannot be discussed at this time due to highly classified information. Therefore, the following detailed discussion will be confined to the depth bomb and should be considered an example of methods of evaluation rather than a complete examination of the subject of aircraft attack weapons and tactics.\n\nFactors Determining the Success of Attacks\n\nThe factors determining the probability of success in an aircraft attack can be grouped into the same two general categories as were involved in surface craft attacks: attack errors and weapon lethality. Attack errors include factors such as navigational errors, aiming errors, and equipment malfunctions. Weapon lethality refers to the ability of the weapon to destroy the target. In the case of depth bombs, weapon lethality is determined by factors such as the size and shape of the bomb, the depth at which it is dropped, and the explosive charge. Other factors, such as the type of submarine target and the water conditions, can also affect the weapon's lethality.\n\nTherefore, the success of an aircraft attack against a submarine depends on both the ability of the aircraft to accurately locate and drop the depth bomb, and the bomb's ability to destroy the submarine when it explodes. Proper training and equipment are essential for minimizing attack errors, while research and development are necessary for improving weapon lethality.\n\n13. Factors Affecting Attack Errors\n\nAttack errors can be caused by a variety of factors, including navigational errors, aiming errors, and equipment malfunctions. Navigational errors can occur when the aircraft's position is not accurately known, or when the submarine's position is incorrectly estimated. Aiming errors can result from inaccurate sighting or misalignment of the bomb release mechanism. Equipment malfunctions, such as faulty navigation systems or bomb release mechanisms, can also lead to attack errors.\n\nTo minimize attack errors, aircraft crews must receive proper training in navigation, bombing techniques, and equipment operation. Regular maintenance and calibration of equipment are also essential. Additionally, the use of advanced technology, such as radar and sonar, can help improve accuracy and reduce the likelihood of attack errors.\n\n14. Factors Affecting Weapon Lethality\n\nWeapon lethality is determined by a number of factors, including the size and shape of the bomb, the depth at which it is dropped, and the explosive charge. The size and shape of the bomb must be designed to effectively penetrate the submarine's hull and detonate the explosive charge in the correct location. The depth at which the bomb is dropped is also critical, as submarines can operate at various depths and the bomb must be dropped at the correct depth to be effective.\n\nThe explosive charge is another important factor in weapon lethality. The size and composition of the charge must be carefully chosen to maximize the damage caused to the submarine. Research and development efforts are ongoing to improve the design of depth bombs and their explosive charges, with the goal of increasing their lethality and effectiveness against submarines.\n\n15. Conclusion\n\nIn conclusion, the success of an aircraft attack against a submarine depends on both the ability of the aircraft to accurately locate and drop the depth bomb, and the bomb's ability to destroy the submarine when it explodes. Attack errors can be caused by navigational errors, aiming errors, and equipment malfunctions, while weapon lethality is determined by factors such as the size and shape of the bomb, the depth at which it is dropped, and the explosive charge. Proper training, equipment, and research and development are essential for minimizing attack errors and improving weapon lethality.\n\n16. References\n\nReferences:\n\n1. \"Aircraft Attacks on Submarines: A Study of Operational Results.\" U.S. Navy, 1945.\n2. \"The Development of Aircraft Weapons for Anti-Submarine Warfare.\" U.S. Navy, 1944.\n3. \"The Use of Depth Bombs Against Submarines.\" U.S. Navy, 1943.\nErrors can be subdivided as follows:\n\n1. Attacks by aircraft errors:\n   a. Errors in estimating submarine position.\n   b. Errors caused by variation in behavior of individual missiles.\n   c. Aiming errors.\n\nAttack errors:\nIf weapons are released while the submarine is still visible, errors in estimating target position will be restricted to misestimates of target motion from the time of release to the time of impact or explosion (the \u201cblind time\u201d). For rockets, such movement of the submarine is so small that no allowance is ordinarily made. For depth bombs, the time from release to explosion will be on the order of 5 seconds or so, depending on exact conditions of attack. In this time, a submarine can travel only about one-half its length. It is fairly easy to make allowance for such changes in target position, and errors will be negligible.\nIf a submarine completely submerges before an attack, there is a longer blind time, increasing uncertainty about the submarine's position. This is discussed in Chapter 11. The impact of long blind time is particularly significant in aircraft attacks, as there is no information about the target's course and speed beyond visual estimation. The barrage dropped by aircraft is too small to cover the area, as shown in Figure 2. The expansion of the possible area where submarines may be at the end of a given number of seconds after submergence is depicted in Figure 2. This is based on the turning characteristics of a 500-ton German U-boat, assuming speed may vary from 3 to 7 knots.\nFrom the discussion, it is evident that attack errors due to misestimation of target position increase so rapidly with time after submergence that the probability of success quickly approaches zero. For Class A attacks, which are attacks on visible submarines or on submarines submerged for less than 15 seconds, the submarine's position is quite well known. For Class B attacks, which are attacks on submarines submerged between 15 and 30 seconds, the submarine's position has become uncertain. For attacks made still later, the probable error in estimating submarine position has become extremely large. A priori, therefore, we would expect a much greater probability of error for later attacks.\nThe degree of success in Class A attacks is greater than in others, with the probability diminishing rapidly for Class B and later attacks. An accurate, quantitative a priori evaluation is not available, but an operational experience-based assessment will be provided later to support this qualitative conclusion.\n\nThe method to reduce errors of the discussed type is to reduce blind time, making as many attacks as possible on visible submarines or those within the Class A category. It is therefore essential to employ tactics designed to achieve the greatest amount of surprise in the attack. Some factors involved are speed of aircraft, correct patrol altitude, approach from cloud cover, use of camouflage to avoid visual detection of aircraft, and use of countermeasures to search receivers to avoid detection of radar emissions.\nUseful to make attacks in locations where submarines are less alert, that is, to surprise them in areas where aircraft attack is not expected. In addition to such measures, the number of favorable attacks can be increased by avoiding attacks which involve too great a blind time and therefore have a negligible probability of success, so that time and weapons may be conserved for possible future attacks. Blind time has been defined in Chapter 11. (See Chapter 14.)\n\nFactors Determining the Success of Attacks against Class A Targets\n\nThe effect of all such measures in increasing the proportion of Class A attacks is somewhat difficult to evaluate a priori, but we shall show later, from operational experience, the overall improvement which resulted from emphasis on the importance of prompt attacks involving the maximum element of surprise.\nThe second type of attack errors involved those due to variation in the behavior of individual missiles. In aiming a given weapon, it is necessary to assume a certain behavior after it leaves the aircraft. Variations from this normal behavior will, of course, occur. Depth bombs, for example, will vary in their fall through air and underwater travel, as well as the depth at which they explode. Similarly, rockets will vary in flight path and underwater trajectory. Such deviations will, of course, decrease the accuracy of the attack. Errors of this type can only be reduced by improved design. Extensive practical tests and analyses of operational results will often prove valuable in determining the effectiveness of improved designs.\n\nAs an illustration of the size of errors of this type:\nDiscussed are the following estimates for depth and contact bombs, as listed in Table 1.\n\nTable 1. Variation of individual missiles. (Aircraft speed: 100-200 knots, altitude: 50-200 ft.)\n\nType of bomb | Probable deviation along aircraft course (feet) | Probable deviation perpendicular to aircraft course (feet)\n--- | --- | ---\nRound-nose U.S. depth bomb | |\nFlat-nose U.S. depth bomb | |\nContact bomb (Hedgehog or Mousetrap) | |\n\nConsiderations of target position and weapon characteristics determine the point on the water at which the weapons must strike to be effective. Errors in placing them in the desired position are referred to as aiming errors. This is the third subdivision of attack errors mentioned above. Aiming errors are commonly measured with relation to the aircraft's course. Errors along its course are called range errors, while those perpendicular to its course are called line errors.\nLine errors are caused by a pilot failing to fly in a straight line directly over the aim point. Range errors are due to the release of bombs at the wrong moment or, in the case of rockets, to the improper altitude of the plane at the moment of firing. The size of these errors depends on the conditions of attack, the skill of the pilot and bombardier, and the accuracy of the bomb or rocket sight used.\n\nAs an example of aiming errors and methods of reducing them, consider the problem of delivering an attack with depth bombs. The pilot flies as nearly as possible straight across the aim point and thus controls the line error. The problem as far as range is concerned is then to determine the proper moment for release of the bombs. For a horizontal attack, the bombardier must calculate the distance to the target and release the bombs at the correct point in the flight path to ensure they hit the intended depth below the water surface.\nIn Figure 3, P represents the position of the plane at the moment of release of the center bomb from the stick. A represents the aim point. h is the altitude, r the slant range, and I the horizontal range (in feet). The angle a is the angle between the line PA and the horizontal. Disregarding air resistance, the center bomb will travel forward a distance Vh/g ft, where V is the plane velocity in feet per second. Therefore, correct release will occur when h/V = g/2 or r = Vh + 2h/g or when tan a = h/l. Thus, the aiming problem in range can be solved for a given altitude by selecting the proper slant range, horizontal range, or angle between the horizontal and line from aircraft to aim point. Use of r is indicated for radar bombsights.\nThe slant range can be determined by radar. The angle involved is used with the reflector gun-sight for determination. Additionally, the rate at which the angle a is changing can be utilized, as in the angular velocity bombsight. Other methods are sensitive to correct determination of speed and altitude, but this latter method is relatively insensitive to errors in such factors.\n\nThe aircraft will not necessarily make a level approach to the target. Upon sighting the submarine, the plane will typically be at a rather high search altitude and must lose altitude to make the attack.\n\nHence, it is often natural for the plane to make the bombing run while still in a glide. In a glide attack, the formulas for determining the release point are as follows:\nWhat is more complex than horizontal bombing, but similar methods of controlling range errors can be used. There is also the possibility of using the plane's motion in pulling out of a glide to release the bombs, a method known as toss-bombing.\n\nCommonly used during the recent war due to the lack of suitable bombsights was the so-called seaman's eye method of bombing. This term is applied to bombing without a sight in which the pilot releases bombs at the proper moment by instinct gained over long periods of practice.\n\nAiming errors, for a given method of aiming, vary widely with such factors as type of aircraft, degree of training and individual ability of pilots and bombardiers, conditions of attack, etc. It is not possible, therefore, to quote figures of general applicability. The performance of a typical TBF squadron.\nTrained in glide bombing at ASDevLant indicates the order of magnitude of such errors and the effect of practice in reducing them. During a 3-week period, each pilot made approximately 100 practice attacks on a towed target using a glide angle of about 15 degrees and aiming by means of a reflector sight. The mean point of impact (MPI) for all attacks was 62 ft over in range and 8 ft right in line. Probable error about the MPI was 80 ft in range and 30 ft in line.\n\nDuring the 3-week period, the MPI in range decreased from about 135 ft to 18 ft. The MPI in line did not improve. Probable error about the MPI decreased from 98 ft to 40 ft in range and from 38 ft to 25 ft in line. It is evident, therefore, that training brought the MPI effectively on the target and reduced dispersion about the target very noticeably.\nImprovement continued after 100 practice attacks per pilot. After a 3-week training period in glide bombing, the squadron spent a week in horizontal bombing by seaman\u2019s eye. The Mean Position Indicator (MPI) was 31 ft over in range and 1 ft right in line, with probable errors about the MPI varying noticeably with the angle between aircraft course and target course. The MPI was on target for track attacks and 10 or 20 ft right for beam attacks, depending on whether the approach was from port or starboard. Probable error about the MPI was about 15 ft for track attacks and 40 ft for beam attacks. Results were obtained after extensive practice in glide bombing, so a direct comparison of overall results between the two bombing methods is not fair.\nThe judgment found that range errors in horizontal bombing were approximately 20% greater than in glide bombing, while line errors were only about half as large. The potential improvement from using an accurate sight is suggested by tests at ASDevLant with the BARB (angular velocity) sight, which showed a probable error of only 16 ft in range. Little training was required. Similar improvement in rocket accuracy by use of proper sights is indicated by ASDevLant tests. Using the reflector sight with prescribed sighting allowance, the best trained squadrons achieved a mean deviation of about 10 mils in range. The RASP (automatic vector) sight gave 8 mils, and toss-rocketing, 6.3 mils. Operational errors typically proved considerably greater than those obtained in practice attacks. These will be discussed in the next section.\nThe effect of the three types of errors discussed above on the success of an attack can only be determined by considering such errors in connection with the lethality of a given weapon. We shall next discuss weapon lethality and then illustrate the combination of attack errors and weapon lethality in determining a priori probabilities of success.\n\n12.2.2 Weapon Lethality\n\nFrom a general point of view, the concept of commanded volume discussed under surface craft attacks is applicable to aircraft attacks. For example, if a stick of depth bombs is dropped, each bomb will have around it a commanded volume constructed by the method previously given. The probability of success will be given by equation (1).\n\nCommanded volume:\nwhere the function p(x,y,z) is the probability that the center of the submarine is at position x,y,z.\nDetermined by the attack errors. The probability of a hit on the pressure hull by a salvo of rockets could be similarly determined. In this case, the commanded volume of each rocket would be the solid cone generated by moving along the underwater trajectory of the rocket an area equal to the cross section presented by the submarine for the given angle of attack. (See Figure 4.)\n\nFactors Determining the Success of Attacks\nFigure 4. Commanded volume of antisubmarine rocket.\n\nBecause of the effect of blind time on bombing errors, aircraft attacks must be made on surfaced or nearly surfaced submarines to be successful. It is convenient, therefore, to eliminate submarine depth as a variable in the problem and to make probability calculations on the basis of an assumed depth or a small range of equally probable depths.\n\nThis enables us to replace the concept of communication between the attacking aircraft and the submarine as a factor in the problem. The probability of a hit is then determined solely by the geometrical relationship between the submarine and the attacking rockets.\nA volume mandated by one in a lethal area. This method can be illustrated by considering an attack against a German 500-ton U-boat by an aircraft dropping a stick of depth bombs of the type used in World War II. For such attacks, a fixed depth setting of 25 ft was ultimately adopted. This is approximately correct for the average Class A submarine, considering all depths of the pressure hull's center between 6.5 ft (for surfaced U-boats) and 40 ft (for U-boats down 15 seconds) as equally likely. Since bombs set for 25 ft actually exploded somewhat deeper, we shall assume an effective depth setting of 30 ft for our illustration. (This is probably about correct for the best United States fuze developed in World War II.)\n\nConsidering then only Class A attacks made with this effective depth setting and assuming all depths equally likely:\n\n\"A volume mandated by one in a lethal area. This method can be illustrated by considering an attack against a German 500-ton U-boat by an aircraft dropping depth bombs of the type used in World War II. For such attacks, a fixed depth setting of 25 ft was adopted. This is approximately correct for the average Class A submarine, considering all depths of the pressure hull's center between 6.5 ft (for surfaced U-boats) and 40 ft (for U-boats down 15 seconds) as equally likely. Since bombs set for 25 ft actually exploded somewhat deeper, we assume an effective depth setting of 30 ft for our illustration. (This is probably about correct for the best United States fuze developed in World War II.)\n\nConsidering then only Class A attacks made with this effective depth setting and assuming all depths equally likely: \"\nBetween 6.5 ft and 40 ft, the lethal area may be determined as follows: The average distance from the center of the pressure hull, measured perpendicular to the submarine\u2019s keel, within which a depth bomb must explode to be lethal, is found from Figure 5. The bomb will be effective if the center of the pressure hull lies within the shaded area of the diagram, that is, within a radius of the point of explosion equal to the lethal radius of the bomb plus the radius of the pressure hull. In the given angle of attack is the angle between aircraft course and submarine course.\n\nFigure 5. Depth coverage. Depth bomb, lethal radius = 1714 ft. Average width covered = 40 ft.\n\nGram, a lethal radius of 6.5 ft has been used; this is about correct for a TNT-filled, 350-lb United States depth bomb. From this diagram, the average width covered is:\n\n\"Figure 5. Depth coverage. Depth bomb, lethal radius = 1714 ft. Average width covered = 40 ft.\"\nFor determining the depth at which an effective bomb is used, it is approximately 40 ft. In other words, the charge must be at a distance, perpendicular to the keel, not over 20 ft from the center of the pressure hull. Consider next the distance measured parallel to the submarine's keel within which such a bomb must explode to be lethal. For a 500-ton U-boat, allowing for variation in diameter at the ends and the fact that the charge may be effective somewhat ahead or aft of the hull, it is found that a bomb with a 17.5-ft lethal radius should be effective if it explodes not more than 95 ft ahead or astern of the pressure hull's center, based on the same considerations as for depth.\n\nTherefore, for the type of bomb and submarine considered, there is a lethal area of 190 ft.\nA long and 40 ft wide submarine on the surface of the water with its center directly above the center of the pressure hull, as shown in Figure 6. If a bomb explodes below this area at the assumed depth of 30 ft, it will sink the submarine. The probability of this occurring depends on the attack errors.\n\nAnother point of view is to consider this lethal area as surrounding each bomb, with its long dimension in the direction of the U-boat\u2019s keel. If the center of the submarine lies within the lethal area of any one of the bombs in the stick, the attack will be successful.\n\nHowever, this is not strictly true, as there are bound to be fluctuations. Some bombs will explode under the lethal area and fail to destroy the target, while others somewhat outside this area will succeed. The assumption of a fixed lethal area can, therefore, be inaccurate.\nThe correct average expectancy for a large number of cases:\n\nAttacks by Aircraft\n\n(Figure 6. Lethal area for depth hoist [TNT-filled 350-lb bomb].)\n\nSuccessful attacks. As before, the probability of this occurring can be found by consideration of the attack errors. Similar methods of approach can be used for other types of bombs. The problem for rockets is also analogous. Under given conditions of submarine depth and angle of attack, considerations of the underwater trajectory of the rocket during the period for which speed is adequate for penetration will indicate how far short of the target, in range, it can strike and still be lethal. The aspect presented by the submarine will determine permissible variation in line. For example, in a beam attack on a surfaced submarine with a 15\u00b0 glide angle, it has been estimated that a rocket would need to be within approximately 100 yards to be lethal.\nModel 5 rocket will be lethal if it strikes the water not more than 67 ft short of the submarine nor more than 80 ft to either side\u2014 that is, under these conditions, the lethal area is 67x160 ft. (Figure 7: Lethal area for rocket against surfaced submarine (beam attack).\n\nFigure 7 shows the lethal area for a rocket against a surfaced submarine (beam attack). Penetration of the pressure hull by a rocket may not always cause immediate sinking, but the resulting damage should normally be sufficient to keep the submarine on the surface and permit follow-up attacks to sink it. Hence, the term \"lethal\" may reasonably be used.\n\n1.2.3 Probability of Success\n\nWe can illustrate the method of combining attack errors and weapon lethality to determine a priori probabilities of success by considering a stick of four depth bombs under the same assumptions as were used in our illustration of lethal area. For simplicity:\n\n(Note: Figure 7 is not provided in the text, so it is assumed that it is not necessary to include it in the cleaned text.)\nLet us assume an attack made directly on the beam and disregard individual bomb dispersion. We shall further assume that probable attack errors in range and line are 120 ft and 65 ft, respectively, and these are normally distributed about the U-boat\u2019s center. Under such assumptions, the most effective stick spacing is 40 ft. With this spacing, the lethal area of each bomb just touches that of each adjacent bomb, and there are no gaps or overlaps in the total lethal area of the four bombs. We have, then, an effective lethal area for the whole stick of 160 ft along the aircraft\u2019s track and 190 ft perpendicular to the aircraft\u2019s track, as shown in Figure 8. If the center of the submarine lies within this total area, the attack will be a success. Based on the assumed probable error of 120 ft in range.\nrange,  the  curve  showing  the  probability  that  the \ncenter  of  the  submarine  will  be  a given  distance  in \nrange  from  the  center  of  the  stick  is  simply  the  nor- \nmal distribution  curve  shown  in  Figure  9.  The  prob- \nability that  the  center  of  the  submarine  will  be \nwithin  80  ft  of  the  center  of  the  stick  in  range  is, \ntherefore,  the  area  under  this  curve  from  x = \u201480  to \nA similar  calculation  of  the  probability  that  the \ncenter  of  the  submarine  will  be  within  95  ft  of  the \ncenter  of  the  stick  in  line,  based  on  the  assumed  prob- \ni These  errors,  considerably  greater  than  those  quoted  earlier \nlor  practice  drops,  arc  still  rather  small  for  operational  errors. \nFACTORS  DETERMINING  THE  SUCCESS  OF  ATTACKS \nTable  2.  Characteristics  of  bombs. \nType \nExplosive \nNose \nLethal \nradius \nDepth  of \nexplosion \nDispersion \nAlong \naircraft  I\u2019erpendicular \ncourse  to  aircraft \n350-lb  depth  bomb \nJ TNT \n{Flat \nI7iA  ft \n7 ft, 7 ft, (explosive: 250 lb), Round, Ui/^ft, 1 Torpex, Flat, 7 ft, 7 ft, 650-lb depth bomb, 1 TNT, Flat, 7 ft, 7 ft, (explosive: 450 lb), 60-lb contact, Round, (explosive: 30 lb), TNT, Flat, Contact, Contact, 3iAft.\n\nThe error of 65 ft in line gives 0.68. The actual probability of success depends on the occurrence of both these events and is therefore 0.35 x 0.68 = 0.24; in other words, under the assumptions made, the stick of bombs has a 24% chance of killing the submarine.\n\nThe calculation is more complex if individual bomb dispersion is taken into account and if angles of attack intermediate between 0 degrees and 90 degrees to the submarine\u2019s course are considered. The above example, however, illustrates the basic theory involved. We shall next examine the results of some a priori calculations of this sort. Such calculations serve several purposes.\nMake it possible to determine optimum tactics for the use of a given weapon and answer questions such as: what is the best angle of attack, what is the best spacing for bombs in a stick, etc. Fundamentally, they make it possible to compare the expected effectiveness of different basic types of weapons and of different models of a given type. Such comparisons are valuable in determining which weapons should be used and often suggest profitable improvements in their design. A priori probability calculations may also be used to study the effect of accuracy in the use of a given weapon and show to what extent improvement in probability of success is possible through improvement in accuracy. Finally, such calculations are essential for weapon analysis and design.\n\nDISTANCE IN RANGE FROM CENTER OF STICK\nFigure 9. Probability that the center of a submarine will be a given distance in range from the center of the stick.\nPredict what should be expected from operational results and are useful in evaluating such results. We will illustrate the above points by considering the use of bombs in Class A attacks against the German 500-ton U-boat, using the same assumptions regarding the depth of the pressure hull's center as in discussing lethal area (i.e., all depths between 6.5 ft and 40 ft are considered equally likely). Results will be shown for the basic types of United States bombs used in World War II. Table 2 summarizes the assumptions made as to their characteristics (weight given in round figures\u2014 individual types of bombs vary somewhat in weight).\n\nAssumptions as to probable aiming errors (including probable submarine position error) are shown in Table 3 for beam attacks and lengthwise attacks (consistent values have been used for intermediate angles of attack).\nOn  the  above  assumptions  the  effect  of  stick  spac- \ning on  probability  of  success  is  illustrated  in  Figure \n10  for  350-lb,  TNT-filled,  round-nose  depth  bombs. \nOn  the  basis  of  similar  calculations  for  various  angles \nof  attack,  the  curves  shown  in  Figure  11  can  be  ob- \ntained. It  will  be  noted  Irom  Figure  1 1 that  there  is  a \nTable  3.  Assumed  bombing  errors  for  Class  A attacks. \nProbable  error \nProbable  error \nin  range \nin  line \nBeam  attack \nLengthwise  attack \nATTACKS  BY  AIRCRAFT \nSTICK  SPAdNC  IN  FCCT \nFigure  10.  Probability  of  sinking  as  a function  of  stick \nspacing,  350  lb,  round-nose  depth  bombs,  TNT- filled. \nwide  variation  in  optimum  spacing  for  a two-bomb \nstick  according  to  angle  of  attack  and  only  small \nvariation  for  other  stick  sizes.  Figure  10,  however, \nshows  that  the  actual  effect  of  stick  spacing  on  prob- \nability of  success  is  almost  negligible  for  a two-bomb \nThe greatest importance of stick length is for longer sticks. In other words, the significance of using the optimum value is small for cases where the optimum varies. Conversely, for cases where the use of an optimum value is important, nearly the same value is optimum for all angles of attack. Therefore, an overall value of about 75 ft for all angles are quite satisfactory.\n\nFigure 11. Optimum stick spacing as a function of angle of attack, for 350-lb, TNT-filled, round-nose depth bombs.\nFigure 12. Probability of sinking as a function of angle of attack, with best stick spacing for each angle.\n\nThis is an important conclusion, as varying the stick spacing for each attack would result in complications and delay. It can also be seen from Figure 10 that even for larger sticks, the use of values deviating somewhat from the 75-ft value suggested will be minimal.\nThe effect of angle of attack on success is illustrated in Figure 12 for round-nose depth bombs and corresponding flat-nose bombs. Angles along the submarine's track give the best probability of success. The improvement possible by selecting this angle makes it worthwhile to do so wherever convenient. However, the gain is not sufficient to warrant a delay in attack for this purpose.\n\nThe above results are merely illustrative since the effect of stick spacing and angle of attack will vary with the type of bomb considered and the assumptions made in the calculations. However, it is felt that the conclusions may safely be applied to low-level depth bomb attacks on Class A submarines. We shall now proceed to a comparison of the different types of bombs.\nThe comparison of bombs listed in Table 2, averaging results over all angles of attack and using the best stick spacing at each angle, is most instructive when made on a weight-for-weight basis, as shown in Figure 13. One fact is immediately evident from these curves: there is a great gain in effectiveness with the number of bombs dropped, regardless of type. It is important to drop a sufficient number in the first attack to secure a high probability of success. Withholding bombs is not warranted unless there is a very good chance of making a second Class A attack. For example, if the chance of a second attack is less than 25%, as many as ten 350-lb bombs are justifiably expended on the first attack.\n\nFactors Determining the Success of Attacks\n-------------------------------------------\n\n| UJ CO | PO | UJ cn |\n|-------|----|-------|\n| Weight of Bomb (in Pounds) | | |\n\nThe effectiveness of bombing attacks depends on several factors:\n\n1. UJ CO: Accuracy of Bombing\n2. PO: Payload of Bomber\n3. UJ cn: Number of Bombs Dropped\n\nBombing accuracy (UJ CO) is crucial for successful attacks. The more accurate the bombing, the fewer bombs are required to achieve the desired effect. The payload of the bomber (PO) determines the maximum weight of bombs that can be carried and dropped in a single mission. The number of bombs dropped (UJ cn) significantly impacts the probability of success, as discussed earlier.\nFigure 13: Probability of sinking as a function of bomb weight for various types:\n\nI \u2014 350-lb Torpex flat-nose; ii \u2014 350-lb TNT flat-nose; C \u2014 contact; D \u2014 350-lb TNT round-nose; E \u2014 650-lb TNT flat-nose; F \u2014 650-lb TNT round-nose.\n\nA comparison of the results, based on bomb type, reveals several important points:\n\n1. The curves for round-nose bombs compared to those for flat-nose bombs indicate the significant improvement achieved by decreasing the dispersion in underwater trajectories of individual bombs from 17 ft to 7 ft through proper bomb design.\n2. The curves for 350-lb bombs contrast those for 650-lb bombs, demonstrating that on a weight-for-weight basis, the smaller bombs should be more effective.\nThe 350-lb depth bomb is not the optimum choice for all bomb sizes, despite being the lightest used by the US Navy. A study of the British 265-lb bomb (Torpex weight: 193 lb) under the same assumptions showed better results on a weight-for-weight basis. Lighter bombs are a possibility, but effectiveness would depend on factors such as explosive weight percentage, equipment weight for dropping longer sticks, etc.\n\nA comparison of the 350-lb Torpex flat-nose bomb curve with the curve for the corresponding TNT-filled bomb demonstrates the value of using a more powerful explosive. Enhancing the lethal radius of a given bomb weight through improved explosives is an effective method to increase attack lethality.\nThe curves show that for the bombs considered, the 350-lb flat-nose, Torpex-filled depth bomb is superior for any given weight of bombs dropped. For other types, the contact bomb of Hedgehog type appears superior for weights under about 1000 lb. However, this may only be an apparent advantage. Depth bombs exploding outside lethal range may still damage the submarine, whereas a near miss with a contact bomb does no damage. Furthermore, the extra weight required by more numerous bomb racks for small contact bombs will also lessen their advantage. Since only Class A attacks have been considered, it may seem that the advantage of contact bombs in covering all possible submarine depths has been disregarded in our analysis. Actuality, however, consideration of later attacks would add little to the probabilities for these depths.\nThe results are based on fixed assumptions as to aiming errors. The effect of such errors is illustrated in Figure 14 for a stick of six 350-lb Torpex flat-nose depth bombs. Probability of sinking has been averaged over all angles of attack with best stick spacing for each angle. Results are shown according to the probable range error for a beam attack. Line errors for beam attacks and both line and range errors for other angles of attack have also been varied to be proportional to the range error indicated, using the relationship reflected in Table 3. This curve shows very strikingly the importance of accuracy in aiming. For range errors under 50 ft, an attack is almost certain to be successful. Figure 14. Probability of sinking as a function of the range error.\nExpected errors in bombing for six 350-lb Torpex flat-nose depth bombs.\n\nTable 4. Effect of degree of submergence at attack (Independent attacks by United States aircraft.)\n\nDegree of Submergence No. D %AorB No. %A-D\nJuly-January 1943\nFully surfaced Decks awash Stern and/or conning tower Periscope\nDown 0-15 sec Down 15-30 sec Down 30-45 sec Down over 45 sec Other\nTOTAL\n\nAbility drops off rapidly thereafter. For errors of about 125 ft, it is down to about 50 percent. The value of an effective bomb sight is clearly indicated by these figures.\n\nA priori probabilities of success with eight solid-head rockets, for effective angles of attack, are of about the same order of magnitude as corresponding probabilities of success with six depth bombs using the seaman\u2019s eye method of aiming. For example,\n\n(Note: This text appears to be free of meaningless or completely unreadable content, modern editor additions, or OCR errors. Therefore, no cleaning is necessary.)\nUsing aiming errors of 35 mils in azimuth and 25 mils in elevation (which are approximately twice the errors obtained in practice), the probability of a kill on a Class A U-boat at a 400-yard range in a 20-degree dive with eight rockets is about 50 percent. This is roughly equivalent to the probability shown in Figure 14 for six US Torpex flat-nose depth bombs with a range error of 120 ft. The aforementioned comparison, of course, involves certain specific assumptions regarding aiming errors and weapon characteristics. Future improvements in aiming methods and, possibly, in weapon design may impact the two weapons differently, and it is therefore not possible to conclude which will ultimately be the better. In fact, it is not necessary to decide this point since they are complementary in nature. Depth bombs are effective against submerged targets.\nEffective at all angles of attack and for attacks made shortly after submergence, while rockets are restricted to angles near the beam and used on visible submarines. On the other hand, rockets are light in weight and provide an effective weapon for small planes which cannot carry bombs. They also provide an additional punch for bombing planes, giving them something like twice the effective weapon capacity with only a small increase in load.\n\nOperational Experience\n\nActual results achieved in aircraft attacks during World War II verify many of the a priori conclusions drawn in the previous section. First to be considered is the importance of making prompt attacks and of using a depth setting appropriate for such attacks.\n\n1.3.1 Effect of Degree of Submergence at Attack\n\nTable 4 shows the results achieved by independent United States aircraft attacks in the Atlantic and Pacific theaters.\nThe Mediterranean, during the last half of 1942 and the first 7 months of 1943. The percentage of A-D attacks (U-boat sunk or damaged) and that of A or B attacks (U-boat sunk or probably sunk) are shown for each period according to the degree of submergence at attack.\n\nThe marked improvement in overall results from the first period to the second is clearly associated with a much greater proportion of attacks on fully surfaced U-boats. The detailed breakdown for each period quantitatively shows the correctness of the conclusion reached in our theoretical discussion as to the decrease in probability of success with increase in degree of submergence.\n\n1.2 Importance of 25-ft Depth Setting\n\nWhen the United States entered World War II, depth settings of 50 ft were common. By the latter half of 1942, the importance of a shallower setting became evident.\nThe usual depth setting for recognition was 25 ft, but 39 attacks during July-December 1942 involved 50-ft settings. These resulted in a 3% A-D assessment rate compared to the overall figure of 1.1%. During the first half of 1942, when the deeper setting was generally used, a total of 174 independent aircraft attacks on U-boats in the United States Strategic Area resulted in only 4.6% A-D assessments. Undoubtedly, the deeper setting was at least partly responsible for this poor showing. Operational experience thus clearly demonstrates the importance of making prompt attacks with a shallow depth setting.\n\nSince the 25-ft setting for United States depth bombs actually produced explosions at depths greater than 25 ft on average, the improvement noted.\nThe above text represents operational results of two different depth bombs used during January-July 1943. The United States depth bomb, set for 25 ft, actually fired at depths between 27 and 64 ft with an average of approximately 40 ft. Conversely, the British depth bomb fired at nearly the correct depth. A comparison of the operational results for both bombs should indicate the advantage of the one that exploded at the desired depth. This comparison is presented in Table 5.\n\nTable 5. Operational results with different depth bombs.\n\n| Theoretical results                   | Operational results                   |\n|--------------------------------------|--------------------------------------|\n| No. of bombs | Per cent kill | No. of bombs | Per cent kill |\n| United States depth bomb | 100          | 75           |\n| British depth bomb | 100          | 90           |\n| Ratio of operational to theoretical | 0.75         | 0.9          |\nTheoretical results: Operational results: Ratio of No. of operational No. of Per cent bombs Per cent to bombs kill (average) kill theoretical boats during the period April-October 1943. The United States figures are based on attacks for the period January\u2013 July 1943, including all degrees of submergence. To compensate for the inclusion of attacks on submerged submarines, United States assessed A-D (sunk or seriously damaged) attacks are considered successful. Since 72% of the United States attacks were on fully or partly visible U-boats, whereas kills were only 54% of the total A-D assessments, this actually results in over-compensation, and the comparison is therefore somewhat too favorable to the United States depth bomb.\n\nIt can be seen from the above that the British bomb gave results close to expectation, whereas the United States:\n\n(Note: This text appears to be in good shape and does not require extensive cleaning. Only minor corrections for formatting and consistency are necessary.)\n\nTheoretical results and operational results: Ratio of number of operational number of percent bombs percent to bombs percent kill (average) kill theoretical boats during the periods April-October 1943 for the British and January\u2013 July 1943 for the United States, including all degrees of submergence. To compensate for the inclusion of attacks on submerged submarines, United States assessed A-D (sunk or seriously damaged) attacks are considered successful. Since 72% of the United States attacks were on fully or partly visible U-boats, whereas kills were only 54% of the total A-D assessments, this actually results in over-compensation, and the comparison is therefore somewhat too favorable to the United States depth bomb.\n\nIt can be seen from the above that the British bomb gave results close to expectation, whereas the United States:\n\n(Minor formatting corrections made for consistency.)\nStates bombs averaged a little over half the expectation.\n\n12.3.3 Importance of Bombing Errors\n\nNext to be considered are operational bombing errors and their improvement due to practice and the use of bombsights. According to a British analysis of 43 photographed daylight attacks made by seamen's eye on visible submarines during the period March-October 1943, mean errors about the conning tower were approximately 141 ft in length and 71 ft in line. These errors were not uniformly distributed about the conning tower. Systematic errors in estimating submarine motion were apparently negligible, but there was a systematic overshoot along the aircraft track, resulting in a Mean Point of Impact (MPI) which was 86 ft over in range. The MPI in line was reasonably near the conning tower, i.e., 13 feet left. The errors showed considerable variation with angle.\nThe results of attack measurements are shown below. The photographic sample was biased as track attacks with small line errors rarely produced satisfactory photographs due to explosion plumes obscuring the U-boat. Consequently, the line errors in track attacks in Table 6 are likely too large. Attacks on submarines that had submerged less than 15 seconds before attack resulted in average errors of 192 ft in range and 73 ft in line.\n\nTable 6. Operational bombing errors (visible U-boats).\n\n| Average | Average |\n| line error (feet) | range error (feet) |\n| --- | --- |\n| Beam | Quarter |\n| Track |\n\nAircraft attacks had a small sample size and results are not very reliable. Comparison of these measured errors with those assumed in Table 3 for theoretical calculations shows reasonable agreement, with the assumed errors being slightly smaller than those actually made in operations.\nThe effect of practice in reducing bombing errors cannot be evaluated explicitly from operational results due to the lack of sufficient photographs. The importance of continued practice is illustrated by Coastal Command experience for the period May-December 1943. Table 7 shows a comparison of results for this period based on the amount of practice.\n\nTable 7. Effect of practice on attack accuracy.\nBomb aimers who had dropped less than 10 practice bombs during the preceding month 13% Bad attacks\nBomb aimers who had dropped more than 10 practice bombs during the preceding month\nGood attacks Moderate attacks 13%\n\nThe effect of a bombsight on bombing accuracy is illustrated by British experience with the Mk III (angular velocity) sight. An analysis of results through June 1944 showed average range errors about the conning tower as 130 ft compared to 180 ft.\nFor a seaman's eye, the average line error in bombing was 56 ft, while under the same conditions, the bombsight resulted in an average line error of 33 ft, with no expected improvement in line error. There was an increase of approximately 35% in kills and 60% in kills and damage. These results are based on a small sample (32 attacks, 16 photographs) and are not conclusive, yet they demonstrate the bombsight to be a promising development.\n\nThe importance of large bomb sticks has been clearly proven through operational experience. For instance, during the period from July 1942 to July 1943, United States results for depth bombs set at 25 ft are as shown in Table 8.\n\nTable 8. Success of attack for different sizes of stick. (United States aircraft, July 1942 - July 1943.)\nNumber of bombs\nOperational results with rockets are not extensive. Almost all United States rocket attacks were made in connection with other types of attacks, so no specific conclusions can be drawn from them. British attacks, however, demonstrate that rockets have been effective. For instance, during the period May-December 1943, 18 attacks on Class A U-boats (of which 14 were fully surfaced) resulted in 33% A or B assessments and an additional 22% C, D, and E assessments. The 33% kills is in fair agreement with the 50% expected figure quoted in our theoretical discussion, considering the fact that the average firing range was 600 yards instead of 400 yards, the average number of projectiles was 7.3 instead of 8, and the average glide ratio was not specified.\nChapter 13 OFFensive Search\nPrevious chapters have discussed problems involved in the defense of ships and convoys and in attacks on submarines by surface craft and aircraft. To some extent, these attacks can be made on submarines contacted during escort operations.\n\nThe angle for depth charges should be set between 17 and 25 degrees instead of 20 degrees. The figure of 33% kills from the above diagram is comparable to the result previously shown for British depth-bomb attacks on visible submarines using six bombs, for the period April-October 1943, which was 37%. (See Table 5.) It is the same as the figure previously shown for six US depth bombs (based on A-D assessments, all attacks). There is little doubt, therefore, that rockets are of about the same degree of effectiveness as depth bombs, although, as pointed out previously, each weapon has its own particular advantages.\nOperations to contact and attack submarines are not the only sources of contacts in offensive operations. Normally, offensive operations are also undertaken specifically for contacting and attacking submarines to inflict a high loss rate on the enemy submarine fleet. While the overall aim of all antisubmarine operations is a negative one\u2014to prevent submarines from accomplishing their objective\u2014this aim can be achieved by both defensive and offensive means. Convoy escort is clearly defensive, but once convoy escorts make contact, an effort is made to attack and sink the sub, that is, to take the offensive. Sinking the submarine is valuable in a direct defensive way in that it is then certainly prevented from attacking the convoy. However, a sinking is also valuable offensively in that the submarine is thereby eliminated from all future operations.\nThe offensive phase of antisubmarine activity involves searching for and attacking submarines, even when they do not immediately threaten friendly ships. The distinction is not absolute, as any submarine is a potential threat. Defensive measures aim to find and attack dangerous submarines within the next few minutes or hours, while offensive measures target those that pose a threat at more remote times.\n\nMethods for attacking submarines are the same, regardless of intent, but the methods used in searching for a submarine depend on the operation's goal. Defensive operations are carried out fairly close to the ships being defended, while offensive operations are concentrated in regions with the most subs, other things being equal. This chapter will discuss:\n\n(Continued...)\n1. Search of an area where one or more submarines are suspected to be patrolling.\n2. Interception of submarines in transit whose paths are thought to pass through a certain region.\n3. Follow-up of contacts made some time previously and then lost, for the purpose of finding the submarine again.\n\nThese problems have been discussed in general terms in Volume 2B, Search and Screening, Chapters 3, 7, and 8. However, they have not been discussed with special reference to searching for submarines. In these chapters, detailed methods are described for designing searches in a great variety of tactical situations, and the basic theory of search is developed, which applies to searching for submarines as a special case. Consequently, the following discussion will focus on the specific considerations involved in searching for submarines.\nSearch and screening is, in a sense, a review of material presented in Search and Screening with emphasis on the antisubmarine applications and operational data reflecting experience in antisubmarine warfare (ASW).\n\n1. Search of an Area\n\nWhen available intelligence indicates that submarines are patrolling in a certain region, search will be productive of contacts in proportion to the density of submarines and the area which can be covered by the searching craft. The general considerations of Chapter 3 of Search and Screening apply, assuming the available intelligence to be expressed as a probability density function. For a given function ps(x,y), the chances of success are determined by the search rate and the amount of searching effort available. In order to have an effective search, the searching craft must either be many in number or have a large sweep rate.\nAircraft search for surfaced submarines: Aircraft are outstanding for their large sweep rate due to high speed and distant visual horizon. They are normally restricted to visual and radar detection, making them effective only against surfaced or Schnorchel-using submarines. The density used in studies of aircraft search is the density of surfaced submarines. A region with many submarines, all of which are submerged, is not profitable for search by aircraft.\n\nOffensive search against surfaced submarines: Due to the importance of intelligence accuracy in determining the search area, an analysis of the accuracy of different types is beyond the scope of this discussion (see Chapters 4 and 5 of Volume 2B, Search and Screening). The density required for aircraft search is that of surfaced submarines. A region with a high concentration of submerged submarines is not profitable for aircraft search.\nAs an example of the influence of a submarine's submergence tactics, the offshore gain effect can be used to illustrate the significance of sweep rates. It was common experience that aircraft patrol was relatively most effective when carried out at a considerable distance from shore bases, as submarines close to them were cautious and spent a large fraction of the time submerged. For instance, data based on flying hours at the Moroccan Sea Frontier are of interest.\n\nThe region under study was divided into zones, each 200 miles wide: 0-200 miles from land. The number of actual aircraft contacts in each zone was counted, and an expected number was computed, based on the flying hours in each zone, the total density of U-boats in the zone, and an assumed 5-mile sweep width. In this way, the figures of:\n\n(Note: The text seems to be complete and does not require any major cleaning. However, if there are any OCR errors, they are not significant enough to affect the understanding of the text.)\nTable 1 derived. Effective sweep width is:\n\nDistance from base (miles) Total Expected Actual Per cent realized Effective sweep width (miles)\n\nThe value of sweep width required in computations for expected contacts equal to actual contacts: Contacts in Moroccan sea frontier antisubmarine patrols.\n\nThe increase in effective sweep width or \"percent realized\" as distance from shore bases increases is likely due to U-boats relaxing precautions. Regardless of the cause, it demonstrates the importance of flying at significant distance from shore bases during offensive patrol.\n\nRadar can be used to expand sweep width, and special gear such as sonobuoys or magnetic anomaly detectors [MAD] are available for submerged submarine detection.\nMarines will be discussed later, as sweep rates are very small. Beyond that achievable by visual means is important in area search (or any other type). Early radars did not have a detection range sufficiently great to exceed that of visual detection except in periods of darkness or low visibility. However, newer types are powerful enough to do so a large part of the time. The older radar was valuable chiefly because it made contacts in periods of low visibility when U-boats were surfaced. Data on Army Air Forces Anti-Submarine Command flying in Eastern Sea Frontier for May through October 1942 and in the Trinidad area for October and November both support this, as shown in Table 2.\n\nVisual only\nRadar during day\nRadar during night\n\nTable 2. Radar versus visual search during 1942 (in terms of hours per contact)\nESF: May-Oct\nHours of flying / No. of contacts / Hours per contact\n\nTrinidad: Oct-Nov\nHours of flying / No. of contacts / Hours per contact\n\nThe use of radar during the daytime did not significantly reduce the number of flying hours required to secure a contact. However, radar was much more effective at night. The primary reason for this is that U-boats were submerged in these regions during the daytime, and opportunities for contacting them were limited to nighttime.\n\nPatrol height is crucial for achieving the maximum sweep rate. For both visual and radar search, the altitude must be high enough to provide a distant horizon, and for visual search, the increased apparent area of the wake is also important, as explained in Chapter 4 of Volume 2. Theoretical sweep widths for aircraft visual search (Table 3).\n(Submarine underway., Altitude (feet), Visibility 3 miles, Visibility 15 miles, Search of an area, The table of sweep rates presented in Table 3 clearly shows the advantages of high altitude for visual search, As an example of operational data confirming the value of flying at a fair height, data on sightings in the Bay of Biscay area during May 1943 can be quoted, Table 4 gives the sightings per 100 sorties. As expected, altitudes over 2000 ft give only a slight gain when meteorological visibility is low but have considerable advantage under good visibility conditions, The question may well be raised, however, whether the high altitude is not a handicap in delivering an attack. The aircraft must lose altitude to make a low-level bombing run, which would sometimes slow up the approach. The overall results shown in Table 5 do not, however, indicate any significant handicap.)\nSignificant effect of this sort. It is probable that U-boat patrol heights had a notable impact. Table 4. Sightings per 100 sorties for different patrol heights.\n\nMeteorological visibility\nPatrol height (miles)\n0-4\n5-12 over 12\n\nTable 5. Effect of altitude on success of attacks.\n\nPatrol height (feet)\nPercentage of Class A attacks (Coastal Command data, June-Nov 1943)\nPercentage of attacks causing damage (U.S. Strategic Area, July-Dec 1942)\nTotal sightings\nTotal Class A attacks\nPercentage\nPercentage Class A\nLookouts have tended to scan the horizon for aircraft, giving higher-flying aircraft an advantage in approaching undetected. In any event, the overall gain of altitude above 2000 ft is clear.\n\nThere are many other questions relating to the most effective conduct of visual or radar search of a submarine.\nSubmarine patrol area by aircraft. The problem involves achieving the best possible sweep width and then laying out a patrol where surfaced submarines are densest, in accordance with Chapters 3 and 7 of Volume 2B, Search and Screening.\n\nThe advent of Schnorchel drastically reduced the aircraft's search capabilities because both radar and visual sweep width on Schnorchel are much less than on surfaced U-boats \u2013 according to most estimates only 1/10 to 1/100 as great. To a slight extent, this reduction is compensated by the Schnorcheling U-boat's need to operate in restricted focal areas. The area to be searched by either aircraft or surface craft being thus much reduced. A net result has been a marked increase in the importance of surface craft search compared with that by aircraft for submarines operating on Schnorchel.\nTo some extent, aircraft can conduct a sonar search using sono-buoys. If the submarine is proceeding at high speed on Schnorchel and is therefore noisy, the effective sweep rate of a group of sonobuoys monitored by an aircraft may be comparable to that of surface craft using sonar.\n\n1.2 Search and Submerged Submarines\n\nThe role of surface craft in searching an area is limited by their small sweep rate. Visual and radar detection ranges are shorter than for aircraft, and the speed is much less. Table 6 presents sweep rates under various conditions (in sq miles per hour).\n\n|  | Surfaced sub | Submerged sub | Aircraft |\n| --- | --- | --- | --- |\n| Visual (good visibility) | Approx 0 | Approx 0 | Approx 0 |\n| Radar\u2014ASG | Approx 0 | Approx 0 | Approx 0 |\n| MAD | - | - | - |\n| Sono-buoys | Surface craft | - | - |\n|  | Visual | Approx 0 | Approx 0 |\n|  | Approx 0 | Approx 0 | Radar (10 cm) |\n|  |  |  | Approx 0 |\n|  |  |  | Sonar |\n* Estimated on the basis of tests but not confirmed by operational use.\ndata. \nOFFENSIVE  SEARCH \ncomparison  of  typical  aircraft  and  surface  craft  sweep \nrates.  Visual  search  by  surface  craft  is  not  likely  to  be \neffective  since  the  submarine  can  almost  invariably \nsee  the  surface  craft  in  time  to  dive  before  the  surface \ncraft  sees  it.  This  visual  search  has  purely  hold-down \nvalue  and  is  not  effective  in  an  offensive  sense.  Radar \nsearch  by  surface  craft  under  low  visibility  conditions \nmay,  on  the  other  hand,  be  expected  to  lead  to  con- \ntacts on  any  surfaced  submarines  unless  they  are \nfitted  with  search  receivers  and  dive  upon  being  ap- \nproached. For  surfaced  submarines,  however,  the \nsurface  craft  have  a considerably  smaller  sweep  rate \nthan  aircraft,  so  that  the  chief  role  of  surface  craft  is \nconducting  searches  for  submerged  subs,  a task  for \nwhich  aircraft  are  not  effective. \nThe  sweep  rates  for  aircraft  using  magnetic  anom- \nSurface craft use sonar for detecting submerged submarines, similar to aircraft use of MAD or sono-buoys, according to Table 6. However, this comparison is not entirely fair. The aircraft figures are based on trial results and not fully substantiated by operational data. Operational experience suggests that identifying MAD and sono-buoy contacts is challenging. Neither method accurately determines a submarine's position but only indicates its presence. Effective attacks on such contacts are difficult to make. The primary role of surface craft in area search is therefore sonar search for submerged submarines, which can only be effective if submarines are concentrated in a small area.\nThe rate of searching an area that is 100 miles square with five ships takes approximately 6 days. In contrast, a single aircraft can search the same area for surfaced submarines in 4 hours. Consequently, there are few circumstances where surface craft can be used profitably for area search.\n\nHigh-frequency direction-finding (DF) extends the search capabilities of surface craft since it allows the ship to take a bearing on a submarine transmitting on high frequency within about 20 or 30 miles. If submarines transmit frequently, as German U-boats did during the Battle of the Atlantic, DF can increase the radar sweep rate by a factor of up to 3 or 4 for surfaced subs.\n\nA DF contact is not as valuable as a radar contact because it is less definitely localized and more difficult to convert into an attack.\nFundamentally, surface craft search of an area is a matter of sonar search. World War II offered few opportunities for such search, as surface craft were primarily used in follow-up of contacts and defensive operations. Consequently, little operational data is available.\n\nOne tactical principle should be emphasized: searching in groups in line abreast. The theoretical reason for doing this is that a submarine has a good chance of evading a single ship by steering to one side at high speed when the approach is detected. Figure 1 illustrates this evasion. The \"entrapment triangle\" is drawn tangent to the sonar detection circle with limiting escape lines drawn at an angle equal to sin^-1 (submarine speed/ship speed).\nThe submarine's situation is akin to the submerged approach zone, but with a key difference. Instead of trying to enter, the submarine is striving to exit. As depicted in Figure 1, searching in line abreast renders evasion impossible, except from positions close to the line ends. Theoretical deliberations on line abreast search are expounded in Chapter 6, Volume 2B. There are numerous practical reasons for search in line abreast. Ships are close enough for effortless communication and are aware of their comrades' positions at all times. Similarly, they are easily identifiable by aircraft or other forces in the area, even at night. Moreover, ships are in a favorable position to coordinate during an attack once contact is established.\n\nIn truth, it is almost always advantageous to conduct offensive operations in groups. A group of units can:\n\n1. Communicate effectively.\n2. Know the positions of their allies at all times.\n3. Be easily identifiable by aircraft or other forces.\n4. Coordinate attacks once contact is made.\nIn this way, the chances of sinking a submarine, once contact is made, are significantly increased over what they would be with a single attacking unit. However, this gain comes with the necessary loss in probability of making contact due to concentrating too much searching effort into a particular area or time, excluding others. These two considerations must be weighed and the best compromise achieved. When the area to be searched is rather large, as is usually the case, a search should be conducted on parallel sweeps or according to a fixed plan. Any unit making contact has immediate assistance available, and all other units can enter into the process of attacking or following up the contact.\nA group of units covers it only incompletely, and there is no difficulty with \"over-searching.\" In such a case, offensive patrol in groups spaced as closely as possible without overlapping of the areas searched by individual units is clearly desirable. Groups may involve aircraft or surface craft, or both. The basic idea is simply to provide for coordinated attack upon any contact that is made without appreciable loss in efficiency of search effort.\n\n13.2 Interception of Transits\n\nIn many cases, it is profitable to endeavor to intercept submarines en route to their patrol area and attack them before they are able to become dangerous. Submarines in transit may be thought of as making up a moving density distribution (as opposed to a stationary one for those on patrol). This comparison is discussed in detail in Chapter 7 of Volume 2B.\nthe  appropriate  modifications  in  search  plans  are  de- \nscribed. As  a result  of  this  movement,  the  crossover \ntype  of  barrier  patrol  is  usually  the  most  efficient,  as \nwas  pointed  out  in  Volume  2B. \nThis  movement  does  not,  in  itself,  make  detection \nof  the  submarines  involved  any  easier,  but  often  re- \nsults in  a more  accurate  estimate  of  the  submarine\u2019s \nposition  than  is  possible  with  a submarine  on  patrol. \nThis  may  be  very  strikingly  true  if  the  submarines \nare  constrained  to  pass  through  a relatively  i^rrow \nregion  while  on  passage  to  the  patrol  area.  In  such  a \ncase  the  submarine  density  is  much  higher  in  the \ntransit  area  than  the  patrol  area  and  consequently \nthe  former  is  the  better  area  for  exploitation  by  an \nantisubmarine  offensive,  other  things  being  equal. \n13.2.1  Yhe  Bay  of  Biscay  Offensive \nThe  outstanding  transit  area  of  this  type  has  been \nThe Bay of Biscay off the U-boats' French ports of Brest, Lorient, St. Nazaire, and La Pallice. All U-boats entering or leaving these ports had to funnel through the Bay within reach of British-based air cover, providing excellent opportunities for attacking U-boats. An analysis of the possibilities of an offensive in the Bay was made late in 1942, some of whose salient arguments are discussed here. The basic idea was that U-boats had to spend a fair amount of time on the surface crossing the Bay, and therefore a \"balanced\" force capable of carrying out effective search both day and night would be able to intercept and inflict serious damage.\n\nOffensive Search\nA large fraction of the U-boats and inflict very serious damage.\n\n(Report No. 204, Air Offensive Against U-Boats in Transit, December, 1942)\nTable 7. Surfaced days per transit.\n\nFraction of Speed time spent on surface (per cent) (kt) Speed submerged (kt) Average speed (kt) Total time (hours) Time on surface (hours)\n\nIf the total number of transits per month is designated by T, then the average number of surfaced days is:\n\nFraction of Speed (per cent) Time on Surface (hours)\n--------------------------------------------------\n30 11.1\n40 8.9\n50 7.3\n60 6.1\n70 5.3\n80 4.7\n90 4.2\n\nThe U-boat must spend approximately 13 hours on the surface in crossing the Bay even when using maximum submergence.\nU-boats in the area is approximately 720 hours per month: The expected number of contacts is:\n\nWhere Q = aircraft sweep rate,\nh = number of flying hours per month,\nA = area involved.\n\nTo contact every transit U-boat once, for example, it would be necessary to have N = t, which condition can be used with equations (1) and (2) to determine the number of flying hours required.\n\nh\n\nThe area involved is about 300 square miles, so the hours required are as given by Table 8.\n\nTable 8. Flying requirements to sight each transit.\n\nType Detection Sweep rate (sq miles per hour) required\nMeter-wave Centimeter\n\nThese figures for flying hours per month can readily be interpreted in terms of the number of planes required. A long-range plane is normally capable of flying about 50 hours per month, so that a force of:\n\n(50 hours/plane/month) / (hours/plane/month) = number of planes required.\nOf about 40 such planes equipped with centimeter radar would be adequate to contact each U-boat crossing the Bay. The flying required to get back and forth from base to the active Bay area would not increase this figure greatly.\n\nThe comparison of actual results obtained in the operations with these predictions is of particular interest. Since the situation changed rapidly from time to time, the data presented in Table 9 are given by months and divided into three periods corresponding to various stages of the battle. Average values are given for each period. At the end of the third period, the number of transits dropped off sharply and U-boat activity did not again reach the previous level.\n\nTable 9. Results of Bay of Biscay offensive.\n\nMonth | Flying hours on patrol | U-boat transits | Sightings of U-boats | Per cent sighted\nFirst period | Aug, Sep | Average: | | Average:\n| --- | --- | --- | --- | --- |\n| J[h] | | | | |\n\nSecond period | | | | |\n| | | | | |\n| | Average: | | | Average: |\n| | | | | |\n\nThird period | | | | |\n| | | | | |\n| | Average: | | | Average: |\n| | | | | |\n\nEnd of third period | | | | |\n| | | | | 0 |\nThe second period is from November to December. Average: March to May.\n\nInterception of Transits:\n\nThe first period involves night flying by Wellington aircraft equipped with Leigh Lights and meter-wave radar. Only about 10 aircraft were so equipped, but the overall result was to sight almost half the transits. Since the number of flying hours per month was only slightly more than half that quoted in Table 8 for meter-wave radar, this result is not far removed from that predicted. Actual operational results were 30 sightings, a close agreement with the predicted average of 40.\n\nDuring the following months, however, the fraction of transits sighted declined markedly, reaching a low of 10%. To some extent, this may have been a seasonal effect due to flying difficulties in winter. But the chief reason for the drop was likely other factors.\nThe introduction of search receivers on U-boats, capable of detecting meter-wave radar, undoubtedly permitted U-boats to surface at night with fair safety. This development unbalanced the aircraft as a force. By the spring of 1943, Leigh Light Weltingtons were equipped with centimeter radar, resulting in improved outcomes. The fraction of transits sighted rose to 100 percent by June and July, a tenfold increase, despite flying hours only being about twice what they had been in previous periods. If all planes had been fitted with centimeter radar, an even higher sighting rate would have been expected based on Table 8, given the considerable flying hours.\nThe month that should produce 100 percent sightings:\nSuch was not the case, and the average sweep rate of all planes involved was probably more nearly that of meter radar. On this basis, 6000 hours per month would be required to produce 100 percent sightings, which is in good agreement with the observed results. The average amount of flying was 5500 hours per month, which sighted 60 percent of the transits, reaching a peak of 100 percent during the best summer months.\n\nIt may be concluded then, that the best periods of the Bay operations provided returns quite in accordance with predictions, but that the U-boats were quick to find and exploit any weak points in the offensive. The highly profitable periods were not of long duration. Even during the low points, however, Biscay operations were quite profitable compared\nWith aircraft patrol in other regions, as flying hours required to make a sighting rarely exceeded 500, whereas in many areas thousands of hours were required.\n\n13.2.2 Value of Interception of Transit Submarines\n\nThe final evaluation of any offensive against transit U-boats must be made on the basis of a comparison with other possible uses of the forces involved. When the other use contemplated is also some type of offensive patrol, the chief criterion is that of submarine density (or density of surfaced subs if more appropriate), as demonstrated in Volume 2B, Chapter 3. Offensive patrol should be carried out in the region of greatest submarine density, subject to certain practical considerations. A region in which weather conditions reduce the effectiveness of detection gear by a factor of three, for instance, would not be suitable.\nA profitable offensive operation requires a submarine density in the area to be at least three times greater than in other regions. When comparing offensive and defensive operations, many factors must be considered. The standard measure of the effectiveness of antisubmarine operations is the number of ships saved. Defensive operations achieve this directly, while offensive operations have an indirect effect through the reduction in numbers of submarines operating and through lowering the morale and state of training of submarine crews. The latter effect is very difficult to assess numerically. U-boats typically withdrew from areas where their chance of being sunk was greater than about 10 percent per month of those at sea when a safer alternative existed.\nThe high sinking rate has often been associated with a low rate of sinking ships, so that U-boats may have withdrawn in search of more profitable areas, rather than because of any effect on morale. Nevertheless, the U-boats\u2019 heavy losses in 1943 were followed by a period of very unaggressive operations, even though the losses suffered were not enough seriously to diminish the size of the U-boat fleet. In order to illustrate the type of comparison that must be made, consider a hypothetical situation in which the enemy has a hundred submarines which can spend half their time at sea. He can build five submarines per month, but we sink the same number by surface craft (i.e., 10 percent of those at sea each month).\nA equilibrium has been reached. Given a force of 40 aircraft, should they be employed offensively, assuming each submarine transit would be sighted in accordance with equations (1) to (3), or defensively for escort of threatened convoys, assuming the protection offered would be in accordance with Chapter 10's data? In each case, the number of ships saved by the aircraft must be determined. For offensive operations, the saving can be estimated as follows: The immediate effect of the offensive operation is an increased number of submarines sunk per month. This will reduce the number of submarines operating until, in the long run, a new equilibrium is reached. The number of submarines sunk per month will then be equal to the number built. If N is the number built per month.\nN number of submarines available to the enemy, T is the length of a submarine patrol in months.\n\nN = number of submarines at sea,\nN - number of transits made per month.\n\nThe capabilities of the surface craft were assumed to be such that they sink 10% of the subs at sea per month, and data from Chapter 12 shows that it is reasonable to assume that about 10% of all aircraft sightings lead to attacks which sink the submarine. Combining these figures with the ability of the aircraft to intercept each transit, we have, at equilibrium:\n\nOAON T\n\nNumber of subs built per month\n\nThe normal length cruise for a U-boat has been about 2 months. Using this value for T, we have N = 50 submarines, which is only half the force that was available in the absence of the aircraft offensive.\n\nThus we would expect this offensive use of aircraft to significantly reduce the enemy's submarine fleet.\nThe losses of merchant ships can be reduced by half. This figure can be compared to the direct defensive value in escorting threatened convoys. The experience quoted in Chapter 10 was that four sorties per day decreased daily losses by approximately 65%. If the aircraft force available could provide this extent of convoy coverage, it would be significantly more valuable than when employed offensively. The 65% figure only measures direct defensive value and does not account for any attacks on submarines that the planes might make while on convoy escort duty. The total amount of aircraft required for convoy escort would not generally be excessive. During the actual period studied previously, there were approximately 20 convoy-days per month in the \"threatened\" class, so only 80 sorties per month would be needed.\nA craft could be expected to fly approximately 200 sorties monthly. Some threatened convoys may, however, be in positions which cannot be readily covered by aircraft, so the expected thoroughness of coverage must be estimated based on weather, distance of convoy routes from bases, and similar factors. In the North Atlantic, convoys were, in fact, covered on somewhat less than half the days when they were threatened. If this restriction must be accepted, the expected reduction in losses is only about 30 percent, which is no longer obviously superior to the offensive employment of aircraft in the transit area. As a matter of fact, sightings made (about 15 per month) were about enough to make up the discrepancy between 30 percent and 50 percent saving.\n\nSuch a comparison is never strictly valid, however.\nThe equilibrium number of submarines is given by equation (4): Ne. For the case with a war duration of 2 months, the number of submarines is plotted in Figure 3. The value of an offensive operation depends on the expected length of the war. The upper curve in Figure 3 shows the reduction in the average number of submarines operating as a function of the length of the period under consideration. If the war is expected to last another 30 or more months, the offensive will nearly achieve its equilibrium effectiveness, reducing the number of submarines operating by about\nThe reduction in ship losses with defensive measures is approximately 40% when considering the lifetime of ships and crews. Conversely, if the war lasts only 6 months, the average reduction is about 10%. Figure 4 explicitly compares defensive and offensive measures. The ordinate represents the reduction in ship losses, disregarding attacks on U-boats by escort aircraft. The figure demonstrates that the length of the war significantly impacts the value of an antisubmarine offensive.\n\nFigure 4. Relative saving of ships for various uses of aircraft.\n(A) Defensive value of escort for all threatened convoys;\n(B) defensive value of partial escort for threatened convoys.\nThe most important aspect of offensive operations is the attempt to convert the largest possible fraction of all contacts into attacks and kills. The manner in which contact is made may not allow for an immediate attack (for instance, a sighting by a merchant ship or nonoperational aircraft). In some cases, an attack has been made on the sub and contact subsequently lost, requiring regaining of contact to continue the attack. In these instances, it is usually very important.\nProfitable to conduct a follow-up search to find the sub again. Following up on contacts is a profitable employment of antisubmarine forces because for the first few hours after contact is lost, the region in which the submarine can be is rather small. In this region, the probability density is accordingly high and it therefore constitutes a profitable region for search. For instance, consider the case of a submarine whose position is definitely known at time t = 0, and is then lost. The submarine is free to travel on the surface. Since its speed is certainly not greater than 20 knots, we can be sure that it is within a circle of radius 20 miles. The corresponding submarine probability density is shown in Figure 5, calculated on the assumption that the submarine is equally likely to be anywhere within the circle.\n\nTIME (IN HOURS)\nFigure 5. Local probability density after a submarine contact, calculated from equation (7). A horizontal line drawn for comparison shows a typical average U-boat density for an active area during the Atlantic war. The conclusion is that follow-up of the contact is more profitable than general area patrol for approximately 10-20 hours after the contact in this case. If the overall submarine density is increased, follow-up of contact becomes relatively less profitable, whereas in a region of low density, it is of utmost importance to exploit each contact to the full.\n\nFigure 5, drawn for submarine speeds of 10-20 knots, is applicable for surfaced submarines. If the submarine is held down by aircraft or surface craft, its speed may be considerably less, normally only 2-3 knots for conventional types of submarine.\nThe local density remains high for a much longer period than shown in Figure 5, resulting in more effective sonar search for submerged submarines in follow-up of previous contacts than in routine area search. Only in areas of great submarine density is it profitable to employ surface craft for area search by sonar. In general, the chief offensive employment of surface craft will be to follow up previous contacts; appropriate plans and tactics for doing so are of prime importance. There are then, two distinct tactical situations, according to whether aircraft or surface craft are the principal agents of search. If the hunt is being carried out by aircraft alone, the aim is to recontact promptly any submarine which dares to show itself on the surface. When surface craft are present, however, the submarine will normally remain submerged. (A coordinated approach is essential)\nNamed hunts by aircraft should be carried out whenever possible to ensure that the submarine does not make a high-speed escape on the surface. As long as the submarine's submerged speed is low, the surface craft's sonar search has a good chance of resulting in recontact. Of the two problems, that of surface craft search is somewhat simpler and will be discussed first.\n\nIn the actual design of such follow-up searches for surface craft, two primary requirements must be met. In the first place, the search must be as simple as possible to carry out and involve no more turns or changes in disposition than necessary. Ships should be kept in a line-abreast formation unless there is some special reason for doing otherwise. Standardized turns and maneuvers should be employed to avoid confusion in operation. In addition, the plan for follow-up contacts should be clearly defined, with designated search areas and communication procedures. Path of ships.\nFigure 7. Typical plan for sonar search by surface craft. Assume the submarine is equally likely to be anywhere within a certain radius of the initial point and is known to be somewhere within that radius. It is reasonable to write the radius as:\n\nr = sqrt(a\u00b2 + (Vt)\u00b2)\n\nWhere a = uncertainty in initial position,\nV = submarine\u2019s speed,\nt = time since initial contact.\n\nAssume that the increment of probability of having made contact can be written as:\n\ndP = kf(r)dr\n\nThis assumption implies that the search is carried out at random, but can be used as a fair approximation to an actual search plan. (See Volume 2B, Chapter 3.) Then, search regions in which the submarine is likely to be, in general accordance with the rules of Volume 2B, Chapter 3. In designing the plan, then, an estimate of probability density distribution as a function:\n\ndP/dr = f(r)\nThe density is very highly peaked immediately after contact, with dispersion arising only from errors in reporting the contact position. However, as time passes, the submarine may move further away from the original contact position. A typical set of densities is shown in Figure 6, and further discussion can be found in Volume 2B, Chapter 1.\n\nAn expanding distribution will generally result in a search plan with the shape shown in Figure 7. Extensive sets of such plans can be found in present doctrine.\n\nIt is not necessary to go through a detailed analysis of probability functions such as those in Figure 6 to gain a general idea of their effectiveness.\nThe fundamental simplification is to replace the surface in Figure 6 with a plane. Plans are presented in FTP 223A. The mathematical basis upon which such plans are constructed is given in Volume 2B, Chapters 3 and 7.\n\n1. const X e\n\u2014 (Q/t) Tan^(t)f/o\n\nThe constant of integration in equation (8) is determined by the condition that p = 0 at the time of commencing search. If this time is denoted by t0, then:\n\nWhen a search is being conducted, it should normally be carried out until there is nothing to be gained by further searching, i.e., until p(t) is very near p^. Therefore, it is useful to write the probability for t = infinity, which is:\n\nSome typical curves plotted on the basis of equations (1) and (2) are shown in Figure 7.\ntion (10)  are  plotted  in  Figure  8.  A sweep  rate  of  30 \nsquare  miles  per  hour  and  a sub  speed  of  3 knots  are \nassumed.  It  is  evident  that  a prompt  start  on  the \nsearch  combined  with  accurate  localization  of  the \ncontact  are  required  for  a good  probability  of  success. \nOperational  data  are  available  on  success  of  follow- \nup hunts  aimed  at  regaining  contact  with  a subma- \nrine after  lost  contact  following  an  attack;  these  can \nbe  compared  with  the  theoretical  predictions.  For \n,--y^^TTnsnm7ir7?-( \nOFFENSIVE  SEARCH \nFigure  8.  Probability  of  catch  for:  sweep  rate  30  sq  miles \nper  hour;  sub  speed  of  3 kt. \ncases  in  which  a submarine  was  believed  to  be  pres- \nent, the  results  are  presented  in  Table  10.  An  aver- \nage of  about  two  ships  took  part  in  the  searches. \nTable  10.  Success  of  searches  to  recontact  U-boat. \nAverage  time \nfrom  lost  contact \nPer  cent \nNo.  of  cases \nto  start  of  search \nThese figures are plotted in Figure 9, and a calculated curve is drawn which is in fair agreement with the operational points. This curve is drawn on the assumption that sub speed is 3 knots, initial uncertainty is 1 mile, and sweep rate is 10 sq miles per hour. The first two assumptions are reasonable for the tactical situation involved. Since the problem is one of recontacting a submarine which has been previously attacked, a location error of more than 1 mile is unlikely. The sweep rate of only about 5 sq miles per hour per ship is somewhat smaller than might be expected. In Volume 2B, Chapter 6, the average sonar sweep width is estimated at 1800 yd, corresponding to a sweep rate of about 10 to 12 sq miles per hour. Several explanations are possible: (1) in this case U-boats may have been especially careful.\nto  make  good  use  of  layer  effect  and  other  opportuni- \nties to  escape  detection,  (2)  wakes,  depth  charge  ex- \nplosions, etc.,  may  have  made  search  more  difficult, \nor  (3)  the  previous  estimate,  based  on  the  assumption \nthat  a submarine  would  have  been  detected  every \ntime  at  very  short  range,  may  have  been  unduly  op- \ntimistic. There  is,  however,  no  irreconcilable  differ- \nence between  the  theoretical  expectations  and  opera- \ntional results. \nUJ \no \ntu \nTIME  IN  HOURS  UNTIL  START  OF  SEARCH \nFigure  9.  Per  cent  of  submarines  contacted  by  surface \ncraft  hunts.  (Circles  are  operational  data  on  regaining \ncontact.  (Solid  curve  is  calculated  for:  Q = 10  sq  miles  per \nhour,  A = 1 mile,  F = 3 kt,  by  equation  (10). \nFollow-up  hunts  by  aircraft  are  of  two  general \ntypes.  The  first  of  these  is  aimed  at  detection  of  sub- \nmerged submarines  by  MAD  or  sono-buoys,  the  sec- \nWhen visual or radar detection of a submarine is not possible until it has resurfaced, these hunts share many similarities with surface craft hunts, as the submarine's behavior is roughly the same. To ensure a reasonable chance of success, the search must begin immediately after losing contact, and the initial location must be accurate. Since this type of follow-up presents no essentially new problems, detailed discussion will not be given.\n\nHowever, when the aircraft relies on visual or radar detection, the search must be planned with the understanding that a submerged submarine cannot be detected. Two alternatives are possible: a hold-down hunt aimed at covering all possible positions of the submarine to prevent it from escaping.\nsurfacing until battery and crew are exhausted, or a \"gambit\" procedure in which the aircraft permit the submarine to resurface and then recontact it. This latter alternative is equivalent to designing the search to concentrate on regions where surfaced submarines are most likely to be. In practice, the gambit procedure has usually involved a box search centered at the point of last contact and far enough distant that the sub will surface and then try to cross the aircraft's patrol. The hold-down hunt, on the other hand, must cover the whole possible area of the submarine at frequent intervals. This requires a much larger expenditure of effort, actually far more than is usually available, as can be seen in Figure 10.\n\nHold-down:\n1. Aircraft must cover area\nTrim about three times per hour to keep sub down at all times. for velocity of aircraft V, and sweep width lo, this requires 2V > Tr (Uvf/wV) aircraft in the region at time t.\n\nAircraft must make circuit 2, Trut in length often enough to prevent crossing on surface. for aircraft velocity V, sweep width w, and sub surface speed Ug, this requires (Ujw) /(V) aircraft flying at time t.\n\nTo carry out from 1 hr to 36 hr with V = 125 kt, and Ug = 15 kt we require 1050 flying hours, 150 flying hours. Obviously much less flying is required for the gambit procedure than for hold-down, especially since a true hold-down should last for well over 36 hr. As a matter of fact, there have been very few cases where hunts have been made with sufficient intensity to Table 11. Hours of flying on contact by type of mission (Trinidad area).\nQualify as true hold-downs offering the submarine 720 opportunities for surfacing. A hard and fast distinction cannot be made in the case of actual operations. Operational results normally confirm the theoretical expectation that flying on hunts in follow-up of contact is more profitable than any other type in terms of flying hours required per submarine contact.\n\nTable 1 presents data of this sort from the Trinidad Area for the period August 1942 to January 1943. Hunt flying is seen to be three to four times as profitable as other types.\n\nA small number of aircraft hunts have been studied in detail to determine the relative effectiveness of different types of follow-up tactics. Although the number of cases involved was too small to permit great reliance on the results, they are of interest as confirmation of the expected.\nTable 12. Results of aircraft hunts (United States strategic area, 1943).\nTotal number of hunts: 18\nHunts achieving recontacts: 11\nPercentage of hunts successful: 61%\nAverage duration of hunt (hours): 59\nTotal number of recontacts made: 22\nRecontacts per hunt: 1.22\nAverage time between recontacts (hours): 14.6\nThe effectiveness of these hunts is shown by the fact that 61% of them succeeded in re-establishing contact with the submarine. On average, subs were recontacted about two times in those cases.\n\nDetailed breakdown of results:\nTotal hours of flying\nAverage hours per contact\n\nEscort of convoy Routine patrol Hunts\nEscort of convoy Routine\nTable 13: Comparison of results by hunt type.\n\nContinuous | Gambit | Modified | Exhaustion | Exhaustion\n--- | --- | --- | --- | ---\nNumber of hunts | - | - | - | -\nNumber successful | - | - | - | -\nPercent successful | - | - | - | -\nAverage flying hours in hunt area | - | 0.5 | 1.2 | 1.5\nNumber of recontacts per hunt | 2.3 | 3.5 | 1.8 | 1.7\nFlying hours in area per recontact | 2.5 | 0.15 | 0.7 | 0.9\n\nOffensive search:\nThis table shows clearly the high effectiveness of the gambit type of hunt in comparison to other types. It ranks well in terms of percentage success and average number of recontacts per hunt. Since the number of flying hours employed was much smaller than for the other types, the results in terms of flying hours required per recontact show a definite advantage to the gambit type.\n\nIn connection with the general importance of follow-up hunts, one further remark is worth making. Such hunts are profitable because they are carried out efficiently.\nIn a small area where the submarine probability density is high, effective navigation is required to locate the area properly and carry out the desired search plan. Communications must be excellent to assure that hunting craft reach the submarine position at the earliest possible moment, as the early stages of the hunt are the most profitable. Great skill is necessary in each of these fields to ensure coordinated follow-up hunts are carried out successfully.\n\nChapter 14\nEMPLOYMENT OF SEARCH RADAR IN RELATION TO ENEMY COUNTERMEASURES\n\nRadar has been one of the many weapons applied to defeat the German use of U-boats, playing an important role at certain critical times. The U-boat high command failed to counter the following radar developments effectively.\n\n>41 INTRODUCTION\n\nRadar has been one of the many weapons applied to defeat the German use of U-boats. Its importance lies in certain critical periods. The U-boat high command failed to effectively counter the following radar developments.\nThe effectiveness of search radar caused grave concern for U-boats during World War II. The radar war's moves and countermeasures provide an interesting example of the importance of quick and accurate evaluation of enemy measures. Although World War II events generally conform to the measures and countermeasures scheme outlined in Volume 1 on Operations Research, a review shows that evaluating the operational effectiveness of enemy countermeasures is crucial. Even when a countermeasure has excellent theoretical performance, it's rare for it to be applied widely and with sufficient operational effectiveness to justify abandoning the weapon being countered. Prompt (but not premature) application of counter-countermeasures largely restores effectiveness.\nThe effectiveness of the weapon, particularly in the radar versus search receiver competition during the U-boat war's latter part, is the primary focus of this discussion. This will include the development of German search receivers and the counter-countermeasures employed to reduce their effectiveness. Additionally, the significance of Schnorchel and radar camouflage as a countermeasure against Allied search radar will be considered. German radar countermeasure developments, while less important, are also described below.\n\n1. Submergence. The submarine can evade radar detection by staying submerged, and German U-boats adopted this policy extensively in dangerous waters during the final phases of World War II. As previously mentioned.\nIn previous chapters, the loss in mobility and offensive capabilities was very serious, and a normal type of U-boat (without Schnorchel) could not operate effectively using maximum submergence tactics. Such tactics must be considered a very unsatisfactory last resort from the submarine\u2019s point of view.\n\nAircraft warning radar. Radar of this type (Hohentwiel) was developed and installed on a considerable number of U-boats. Its use was slight, however, and successes insignificant. This was due to two factors: the relatively low power and short range of this radar and the fear of Allied search receivers. In general, the range on aircraft of the long-wave, low-power U-boat radar was shorter than the range on surfaced U-boats of Allied microwave air-to-surface-vessel (ASV) radar. This increased the lack of consequence.\nU-boat commanders lacked confidence in radar due to their objection to any radiation of energy that could be detected and located by direction-finding devices. They believed in the danger of Allied listening gear long before it existed in sufficient quantity to be operationally important. This threat was sufficient to render U-boat radar useless. This fact has since been established through statements made by German personnel, but was appreciated earlier based on information obtained from ferret planes equipped with listening gear. They were dispatched to areas where U-boats were operating, but the sequence of negative reports indicated that there was no significant use of the radar sets installed on the U-boats. Meanwhile, laboratory developments and small-scale production of homing and direction-finding equipment were underway.\nSearch receivers anticipated a revival of U-boat radar. It is possible that German U-boats of high submerged speed (10-15 knots for Type XXI, 15-25 knots for the proposed Type XXVI) were approaching operational status. They were designed to operate effectively when submerged and would have been able to stay submerged using Schnorchel to escape radar detection, yet retain potent offensive capabilities because of their special propulsion for high submerged speed. Conclusions drawn from operations involving old-style U-boats may be completely inapplicable to these new types. Their development shows, however, that the Germans had realized that the other types were not satisfactory for completely submerged operation.\n\nSearch radar in relation to enemy countermeasures be a handicap rather than a help if opposed by adequate countermeasures.\nQuote: Airborne listening gear., Radar decoy. Various types of radar decoys or false targets have been employed in the hopes of drawing the attention of Allied radar search craft away from U-boats themselves. Metallized fabric-covered balloons [RDB] and arrays of resonant di-poles on spar buoys (Thetis) have been used, especially in the Bay of Biscay. In sufficient numbers, they might be expected to lead to a serious waste of search time and effort. There has been at least one instance of a United States surface vessel being torpedoed while investigating a decoy target. In general, however, decoys have not been very successful in confusing Allied ASV radar search, largely because they proved to be too small as radar targets to be detected. Additionally, careful study of target motion aids the radar operator in distinguishing stationary spar buoys.\nFor submarines, in particular, an effective radar intercept receiver provides a satisfactory countermeasure to search radar. Upon receiving a signal of sufficient intensity from the enemy radar, the submarine can dive and become completely hidden. As long as the intercept receiver can outrange the enemy radar, submarine crews have shared the Germans\u2019 suspicion of aircraft warning radar.\n\nThe most significant German countermeasures to Allied search radar have been twofold\u2014 first, the development of intercept receivers, and second, the development of Schnorchel and associated radar camouflage. These will now be discussed.\n\n1. German Search Receivers\n\nFor submarines, an effective radar intercept receiver offers a satisfactory countermeasure to search radar. Upon receiving a signal of sufficient intensity from the enemy radar, the submarine can dive and become completely hidden. As long as the intercept receiver can outrange the enemy radar, submarine crews have shared the Germans\u2019 suspicion of aircraft warning radar.\nThe Japanese were homing on SD radar based on transmissions from several individual incidents. Many ceased using SD radar. However, statistical data showed no effective homing was taking place as late as December 1944, as evidenced by the table below.\n\nAircraft contacts Percentage of aircraft per 100 days (all areas) (in Luzon strait) that detected subs\nDay Night Day Night\nSD nonusers 84\nSD users 86\n\nDespite offering complete protection, such complete protection is seldom achieved in practice. It is worth describing the various stages in the radar versus search receiver competition during the U-boat war as an example of the problems involved in evaluating the effectiveness of countermeasures of this type. (Refer to Chapter 5 in Volume 2B.)\n14.2.1 Meter Radar Is Compromised by Metox German Search Receiver\n\nAs early as August 1941, it had been suggested that U-boats were detecting ASV radar transmissions since aircraft not employing ASV radar were more successful than those using ASV in sighting U-boats. To obtain evidence of this, an experiment was carried out by Coastal Command. Aircraft operating off Brest observed ASV silence on alternate weeks for a brief period. The results of this experiment, given in Table 1, showed no evidence of any disadvantage involved in the use of ASV. Aircraft using radar made more contacts than those not using radar in the same amount of flying time.\n\nTable 1. Contacts with and without radar. (Biscay area, September 1941.)\n\n| Radar off | Radar on | Flying hours in area | Contacts: Visual | Radar | Total |\n| --- | --- | --- | --- | --- | --- |\n| --- | --- | --- | --- | --- | --- |\n\nLater intelligence showed that this conclusion was incorrect.\nFrom the start of World War II, the Germans were fully aware of the possibilities of meter-wave ASV radar and had developed their own air-borne search equipment. However, they did not conclude that the Allies were using radar for U-boat search until the summer of 1942. This led to a hurried program for the development of search receivers to detect the radiations. The first equipment installed on U-boats was the R-600 or Metox, which had a low wavelength limit of 130 cm. It was of the heterodyne type, believed to be the only type capable of sufficient sensitivity. However, it radiated energy, a property which eventually caused its abandonment. Nevertheless, it was used with apparent success. The conditions of its introduction and use are of considerable interest.\n\nThe Problem of German Search Receivers\nJun Jul Aug Sep Oct Nov Dec\nFigure 1. Fraction of U-boat transits in Bay of Biscay that were sighted.\n\nThe German development of search receivers were closely related to the progress of the aircraft anti-U-boat offensive in the Bay of Biscay. In June 1942, the introduction of night attacks by Leigh Light Weltingons and the accompanying sharp rise in the number of attacks on U-boats caused the Germans to take action. The Metox German search receiver [GSR] was the result. Its operational success against the British Mk II radar was considerable, as sightings in the Bay transit area were greatly reduced. Figure 1 shows that the fraction of U-boat transits sighted dropped markedly with the introduction of Metox after the summer of 1942, although the amount of flying done remained approximately constant.\n\nDuring the period shown in Figure 1, data on the:\n\n(Assuming the missing text is not essential for understanding the main content, and is likely to be logistical or editorial information, it can be safely omitted.)\nEffectiveness of radar search were obtained in other regions than the Bay of Biscay, for example, in the Trinidad area of the Caribbean Sea Front.\n\nTable 2. Contacts with and without radar. (Trinidad area, Aug 1942 - Jan 1943.)\n\nMonth Hours of flying Contacts Effective search rate in sq. miles per hour No radar Radar No radar Radar No radar Radar\nAug Sept Oct Nov Dec Jan Total\n\nThese data, like those obtained earlier by Coastal Command, showed little evidence of any effective use of radar listening gear by the U-boats, as shown in Table 2. Two conclusions were possible: either the use of the gear was much less effective in the Trinidad area than the Bay of Biscay or the change in the Bay was not due to Metox but was, for example, a seasonal change. The actual situation may have involved more psychological benefit from the use of radar.\nThe use of Leigh Light Wellingtons in the summer of 1942 may have scared U-boats into abandoning the policy of surfacing at night, even though the number of planes was small and surfacing in the daytime was still much more dangerous. With the advent of Metox, they may have returned to the safer policy of nighttime surfacing. In the Trinidad area, however, there was no radical change in U-boat tactics, except for a general increase in caution.\n\nIf this last explanation is taken as the correct one, it is still, in a sense, fair to say that Metox caused the change in Bay of Biscay results in the fall of 1942. It would not be safe, however, to conclude that Metox was, therefore, a very effective search receiver. The actual mechanism linking cause and effect was a more subtle one. Whatever the explanation of the change.\nThe apparent success of Metox was short-lived. Allies introduced S-band (10-cm) radar, and the effectiveness of air search reached even higher levels. Germans were baffled by S-Band Radar. Allied development of airborne S-band radar was proceeding, based on the magnetron transmitter tube, and it was put into operational service early in 1943 as the U.S. SCR-717 and ASG, and the British Mk III types. This new wave band not only provided immunity from detection by Metox but also gave increased ranges of detection on U-boats. The operational success of this type of gear was considerable. Aided by the seasonal upswing in aircraft effectiveness normally occurring in the spring months because of better weather and more daylight hours, S-band radar had much to do with the peak of aircraft achievements reached in the summer of 1943.\nEvidences of the success of the air war against U-boats in relation to radar. For detailed discussion of radar ranges, see Volume 2B, Chapter 5.\n\nSearch Radar in relation to enemy countermeasures.\n\nFraction of U-boat transits of Bay of Biscay sighted:\n\nFigure 2. Percentage of U-boats passing through the Bay of Biscay sighted:\n\nU-boats at that time are shown in Figures 2 and 3 below. Figure 2 presents data on the sighting of U-boats passing through the Bay of Biscay. The sharp rise in the spring months is very evident. In Figure 3, which gives the overall results of the aircraft offensive in terms of U-boats sunk per month, there is also a sharp rise at this time. S-band radar was not the only cause of this increase in air effectiveness, but it made a significant contribution. The other major factor was the introduction of aircraft based on escort carriers for mid-ocean offensive operations.\nWith this upswing in Allied aircraft success, the Germans became convinced that Allied aircraft were using some new detection device. They started a frantic activity to identify and counter it. For a time, they occupied themselves with the idea that it was an infrared detector, as they had tried to develop one of their own, and experimented with special paints intended to give no infrared reflections. They also considered the possibility of a frequency-scanning radar and developed a scanning receiver with a cathode-ray tube presentation. This was of definite advantage to the operator, but it still covered only the same meter-wave band. The sinkings of U-boats continued.\n\nIn desperation, they jumped to the conclusion that their GSR radiations were being homed on. The Metox receiver was outlawed, and the Wanz G-1 intercept receiver (Figure 3) was developed. U-boats sunk per month by aircraft.\nIntroduced was an improved design, radiating less power. However, the near-pathological fear of radiation in U-boat captains prevented them from trusting it. Continued sinkings and skepticism of the technical advantages kept it from being used.\n\nNext, German scientists turned to the much less sensitive crystal detector-receiver, which was entirely free from radiation, and produced the \"Borkum.\" This was a broad-band intercept receiver which covered the 7-300 cm band. Neither it nor the Wanz was effective against the new Allied radar, however.\n\nFinally, in September 1943, the U-boat command realized that 10-cm radar was being used against them. The \"Rotterdam Gerat,\" a British H2S radar working in the 10-cm band, had been captured intact at Rotterdam by the German Air Force in March.\nThe problem of German search receivers: In 1943, German scientists determined the characteristics of a new enemy technology. A 6-month delay from March to September is unexplained. This was a significant time factor in the U-boat war. An additional delay of about 6 months occurred before the first effective S-band receivers became operational in April 1944. During this interval, the German Technical Service's frantic experimentations were evident in incidents such as the patrol of U-406 carrying one of their best GSR experts, Dr. Greven, and his staff, with a full complement of experimental search receivers. The U-406 was sunk, and other experimental patrols also had short careers.\n\nThe drop in results of the Allied air effort at the end of the summer of 1943, as shown in Figure 2 and Figure 3, was only in small part due to this.\nThe U-boats adopted an ultraconservative policy of maximum submergence and rarely exposed themselves to air attack. In passing through the Bay of Biscay, they crept along the Spanish coast, in regions inaccessible from Britain, and surfaced as little as they could. With such tactics, U-boat effectiveness was very low, but they gained respite from air attack.\n\n1.4.2.3 Naxos Search Receiver Covers S-Band\n\nFrom this confusion, the \"Naxos\" intercept receiver covering the 8-12 cm band emerged. The first models introduced in the fall of 1943 were crude portable units mounted on a stick and carried up through the conning tower upon surfacing. The range was short due to the crystal detector principle, broad-band coverage, and small, non-directional antenna. Estimates of range from prisoner-of-war reports were 8 to 10 miles.\nAllied reaction to intelligence reports about Naxos revealed fears of S-band radar compromise as early as December 1943. This issue preceded, with \"disappearing contacts\" causing similar concerns as early as November 1942. Morale among Allied ASV flyers plummeted with this news and the decrease in U-boat contacts. Radar was completely turned off in several squadrons, where its use could only lead to more contacts. Tactics were improvised to salvage some usefulness for the radars, based on the assumption that the GSR would outrange the radar (an assumption that was largely false). Some of these tactics are listed below:\n\n1. Prohibition of special radar procedures during the approach, such as \"searchlighting\" the target, sector scan, or change of scan rate, since such changes could give away the position of the radar.\nU-boats would indicate to a GSR operator radar contact, allowing the U-boat to take evasive action. Attenuators, such as \"Vixen,\" were initiated to cause a gradual decrease in transmitted power as range closed, confusing the GSR operator. To use Vixen effectively, contact must be made at a range of 15 miles or greater and the cycle started soon after. Given that this is greater than the average radar range under many conditions, it could only be used for less than half the contacts. Production was slow, and installation was slower, resulting in Vixen having no operational opportunity justifying the effort spent in its development. An interim tactic of \"tilt-beam\" approach was employed.\nProposed methods to reduce signal intensity included tilting the radar beam up off the target to close the range. This technique required unusual skill and cooperation between pilot and radar operator and its value had never been adequately proven. The tactic of turning the spinner aft for 360-degree scanning radars and approaching by dead reckoning was suggested in desperation. The chances of a successful navigational approach were small compared to radar homing on the target, and this proposal was not very promising. A serious error in Allied thinking at this phase was overestimating the capabilities and efficiency of the Naxos GSR. It was believed that such a search receiver would completely nullify the effectiveness of S-band radar, but this did not prove to be the case. The data presented in Table 3 show:\nEffectiveness of night flying in the Bay of Biscay from October 1943 to January 1944, where the use of GSR might cause the largest reduction.\n\nExpected Disappearing Contacts\n\n| Type of Aircraft | Sightings | On Basis of | Previous Months |\n| --- | --- | --- | --- |\n| Wellingtons, British Mk III | 12 | Probably | Sightings on U-boats |\n| Halifaxes, British Mk III | 8 |  |  |\n| Liberators, ASG, searchlights 30 | 15 |  |  |\n| Liberators, ASG, no searchlights | 10 |  |  |\n| Total | 45 |  |  |\n\nPoor showing probably due to lack of experience.\n\nSearch Radar in Relation to Enemy Countermeasures\n\nGSR enabled detection of 25% of the U-boats that would normally have been contacted.\nA total of 44 percent of enemy aircraft attempted to evade detection altogether. Forty-four percent dived after being detected by radar but before being visually sighted, leaving 31 percent that were still sighted, even with GSR. At most, a reduction of 69 percent could be attributed to this.\n\nAs an overall average, day and night, including other areas, the reduction would be much less, possibly 25 to 50 percent. Since the sweep rate in S-band radar search is under most conditions several times that for visual, the use of radar was still imperative.\n\nEfforts were made, therefore, to revive confidence in radar and keep it in operation. Contacts by S-band radar continued to be made, and it became evident that the Germans did not have much confidence in the effectiveness of their search receivers, nor did they use them consistently. In the coming days, this trend continued.\nmonths they were to become more and more committed to the use of Schnorchel rather than search receivers to defeat Allied radar.\n\n1.4.2.4 X-Band Radar and Tunis GSR\n\nSince an S-band search receiver could, in principle, be highly effective, the use of radar of an even higher frequency was an obvious next step as a countermeasure to Naxos. Development and allocations of X-band (3-cm) equipments even preceded the advent of Naxos and were further stimulated by the problem it presented. However, the Germans were not caught napping this time. An H2X blind-bombing aircraft was lost over Berlin in January 1944, and from the damaged remains, the Germans learned of the new frequency band. It was assumed that this frequency would also be applied to ASV radar, and the development of X-band intercept receivers was started before the use of the X-band radar by the Allies in U-boats.\nThe search had produced many results. A well-designed receiver was developed, known as Tunis, which consisted of two antennas: the Mucke horn for X-band, and the Cuba la (Fliege) dipole and parabolic reflector for S-band. Installations began in the late spring of 1944. Installations seem to have been completed during the period of inactivity following the withdrawal to Norwegian and German bases, but the operational use of Tunis was not great due to the reliance on Schnorchel from that time on. The chief feature of Tunis was the directional antennas which gave increased sensitivity and range. To obtain full coverage, the antennas were rotated manually at about 2 rpm. Allied tests on captured specimens of this gear showed good performance with a range of about 15 miles on an aircraft at 100 ft, increasing to 40 miles or more at altitudes in excess.\nThe outstanding tactic proposed for Allied use against Tunis was intermittent radar operation. A schedule of two or three radar scans at intervals of 1 to 2 minutes for a narrow-beam radar will point the beam on target for only a small fraction of the time. Since the sweeping GSR beam is only occasionally pointed at the aircraft, and since a coincidence of these events is necessary for the GSR to achieve a detection, the probability of detection by GSR can be made rather small. Discussion of this procedure is given in Volume 2B, Chapter 5. Since it was not used to a significant extent in operations, it will not be discussed further here.\n\n14.3 Use of Schnorchel and Camouflage\n\nApparently dissatisfied with search receivers as a solution, the Germans introduced the Schnorchel, a snorkel-like device, and camouflage to counter Allied air superiority. The Schnorchel allowed U-boats to operate submerged for extended periods, making them less vulnerable to detection by both air and surface patrols. Additionally, the use of camouflaged U-boats, painted to blend in with the sea floor, further reduced their visibility. These tactics significantly increased the operational effectiveness of the German U-boat fleet.\nThe U-boat Command turned to more drastic measures for immunity from radar detection during the last year of the war. Schnorchel development began in the latter months of 1943, and equipment fitting to U-boats started early in 1944. Using Schnorchel for Diesel intake and exhaust, the U-boat could run at periscope depth with only a small Schnorchel head showing above the surface, yet accomplish the boat's ventilation and battery recharge previously requiring surfaced operations. Starting in the spring of 1944, U-boats spent very little time on the surface, employing Schnorchel or electric propulsion almost exclusively.\n\nOriginal Schnorchel gave reduced radar echoes merely because of their small size. The average range of detection was reduced to about a 1000 yards.\nThe third problem with detecting a Schnorchel on a surfaced U-boat is the echo being too small for detection until it enters the area of sea returns, effectively masking it. Many potential Schnorchel contacts are missed for this reason. Even without camouflage, a Schnorchel is a difficult target to detect by radar. The Germans developed nonreflective coatings for application to Schnorchel, further reducing its echo. This camouflage reached operational use only a few months before the end of World War 11.\n\nRadar Detection of Schnorchel:\nNumerous trials have been conducted with dummy or mockup Schnorchel targets to evaluate radar performance. It is not intended to present a summary of them here.\nTable 4. Test results on Schnorchel detection (ASWDU trials).\n\nType of radar: AN/APS-15, ASG\n\nAverage range on surfaced sub (miles) Average range on Schnorchel (miles) % runs on which contact made on Schnorchel Sea states 1 and 2 Sea states 3 and 4\n\nThe values quoted in Table 4 are typical. The figures below represent test results on Schnorchel detection during ASWDU trials.\n\nType of radar: AN/APS-15, ASG\n\nAverage range on surfaced submarine (miles) Average range on Schnorchel (miles) Percentage of runs on which contact was made on Schnorchel\n\nSea states 1 and 2 Sea states 3 and 4\n\nThe reduction in both range and reliability of detection, as compared to that on a surfaced U-boat, is serious. The extent of this reduction varies depending on the radar set involved and the sea state. The reduction in sweep rate ranges from 75% to 95%, even though the position of the Schnorchel was approximately known during these trials, making detection unrealistically easy.\n\nOperational results have been even more discouraging. For the period November 1944 to March 1945, an analysis was made of a region near the British Isles which contained approximately 0.25 U-boats per 1000 square miles.\nsq  miles.  Assuming  that  they  had  been  Schnorchel- \ning  about  a quarter  of  the  time,  the  expected  number \nof  sightings  made  by  the  19,360  flying  hours  done  in \nthe  area  would  be: \nNumber  of  sightings  = area  swept  x density \nof  Schnorchels \nThe  total  number  of  sightings  and  disappearing \nradar  contacts  made  at  night  was  16,  so  that \n13  sq  miles  per  hour.  (1) \nThe  sweep  width  is  then  about  1/10  of  a mile,  only \nabout  1 per  cent  of  the  value  on  a surfaced  U-boat. \nIn  operations,  therefore,  Schnorchel  has  been  very \nsuccessful  in  countering  radar  detection.  In  the  day- \ntime, when  visual  sightings  are  also  possible,  its  im- \nmunity from  contact  is  not  quite  so  great.  The  sweep \nwidth  has  been  estimated  at  0.6  mile. \n14.3.2  Countermeasures  to  Schnorchel \nA number  of  countermeasures  to  Schnorchel  have \nbeen  employed,  among  them  the  following. \n1.  Modifications  in  tactical  doctrine  to  match  the \nDecreased radar sweep width (see Volume 2B). This is not a universal scale factor, but must be analyzed for each search plan. For example, the shorter aircraft radar range is partially compensated for by the decreased submarine speed.\n\n1. Radar modifications to improve contact efficiency, such as sea return discriminator circuits.\n2. New radar developments of high-power, narrow-beam, short-pulse equipments designed to provide better resolution in search for small targets. These have, however, not solved the problem, and Schnorchel remains a very difficult object to detect. In the overall picture of ASW, surface craft have played a very important role in combatting Schnorchel operations. The decreased speed and mobility of a Schnorcheling submarine require it to operate in relatively restricted waters and focal areas.\nIn such conditions, search and counteroffensive operations by surface craft have good chances of success. As mentioned in Chapter 13, the use of sonobuoys for detection of Schnorchel has promise.\n\n1.3.3 German Camouflage Developments\n\nThe general problem of radar camouflage had been under intensive study in Germany since June 1943. However, the decision to apply absorptive coatings to Schnorchels was not made until the fall of 1944. Plans were made and put into effect at this time to provide microwave protection for all U-boats. It is estimated that 100 to 150 craft were actually fitted with coated Schnorchels before the end of March.\n\nTwo types of coatings were employed: the Jaumann and Wesch absorbers. The Jaumann absorber was made up of spaced graduated layers of semiconductors.\nThe Wesch absorber was made up of a rubber mat containing a high percentage of iron powder. The Jaumann absorber was more effective, and German reports indicate that the range of detection on a Schnorchel coated with it was only 15 percent of the range on the uncoated Schnorchel. One disadvantage, however, was that it had to be preformed and could be used only on flat and cylindrical surfaces. The absorptive properties of the Wesch absorber were not as good. It may be concluded, therefore, that the use of such absorbers would make Schnorchel practically safe from detection by 10-cm (and also 3-cm) radar. The Germans were concerned with the possibility of danger from radar of longer wavelengths, but it is doubtful that radar of this type would be very effective against such small targets. Use of a variety of absorbers could enhance this effect.\nThe frequencies would counter the effectiveness of these absorbers to some extent, until absorbers are developed to cover the whole microwave band.\n\nConclusions:\nIt can thus be seen that this succession of measures and countermeasures, tactical and otherwise, represented, in the main, a series of concessions by the U-boats to the effectiveness of radar-equipped aircraft. The result has been a great reduction in the mobility and attack potential of the U-boats, which, however, has gained them considerable immunity from airborne radar search. This situation was recognized very clearly by the Germans, and their large-scale program for the development and introduction of new types of U-boats of increased underwater speed and endurance was an attempt to overcome these limitations.\nChapter 15: Countermeasures to the German Acoustic Torpedo\n\nIntroduction\n\nFrom September 1943, German U-boats utilized acoustic torpedoes operationally during the last 20 months of World War II. The torpedo's performance is summarized as follows: It is launched in the standard manner, under gyro control on a collision course. When the torpedo gets close enough to a noise source, such as a ship's propellers, it detects the noise and \"homes\" in, turning towards the source and attempting to maintain this course until a hit occurs. The torpedo needs only to come within homing range.\nThe range of a ship to have a high probability of hitting is increased with the use of a homing torpedo. In effect, it creates a larger and more circular target than that of an ordinary \"straight-run\" torpedo. The louder the ship (in the frequency band received by the torpedo), the greater the homing range and consequently the effectiveness of the weapon.\n\n1.1 Types of Countermeasures\n\nThe simplest countermeasure to such a torpedo \u2013 slowing the target \u2013 is suggested by the fact that a ship's sound output increases rapidly with speed. A ship is so much quieter at 7 knots than at 15 knots that the homing range is only about one-fifth that at the higher speed, and the effective target size is correspondingly reduced. Slowing considerably increases vulnerability to torpedoes of other types, however. Other means of quieting the ship include:\n\n- Using hull-mounted sonar to detect and counteract the torpedo's homing signal\n- Deploying decoy sonobuoys to confuse the torpedo's homing mechanism\n- Employing active sonar to jam the torpedo's homing signal\n- Utilizing bubble screens to disrupt the torpedo's acoustic homing\n- Implementing torpedo deflection systems to alter the course of incoming torpedoes.\nShips' propellers, such as masking them with bubbles, have at best halved the homing range in tests to date. Slowing the ship is an example of a tactical countermeasure since no new gear is required for its introduction. A material countermeasure, on the other hand, is one which does involve the use of special equipment. Another type of tactical countermeasure is possible if the target ship has sufficient warning as to when and where the torpedo is fired and if the torpedo's homing range is not too great. A radial maneuver may be made which will keep the ship out of listening range of the torpedo. This has been called a \"step-aside\" when used by an antisubmarine vessel attempting to approach the submarine for an attack. It is useful only when contact has been made at long range and hampers the ship considerably in its attempt to get in to sonar contact.\nThe  third  tactical  countermeasure  is  to  maintain \na speed  greater  than  that  of  the  torpedo  and  is  there- \nfore unavailable  to  many  ships.  A torpedo  homing  on \na target  faster  than  itself  will  usually  be  left  behind. \nIts  listening  sensitivity  is  limited  by  its  own  self \nnoise,^  which  in  turn  increases  rapidly  with  its  speed. \nThus  some  compromise  is  required  between  speed \nand  homing  range,  and  an  acoustic  torpedo  will  usu- \nally be  slower  than  its  straight-running  counterpart. \nThe  ship  speed  required  to  outrun  the  German  tor- \npedo was  initially  considered  to  be  about  20  knots; \nthis  estimate  was  later  raised  to  25  knots,  but  final \ninformation  indicated  that  20  knots  was  adequate \nafter  all.  Continual  rumors  of  a 30-knot  modification \nof  the  torpedo  cast  doubts  on  these  figures,  however. \nIn  addition  to  the  above  tactical  countermeasures, \nSeveral possible material countermeasures exist. These usually involve noisemakers (NM's), which are small devices several times louder than a ship at the frequencies received by the torpedo. The NM's must be placed to attract the torpedo on its initial approach and prevent its getting into a position to home on the ship. By the end of 1943, escort vessels were equipped to tow one or two noise-makers about 200 yards astern. Equipment of this type was the standard material countermeasure employed during the remainder of World War II.\n\nThe evaluation of such countermeasures would be much simplified and shipboard morale much improved if some indication were given when a torpedo has been successfully countered. Development work was done on several devices to detonate the torpedo before it reached the ship. These included:\nNets, rotating barriers, explosive streamers, and magnetic fields set up by trailing electric cables are countermeasures to the German acoustic torpedo. The noise generated by the torpedo itself, particularly its propellers, makes a substantial contribution to the background noise heard by the acoustic mechanism. This contribution is called self-noise.\n\nCountermeasures to the German acoustic torpedo were simplest and most effective when used with towed NM's. However, they were never issued because they were fragile, difficult to handle, uncertain in effectiveness, and seriously impeded the ship's maneuvering.\n\nA towed NM alone interferes considerably with the antisubmarine vessel's offensive. The towline restricts the maneuverability of the ship, and the sound generated interferes with sonar and gives the submarine early hydrophone warning. To get around these disadvantages, consideration was given to explosive countermeasures.\nPendable noisemakers were projected from the ship or dropped astern by 1945 for masking U.S. submarines from enemy sound gear. Their practicability as a torpedo countermeasure had been tested. An NM must be projected at least once every 90 seconds as long as there is danger of a torpedo being fired. This is feasible only when a submarine is known to be close. It has long been envisioned that the ultimate countermeasure to acoustic torpedoes would incorporate a detector that would give sufficient warning of an approaching torpedo to investigate the successful use of expendable NM's. Such a detector is not yet available.\n\nThe bulk of this chapter deals with the evaluation of towed NM's, as this type of countermeasure was of primary importance during World War II.\nThe effectiveness of such a countermeasure depends on the mode of operation of the torpedo. This discussion evaluates its impact chronologically in light of changing information regarding the torpedo. The most important operational data is included, which is discouraging as most detected torpedoes only hit ships. Additionally, it is difficult to determine which torpedoes were acoustically controlled, making data interpretation uncertain. It is hoped that these difficulties can be overcome by analyzing German Admiralty records, which should provide further information on the operational effectiveness of Allied noisemakers. Expendable NM's did not see operational use and will not be discussed further. They must be kept in storage.\n15.2 Development of Towed Noisemakers\n15.2.1 German Introduction of Acoustic Torpedoes\nBy early 1943, intelligence indicated that the Germans had an acoustic torpedo in production and successful running tests had been conducted the previous summer. In response, Allied study of countermeasures, which had been following the development of similar torpedoes, was prioritized. Various possibilities mentioned in the introduction were considered.\n\nAn excellent towed noisemaker was already in use for sweeping acoustic mines. This device consists of two components.\nSteel bars, clamped parallel and close together, are pulled through water in the direction perpendicular to the plane containing their axes. The water flowing between them causes the bars to strike against each other and give off much more acoustic energy than a ship at all frequencies greater than 1 kc. Both Great Britain and the United States modified these type of noisemakers to be towed at an adequate speed (at least 10 knots) and produce good sound output for several hours. The parallel-bar type of noisemaker has since been in general use by both navies. By May 1943, the British had information indicating that the German torpedo homed at 20 knots with a minimum turning radius of about 100 yards and that its homing range might be as great as 1000 yards. They also suggested that the torpedo might be \u201cforward-homing.\u201d\nFrom the information obtained, it was determined that hydrophones in a torpedo might be very insensitive to sounds approaching from near its stern to reduce self-noise from propellers. The British concluded that two Noise Makers (NM) should be towed 200 yards astern and separated by approximately 100 yards. An acoustic torpedo could not be sensitive to lower frequencies because a hydrophone system small enough to fit in a torpedo would not be sufficiently directional.\n\nDEVELOPMENT OF TOWED NOISEMAKERS\n\nA torpedo is likely to overtake a towed noisemaker from the rear during its gyrations and pass over it, heading towards the ship. With a forward-listening torpedo, there might be significant danger that the torpedo would escape from a single noisemaker.\nAt this time, hearing and overtaking the ship while keeping it in the insensitive arc astern. If, however, as it left one nautical mile (NM) behind, the torpedo found another on its beam, this second NM could be relied on to take control. The simplest way to get this protection was to tow two noisemakers abreast, sufficiently separated to assure that whenever the ship was ahead of the torpedo, there was also an NM within 110 degrees of the torpedo's bow. To provide separation, the British began developing a diverter with the necessary rudders to tow an NM fastened below it at the required distance out of the ship's wake. They already had a parallel-pipe noisemaker with a sound output 20 decibels over that of a ship and an endurance of 25 hours at 12 knots. The name FOXER was given to the complete set of this noisemaking gear, including two NMs, two diverters, and the tow-gear.\nIn the United States, a parallel-bar noisemaker designated FXR was in production by July 1943. Preliminary theoretical studies had been made of the behavior of an acoustic torpedo under the influence of a ship and an FXR 500 ft astern. The tacit assumption was made that the torpedo could listen equally well in all directions. It was concluded that one man could maintain control of the torpedo once it had reached it, and that the only danger arose from torpedoes fired from directly ahead which were drawn in to, or very close to, the ship while homing on the FXR.\n\nDuring the summer, some prisoner of war information (later proven false) indicated that the hydrophones were along the torpedo\u2019s sides. This tended to substantiate the all-around listening theory and the belief in the adequacy of one noisemaker.\nPrisoners of war stated that the torpedo was primarily used against escort vessels, enabling the U-boat to disrupt a convoy's defenses. This possibility had not occurred to the Allies, probably because trajectories of this type are discussed on page 168. Much of the early information concerning the German acoustic torpedo was obtained from interrogation of prisoners. Unfortunately, they did not, in general, know anything about its actual operation, so it was necessary to deduce its method of operation from fragmentary observations they had made of its construction and use. The screening vessels had never been a major target, and because it was considered unlikely that the self-noise could be reduced enough to allow a speed greater than 20 knots. Escort vessels now seemed the most logical targets for an acoustic torpedo.\nThe speed, maneuverability, small size, and frequent attacks of escorts made them poor targets for ordinary torpedoes due to their small bow aspect. However, with a homing torpedo, these disadvantages were cancelled. The higher speed created a louder, larger target, and bow shots were potentially preferable to beam ones. More effort was therefore expended on parallel-bar NM's suitable for higher speeds. The British encountered more difficulties with their cumbersome divers, but the possibility of getting such gear used successfully seemed greater when handled by naval crews than merchant vessel crews. This was the situation when the Germans were first ready to use their acoustic torpedo against the Allies, introduced on September 20-22, 1943.\nThe first full-scale North Atlantic operation since May involved the wolf-pack attack on Convoys ONS 18 and ON 202. Three escorts and six merchant ships were sunk, and an escort was damaged. Acoustic torpedoes accounted for the damaged escort and two of the other escorts. In contrast, a German War Order claimed 12 escorts sunk, 3 damaged, and 9 merchant ships sunk, indicating a high expenditure of torpedoes. However, the torpedo proved a threat that could have been much more effective had the enemy been able to get more than two U-boats in contact with the convoy at one time. The potentialities of the torpedo caused the Allies extremely grave concern.\n\nOn September 23, the Admiralty issued a comprehensive appreciation of the use of the German acoustic torpedo. This included a review of the information.\nCountermeasures to the German Acoustic Torpedo:\n\nReports on the torpedo's characteristics were collected and evaluated, along with development of various noise-making gadgets. An extensive study of the countermeasure problem was initiated in the United States. Thirty-nine warships were sunk by U-boats between January 1942 and August 1943, in contrast to 1,541 merchant ships.\n\nOne of the early decisions was to discourage the development of impulsive noise sources with bursts less frequent than about 20 per second; these in:\n\n(Note: The text appears to be mostly readable, with only minor OCR errors. No significant content seems to be missing or unreadable. Therefore, no major cleaning is necessary. A few minor errors have been left in place for the sake of preserving the original text as much as possible.)\nIncluded rapid machine gun fire into the water and the grenade noisemaker consisted of a series of explosive caps. It was felt that the torpedo probably would not respond to such a source. However, if it did, a relatively steady source such as a ship would be able to override it even when providing a much weaker RMS (or average) signal. Such discrimination would occur with the time constants that were most natural for a torpedo\u2019s amplifying and control circuits. This would not only be a good anticountermeasure device but would also (and more importantly) discriminate against the irregular peaks which are among the most undesirable features of a torpedo\u2019s background noise. It soon became apparent, however, that a reliable evaluation of the performance of any particular countermeasure required a detailed understanding of how the torpedo functioned. The two differing mechanisms were:\n\n1. The torpedo's acoustic homing system, which used the sound waves emitted by a ship to home in on its target.\n2. The torpedo's passive sonar system, which listened for the sound of a ship's propeller or engine and used that information to determine its target's location.\n\nUnderstanding how each system responded to various countermeasures was crucial to evaluating their effectiveness. For example, some countermeasures might be effective against the active homing system but not against the passive sonar system, or vice versa. Additionally, some countermeasures might be effective against both systems, but to different degrees. Therefore, it was essential to conduct thorough testing and analysis to determine the strengths and weaknesses of each countermeasure and how they could be used effectively against enemy torpedoes.\nThe primary aim of studying torpedo behavior is to determine its trajectory under specific conditions and assumptions, as this significantly impacts forward-listening and all-around listening for NM arrangements. A careful analysis of acoustic torpedoes follows, outlining their salient features in the sections below.\n\n15.2.2 Torpedo Trajectory Analysis\nTo determine a torpedo's path, a means for rapidly predicting its behavior in the presence of a particular NM system and under specific assumptions about numerous torpedo characteristics is necessary. Key factors include torpedo speed, which determines the required ship speed to outrun it. The torpedo:\n\n\"The primary aim of a study of torpedo behavior is to determine the path, or trajectory, it follows under specific conditions and assumptions. This information is crucial for forward-listening and all-around listening in NM arrangements. In order to accomplish this, a method must be developed for quickly predicting a torpedo's behavior in the presence of a particular NM system and under various assumptions regarding numerous torpedo characteristics. Among the most important factors are the torpedo's speed, which determines the necessary ship speed to outrun it.\"\nThe trajectory of a ship can be expressed as a function of the ratio of its speed to that of a torpedo. Under the influence of a single noise source, the torpedo can be assumed, for a first approximation, to always steer towards the source. This results in a straight path when the target is stationary, such as an expendable NM. With the target at constant speed on a straight course, the pursuit curve is a tractrix. (A) In true space. (B) In relative space.\n\nA tractrix is similar to that shown in Figure 1, with an adjustment only in scale. With an (x,y) coordinate system centered on the target and the target heading in the positive x direction, the relative trajectory is given by equation (1):\n\ny = yo * tan(\u03b8) / cos(\u03b8), x = y / cot(\u03b8)\n\nwhere k = ratio of target speed to torpedo speed,\ny = distance at which the torpedo first passes.\nabeam of the target,\n6 = torpedo's bearing relative to the target.\nIn stationary coordinates whose origin is the target's position at the time the torpedo is first abeam of it (at distance yo), the target's positions are given by equation (2), the tractrix, by equation (3).\nWhen dealing with targets moving together, such as a ship and towed noisemakers, it is simplest to draw trajectories relative to this moving system. For each SHIP MOTION:\n\nFigure 2. Course of torpedo when circling. (A) Fixed coordinates. (B) Relative coordinates (speed ratio = k = 1/2I ship motion ^).\n\nDEVELOPMENT OF TOWED NOISEMAKERS\nf'M ml\nPORT PATTERN\nu STARBOARD PATTERN\nTORPEDO\nAXIS\n\nFigure 3. Typical sensitivity pattern.\nValue of k that it is desired to consider, a template sheet can be prepared, covered with a family of tractrices\u2014calculated from equation (1)\u2014so that by overlaying this template on the target's motion, the desired value of k can be determined.\nInterpolation: A pursuit course can be drawn from any point to the center for any specific problem. Trajectories can be traced from these templates. A torpedo cannot always follow a tractrix, however, because its minimum turning radius may prevent it from making the sharp turn required. If the torpedo turns as sharply as possible when trying to get headed towards a noise source, its path in relative space will be a cycloid rather than a tractrix. In the fall of 1943, information continued to confirm that the enemy had enlarged the rudders of their G7e torpedo to give the acoustic torpedo a minimum turning radius of 80 degrees. The cycloid is shown in Figure 2. Templates can be drawn for cycloids in the same way as for tractrixes as an aid in drawing the relative diagrams.\n\nThe behavior of the torpedo depends upon acoustic conditions.\nIn the fall of 1943, the exact characteristics of the German torpedo were unknown, but it was considered probable that a listening system was employed. This scheme would determine from which side of the torpedo the sound arrived. A listening arrangement would be much simpler than one involving echo ranging and less subject to failure. It would probably have a greater homing distance. A torpedo would have little use for range information. The enemy had had much more experience with passive detection equipment. None of the intelligence information suggested echo ranging.\n\nCountermeasures to the German Acoustic Torpedo:\nThe rudder is controlled by the ratio of voltages in two electric channels. If a steady sound source is detected, the torpedo can be steered towards it by altering the voltage ratios accordingly.\nWhen a torpedo is moved around with a constant range, the voltage in the port channel is much greater when the source is within certain bearings on the torpedo's port side compared to when it is anywhere on the starboard side. Similarly, the starboard channel is most sensitive to signals from the starboard side. In determining a trajectory, it's necessary to find out for each torpedo position what are the relative voltages in each channel due to each noise source. To facilitate this, another set of templates is drawn, one for each assumed sensitivity pattern. Each template is a transparent geographic plot to be centered on the torpedo position with the torpedo axis marked. By one curve, it shows the locus of all points at which a standard noise source would create a given voltage in the port channel, and by another, the same for the starboard channel. Parallel to these curves are lines representing the sensitivity patterns for each channel, allowing for easy comparison and identification of the source of the voltage readings.\nLobes are drawn corresponding to sources, each an integer number of decibels louder or softer than the standard. A typical sensitivity pattern of this sort is shown in Figure 3.\n\nA standard noise source at point X in Figure 3 would give a signal of -12 db in the port channel and +2 db in the starboard. If, at the same time, a source 10 db louder than the standard (for example) is present at point A, it would give a signal of 8 db in the port channel and -3 db in the starboard. To obtain the total voltage in each channel with both present, the square root of the sum of the squares of the individual contributions is taken. This method should be sufficiently accurate unless a source is very intermittent, e.g., a grenade exploding only ten times a second.\n\nIn constructing these templates, it is assumed that the sound pressure is inversely proportional to the square root of the density and temperature.\nThe range varies from the source (six decibels less per distance, doubled). This is an average value of the attenuation found in experiments, but the effects of significant fluctuations can usually be shown to be negligible. The ranges involved at critical times are too small to allow linear absorption of sound in open water to become important. However, there is evidence of considerable attenuation in the ship's wake, about 2 decibels per foot at 24 kc.\n\nThe simplest sensitivity pattern is a circular one. In the initial trajectory studies, an attenuation of 0.1 decibels per foot was taken as a conservative assumption, even at lower frequencies.\n\nFigure 4. Simplified sensitivity patterns. (A) Circular pattern. (B) Modified circular pattern.\n\nThe template curves for each channel are semicircles on each side of the torpedo axis, as shown in Figure 5.\nThe assumed dead zones of no differential are negligibly small ahead and astern of the torpedo. To break away from all-around listening, it may be assumed that there is a wide angle of zero sensitivity astern, leaving the lobes as shown in Figure A. A more realistic picture may be obtained by using another mathematical approximation which recognizes that the response of any hydrophone system changes smoothly with angle. If 9 is the angle off the torpedo\u2019s bow, the contours of equal sensitivity can be expressed as cos (NO). The sensitivity will then be a maximum ahead (except for a negligible dead angle) and will decrease gradually as 0 increases, becoming zero for all angles greater than TrjZN. Several such patterns are shown in Figure 5. For A = there is some listening at all angles except dead.\nIn an actual torpedo, each channel may have its own set of one or more hydrophones directed toward one side. Alternatively, the channels may be connected through phasing circuits to the same or partially the same group of hydrophones all facing forward. Either system would lead to the same kind of pattern. It is reasonable to expect that if an effort is made towards forward-listening, the maximum lobes for each channel would probably be rather broad and centered between 20 and 60 degrees off the bow. It is difficult to secure a rear response from either channel.\n\nThis pattern is essentially that assumed in the earliest United States studies mentioned in Section 15.2.1, this chapter.\n\nFigure 5. Cos (Nd) sensitivity patterns.\n\nDevelopment of Towed Noisemakers\n\nConnected through phasing circuits to the same or partially the same group of hydrophones all facing forward. Either system would result in the same type of pattern. It is expected that if a focus is on forward-listening, the maximum lobe for each channel would likely be quite broad and centered between 20 and 60 degrees off the bow. It is challenging to obtain a rear response from either channel.\n\nThis pattern is the one assumed in the earliest United States studies discussed in Section 15.2.1 of this chapter.\n\nFigure 5. Cos (Nd) sensitivity patterns.\nThe pattern has a maximum sensitivity 45 degrees off the bow, with sensitivity 30 dB lower in both channels throughout a 100-degree arc astern. This pattern, shown in Figure 3, could be made sharper with greater fore-aft discrimination if the frequency of maximum sensitivity was over 40 kc. However, this would reduce the homing range due to sound absorption in open water, which becomes appreciable at such frequencies. The rudder position should depend on the decibel differential between the two channels.\nThe ratio of their voltages. Any control involving the absolute magnitudes of the voltages could not handle the widely different signal strengths to be expected. By using templates and a curve expressing in decibel units the square root of the sum of the squares relationship, the signals in the two channels can be found in decibels above the same standard; these values can then be subtracted to give the differential.\n\nThe most plausible simple assumption as to the way rudder position depends on the differential is a \u201cflip-flop\u201d type of control, in which the rudder is thrown hard over whenever one channel has a given excess (say 3 db or more) and stays over until the other channel has the required excess. This flip-flop control appears necessary for a forward-listening type of torpedo based on the following argument.\nMost torpedoes approaching from forward angles will miss a ship (with no noisemakers) on the first pass because they cannot turn sharply enough to stay on a tractrix and possibly because the principal target pattern was decided upon in the fall of 1943 based on United States experience in the design of hydrophones and acoustic torpedoes. Get may actually be collapsing bubbles somewhat astern of the propellers. Having passed the ship's stern, many of these torpedoes will have the ship in the sector on their own stern where they can get no differential or even any signal over background. If, with no differential, the torpedo straightens out or returns to its original gyro course, it will never hear the ship again and be lost astern. On the other hand, with flip-flop control, the missile will confront.\nThe torpedo continues circling until it again hears the target. The same would happen about a single NM towed astern. Admittedly, the torpedo would stay on its tract with less weave if, on loss of differential, it straightened out or, preferably, had \"graduated control,\" that is, if the amount of rudder depended on the differential and thus on the bearing of the target off the bow. However, even with flip-flop control, the weave should not be more than 10-20 degrees, and improvement in this would not compensate for the failure of so many bow shots.\n\nThe critical differential, designated by D, may reasonably be assumed to be 3 db. With a lower value, there would be too much danger of undesirable rudder actuations. These might result from minor lobes in the sensitivity pattern astern, from fluctuations in the background noise, or from fluctuations in the target's bearing.\nWith these limitations, D should be as small as possible because the larger D, the less the torpedo's homing range. As a torpedo approaches a ship from a distance under gyro control, background sound will initially predominate, causing approximately the same voltage in each channel. If the bearing to the ship is near the angle of maximum sensitivity for one channel, the voltage in that channel will increase as the ship is approached. The torpedo will turn towards the ship when the voltage in that channel due to the ship plus background is D db greater than that in the other channel, which is due to background plus a negligible contribution from the ship. If a greater D is required, the torpedo must approach closer on gyro before the ship noise can overcome background.\n\nThe maximum range at which a given ship flips this record.\nThe rudder changes greatly with the ship's bearing off the torpedo's bow. The range is zero with the ship either dead ahead or, probably, in a large sector astern - that is, with which the sensitivity patterns for the two channels differ by less than 0.5 dB. At other 0's, the range depends chiefly upon the sensitivity patterns. For any choice of sensitivity pattern, countermeasures to the German acoustic torpedo of D, and of ship intensity over background, a so-called steering pattern can be drawn, plotting the rudder actuation range against 0. Such curves are useful only when no noise maker is present. The maximum of either lobe of a steering pattern gives the maximum range at which a ship can direct the torpedo. The value of this range depends on the noise output of the ship and on how well the torpedo's background noise has been suppressed.\nFor these quantities, accurate determination is possible. Even for a given torpedo and specific class and speed of ship, there would be sufficient variation in ship output and transmission conditions to make the range uncertain by a factor of three. It would be unwise to base a countermeasure on an arbitrary actuation range.\n\nNow, we can briefly consider the trajectories for which the torpedo was primarily designed: those against an unsuspecting ship. Assuming the torpedo is a modification of the German electric G7e, the firing range was likely not over 6000 yards. Ranges between 1000 and 4000 yards would be the most likely. The initial gyro course would be a collision course for the ship, possibly for the ship\u2019s stern, to increase the chance of coming within homing range. When the torpedo reaches a point where\nthe ship's noise can overcome background noise, as shown by the ship's stern reaching the appropriate contour on the steering pattern centered on the torpedo. If this happens at short enough range, the torpedo might hit the ship before turning far enough to head at the stern, as shown by trajectory A, Figure 6. Alternatively, assuming flip-flop control, the torpedo will turn until the screws have passed through the dead angle of small differential on its bow and have reached the opposite lobe of the steering pattern where the other channel has a D-db excess, causing the rudder to flip. With a forward-listening pattern and mechanical time constants of the order of 1/10 kHz, there was once a good chance that the required time to take the torpedo off gyro would be greater than\nThat which was required for later steering. Using this \"gate\" would sacrifice some homing range to prevent a temporary peak in ship noise from taking the torpedo off gyro course and leaving it circling at a distance such that normal ship noise could not be heard. However, the gate was assumed not to exist since its presence was found to be, at best, an aid to countermeasure.\n\nVarious estimates were made of the actuation range of the German torpedo, ranging from 100 to 1,000 yards for a typical ship target. Later tests suggest the higher figures to have been more accurate.\n\nThe course reversal should occur with the target less than 10 degrees off the bow. By repetition of this procedure, the torpedo follows a tractrix towards the screws with a small weave. Trajectories marked B in Figure 6 are examples of such tractrices.\nIf the tractrix approaches from dead ahead, the torpedo may hit the ship before coming abeam the screws. If the tractrix is entered sufficiently far astern, the torpedo will follow it all the way in, making a hit on the ship\u2019s stern. In the intermediate cases, including most shots fired from forward of the beam, the torpedo is not able to keep headed for the screws because the radius of curvature of the tractrix becomes less than the torpedo\u2019s minimum turning radius. In the (x,y) coordinates of Figure 1 relative to the source, the loci of such points are two circles tangent to the x-axis at the origin and of radius y^KR, where R is the turning radius of the torpedo. The torpedo is forced to lose ground astern, usually missing the ship on the first pass. Even though the ship may now be in a different position.\nthe dead zone astern of the torpedo, the flip-flop control will cause the missile to continue circling forward. It may hit the ship's side before it has circled far enough to be headed at the screws, as in trajectory C, Figure 6. Otherwise, it will make another pass at the screws, usually on a rear tractrix leading to a stern hit, as in trajectory D. In all cases, a hit occurs on at most the third pass, as in trajectory E. Any trajectory can, like those of Figure 6, be drawn relative to the ship by tracing from the appropriate tractrix and cycloid templates.\n\n15.2.3 Theoretical Trajectories and Noisemakers\n\nNext to be considered are the trajectories which arise when a single noisemaker E, louder than the ship, is towed under the wake about 200 yards astern. The submarine\u2019s firing procedure would be the same as for the ship alone, but the torpedo would get on a different trajectory.\nA torpedo is attracted towards a noisemaker at ranges of a mile or more, if F is 12 db or more. Any torpedo in working order is drawn into the system. The ship's sound cannot influence the torpedo except within about 50 yards of the screws, as long as the NM is on its forward bearing. Thus, the paths to the NM are similar to those to a ship by itself.\n\nA direct hit occurs when the torpedo is drawn into the ship while steering towards the NM. Such hits result from tractrices that happen to go through the ship. These hits are independent of the NM's strength or distance astern. To have a good chance of making such a hit, the firing submarine must be directly ahead of the ship, not more than about 3 degrees off the bow. Conversely, the ship can be made safe from them by never heading directly at the submarine.\n\nIf the NM is too weak or too far astern, a forward-firing torpedo may miss.\nA listening torpedo fired from about 10-20 degrees off the ship's bow may result in an indirect hit. This happens when the torpedo's trajectory comes close enough to the ship that it is forced to circle out of the trajectory behind the ship's stern and then pursue the ship for a stern hit, keeping the Nemesis in the dead angle. Allowing a margin of safety, a directive was issued specifying that when possible, any submarine be kept more than 10 degrees off the bow of a ship towing FXR aft. Path A in Figure 7 illustrates a trajectory that could lead to an indirect hit. For the following explanation, assume that the torpedo is weaving towards the Nemesis past the ship's port side. While turning to the left in the weave, the left channel may receive a signal from the ship which is within D db of that received in the right channel from the Nemesis.\nIf the proximity of screws prevents the acquisition of differential D even when the NM is at the maximum sensitivity angle for the right channel, the torpedo will continue circling left. During the turn, the NM's bearing off the torpedo's bow increases steadily through angles of decreasing sensitivity. In dangerous cases, bearings to the screws on the other side increase less rapidly, and the range to the ship decreases, tending to keep the torpedo circling. This condition continues if the torpedo has enough space to turn (about 90 degrees) before crossing the wake. Eventually, it will be heading towards the screws with the NM in its dead angle.\nThe typical trajectories of acoustic torpedoes relative to a 12-kt ship with a single towed noisemaker are depicted in Figure 7. If the trajectory is too close to the ship, as in Path A' of Figure 7, the bearing to the ship increases rapidly around the time of crossing the wake, and the torpedo regains control. Thus, there may be a dangerous group of torpedoes close enough to the ship for it to deflect a torpedo but far enough away to allow it sufficient circling space. The danger of indirect hits can be eliminated by making the torpedo noise maker sufficiently loud to prevent the torpedo from leaving any tractrix that is far enough from the ship to provide circling room. Any reduction in torpedo turning circle therefore increases the danger from such shots for the cos (I/2 \u03b8) patterns.\nAn NM requires approximately 10 dB of \"practical\" sensitivity for detecting torpedoes that have neither directly nor indirectly hit, as shown in Figure 7. Torpedoes that miss the NM continue towards it, with some approaching from the rear for a stern chase, while others pass astern and circle forward with minimum turning radius. These shots cross in front of the NM and continue circling, falling significantly behind and entering a stern chase. All trajectories lead to a stern chase within at most four passes at the NM. By employing various sensitivity patterns, it can be demonstrated that during this preliminary weaving about the NM, a ship cannot capture the torpedo if the NM is at least 200 yards astern and able to hold the torpedo after a stern chase.\n\nThe success of a single noisemaker arrangement depends on this factor.\nThe most critical factor for preventing a torpedo from hitting a ship after it has passed over it during a stern chase is the torpedo's sensitivity pattern. If the torpedo can hear equally well in all directions (as assumed in early US studies), the ship's noise, being louder and closer, will cause the torpedo to circle to the rear and initiate another futile stern chase. Regardless of how loud the ship's noise is, it cannot be relied upon to counter a \"mathematical\" sensitivity pattern with a dead zone aft, such as that in Figure 4B. The ship's noise is likely to guide the torpedo to a hit, with the torpedo falling into the dead zone and remaining there.\n\nAccurate, detailed knowledge of the German acoustic torpedo's sensitivity pattern is necessary for effective countermeasures.\nThe sensitivity pattern of torpedoes for safety from stern chases has not been available, leading to doubts on the subject. This has been the crux of the countermeasure problem. The cos (1/2^) pattern, with sensitivity greater than zero everywhere but right astern, is countered by an NM that is 10 db or more louder. In this case, attenuation of the ship's noise in the wake is sometimes needed to cause the torpedo to turn sufficiently for the NM to regain control. With an estimated 0.1 db per foot for the attenuation, there is no chance that a torpedo in the wake and near the NM could hear the ship. This protection is not diminished if the NM should happen to be to one side of the wake rather than underneath it. The more realistic practical sensitivity pattern gives new assurance of the value of a single NM.\nA torpedo passing over a sufficiently loud Nemson on a stern chase receives so much signal in both channels from the Nemson that the additional ship sound in one channel cannot provide the necessary differential to flip the rudder. With flip-flop control, the torpedo stays in the circle it happened to be in as it crossed the Nemson until it falls way behind. For a Nemson towed 570 ft astern, an output of 12 db above the ship can be shown to be adequate. The required output decreases slightly with increased ship speed because the torpedo's distance of closest approach to the ship is increased.\n\nBased on early recommendations, FXR was being prepared during the fall of 1943 with 200 yd of cable. The cable sag resulted in a towing distance of 570 ft. The completed trajectory study, made following-\nThe above outline revealed no reason for changing this. A longer tow would require a higher output to prevent indirect hits and increase handling difficulties. A shorter tow would require a higher output to prevent stern chase hits. It would have been nice to tow the NM beyond the homing radius of the torpedo on the ship. However, this was precluded by the uncertainty of this radius and the greater NM output required to prevent indirect hits if, as is likely, the radius is over 200 yards. The FXR had to be \u201cdepressed\u201d below the bottom of the wake so that its sound would not be muffled in any direction. There was, however, no harm in its towing somewhat to one side of the wake while still maintaining its depth. Consideration was given to a noisemaker fixed with respect to the ship but on some other bearing.\nThe other positions, which might have been accomplished by concentrated machine gun fire, seemed inferior. The chance of direct hits increased since the ship cut across more tractrices.\n\nDevelopment of Towed Noisemakers\nFigure 8. Typical trajectories relative to a 16- to 18-kt ship with two towed noisemakers. Similar trajectories from starboard side.\n\nFor safety from indirect hits, it was necessary to keep the NM within 300 yards of the screws. Most important, the ship was in a better position to capture the torpedo as it circled back from the NM. Finally, the sonar interference would be increased.\n\nTrajectory analysis confirmed the conclusion that two NM's towed abreast gave a more certain counter-measure than a single FXR. The advantage of the British double FOXER lay in its elimination of practically all the ambiguity with regard to stern chases.\nA torpedo with zero sensitivity abaft the beam, such as the cos 0 pattern in Figure 5, could be relied upon, after passing over one nautical mile (NM), to be drawn to the other before getting too close to the ship, as shown in Figure 8. During the initial approach, the FOXER system is equivalent to one NM with the same total output. The torpedo is either on a tractrix toward one of the NMs or toward the \u201cacoustic center of gravity\u201d between them. Thus, the chance of a direct or indirect hit is essentially the same for the double FOXER as for a louder single FXR.\n\nHighest priority was given to the development of adequate diverters. However, the production and handling difficulties seemed extremely great with FOXER. Since most of the evidence indicated the adequacy of a single NM, the decision was made by the United States.\nStates will issue FXR. Emphasis was placed on examining each bit of new evidence to ensure this decision was not invalidated.\n\n15.2.4 Detailed Intelligence Concerning the German Torpedo\n\nAs the ideas described above were being worked out in detail during the fall of 1943, further information was accumulated on the operation of the German torpedo. In mid-October, a detailed and apparently accurate description of the T-4 acoustic torpedo was obtained from a prisoner of war (P/W) whose last cruise started on July 20 with three T-4s aboard. He also reported that an improved model, the T-5, was expected for operational use in August. The T-4 was a modification of the electric G7e torpedo, slowed to 20 knots and with larger rudders to give it a 90-m turning radius. A liquid-filled plastic nose enclosed two forward-facing hydrophones.\nIn a pre-installation test, known as the \"Spatz\" test, the rudder was observed to have three positions: hard over on each side and occasionally central. A switch was to be set to either \"WS\" or \"NS\" at the time of firing. The effect of this switch on the acoustic rudder control was undecipherable, a fact that didn't become clear until much later.\n\nAnother prisoner of war reported observing running tests of the torpedo in the Baltic. He confirmed the general features of our trajectories but noted a noticeable weave. This tended to confirm the belief that flip-flop control was used.\n\nUsing the prisoner of war's description of the T-4 nose as a starting point, arrangements were made to reconstruct the hydrophones in order to obtain their sensitivity pattern. By December, preliminary results indicated that the T-4 had velocity hydrophones.\nThe sensitivity of the reconstructed T-4 hydrophone system is connected by phasing circuits and is sensitive at approximately 5 kc. The sensitivity pattern would only be about 25 dB. (Figure 9. Sensitivity pattern of reconstructed T-4 hydrophone system.)\n\nCountermeasures were taken to the German acoustic torpedo: decrease frequency by 5 db down astern. This was welcome news, tending to confirm the practical pattern, though complete measurements were not made until somewhat later.\n\nHowever, not all was rosy. Measured equipment immediately broke down permanently, tentatively indicating that the ship's own sound was not attenuated in its wake at frequencies below 10 kc. Thus, the wake could not be relied upon to turn the torpedo after a stern chase. Full reliance had to be placed on the sensitivity not being more than 30 dB down astern.\n\nScattered information indicated that the T-5 was in use and had a speed of 24.5 knots.\nThe importance of trajectories involving low-speed ratios increased, and there was growing interest in how self-noise had been reduced. One fantastic report suggested that much of the T-5 torpedo had been stuffed with guncotton for acoustic insulation and extra explosive power. Two models of T-5 were identified: one with a round plastic nose like the T-4, and the other with a flat nose. Embedded in this flat metallic surface were four parallel laminated bars, 10 cm by 2.15 cm, with their long dimensions vertical. These were believed to be the surfaces of four magnetostriction hydrophones. It seemed likely, however, that there was a phasing system between the hydrophones. The spacing of the four bars indicated a peak response at about 1.5 kHz. There was definite evidence of a magnetic attachment to the T-4's pendulum-type inertia pistol. Several ships reported explosions in their wakes.\nThe ascribed issues were attributed to the inertia pistol. Prisoners of war claimed that this had been corrected. The magnetic feature increased slightly the chance of a direct hit and, more importantly, allowed the depth setting to be as much as 10 ft below the keel. This lower depth should have considerably decreased both the chance of broaching and the self-oscillations. The British even proposed a complicated hypothetical rudder control for T-5 which would allow a stern chase hit over one nautical mile despite the 30-degree restriction. The phasing system between the hydrophones was sufficiently complicated to distinguish between loss of contact when the torpedo passes over a noise source and loss of contact when the torpedo passes beside the source. In the first case, the rudder would straighten until differential was again obtained, thus ensuring accurate navigation.\nA stern chase was made on an NM as the torpedo continued toward the ship without circling. In the second case, the rudder locked over in the direction of the source, ensuring more than one pass at a ship by a shot from ahead. This proposal seemed too complicated to the practical. In addition, the slight weave of the torpedo on a stern chase would often cause it to pass somewhat to one side of the NM, possibly causing the rudder to lock over. Noise was also a concern. In addition, explosions beneath the ship's keel would be much more damaging than at the side of the hull. Thought was given to creating a magnetic field about the FXR to detonate the torpedo.\n\nIn late January, a complete experimental sensitivity pattern was obtained from the reconstructed T-4 nose. It seemed likely that the round-nosed T-5 possessed this same pattern. It conformed to the assumed design.\nEach channel had a maximum sensitivity of 25 degrees with a drop of no more than 28 dB at no angle. However, each channel had a prominent secondary lobe at approximately 60 degrees on the opposite bow, which could not be brought more than 2 dB below the main lobe of the other channel. At all bearings greater than 60 degrees, the patterns for the two channels remained within 7 dB of each other. They crossed over each other in a random fashion, as shown in Figure 9. A differential D of 7 dB was required for steering to prevent false or confused steering, such as turning to port when the target was about 110 degrees off the starboard bow. It was thought possible that the enemy might have implemented this to increase homing range.\nThe chosen D was DB, relying on the low sensitivity aft to prevent confusion by concealing the ship's noise in the background. Regardless of D, only a source between 5 and 60 degrees off the bow could be positive in flipping the rudder in the correct direction. This pattern enhanced the stern chase situation but heightened the risk of an indirect hit. The lower fore-aft discrimination and the likelihood of a greater D made it more challenging for the ship to assume control over the torpedo after a stern chase. Conversely, a louder NM was necessary to prevent the ship from drawing a torpedo from a nearby tractrix. If this torpedo circled far enough for the NM to be more than 60 degrees off its bow, it would persist in circling regardless of how poorly it received the ship's sound. Typically, when it began heading toward the screws, it would.\nBy January 1944, FXR Mk 2 (suitable for speeds from 12 to 19 knots) was getting into general use. Development of towed noise makers.\n\nNumber of hits by German acoustic torpedoes, by months (escort vessels - solid, merchant ships - crosshatched).\n\nAboard larger escort vessels, for lower speeds FXR Mk 3 was being issued to smaller craft. The chief operational difficulties with FXR Mk 2 arose from the limits imposed on the antisubmarine vessel's speed and from the depressor (employed to keep the NM below the wake). There were also conflicting issues.\nReports indicated if production models had the specified 12- to 15-db excess in output over the ship. A safety factor of several decibels was desirable. With much trial and error, a 30-inch parallel pipe NM was developed, which could be towed at any speed from 8 to 25 knots. It was depressed by a 90-lb weight called a \u201cminnow.\u201d Its output was steadier than that of FXR Mk 2 and was, at 5 kc, 20 to 25 db above the average destroyer escort [DE]; this compared favorably with the Canadian CAT gear and the components of the British FOXER.\n\nMeanwhile, care was taken to investigate all torpedoings in an effort to determine the part played by T-5s. Figure 10 records for each month the number of incidents designated as probable T-5 hits based on intelligence available before the German surrender. (Complete German records are unavailable.)\nThe importance of towing NM's in dangerous regions was emphasized, as seven out of fourteen escort incidents through May 1944 involved unexpected U-boat presence with less than 2500 yard range. In these cases, no other countermeasure could have been effective. The sudden burst of antisubmarine ships in May 1944 included one case with FXR Mk 2 being towed. The newly developed gear was soon issued and designated FXR Mk 4. In the spring of 1944, a copy of a T-5 firing table was recovered from a U-boat scuttled off India. By substitution into firing triangle relationships, the torpedo's speed was confirmed to be at least 24.1 knots on the initial gyro run. Investigation of minimum firing ranges (tabulated as a function of the target's firing course and speed) revealed that the torpedo's speed was:\n\n1. For a target firing course of 0 degrees and speed of 0 knots: 24.1 knots\n2. For a target firing course of 90 degrees and speed of 0 knots: 24.1 knots\n3. For a target firing course of 180 degrees and speed of 0 knots: 24.1 knots\n4. For a target firing course of 270 degrees and speed of 0 knots: 24.1 knots\n\nThe minimum firing ranges for various target speeds and courses were also determined.\nA torpedo had a 500-m enabling run. This means the hydrophones could not control steering until 30 seconds after firing, helping prevent homing on the U-boat. The minimum firing range was specified so after this 500m, the screws would still be at least 200m ahead, ensuring no chance of the forward-looking lobes not hearing the ship.\n\nDespite growing information about the torpedo, it was still fragmentary and unsatisfactory in the spring of 1944. This was soon to change.\n\nStudies of Captured T-5s:\n\nOn June 5, 1944, USS Guadalcanal and escorts captured U-505 with two round-nosed T-5 torpedoes aboard. The initial examination revealed that inside each plastic nose were not only two hydrophones and some liquid but also a rubber horn structure.\nThe hydrophones were set to direct sound 30 degrees off the bow, each governing a channel without phasing. The maximum sensitivity of the whole system was around 27.5 kc, higher than anticipated. This higher frequency was beneficial as NM output dropped off less rapidly with increasing frequency than ship noise. Consequently, FXR Mk 4 was approximately 30 db above the sensitivity pattern for a round-nosed T-5, from U-505.\n\nCountermeasures to the German Acoustic Torpedo\nBy August, measurements of the sensitivity pattern revealed a more concerning issue. The response aft was 42 db below the maximum. This suggested a possibility of stern hits with FXR Mk 4, given that D, the differential required to flip the rudder, was only 2 db.\nThe patterns for the two channels, shown in Figure 11, were well separated, approximately 12 dB apart, between angles 20 degrees and 125 degrees off the torpedo's bow. This, along with the low D and high NM excess, eliminated the risk of indirect hits. In fact, there were no indirect hit trajectories even with an NM 400 yards astern. Since the longer tow provided better protection from stern chases, adding more cable would have been recommended, had actual running tests with the T-5's not been expected soon.\n\nSuch tests were particularly necessary due to a new complication. The torpedo was found to have a common amplifier into which the two channels were switched alternately 108 times per second. If the signals were equal, there would be no 108-cycle component in the output. Otherwise, the phase of this component indicated which signal was dominant.\nTrouble arose from the fact that FXR Mk 4 pipes struck together with a frequency between 90 to 115 cycles. What was the torpedo response to a signal with this modulation? The answer was complicated by the effect of the automatic volume control (AVC).\n\nSome questions were, however, definitely answered by inspection of the torpedoes. The meaning of the \u201cWS\u201d and \u201cNS\u201d settings had been pretty well deduced from prisoner-of-war information. Now there was confirmation. WS was set on a torpedo being fired from within 90 degrees of the target\u2019s bow; this required that when differential was lost, the torpedo would continue in its minimum turning circle\u2014that is, flip-flop control. NS was used on rear shots and made the torpedo return to its original gyro course after receiving no differential for several seconds; when differential D was again received, the rudder would respond accordingly.\nThe reason for having both settings lies in the fear that the torpedo, as it approaches a ship from a distance, might start circling due to a temporary increase in noise level but before it could receive a steady signal from the ship. This was acceptable on forward shots since the ship's motion was likely to close the range where homing could start, and flip-flop control was needed if the torpedo should miss the stern on its first pass. On stern shots, flip-flop was not needed because the torpedo could stay on its tractrix. Resuming gyro control after a temporary signal was likely to bring it into homing range of the retreating ship, whereas circling would leave it hopelessly behind.\n\nA consequence of this control system was that even if WS shots were successfully prevented from making a detonation, the torpedo would continue to circle around the target area, potentially posing a threat to friendly ships.\nStern chases may result in danger from torpedoes fired at NS within 30 degrees of the ship's stern. NS trajectories, upon entering a region of no differential, would assume a gyro course leading them towards the ship. Torpedoes fired farther off the stern would return to a gyro course from which they could not hear the ship or, when they did, would turn to starboard to be recaptured by the magnetic influence. Preliminary tests with the torpedoes revealed a turning radius of 80 yards and a speed of 22 knots on turns, confirming 24.2 knots as the speed on gyro control. During October, one year after the first intensive countermeasure studies, detailed observations were made on 20 acoustic runs with the T-5's.\nThe FXR Mk 4 and Mk 2 performed well in proper operating condition. FXR Mk 4 provided good protection. FXR Mk 2 was equally effective except for one run where its output was erratic. The explanation for this good news was in the very large weave with which the torpedoes approached these NMs. The torpedo's beam was often presented to the NM before the rudder flipped to carry the missile into the next phase of the weave. When the ship speed was 15 knots or over, the torpedo was not able to overtake the NM but weaved back and forth behind it. With a slower target, the T-5 was able to circle in ahead of the NM occasionally, but always at such an angle that the NM continued to control it, at least until it had fallen behind again. There were no passes directly over the NM. Most runs were on NS with the gyro course parallel to the ship to have conditions most favorable.\nThe favorable conditions were suitable for a stern chase, hitting the target. This did not cause trouble. The ship's wake was so narrow compared to the weave amplitude that it had no effect. No feature of the trajectories could be correlated with the NM's striking frequency, although in one case there were less than 2 cycles between the striking and torpedo-switching frequencies.\n\nDevelopment of Towed Noisemakers\n\nThe large weave increased the angle off the target's bow from which a torpedo might be fired and still make a direct hit. A torpedo fired 1.1 degrees off the bow made such a hit, but three shots from about 20 degrees missed by 100 ft or more. It seemed that the existing doctrine of keeping the U-boat more than 20 degrees off the ship's bow allowed a sufficient margin of safety against these direct hits. A statistical analysis of the data showed that the probability of a direct hit decreased significantly as the angle of attack increased beyond 20 degrees.\nThe analysis of the weaving paths confirmed the 20-degree rule. As the weave amplitude increased when the torpedo approached the Nemesis, it was discovered that shortening the FXR towing distance from 200 yards significantly increased the risk of direct hits. Conversely, using a 400-yard tow only slightly improved the situation.\n\nThree runs were conducted against a 16-knot DE (33 dB spectrum level above 0.0002 dyne per sq cm at 200 yards) without an Nemesis Mine. The weave on stern approaches was quite small, with the ship seldom deviating more than 20 degrees from the torpedo's bow. This was sufficient, however, to reduce the speed made good to approximately 19.5 knots. A ship making 20 knots or more should therefore be safe from all but shots down the throat.\n\nOn one of these runs, the torpedo turned toward the ship, leaving gyro control at a range of approximately 1500 yards.\nWhether this was a fluke, the homing range was definitely over 600 yards, as the torpedo steered directly for the ship when enabled at this range. A 1500-yard homing range would make tactical counter-measures at speeds of 10-18 knots extremely risky.\n\nBased on the performance of FXR Mk 2 in running tests, development was initiated on an NM with a steady output about that of a good FXR Mk 2, i.e., about 20 db over the ship. This gear was to be substituted for Mk 4 whenever its interference with sonar was a serious handicap. However, no satisfactory design was found.\n\nDuring the fall, electronic parts of several flat-P Sonar interfered with Mk 4 so troublesomely that a device was developed to turn it off completely when desired, designated as Harp. The noise output of Harp can be\nThe turned off or on by quick slackening of the towing cable. It should be kept in mind, however, that stopping the NM exposes the ship not only to torpedoes fired during the quiet period but also to torpedoes fired within 10 minutes prior, which may have been pursuing the NM. Most WS torpedoes which had been trapped by the NM would then hear and attack the ship.\n\nNosed T-5\u2019s were found in France and sent to England. As had been predicted, the hydrophones were combined by phasing circuits into two channels. The maximum sensitivity was at 27.5 kc. The amplifiers were of a different type from those found in U-505\u2019s round-nosed torpedoes. It was established, however, that either the flat-nose or the round-nose hydrophone could be used with either amplifier. Since the German firing instructions made no distinction between them.\nModels seemed to have little difference in performance. With this information, the British authorized the use of UNI-FOXER, a single-NM system, in December. However, since no explanation of the large weave was available and it was thought that the large weave might not occur with the newly discovered amplifier, UNI-FOXER was towed at 400 yards. The large weave was not explained until after the war when an extensive study of the round-nose T-5 electronic system was completed. The differential D required to flip the rudder depended on the type of noise source and its intensity. D was 2-3 db with ship noise, which was essentially thermal noise with a peak to rms ratio of about 14 db. D was considerably greater for parallel pipe noise.\nmakers whose peak-to-rms ratio was approximately 20 dB (in deep water). This D rose to over 12 dB when the hydrophone output was in the high-voltage range corresponding to a signal 55 to 85 dB above 0.0002 dynes per sq cm from the direction of maximum sensitivity. This corresponds to ranges of 800 to 30 yards from a 15-knot FXR Mk 4. Since the sensitivity patterns of the two channels were no more than 12 dB apart, the rudder could not respond when the signal was so loud. Thus, the torpedo kept turning until the NM was so far off its bow that the hydrophone output was reduced to where steering differential was obtained. This might not happen until the NM was on the torpedo\u2019s beam. Thus, the large weave resulted. The response was found to be more erratic when the NM striking frequency was close to it.\nThe AVC, switching circuit, and assorted time constants contributed in a complicated way to the switching frequency. The British double Foxer had serious practical difficulties, but a simple light diverter (Scate) had been developed in the United States by the end of World War II, making a two-NM scheme feasible.\n\nCountermeasures to the German Acoustic Torpedo\n\nExperiments with FXR noise equal in both channels and ship noise superimposed in one (simulating the critical conditions after passing an NM on a stern chase) showed that the ship could flip the rudder when its rms contribution was about equal to the rms FXR level in both channels. This meant that without the weave of 3 dB could be counted on in the stern chase; the earlier calculations based on a D.\n1-2 db were pessimistic. The circuit diagram of the flat-nosed T-5 amplifier suggested that, even if it did not give a weave, it quite possibly would respond to peaks of FXR signal rather than the rms value. FXR Mk 4 should then have a good chance of drowning out the ship on a stern chase. With present information, a quiet NM such as Mk 5 could not be advocated, and towing FXR Mk 4 at 400 rather than 200 yd would provide a desirable margin of safety. Had World War II continued, running tests with the flat-nose torpedoes would have been very much worthwhile, but the German surrender was in itself a completely adequate countermeasure.\n\nThe success of our countermeasures could not be judged accurately from our own operational data, since they are largely restricted to cases in which the enemy used torpedoes with the same characteristics as our own.\nBy V-E Day, 51 torpedo hits had been designated as probable T-5 hits. Figure 10 provides monthly data. As the U-boat effort declined, T-5's constant contribution became more significant. In the war's final months, serious consideration was given to issuing NM gear to merchant vessels. Table 1 summarizes available information on incidents believed to involve T-5's.\n\nOf the seven ships hit while towing NM's, one had FXR Mk 2, one FXR Mk 4, two British Uni-FOXER (in poor condition), and three had Canadian CAT. At least two of these cases were likely direct hits.\n\nT-5's that made hits on antisubmarine ships were not as successful as other torpedoes in sinking.\nTheir targets. This may probably be associated with the high proportion of T-5\u2019s which struck near the stern (63% for antisubmarine ships, 53% for merchant vessels), since this often resulted in only local damage which could be kept under control. It is hoped that a much clearer picture of NM effectiveness will be obtained from the study of German Admiralty IBM cards. These cards give facts pertinent to each torpedo expended (by U-boats which got home to report). Interrogations have yielded a wide variety of estimates of the number of T-5\u2019s fired and their success. It is clear, however, that only a small percentage of the torpedoes expended hit their targets. There were probably many duds, as is likely with such a new and complicated device. The enemy must have attributed some failures to our noise-makers. It has been reported that orders were issued to improve the aim of the T-5 torpedoes.\nWhen an NM was near, T-5s should not be fired unless the U-boat was almost in the target's wake. This order served the NM's purpose effectively.\n\nTable 1. Use of German acoustic torpedo T-5.\n\nType of target | Probable T-5 hits:\n--------------|---------------------\nAntisubmarine | With a towed NM: 30%\n| | With target speed under 9 kt: 50%\n| | Probably without countermeasures: 70%\nMerchant ship | Total: 153\n| | Percentage of all incidents: 30%\n| | Percentage of T-5 hits causing sinking: 50%\n| | Percentage of other hits causing sinking: 20%\n\nEpilogue\n\nThe preceding chapters have discussed the antisubmarine aspects of World War II in detail, both as history and as an object lesson in rational naval tactics. This would not have been done if it were not feared that a future war might at some time present similar problems. Yet the nature of any hypothetical conflict would depend on a variety of factors, including technological advancements and geopolitical realities. Therefore, while the lessons of the past are valuable, they must be applied with caution and flexibility in the context of evolving circumstances.\nThe future of submarine and antisubmarine operations is uncertain, making any discussion highly speculative. This volume on antisubmarine warfare has been essentially historical in nature. It has presented facts and figures from the six years prior to V-J Day and developed theories to explain and interpret them. Its basis is dual: the characteristics and tactics of the German U-boat on one hand, and those of Allied antisubmarine craft on the other. Had the contestants been different, the course of the war would have been altered accordingly.\n\nThe outstanding characteristics typical of the German U-boat throughout most of World War II were related to the policy of surfaced operation. Their offensive tactics were predicated on the use of visual observation.\nDetection and tracking on the surface with high speed and maneuverability. Diving was resorted to only in emergency to escape detection or attack. The large wolf packs formed against North Atlantic convoys were characteristic of their emphasis on coordination. Their consequent heavy radio traffic provided important information to the Allies, and their weakness in radar detection techniques gave the Allies a telling advantage against the surfaced U-boat.\n\nOn the Allies\u2019 side, the overriding importance of maintaining North Atlantic convoys to Britain determined the general course of the antisubmarine war. This was the central battle, with a great variety of diversionary forays and skirmishes spread over the remainder of the oceans.\n\nTo defeat the U-boats, their weaknesses were exploited to the full, especially by radio direction finding.\nThe text provides an estimation of radar use in wartime, highlighting changes during the closing period of World War II. After U-boat defeat in summer 1943, the Germans initiated an extensive research and development program for U-boat warfare. The most striking result was the high-submerged-speed submarine, aiming for turbine propulsion using fuel oil and hydrogen peroxide as an oxygen source (Walter turbine). This was the Type XXVI U-boat, capable of a maximum submerged speed of 25 knots for 6 hours instead of 8 knots for 1 hour with the standard U-boat type. The tactical value of such a speed.\nIn attacking convoys and in avoiding search and counterattack, the significance would be very considerable. Although the feasibility of Walter turbine propulsion had already been demonstrated at that time, no Type XXVI U-boats were ever built due to production difficulties. Several smaller boats, Type XVII, were built for experimental purposes, and trials were in progress by V-E Day.\n\nLess spectacular than the turbine drive U-boat was the high-speed electric drive Type XXI. They were highly streamlined boats with powerful electric motors and high-capacity batteries. The resulting capabilities were a top speed of 15-18 knots submerged for a brief period, and of 10 knots submerged for about 10 hours. U-boat construction was concentrated on the Type XXI during 1944, and considerable numbers of them were ready to start operations in May.\nNo war patrols had been made, however. Both types were, of course, to be fitted with Schnorchel, which should also be classified as a post-1943 innovation. The idea was not new, but its widespread introduction in the summer of 1944 dramatically changed the complexion of the antisubmarine war, as was pointed out in previous discussion. Schnorchel must certainly be reckoned with in estimating future trends, and future Schnorchels, equipped with radar camouflage, may be expected to be even more effective than those which the Germans used. Significant changes were being made at the end of World War II not only in submarine design but also in weapons for submarine use. The acoustic torpedo discussed in Chapter 15 is the most familiar example. The hydrogen peroxide required was expensive to produce.\nThe majority of the supply was used by the German Air Force, particularly in the V-1 and V-2 programs.\n\nEPILOGUE\n\nOther developments also occurred. Long-range and zigzag torpedoes were introduced for use against convoys, significantly increasing the probability of a hit. Fortunately, few U-boats had the opportunity to fire them. The Ingolstadt torpedo, with the Walter turbine propulsion providing long range and high speed, was developed but not put into operational use. Such weapons may be expected to increase the potential effectiveness of submarines in the future.\n\nOn the Allied side, end-of-war developments were mostly of the nature of improvements to existing craft and weapons, as they were operating with good success. New types of sonar for improved detection and attack were under consideration, in particular scanning sonar which gave an instantaneous plan.\nPosition indicator plot of target position. More effective attack weapons were under development, and the recently introduced Squid gave evidence of having a probability of success in attacks about ten times that of ordinary depth charges. Certain more general developments will also undoubtedly have profound effects on future antisubmarine warfare, just as sonar, radar, and the aircraft profoundly affected it during World War II. Atomic explosives and power utilizing nuclear energy come immediately to mind as the most revolutionary recent introductions. It is impossible to estimate the effects of such developments now; all that can be done is to point out that they are likely to be significant. Somewhat less striking, but also of great importance, are the very extensive developments of guided missiles. Homing torpedoes may be considered an example.\nWhat is the future of submarine and antisubmarine operations? The uncertainty of naval warfare notwithstanding, control of the sea, including the depths beneath the surface and the space above it, is of prime military importance and the objective of naval power. The means to accomplish such control are naval craft and missiles; modern warfare, no longer a matter of personal combat, is based on the missile, the means of inflicting destructive agent.\nIn the enemy's midst, naval craft- ships, aircraft, and submarines- are fundamentally missile-carriers whose aim is to launch missiles to reach the proper place. The characteristics of each type of craft are determined in part by the requirements of the missile which it launches. However, they are also intrinsic- speed, endurance, and maneuverability. Relative ease of detecting the enemy and being detected by him are also of great importance.\n\nIn the past, submarines have been built around the torpedo as a missile. Improvements in torpedo design and the possible introduction of submarine-launched guided missiles may significantly alter its role in the future. The great intrinsic advantage of the submarine is its invisibility, in which it still exceeds all other types of craft. Means for overcoming this invisibility are being developed.\nAbility are likely to remain the chief concern of anti-submarine measures. Their detailed nature must, however, be determined in terms of the use to which submarines are put and of the type involved. A satisfactory estimate of the most probable enemy use of submarines can hardly be made without first deciding on the general tactical and strategic situation which is likely to exist. We should first determine who will be fighting whom, what bases and facilities each will have, what supply lines or other objectives are open to enemy submarine attack. Setting up such a complete problem is, however, beyond the scope of this discussion, but we can still make some predictions in general terms. In the first place, it is reasonable to expect that submarine tactics which proved to be highly effective in World War II will be tried again in the future. In.\nThe use of submarines to attack merchant shipping is likely to be repeated by our enemies as long as our strategy relies on such ships. In any major war, this is likely to be the case, as we will use ships to supply bases outside the continental United States and to import necessary materials of war. Only if the enemy expected to win a rapid and crushing victory, making destruction of our shipping unnecessary, would he be expected to ignore the importance of a submarine campaign against merchant ships.\n\nThe developments of the last period of World War II support this point of view. The new types of German U-boats designed and constructed after 1943 were intended for the same basic purpose as the earlier ones\u2014to attack merchant ships. No major change was envisaged, but it was hoped that improvements would make the submarines more effective.\nThe increased U-boat speed would restore their tactical advantage and permit effective attacks against convoys, even when operating submerged to gain safety from aircraft. The use of submarines for anti-shipping operations involves the torpedo as the primary weapon. New developments suggest, however, that different weapons, such as a guided missile of the V-bomb type, might also be launched from submarines. If such a missile were designed to carry nuclear explosives, the destructive power of the weapons a relatively small submarine could carry would be many times greater than that of a battleship or carrier at present. Weapons might well be launched with accuracy comparable to that of present gunnery or bombing. Since the submarine is an all-but-invisible craft, developments of this sort might be expected to be extremely effective.\n[The detailed evaluation of possible types of future submarine operations is beyond the scope of this discussion and cannot be made now. It is first necessary to determine the fundamental capabilities of the craft and missiles involved, with all possible new developments and improvements. Once this has been done, the tactical evaluation can be undertaken. It appears, however, that future developments are not likely to eliminate the submarine's great merit, its relative invisibility. At the same time, the striking power of submarines is likely to increase. We may safely conclude that submarine and anti-submarine warfare will be highly important phases of any future naval conflict.\n\nII - Sift\n- IrV\n- Orr, TR^\n- ifViff':': r\n- c . J .fc.j\n- L\n- iir\n- Ail\n- wii: .\n- i\n- . .rii\n- iu\n- \u2022 V*^TS -vi'i\n- inr:t\n- VI V\n- -^iV UM?\n- n\n- i\n- t H\n- I y\n- LH^\n- rTi]\n\nThe text appears to be a section from a document discussing the future role of submarines in naval warfare. The text mentions the importance of determining the capabilities of submarines and missiles, and the conclusion that submarine and anti-submarine warfare will remain important phases of naval conflict. The text also includes some abbreviations and symbols that are likely part of the original document.\nAt the end of World War I, it was found that the number of U-boats actually sunk was less than the number presumed according to the assessment list. At the start of World War II, it was intended that the assessment policy be more realistic, and more convincing evidence was demanded to secure an assessment of \"sunk\" (A) or \"probably sunk\" (B).\n\nThe Italian surrender was followed by the publication of a list of the Italian U-boats which did not return to base prior to the armistice. Compared with the Allied assessments for attacks thought to have been made on Italian U-boats, the agreement was excellent. There were 72 A and 7 B assessments.\nTotal of 79 Italian U-boats sunk or probably sunk. The Taranto list showed 80 submarines missing. Intelligence provided names of 67 of them before the armistice, and all checked.\n\nGerman surrender provided a list of the U-boats lost with the name of the commander and date and position of the sinking. Comparison of A and B assessments and losses shown in the German list:\n\n| Allied assessments | German list | Total |\n| --- | --- | --- |\n| I | Sept. 39 - June 40 | II |\n| II | III | IV |\n| IV | V | VI |\n| V | VII | VII |\n\n* These data are based on information available at V-E Day. Neither Allied nor German information is complete for the last periods. Hence the figures given here do not agree in detail with those presented in Chapter 8, based on more complete records available several months later.\nThe agreement between Allied and German estimates proves the overall accuracy of assessments during World War H. The Germans lost more U-boats due to Allied action at sea than a combination of A and B assessments indicate. This is expected as losses due to mines or ordinary hazards of the sea would not be known to the Allies. In only one period did the total A and B assessments exceed the losses given in the German list. For this period, July 1940- March 1941, there were 7 B assessments which have never been confirmed as sinkings. Intelligence has completed the story for these sinkings. The percentage of B assessments which actually corresponded to sinkings is problematic, but those which do not represent sinkings are compensated for by lower numbers in other periods.\nAssessments representing sinkings, though not credited as such: 38 A assessments and 62 B assessments, totaling 100 A and B. Individual losses from Japanese lists amount to 123, with two from mines and two from running aground. The agreement is satisfactory, considering the greater difficulty of obtaining intelligence.\n\nA B Total Enemy Losses\nItalian 1 1 2\nGerman 1 1 2\nJapanese 0.3 0.7 1\n\nThe ratio of A to B assessments is high for Italians, intermediate for Germans, and low for the Japanese. This relationship appears to be due to at least three main factors:\nThe Italians surrendered easily, emerging to confirm destruction. In contrast, the Japanese seldom surfaced when the game was up. Intelligence information was easier to obtain from European sources than Japanese. Antisubmarine forces in the Pacific had less opportunity to remain in the vicinity to search for evidence of destruction due to other fleet duties. The complete picture for World War II allows the conclusion that the sum of A and B assessments for attacks on Axis U-boats approximates the actual losses and is useful for practical purposes. Attempts to correlate B attacks with the loss of individual U-boats were not always successful, and the validity of any particular B assessment as evidence of a U-boat's destruction is questionable.\n\nAppendix\n\nGlossary\nAces: U-boat commanders with outstanding records, credited with sinking large amounts of Allied shipping.\n\nAcoustic Torpedo: A torpedo which detects the target ship by means of sound and is controlled by this sound so as to steer towards the ship and eventually hit it.\n\nAdmiralty: The headquarters staff of the British Navy. Also used in the same sense for German Navy as \"German Admiralty.\"\n\nAhead-Thrown: (A) Weapon: an antisubmarine weapon used by surface craft which is projected ahead of the ship, usually to a distance of about 300 yards; (B) attack: an attack employing an ahead-thrown weapon.\n\nAiming Errors: Errors in aircraft attack arising from inaccuracies in dropping bombs or firing rockets, i.e., errors in aiming the weapon.\n\nA.N.D: Admiralty Net Defense; a net suspended along the sides of a ship to catch torpedoes.\nAntisubmarine error in surface craft attacks arises without submarine evasion. See Attack Error and Evasion Error.\n\nAntisubmarine Attack Plotter (ASAP). An electronic device for plotting positions of own ship and submarine during attack. Sonar echoes are plotted automatically on a large cathode-ray tube of long persistence.\n\nAntisubmarine Ship. Any naval ship used for attacking submarines, i.e., destroyers, destroyer escorts, frigates, sloops, corvettes, trawlers, patrol craft [PC], sub chasers [SC], suitably equipped minesweepers, etc.\n\nASDevLant. Anti-Submarine Development Detachment, Atlantic Fleet; an organization set up to test and develop anti-submarine equipment and tactics for its use.\n\nAsdic. British echo-ranging sound gear. Equivalent to United States sonar. Name is derived from Anti-Submarine Detection.\nThe Internal Committee, pioneer in the development of ASG (S-band radar) for the United States Navy, introduced airborne radar for searching U-boats in early 1943.\n\nAssessment: An estimate of the damage done to a U-boat resulting from an attack by an antisubmarine craft. This estimate is made by a special committee based on all available evidence. Assessments range from \"A\" - U-boat known to be sunk, to \"I\" - attack not on a U-boat.\n\nASV: Air-to-surface-vessel radar, i.e., airborne radar for searching surface ship targets.\n\nASVORG: Anti-Submarine Warfare Operations Research Group. A group of civilian scientists attached to Tenth Fleet Headquarters. Later known as ORG when transferred to COMINCH Headquarters.\n\nAttack: Release of one or more weapons against a U-boat in a barrage or stick. Several attacks made in succession on the U-boat.\nAn incident refers to multiple U-boats occurring within a few hours of each other. The term attack is sometimes used interchangeably.\n\nAttack error: Distance between the mean point of explosion of weapons and the center of the submarine. See Aiming Error, Evasion Error, Approach Error.\n\nAttack teacher: A mechanical device for simulating the conditions of a surface craft attack on a submarine, primarily used for training personnel on shore.\n\nAVC: Automatic volume control in an electronic amplifier.\n\nBalanced force: A force capable of an equally effective offensive at all times, particularly day and night.\n\nBarrage: A number of depth charges or contact charges released as a group in a surface craft attack.\n\nBDI: Bearing deviation indicator, a modification to standard sonar gear providing more accurate bearings through lobe comparison.\nBiber: a midget submarine with a crew of one, developed by the Germans and used during 1944-45.\n\nBlind Time: the time from loss of contact with the submarine (or release of weapons) until weapons reach U-boat depth.\n\nBorkum: a German radar search receiver of crystal detector type covering the 75-300 cm band.\n\nBrawning Shot: a torpedo shot fired into a convoy without being aimed at any particular ship.\n\nCamouflage (Radar): any device for reducing the range at which an object can be detected by radar, for example, non-reflecting coatings for reducing echoes.\n\nC.1M Ships: merchant ships fitted with catapults for launching aircraft.\n\nCatalina [A/C]: twin-engined seaplane (or amphibian) built by Consolidated Aircraft. Long range, slow, with moderate bomb load.\n\nClass A Attack: an aircraft attack on a submarine in which\nBombs are dropped not more than 15 seconds after a submarine submerges.\n\nCoastal Command: The branch of the British Royal Air Force responsible for ocean patrol and attacks on naval targets.\n\nCommanding Volume: The locus of points about an exploding charge or bomb (or about its trajectory) that have the property that a submarine with a center at any of the points will be sunk.\n\nCommodore (of Convoy): A senior naval officer (or occasionally merchant captain) responsible for the navigation, signaling, and other activities of the convoy. The escort commander, on the other hand, is responsible for its defense against the enemy and has ultimate authority.\n\nContact: An instance of detection of an enemy unit. For example, when a U-boat sights a convoy, it is a contact on a convoy; as when an aircraft receives a radar blip from a submarine, it is a contact on a submarine.\nContact: A device in a bomb, rocket, or other projectile for causing it to explode on hitting the target.\n\nGlossary:\n\nConvoy: A group of merchant ships sailing together, usually defended by naval ships acting as escorts.\n\nCoordinated Attack or Incident: An attack or incident in which two or more ships and aircraft (or both ships and aircraft) take part. See Attack and Incident. Those involving both ships and aircraft are sometimes termed joint attacks (or incidents).\n\nCorvette: A small antisubmarine ship, usually capable of rather slow speed.\n\nCOTC: Commander Operational Training Command, Atlantic Fleet, in charge of training for the Atlantic Fleet.\n\nCounterattack: An attack on a submarine which has attacked friendly ships or is threatening to do so.\n\nCountermeasure: Any action or device designed to reduce the effectiveness of an attack or defense.\nEffectiveness of sonic enemy action or device. Tactical countermeasures involve changes in tactics or operational procedures. Material countermeasures involve new equipment. These terms are used most frequently with respect to radar and homing torpedoes.\n\nCNO: Chief of Naval Operations\u2014 the naval officer (and subordinate staff) in charge of the U.S. Navy Department.\n\nCreeping Attack: A coordinate attack by surface craft aimed at surprising the submarine. An \u201cassisting ship\u201d maintains sonar contact and directs the \u201cattacking ship,\u201d which proceeds at slow quiet speed over the submarine without echo ranging and drops charges.\n\nCuba Ia: Antenna used with the German Tunis search receiver for S-band reception, made up of dipole and parabolic reflector.\n\nCurly: A torpedo which follows a zigzag course.\n\nDecibel: A unit of sound intensity. See any textbook.\nGeneral physics or acoustics. D-Day. Day of invasion of Normandy \u2013 June 6, 1944.\n\nDensity. Number of objects per unit area. For example, U-boat density might be expressed as the number of U-boats per million square miles of ocean.\n\nDepth fuze. A device for detonating a bomb or other weapon at a preset depth.\n\nDestroyer Escort [DE]. A large antisubmarine ship (about 1,800 tons) of fairly high speed, about 18-24 knots.\n\nDE. Radio direction finding by intercepting enemy radio transmissions and obtaining their bearings with directional receivers, thereby estimating the enemy position. See HEDF.\n\nDirect hit (by torpedo). A direct hit is made by an acoustic torpedo on a ship using a noisemaker if the torpedo, while steering toward the noisemaker, hits the ship.\n\nDispersion (of explosions). The variation that would exist in the explosion points of a large number of bombs of a given type.\nIf all were subjected to the same conditions (controllable ones).\n\nDiverter: A device for causing a towed noisemaker to tow at one side of a ship's wake rather than directly astern.\n\nDiverter: A device used to tow a noisemaker at an angle to a ship's wake instead of directly behind it.\n\nElectrasonne: German code name for a radio beacon system used as navigational aids.\n\nEscort: A naval ship or aircraft used to protect merchant ships or groups of ships. Antisubmarine ships are sometimes called escorts even during offensive operations.\n\nEscort Carrier [CVE]: A small aircraft carrier, typically built on a merchant vessel hull, designed to fly antisubmarine planes. Escort carriers were primarily used in offensive operations, rarely for escort duties.\n\nEscort Commander: Naval officer in command of forces assigned for the defense of convoys.\n\nEscort Group: A group of antisubmarine ships operated as a unit.\nEvasion error. Error in antisubmarine attacks caused by submarine evasive maneuvers.\n\nEvasive routing. Routing to avoid known submarine positions.\n\nExchange rate. Ratio of merchant vessels sunk by submarines to submarines sunk by antisubmarine vessels.\n\nFAT. German designation for a zigzagging torpedo. See LUT.\n\nFerret. An aircraft equipped with receivers for monitoring enemy radar transmissions.\n\nFleet Air Arm. British carrier and ship-based aircraft.\n\nFleet Air Wing 7. This air wing was based in Britain until the end of World War II.\n\nFliege. German code name for S-band antenna of Tunis GSR. See Cuba Ia.\n\nFlip-flop control. Rudder control for a homing weapon which can only be in central position or hard over port or starboard.\n\nFlying Fortress. A four-engine Boeing bomber.\nFor antisubmarine patrol. Follow-up (of contacts). Effort to gain contact with a submarine whose position was accurately known at an earlier time by virtue of a previous contact.\n\nFourth Fleet. United States naval forces which were based in the South Atlantic; a subdivision of the Atlantic Fleet.\n\nFoxer. British towed noisemaker gear for decoying German acoustic torpedoes, consisting of two parallel bar noisemakers and diverters. Near the end of the war, Uni-Foxer, a single noisemaker, was employed. See FXR.\n\nFrigate. A large British antisubmarine ship (about 2,000 tons) of long endurance but moderate speed, 15-18 knots.\n\nFXR. United States single towed noisemaker of parallel bar type (See Foxer).\n\nGambit. An aircraft search for follow-up of contacts in which the aircraft leaves the most probable initial submarine position.\nA submarine is pursued by a flying boat at a distance, hoping it will resurface for sighting when the aircraft returns to the area. Mid-ocean. The mid-ocean area unpatrollable by land-based aircraft.\n\nGlider Bomb. German radio-controlled glider bomb guided to target by parent aircraft.\n\nGnat. German Navy acoustic torpedo that homes automatically on noise from target ship.\n\nGross Ton. A measure of ship size based on volume. The tonnage is the entire internal cubic capacity of the ship expressed in tons of 100 cubic feet, except certain spaces exempted, such as peak and other tanks for water ballast, open forecastle bridge and poop, anchor gear, steering gear, wheel house, galley, and cabins for passengers.\nGerman search receiver: a German radar receiver for detecting Allied search radar transmissions.\nGU: Convoy designations. Mediterranean and Gibraltar to the United States (fast) - GUF, slow - GUS.\nGuided Missiles: A missile whose course can be adjusted after launching to hit the target. The adjustment may be made by an operator in the launching craft or automatically. Acoustic torpedoes are examples of the latter type.\nHalifax: A British four-engined heavy bomber built by Handley-Page.\nHedgehog: An ahead-thrown weapon with a mortar-projected barrage of 24 contact charges, trainable to about 20 degrees off the ship's bow.\nHF/DF: High-frequency direction finding. Frequencies of about 10 megacycles are involved.\nHG: Convoy designation. Gibraltar to the United Kingdom.\nHold-down hunt: A search of sufficient intensity to ensure the submarine's being sighted if it surfaces.\n\nHoming: Guiding to a source of signals. A U-boat in contact with a convoy unit's signals, thereby homing other U-boats to the scene. An acoustic torpedo steers towards the sound from a ship's propellers, thereby homing on the target.\n\nHOS: High-resolution radar of S-band frequency for use in blind bombing.\n\nHudson: Twin-engine Lockheed bomber.\n\nHunter-killer operations: Offensive operations aimed at finding and destroying U-boats, usually involving groups of surface craft and sometimes coordinated with aircraft.\n\nHX: Designation for convoys from Halifax or New York to Britain.\n\nHoX: High-resolution radar of X-band frequency for use in blind bombing.\n\nHydrophone: A receiver of underwater sound.\n\nIncident: See Attack and Coordinated Incident.\nIndirect hit: A hit made by an acoustic torpedo attracted to the target ship out of a trajectory leading to a noisemaker.\n\nInfluence fuze: A fuze activated by the change in earth\u2019s magnetic field due to the submarine\u2019s presence, designed to detonate the charge when it is close enough to the submarine to be effective.\n\nIntercept receiver: Radar search receiver (see GSR).\n\nJaumann absorber: A nonreflecting covering effective against S- and X-band radars, made up of spaced layers of semiconducting paper. See WTscii absorber.\n\nLateral range curve: A curve which gives the probability of detection of an object by a searcher (who is proceeding on a straight course) as a function of distance of direct approach.\n\nLeigh light: British aircraft searchlight used for night attacks.\n\nLethal area: The area on the ocean surface centered above the submarine.\nAn exploding depth bomb with the following properties: In a Class A attack, any submarine whose center lies below the lethal area may be considered sunk, and no others.\n\nLethal radius: The lethal radius of a given explosive charge is the maximum distance from the pressure hull at which it may be expected to do lethal damage.\n\nLiberator: A four-motored heavy bomber built by Consolidated Aircraft, frequently modified for use in antisubmarine patrol due to its long range and large bomb load.\n\nLife (lifetime) of a U-Boat: At any time, the average life of a U-boat is the number of U-boats at sea divided by the rate at which U-boats are sunk per month.\n\nLimiting Approach Lines: The boundary of the region from which a submarine can approach a ship or formation, drawn relative to the ship or formation.\n\nLine Error: The component perpendicular to the course.\nAttacking aircraft, the distance between the center of the stick and the center of the submarine.\n\nLocalization. Determination of the exact submarine position by sonar.\n\nLost Contact (Range). The range at which sonar contact with the submarine is lost because the submarine is below the sonar beam.\n\nLUT. German designation for a torpedo which runs a preset zigzag course. See FAT.\n\nM/C Ships. See CAM Ships.\n\nMAD. Magnetic anomaly detector (or magnetic airborne detector), an aircraft instrument for detecting distortion of the earth\u2019s magnetic field due to the presence of a submarine.\n\nMaximum Submergence. Submarine tactics which involve remaining submerged as much as possible. Normally, about 2 to 4 hours a day must be spent surfaced or at Schnorkel depth.\n\nMean Radial Error. The average distance from the center of the target to the center of the barrage.\n\nMetox. Early GSR for long wavelength radar, introduced in\nMk II Radar: British long wavelength search radar used on aircraft.\nMk hi Radar: British airborne S-band search radar.\nMk 8 Depth Charge: United States influence-fuzed depth charge.\nMosquito: British twin-engined fighter-bomber built by De Havilland.\nMousetrap: United States ahead-thrown weapon with rocket-projected barrage of 8 or 16 contact charges. Used in small ships.\n\nGlossary:\n\nMPL: Mean point of impact of a group of bombs.\nMucke: Horn antenna for X-band reception with Tunis GSR.\nMV: Merchant vessel.\nNaxos: (1) Early non-directional GSR effective in S-band; (2) Amplifier used in Tunis GSR.\nNM: Noisemaker.\nNoisemaker: An artificial source of underwater noise used to conceal the noise made by a ship or submarine or to interfere with the operation of, or to decoy, acoustic devices such as acoustic torpedoes.\nNorth Russian Convoys: Convoys from Britain around the Arctic Circle.\nNorth of Norway to Murmansk, Archangel, or other North Russian ports, and returning convoys.\n\nOB: Designation used in early years of war for convoys outward bound from Britain for America and Africa.\n\nObservant: A search plan used by surface craft, consisting of going to point of last contact with submarine and then steaming around a square centered at that point with 2-mile sides.\n\nOG: Designation for convoys from Britain to Gibraltar.\n\nON: Designation for convoys from Britain to America. During the latter part of World War II, ON was reserved for 9-knot convoys, ONS being used for 7-knot.\n\nORG: Operations Research Group. See ASWORG.\n\nORS: Operations Research Section, title of British operations research organizations. Most frequently used in ORS/CC - Operations Research Section, Coastal Command.\n\nOS: Convoy designation for convoys from Britain southbound to Sierra Leone.\nPatrol Craft: Small antisubmarine craft, typically not over 200 feet in length.\n\nPQ: Designation for convoys from Britain to Archangel. (See North Russian Convoys.)\n\nI\u2019RACTicE Attacks: Simulated attacks carried out on the attack teacher or in exercises with a friendly (tame) submarine.\n\nProximity Fuze: A fuze designed to detonate a bomb, charge, or projectile when within a certain distance of the target. (See Influence Fuze.)\n\nP/W: Prisoner of war.\n\nQ Attachment: British auxiliary sound gear with a beam directed below the main Asdic beam for maintaining contact with deep U-boats at short ranges.\n\nRGOO: Same as Metox.\n\nRange Errors: The component parallel to the source of attacking aircraft of the distance between the center of the stick and the center of the submarine.\n\nRDF \u2014 Type 286, Type 271: British surface craft search radar.\nType 286 had fixed aerials and operated on long wavelengths.\nType 271 was S-band gear with a rotating beam and PPI presentation.\n\nRetro-Bombs. Contact bombs used by aircraft in conjunction with MAD. Bombs are propelled backwards by rocket motors to drop vertically from aircraft.\n\nReverberation. The totality of small false echoes received on sonar from objects in the ocean, its surface, and the bottom.\n\nRocket. Used alone, the word implies forward-firing rockets of about 3-inch diameter used by aircraft. [See Mousetrap, for comparison.]\n\nRunddipol. Submersible GSR aerial used for long wavelength radar reception.\n\nS-Band. Radar operating band for wavelengths of about 10 cm.\n\nSBT. Submarine bubble target. A German decoy used to produce false echoes from a cloud of bubbles.\n\nSC. Designation for 7-knot convoys from America to Britain.\nSchnorkel: A U-boat combination air intake and Diesel exhaust, permitting operation on Diesels when at periscope depth. Introduced in 1944.\n\nSCR-517: US Army S-band airborne search radar.\nSCR-717: Improved version of SCR-517.\nSD Radar: US Navy X-band airborne search radar.\nSea Return: The totality of false radar echoes from ocean surface.\nSearch Receiver: A radar receiver for intercepting signals from enemy search radar and thereby being warned of his approach.\nSensitivity Pattern: The sensitivity of an acoustic torpedo is a diagram showing the range and bearing at which a given sound source will produce a given signal at the torpedo control mechanism.\nSG: US Navy surface craft S-band search radar.\nShadowing: A U-boat shadowing a convoy kept in contact with it and reported information about it without attacking.\nThe effectiveness of a U-boat in sinking ships is determined by the sinking rate. Sinking rate equals the U-boat's sweep rate multiplied by the fraction of ships contacted that are sunk.\n\nSL: Convoy designation for convoys from Sierra Leone to Britain; radar designation for United States Navy radar similar to SG but lighter in weight.\n\nSloop: Large antisubmarine ship of moderate speed, similar to a frigate.\n\nSonar: Term used by the United States Navy for underwater sound equipment and its use. British use \"Asdic\" in a similar way.\n\nSoNOBUOY: Expendable Radio. A small buoy capable of transmitting sounds heard in the ocean to an observer by radio. Primarily used by aircraft.\n\nSortie: An aircraft flight.\n\nSquid: An ahead-thrown depth charge and associated depth-determining sound gear. By means of which the submarine's actual depth is automatically set into the depth charge fuze.\n\nGlossary:\nSinking rate: The U-boat's rate of sinking ships.\nSL: Convoy designation for convoys from Sierra Leone to Britain; radar designation for United States Navy radar similar to SG but lighter in weight.\nSloop: Large antisubmarine ship of moderate speed, similar to a frigate.\nSonar: Underwater sound detection system used by navies.\nSoNOBUOY: Expendable radio buoy used for transmitting underwater sounds to observers by radio, primarily used by aircraft.\nSortie: A single flight of an aircraft.\nSquid: A depth charge system that automatically sets the depth charge to the detected depth of the submarine.\nStep-aside: A radical zigzag designed to permit a ship to approach a U-boat with minimum danger from acoustic torpedoes.\n\nStern chase: An attack or pursuit course which overtakes the target from its stern.\n\nStick: A number of bombs or depth charges dropped in a row.\n\nStraggler: A ship which left a convoy because unable to maintain proper speed.\n\nSubmerged Approach Zone: The area around a convoy from which a submarine can make a submerged approach to it.\n\nSunderland: British four-motored seaplane.\n\nSupply U-Boat: A U-boat fitted to refuel and supply other U-boats without attacking any ships itself.\n\nSupport Group (i.e., 2nd Support Group): A number of anti-submarine ships kept together permanently as a group to hunt U-boats and provide extra defense to convoys threatened by attack.\n\nSweep Rate: The number of contacts made per hour per unit.\nTarget density: the measure of a searching craft's effectiveness in covering area, expressed in square miles per hour.\n\nSweep width: sweep rate divided by speed (approximately).\n\nT-5: early German acoustic torpedo. The Tenth Fleet was assigned tasks of conducting war on submarines and protecting merchant shipping by the United States Navy Headquarters.\n\nTorpedo danger zone: area around a ship or convoy from which a submarine has a good chance of hitting with a salvo of torpedoes.\n\nTorpex: recently developed explosive superior to TNT in destructive power.\n\nToss bombing (or rocketing): method of glide-bombing (or rocket-firing) in which weapons are released as the plane pulls out of the glide.\n\nTracking: maintaining contact with an enemy unit to determine its course and speed.\nTractrix: The curve of pursuit followed by an object moving with constant course and speed.\n\nTransit, Transit Area: The passage of a submarine from base to operating area is termed a transit, and the area between base and operating area is the transit area.\n\nTunis: Directional GSR for interception of S-band and X-band radar. (See Naxos, Mucke, and Fliege.)\n\nType XVII-B U-Boat: Small experimental U-boats with oil-fired turbine drive for submerged operations, having speeds up to 24 knots.\n\nType XXI U-Boat: New type U-boat with powerful electric motors, and extra batteries permitting high submerged speed operation (up to 15 knots).\n\nType XXIII U-Boat: Similar to Type XXI, but smaller, for coastal operations.\n\nType XXV-I U-Boat: Proposed ocean-going U-boat with turbine drive as in Type XVII.\nType 147B - Asdic: British underwater sound gear for determining submarine depth during an attack\nType 271 - Radar: British shipborne 10-cm search radar\nU-Boat: Enemy submarine of 200 tons or larger\nUG: Convoys from the United States to Gibraltar and Mediterranean; UGS for slow convoys, UGF for fast\nU-Kreuzer: Large long-range U-boat\nV-1: German \"buzz-bomb\" or jet-propelled pilotless aircraft of moderate range\nVLR: Very long-range aircraft\nVixen: Attenuator for use with airborne radar to reduce output as range to the target is closed, thereby confusing the GSR operator\nWanz G-1: Long wavelength GSR, an improvement on Metox\nWeapon Lethality: The effectiveness of a weapon in producing damage, without regard to the accuracy with which it can be placed\nWellington A/C: British two-motored bomber and patrol plane built by Vickers.\nWesch Absorber. A rubber-like coating for reducing radar echoes. See Jaumann Absorber.\nWhitley. British two-motored bomber and patrol plane.\nWolf Packs. Groups of U-boats operating together as a unit.\nX-Band. Band of radar frequencies with approximately 3 cm wavelength.\nZigzag. Frequent course changes to make attack by submarines more difficult.\n\nSubject indexes of all STR volumes are combined in a master index printed in a separate volume. For access to the index volume, consult the Army or Navy Agency listed on the reverse of the half-title page.\n\nAcoustic torpedo, German countermeasures, 98-99, 161-176\nFlip-flop rudder control, 167\nGeier, 75\nTrajectory analysis, 164-171\nAdmiralty net defense, torpedo countermeasures.\nAircraft as convoy protection against aircraft attack on submarines, factors determining success: attack errors (128-130), bombing errors (137-138), characteristics of bombs (133), depth bombs (136-137), effect of altitude on success (141), probability of success (132-136), use of rockets (138), variation of individual missiles (133), weapon lethality (130-132). Aircraft equipment for use against U-boats: Leigh searchlight (30), magnetic airborne detector (30), plan position indicator (29). Aircraft patrol, effect on submarine submergence: 95-98. Aircraft tactics against U-boats: advantages over surface craft (12), against Schnorchel-equipped U-boats: depth bombs (136-137), depth charges for air use (12-13), rocket attacks (56, 138), search for surfaced submarines (139-140), sweep widths for visual search (140). Work of seasearch-attack development unit (29). Aircraft types for use against U-boats.\ncarrier-based aircraft, 55\ncivilian air patrol, 29\nmerchant aircraft carriers, 36-37\n\u201cscarecrows,\u201d 6\nvery long range aircraft, 35-36\nAircraft warning radar, enemy, 153\nAir-surface vessel (ASV) radar, 14\nAN/APS-2 (ASG) radar, 39\nAN, antisubmarine equipment\nantisubmarine nets, 30, 41, 98-99\nAsdic equipment, 8, 16, 60\nbearing deviation indicator, 59-60\nBritish Squid, 60\nexpendable radio sonobuoy, 41\nhigh frequency direction finding, 13,\nLeigh searchlight, 30, 40\nmagnetic airborne detector, 30-31\n\"mousetrap\" projector, 30-31\nPPI scopes, 29\nQ attachment (depth-angle sonar), 41\ntowed noisemakers, 162-171\nAntisubmarine measures, 89-91\nconvoy escorts, 90-91\nevasive routing of convoys, 90\nhigh ship speed, 95-97\nobjective of antisubmarine warfare, 89\nsafety of independent shipping, 93-99\nsubmarine operations, 89-90\nAntisubmarine warfare, effect of end-of-warfare, 89\nwar  and  future  developments, \nAntisubmarine  warfare,  history,  prewar \nto  September  1939;  1-2 \nconvoys,  1 \nlack  of  satisfactory  countermeasures,  1 \nneed  for  scientific  and  technical  ad- \nvice, 2 \nsubmarines  in  World  War  I,  1 \nAntisubmarine  warfare,  history,  Septem- \naircraft,  5-6 \nconvoys,  4-5 \nsinking  of  U-boats,  6 \nsurface  craft,  6 \nAntisubmarine  warfare,  history,  July \naircraft,  12-13 \nconvoys,  11-12 \nsinking  of  U-boats,  14 \nsurface  craft,  14 \nAntisubmarine  warfare,  history,  April \naircraft,  20-21 \nconvoys,  20 \nsinking  of  U-boats,  22-23 \nsurface  craft,  17 \nAntisubmarine  warfare,  history,  January \naircraft,  29-30 \nconvoys,  28-29 \nsinking  of  U-boats,  30-31 \nsurface  craft,  22 \nAntisubmarine  warfare,  history,  October \naircraft,  39-40 \nconvoys,  38-39 \nsinking  of  U-boats,  41 \nsurface  craft,  40 \nAntisubmarine  warfare,  history,  July \naircraft,  54-56 \nconvoys,  53-54 \nsinking  of  U-boats,  60 \nAntisubmarine  warfare,  history,  June \naircraft, convoys, sinkings of U-boats, Antisubmarine warfare (summary: 80-87), Asdic (British sonar equipment), depth predictor (50, 60) in minesweepers, limitations (8), ASV (air-surface vessel) radar (14), attack against submarines (theoretical analysis), attack errors, by aircraft (127-138), by surface craft (110-126), factors determining success (114-115), search and interception (139-152), weapon lethality (119-120), attack errors (aiming errors: 129-130, aircraft attacks: 128-130, estimation of submarine position: 114-124, sonar errors: 114-119, surface craft attacks: 114-119, variation in behavior of weapons: 128-), BDI (bearing deviation indicator): 59-60, Blind bombing aid: 57, Blind time, antisubmarine attacks: 114-, Bombing errors, aircraft attacks: 137-138, Bombs: jet-propelled, German, 45, Borkum: German search receiver: 57, 156.\nDepth charges, 137\nSchid, 60\nstrapped magnetron, 40-41\nCamouflage on ill-hoats, 159-160\nCAP (Civilian Air Patrol), 29\nConvoy defense, 100-112 against Schnorchel-equipped U-boats,\nair-escorted convoys, 39, 109\neffect of convoy size, 106-107, 109-111\neffect of convoy speed, 104-106\nend-to-end escort of convoys, 20\ngain in safety, 100-104\nlimitations, 111-112\nradar equipped, 11\nsurface escorts, 107-109\nCountermeasures to the acoustic torpedo nets, 98-99\ntowed noisemakers, 162-176\nCountermeasures to the U-boat, see Antisubmarine equipment\nDamage from U-boats, see Antisubmarine warfare, history\nDepth charges, comparison of British and U. S., 137\ndepth setting, 21, 136-137\ntorpex-filled, 30\nDepth predictor. Asdic, 50, 60\nDirection finding, high frequency, 13\nDMS-1000, microwave radar, 39\nElectric driven U-boats, 177\nERSB (expendable radio sonobuoy), 41, 74, 56, 48, 163\nFast time constant circuit, 74\nFAT (German torpedo gear), 56\nFoxer (British noisemaker), 48, 55, 163\nFXR (U.S. noisemaker), 48, 56\neffectiveness, 163, 172-173\nGerman acoustic torpedo, 48, 161-176\nelectric driven U-boats, 177\nGeier (homing torpedo), 75\nGnat (acoustic torpedo), 75, 173-176\ndescription, 172-174, effectiveness, 176, speed, 56\nGerman\nGuided missiles, effect on antisubmarine warfare, 178\nHohentwiel (aircraft warning radar),\nhuman torpedoes, 52\njet-propelled glider bomb), 45\nKurier (high speed communication), 75\nUiri' (torpedo gear), 75\nPillenwerfer (submarine bubble radar countermeasures), 151-160\nturbine driven U-boats, 177\nU-boat tactics, 177\nGerman U-boat losses in World War II,\nGlider bomb, jet-propelled, 45\nGnat, German acoustic torpedo, 173-176\ndescription, 172-174, effectiveness, 176\nspeed, 56\ntorpex-filled, 30\nHF/DF (high frequency direction find), 153\nHohentwiel, German aircraft warning radar, 153\nGerman torpedo, 30 (Homing torpedo, German)\nGerman, Human torpedo, 52\nItalian submarine losses in World War II\nJapanese submarine losses in World War II\nJet-propelled glider bomb, 45\nGerman high speed communication, 75 (Kurier)\nI.eigh searchlight, 30, 40\nLUT, German torpedo gear, 75\nMAD (magnetic airborne detector), 31,\nMagnetron, strapped, 40-41\nMark HI radar, 40\nMark 8 depth charge, 59-60\nMark 9 depth charge, 60\nMark 14 depth charge, 74-75\nGerman search receiver, Metox, 40-41 (Metox, German search receiver, 55, 57)\n\"Mousetrap\" projector, 30\nNaxos, German search receiver, 55, 57\nNM (towed noisemaker), 162-171 (description, 162; disadvantages, 161-162; effect on trajectory of torpedo, 169-171)\nOperation Torch, 34-35\nPillenwerfer (submarine bubble target),\nPlan position indicator, 29\nProjector, sonar, 41\nQ. Attachment, sonar depth-angle projector, 41\nRadar, enemy countermeasures to, 151-aircraft warning radar, 153\ncamouflage, 159-160\ndecoy for radar, 154\nSchnorchel, 158-160, submergence of submarine, 153\nRadar detection of U-boats, airborne radar, 13, 151\ndetection of Schnorchel, 159, 176, effectiveness, 151-157\nenemy countermeasures, 57, 151-160\nfast time constant circuit, 74\nMark HI radar, 40\nSCR-517 radar, 39\nshipborne radar, 27\nVixen attenuator, 157\nRadio sono-buoy, 41\nRadio-controlled jet-propelled glider bomb, 45\nRD/F 286 M radar (radio direction-find), 39\nRocket projectiles, effectiveness in aircraft attacks, 138\nSADU (seasearch-attack development), 30\nSBT (submarine bubble target), 30\nScarecrows, aircraft used against U-boats,\nSchnorchel on U-boats, 58-59, 64-78, countermeasures to, 159, 176\nSCR-517 radar, 39\nSearch receivers, German, 30, 154-158\nTunis receiver, 75-76, 158\nSubmarine development unit, 29 Shipping safety necessities, locating submarine's ability to approach ships, 95-98 Reduction in mariner's ability to contact ships, 93-94 Sonar gear, limitations, 114-116 Sonar projector, depth-angle, 41 Sono-buoy, dropped from aircraft, 41 Squid, projection of depth charges, 60 Submarine, countermeasures to detect Antisubmarine equipment Submarine attacks, enemy see Antisubmarine warfare, history Submarine bubble target, 30 Submarine search and interception, 139-147 Aircraft search for surfaced submarine, estimation of submarine position, 128-138 Follow-up of contacts, 147-152 Interception of transits, 143-147 Radar versus visual search, 140 Surface craft search, 141-143 Surface craft attack on submarines, 110-119 Barrage lethality, 120-121 Calculation of probability of success, coordination of independent attacks, 125 Effect of sonar conditions, 123\neffectiveness of attacks, factors determining success, 114-126, listening and echo-ranging attacks, surface craft search for submerged targets, T-4 acoustic torpedo, 171-172 (description, effectiveness, 172-174), T-5 acoustic torpedo, 173-176 (description, effectiveness, 176), torpedo, acoustic, German (see Acoustic torpedo, German), korpedo trajectory analysis, effect of noisemaker, 169-171 (flip-flop rudder control, sensitivity pattern template, 166-168), torpedoes, human, 52, Torpex-filled projectiles, 30, rowed noisemakers, 162-171 (description, disadvantages, effect on trajectory of torpedo, 169-171), Tunis, (German search receiver, 75-78), rurl)ine driven U-boats, 177, U-boat countermeasures (see Antisubmarine equipment), U-boat losses in World War II, German, 181, Italian, 181, Japanese, 181, U-boat warfare (see Antisubmarine warfare, history), U-boat weapons, aircraft warning radar, 153.\n[FAT, torpedo gear, 56, Kurier, high speed communication, 75, LUT, torpedo gear, 75, Pillenwerfer, 30, radar decoys, 154, 'ixen attenuator, radar, 157, 'LR aircraft (very long range), 35-36, 'alter turbine propulsion for submar- Vanz G-1, German search receiver, 57]", "source_dataset": "Internet_Archive", "source_dataset_detailed": "Internet_Archive_LibOfCong"},
{"language": "eng", "scanningcenter": "capitolhill", "contributor": "The Library of Congress", "date": "1946", "subject": ["Military oceanography", "Submarine warfare", "Naval research", "Naval research -- United States", "Submarine warfare"], "title": "The application of oceanography to subsurface warfare", "creator": "United States. Office of Scientific Research and Development. National Defense Research Committee, issuing body", "lccn": "2015490950", "collection": ["library_of_congress", "americana"], "shiptracking": "ST005578", "call_number": "18896905", "identifier_bib": "00434112096", "boxid": "00434112096", "possible-copyright-status": "The Library of Congress is unaware of any copyright restrictions on this item.", "description": ["Title on half-title page: Summary technical report of the National Defense Research Committee", "\"Manuscript and illustrations for this volume were prepared for publication by the Summary Reports Group of the Columbia University Division of War Research under contract OEMsr-1131 with the Office of Scientific Research and Development. This volume was printed and bound by the Columbia University Press\"--Unnumbered page ii", "LC Science, Business & Technology copy no. 239", "In a set of declassified documents held as a collection by the Library of Congress", "Includes bibliographical references (pages 99-101) and index", "xi, 106 pages, 11 unnumbered leaves of plates : 28 cm"], "mediatype": "texts", "repub_state": "19", "page-progression": "lr", "publicdate": "2018-01-23 17:20:42", "updatedate": "2018-01-23 18:26:10", "updater": "associate-mike-saelee@archive.org", "identifier": "applicationofoce00unit", "uploader": "associate-mike-saelee@archive.org", "addeddate": "2018-01-23 18:26:12", "scanner": "scribe1.capitolhill.archive.org", "operator": "associate-richard-greydanus@archive.org", "tts_version": "v1.55-final-2-g653f6b8", "imagecount": "154", "scandate": "20180124200126", "ppi": "300", "republisher_operator": "associate-jillian-davis@archive.org;associate-mike-saelee@archive.org;associate-manuel-dennis@archive.org", "republisher_date": "20180416090957", "republisher_time": "2046", "foldoutcount": "12", "identifier-access": "http://archive.org/details/applicationofoce00unit", "identifier-ark": "ark:/13960/t96754d0g", "scanfee": "300;10;200", "invoice": "1263", "curation": "[curator]associate-mike-saelee@archive.org[/curator][date]20180502174636[/date][state]approved[/state][comment]199[/comment]", "sponsordate": "20180430", "external-identifier": "urn:oclc:record:1039972643", "backup_location": "ia906606_35", "openlibrary_edition": "OL30865676M", "openlibrary_work": "OL22959180W", "publisher": "Washington, D.C. : Office of Scientific Research and Development, National Defense Research Committee, Division 6", "oclc-id": "12008779", "associated-names": "United States. Office of Scientific Research and Development. National Defense Research Committee, issuing body", "ocr_module_version": "0.0.21", "ocr_converted": "abbyy-to-hocr 1.1.37", "page_number_confidence": "79", "page_number_module_version": "1.0.3", "creation_year": 1946, "content": "[DECLASSIFIED by authority of the Secretary of Defense memo 2 August 1960 LIBRARY OF CONGRESS SUMMARY TECHNICAL REPORT OF THE NATIONAL DEFENSE RESEARCH COMMITTEE This volume contains information altering the national defense of the United States within the narrowest interpretation of the Espionage Act, 50 U.S.C., 31 and 32, as amended. Its transmission or the revelation of its contents in any manner to an unauthorized person is prohibited by law. This volume is classified Secret. Other chapters may have had a lower classification or none. The reader is advised to consult the appropriate security regulations.]\nWar  and  Navy  agencies  listed  on  the  reverse  of  this  page  for  the  current \nclassification  of  any  material. \nManuscript  and  illustrations  for  this  volume  were  prepared  for \npublication  by  the  Summary  Reports  Group  of  the  Columbia  Uni\u00ac \nversity  Di\\  ision  of  War  Research  under  contract  OEMsr-1 131  with \nthe  Office  of  Scientific  Research  and  Development.  This  volume \nwas  printed  and  bound  by  the  Columbia  University  Press. \nDistribution  of  the  Summary  Technical  Report  of  XDRC  has  been \nmade  by  the  \\Var  and  Navy  Departments.  Inquiries  concerning  the \navailability  and  distribution  of  the  Summary  Technical  Report \nvolumes  and  microfilmed  and  other  reference  material  should  be \naddressed  to  the  War  Department  Library,  Room  lA-522,  The \nPentagon,  Washington  25,  D.  C.,  or  to  the  Office  of  Naval  Research, \nNavy  Department,  Attention:  Reports  and  Documents  Section, \nW'ashington  25,  D.  C. \nCopy  No. \nSummary Technical Report Division 6, NDRC\nVolume 6 A\nSubsurface Warfare (Declassified)\n\nBy authority of the Secretary of Defense\nApplication of Oceanography to Subsurface Warfare\n\nPlease report errors to:\nJoint Research and Development Board\nPrograms Division (STR Errata)\nWashington DC\n\nYour help will make this book more useful to other readers and will be of great value in preparing any revisions.\n\nInevitably, there are errors which have slipped past readers and proofreaders. There may be errors of fact not known at time of printing. The author has not been able to follow through his writing to the final page proof.\n\nA master errata sheet will be compiled from these reports and sent to recipients of the volume.\nLC REGULATION: BEFORE SERVICING OR REPRODUCING ANY PART OF THIS DOCUMENT, ALL CLASSIFICATIONS MUST BE CANCELED\n\nOffice of Scientific Research and Development\nVannevar Bush, Director\nNational Defense Research Committee\nJames B. Conant, Chairman\nDivision 6\nJohn T. Tate, Chief\n\nWashington, D.C., 1946\n\nNational Defense Research Committee\nJames B. Conant, Chairman\nRichard C. Tolman, Vice Chairman\nRoger Adams, Army Representative\nFrank B. Jewett, Navy Representative\nKarl T. Compton, Commissioner of Patents\nIrvin Stewart, Executive Secretary\n\nArmy representatives in order of service:\nMaj. Gen. G. V. Strong\nCol. L. A. Denson\nMaj. Gen. R. C. Moore\nCol. P. R. Faymonville\nMaj. Gen. C. C. Williams\nBrig. Gen. E. A. Regnier\nBrig. Gen. W. A. Wood, Jr.\nCol. M. M. Irvine\nCol. E. A. Routheau\n\nNavy representatives in order of seniority:\nRear Adm. II. G. Bowen, Rear Adm. J. Purer, Capt. Lybrand P. Smith, Rear Adm. H. A. Schade, Commodore\nCommissioners of Patents in order of service:\nConway P. Coe, Casper Ooms\n\nDuties of the National Defense Research Committee:\n1. To recommend to the Director of OSRD suitable projects and research programs on the instrumentalities of warfare, along with contract facilities for carrying out these projects and programs.\n2. To administer the technical and scientific work of the contracts.\n\nMore specifically, NDRC functioned by initiating research projects on requests from the Army or the Navy, or on requests from an allied government transmitted through the Liaison Office of OSRD, or on its own considered initiative as a result of the experience of its members. Proposals prepared by the committee.\nThe Division, Panel, or Committee for research contracts involved in such projects were first reviewed by NDRC. If approved, they were recommended to the Director of OSRD. Upon approval of a proposal by the Director, a contract permitting maximum flexibility for scientific effort was arranged. The business aspects of the contract, including matters such as materials, clearances, vouchers, patents, priorities, legal matters, and administration of patent matters, were handled by the Executive Secretary of OSRD.\n\nOriginally, NDRC administered its work through five divisions:\n\nDivision A \u2014 Armor and Ordnance\nDivision B \u2014 Bombs, Fuels, Gases, and Chemical Problems\nDivision C \u2014 Communication and Transportation\nDivision D \u2014 Detection, Controls, and Instruments\nDivision E \u2014 Patents and Inventions\nIn a reorganization in 1942, twenty-three administrative divisions, panels, or committees were created, each with a chief selected based on his outstanding work in the particular field. The NDRC members then became a reviewing and advisory group to the Director of OSRD. The final organization was as follows:\n\nDivision 1 \u2014 Ballistic Research\nDivision 2 \u2014 Effects of Impact and Explosion\nDivision 3 \u2014 Rocket Ordnance\nDivision 4 \u2014 Ordnance Accessories\nDivision 5 \u2014 New Missiles\nDivision 6 \u2014 Stabilizer-Suspension for Warfare\nDivision 7 \u2014 Fire Control\nDivision 8 \u2014 Explosives\nDivision 9 \u2014 Chemistry\nDivision 10 \u2014 Absorbents and Chemicals\nDivision 11 \u2014 Chemical Engineering\nDivision 12 \u2014 Transportation\nDivision 13 \u2014 Electrical Communication\nDivision 14 \u2014 Radar\nDivision 15 \u2014 Radio Coordination\nDivision IG \u2014 Optics and Camouflage\nApplied Mathematics Panel, Physics - Session 17\nApplied Psychology Panel, Metallurgy - Session 18\nMiscellaneous - Session 19\n\nNational Defense Research Committee [NDRC] Foreword, Declassified\n\nBy authority of the Secretary of [AS], events of the years preceding 1940 revealed more and more clearly the seriousness of the world situation. Many scientists in this country came to realize the need to organize scientific research for national service. Recommendations they made to the White House were given careful and sympathetic attention, and as a result, the National Defense Research Committee (NDRC) was formed by Executive Order of the President in the summer of 1940. The members of NDRC, appointed by the President, were instructed to supplement the work of the Army and the Navy in the development of new and improved materials, instruments, and methods.\nThe instrumentalities of war led to the establishment of the Office of Scientific Research and Development (OSRD) a year later, making NDRC one of its units. The Summary Technical Report of NDRC is a conscientious effort to summarize and evaluate its work and present it in a useful and permanent form. It consists of seventy volumes, grouped according to the NDRC Divisions, Panels, and Committees. The Summary Technical Report of each Division, Panel, or Committee provides an integral survey of its work. The first volume of each group's report contains a summary of the report, outlining the problems presented and the philosophy of addressing them, and summarizing the results of the research, development, and training activities undertaken. Some volumes may be \"state of the art\" treatises covering various fields.\nSome subjects contain information contributed by various research groups. Others describe devices developed in laboratories. A master index of all divisional, panel, and committee reports, which together constitute the Summary Technical Report of NDRC, is contained in a separate volume, including the index of a microfilm record of pertinent technical laboratory reports and reference material.\n\nSome NDRC-sponsored research, declassified by the end of 1945, were of sufficient popular interest that it was found desirable to report them in the form of monographs, such as the series on radar by Division 14 and the monograph on sampling inspection by the Applied Mathematics Panel. The material treated in them is not duplicated in the Summary Technical Report.\nNDRC: The monographs are an important part of the story of these aspects. In contrast to the transformation on radar, which is of widespread interest to the public, research on surface warfare is largely classified and of general interest to a more restricted group. As a consequence, the report of Division 6 is found almost entirely in its Summary Technical Report, which runs to over twenty volumes. The extent of a Division's work cannot therefore be judged solely by the number of volumes devoted to it in the Summary Technical Report of NDRC; account must be taken of the monographs and available reports published elsewhere. Any great cooperative endeavor must stand or fall with the will and integrity of the men engaged in it. This fact held true for NDRC from its inception, and\nFor Division 6, under the leadership of Dr. John T. Tate, we express sincere gratitude to Dr. Tate and the men who worked with him, some as members of Division 6 and some as representatives of the Division's contractors. Their efforts significantly contributed to the successful and often dangerous naval operations during the war and richly deserved the warm response they received from the Navy. Additionally, their contributions to the knowledge of the ocean and the art of oceanographic research will undoubtedly speed up peacetime investigations in this field and bring rich benefits to all mankind.\n\nThe Summary Technical Report of Division 6, prepared under the direction of the Division Chief and authorized by him for publication, presents the methods and results of widely varied research and experiments.\nThis volume deals with the physical properties of the medium in which subsurface warfare is waged. It is more than an account of the oceanographic research sponsored by the Division. It is a text in which the science of physical oceanography is presented with special reference to the significant applications of that science to naval operations. Because of this, it should prove to be of wide interest to all Navy personnel.\n\nThe Division is deeply indebted to Mr. C. O\u2019D.\n\nVannevar Bush, Director\nOffice of Scientific Research and Development\nJ. B. Conant, Chairman\nNational Defense Research Committee\nDirector Iselin of the Woods Hole Oceanographic Institution, not only for his willingness to undertake the task of collecting and editing the material presented in this report, but also for the fruitful participation of his institution in the research and development program of the Division. Special acknowledgment should also be made to the contributions from the Scripps Institution of Oceanography of the University of California. The staff of that institution provided not only broad knowledge of the problems involved but also specialized knowledge of conditions in the Pacific Areas. From the beginning, this research program has received the most cordial support of the Navy. The Bureau of Ships, Hydrographic Office, and forces afloat united to assist in every way both the progress of the work and the application of the results to operations.\n\nJohn T. Tate.\nChief, Division 6\n\nPREFACE\n\nPhysical oceanography is one of the most backward of the geophysical sciences. In general, it can be said that until quite recent years, the physical aspects of the ocean were studied mainly as an adjunct to marine biology. Practical applications seemed to lie in fisheries problems, and the thinking of some oceanographers has been influenced accordingly. Others have been mainly concerned with the geometric approach. More recently, a number of meteorologists have become interested in the circulation problem in the sea because of the several analogies with atmospheric problems.\n\nPerhaps for these reasons, one finds, on the whole, rather little in the standard oceanographic textbooks that is helpful in understanding the transmission of sound in seawater. The chief aim of the present volume is to fill this gap.\nThis text appears to be in good shape and does not require extensive cleaning. Here is the text with minor corrections:\n\nThe use of this volume is hoped to be useful to those continuing with underwater acoustics, as it provides a simple summary of aspects of physical oceanography that help explain the behavior of sound in seawater. Up until the present time, little oceanographic research has been conducted in conjunction with acoustical studies. For those trained in laboratory sciences, this volume may seem elementary and poorly documented. However, at the present stage of physical oceanography, it would not be profitable to treat the subject more exhaustively. The fact remains that our knowledge of the ocean is still rather superficial. It is hoped that in the future, underwater acoustics and physical oceanography will develop in close association.\nPART I\nPHYSICAL OCEANOGRAPHY AND SUBSURFACE WARFARE\n\n1. Introduction\n\nIf the present volume indicates how closely these two subjects are intertwined, it will have served a useful purpose.\nC. O\u2019D. Iselin\n\nCONTENTS\n\nPART I\nPHYSICAL OCEANOGRAPHY AND SUBSURFACE WARFARE\n1. Introduction\n2. The Development of Methods for Predicting Sonar and Diving Conditions\n3. Transmission of Sound in Sea Water\n4. Submarine Diving Problems\n\nPART II\nTEMPERATURE AND SALINITY OF OCEAN WATERS\n5. The Basic Vertical Thermal Structure of the Oceans\n6. Relationship of Salinity and Temperature\n\nPART III\nGEOGRAPHICAL AND LOCAL VARIABILITY\n7. Ocean Currents\n8. Local Variability\n9. Coastal Waters\n\nGlossary\nBibliography\nContract Numbers\nService Project Numbers\nAs inks the intricacies of warfare at sea have cleansed, and as these instruments are used by skillful operators from faster ships or at more nearly their extreme range, the physical characteristics of the medium frequently impose a limitation. In a real sense, there is an oceanography of naval warfare.\n\nAs far as surface warfare is concerned, naval oceanography has already developed far enough to play a part in both operational and materiel activities. Knowledge of sound conditions makes it possible to use sonar gear more effectively and is sometimes a factor in deciding the proper tactical deployment of vessels. Knowledge concerning the surface distribution of temperature and salinity improves diving operations of submarines and to:\nA considerable degree affects their choice of offensive and evasive maneuvers. Oceanographic limitations have caused considerable modification of standard procedures for operating sonar gear and have in some cases influenced its design. They have also required the development and manufacture of instruments to aid in predictions.\n\nAs time goes on, it becomes increasingly clear that, just as climate and terrain affect the strategy of armies, seasonal and geographical characteristics of the oceans must enter into the planning of the Navy. Winds, waves, and currents influence subsurface warfare, as well as aerial and amphibious operations, in ways that are new and different but no less real than the limitations they placed on the old Navies. There are particular times and places best suited to the operation of the diverse and specialized equipment.\nModern fighting ships and skillful planning include oceanography in the list of operational factors to consider. This report's primary purpose is to discuss the general principles of oceanography, particularly in relation to surface warfare. Special emphasis is placed on the aspects of the subject that are most interesting from a practical standpoint: the temperature and salinity of the upper few hundred feet of water and their seasonal and geographical variations, winds and waves and their effects on sound conditions, and bottom sediments in relation to shallow-water echo ranging. The discussion is not limited entirely to matters of immediate practical importance, as a more general knowledge of physical oceanography is essential for proper interpretation of sonar charts and bathythermograph records.\nThe theoretical aspects of the subject are briefly and non-technically addressed here. For more comprehensive treatment, standard textbooks on oceanography are available. Physical oceanography has developed more slowly than other geophysical sciences due to the expense and difficulties of conducting research at sea and the lack of recognition of the practical advantages of increased knowledge of the ocean's physical characteristics. Initially, the biological aspects of oceanography were emphasized over the physical. The Germans were among the first to recognize the potential importance of physical oceanography for modern naval operations, but it is not known at this time.\nDuring the period between the two world wars, the Deutsche Seewarte at Hamburg and the Institut fur Meereskunde at Berlin were strongly supported by the German government. The German Navy had an oceanographic laboratory at Ahrenshfen. Able staffs were assembled, and German naval vessels were used in extended field surveys. One result of this active interest in oceanography by the German Navy was an atlas of the changes in water density, both horizontally and vertically, found in 1911 on a captured German submarine. Primarily designed to guide the diving officer, no definite information can be cited in connection with underwater sound transmission. The Japanese government has also taken an active interest in hydrological surveys.\nAlthough in our country, the Hydrographic Office had pioneered in the early development of the subject, when currents and weather at sea were more important to navigation than they are today, recent years have seen largely private institutions leading the further exploration of the ocean. Before the present war, only a very small beginning had been made by our Navy in the study of the physical factors influencing underwater sound transmission or the operation of submerged submarines. The relatively few physical oceanographers in this country were only vaguely aware of how their studies might be of interest to the Navy.\n\nThere have been four active centers of research in physical oceanography during the war years: namely, the Oceanographic Unit of the Hydrographic Office, the Scripps Institution, the Woods Hole Oceanographic Institution, and the Lamont Geological Observatory.\nOceanography at SIO (University of California, La Jolla), UCDWR (University of California, San Diego), and WHOI (Woods Hole Oceanographic Institution) conducted research on oceanography of subsurface warfare. UCDWR and WHOI carried out more research in this area, but the interests of these four groups were so aligned that it's difficult to assign credit in this report. Personnel was also exchanged freely. In general, studies at Woods Hole focused on the Atlantic Ocean, while data from the Pacific was analyzed primarily at San Diego and La Jolla. It's worth mentioning that oceanography is important to the Navy in various ways different from those discussed here.\nAnd therefore, at some of these laboratories, active research has been in progress, more or less unrelated to submarine warfare. For instance, on the biological side, studies have been carried out of the fouling of underwater surfaces. In mine warfare, currents and the character of the bottom sediments sometimes must be taken into account. In amphibious operations, results of research on waves are important. A few examples have been cited to explain why the few qualified oceanographers available in this country at the start of the war had to take on many and diverse studies. They have been ably assisted by scientists and technicians from related fields, but there has been too little time as yet to develop any one of the practical naval aspects of the subject fully.\nIt is worth considering in this volume not only what has been done but also what problems remain unsolved in the investigations of the effects of oceanography on subsurface warfare. The report begins with an account of the investigations, the developed instruments, methods of using instruments for prediction purposes, and ways these methods might be improved. It continues with a chapter on the transmission of sound in sea water and another on submarine dying problems. Since other volumes of the series deal specifically with these subjects, both are treated summarily here, giving only such facts as are needed for the practical interpretation of the oceanographic material that follows. The latter is divided into two parts. One deals primarily with temperature and salinity.\nThe structure of the ocean and its daily and seasonal changes due to heating, cooling, evaporation, and various other physical processes at the surface of the sea. One topic is concerned with the effect on sound conditions of geographical and local variability of the oceans. Discussed are ocean currents and eddies, coastal waters and bottom sediments, and special phenomena associated with winds and tides.\n\n1. Prewar Investigations of the Role of Refraction in Underwater Sound Transmission\n\nThe role of refraction in echo ranging was first seriously considered in this country in 1937 during transmission measurements made off Guantanamo, Cuba. Accompanied by measurements of the vertical temperature structure of the water, the latter was determined by means of closely spaced mercurial thermometers.\nThe decrease in sound speed with depth, due to the decrease in temperature near the projector level, could sometimes cause sufficient downward refraction for the beam to pass beneath a shallow target, except at relatively short ranges. This idea was advanced independently at the West Coast Sound School in San Diego. It is important to note that both off Guantanamo and San Diego, echo-ranging operations were carried out in deep water in areas where downward refraction effects are particularly striking. A large percentage of earlier tests of sonar gear had been conducted in places where refraction effects were not so frequent. In the course of transmission measurements off Guantanamo and during a second cruise off New York, downward refraction effects were observed.\n\nDevelopment of the Surface Vessel Bathythermograph\nLondon, the following summer, it became obvious that an instrument which would record temperature continuously against depth as it is lowered into the sea would have a great advantage in refraction studies over the conventional deep-sea reversing thermometers of oceanography. A crude model of such an instrument was at that time being tested at the Woods Hole Oceanographic Institution. This instrument had been named the bathythermograph [BT] and was in fact used on a few occasions during the second series of transmission measurements. Modifications resulted in a somewhat improved BT, which gave fair results when used from a vessel moving at 6 or 7 knots and which was used successfully for oceanographic studies.\n\nBeginning in October 1940, the performance of the surface vessel bathythermograph.\nBT was further modified by WHOI working under contract with the National Defense Research Committee with the idea of using it as a naval instrument. It was then realized that for use by the surface vessels of the Navy such an instrument had to be workable at speeds of at least 12 to 15 knots, and this imposed definite limitations on the design.\n\nFirst of all, it was essential to have a light, rugged instrument that could utilize the sounding-lead principle of falling freely through the water in order to gain sufficient depth before the drag of the wire by which it is recovered becomes limiting. The alternative would be to give the instrument diving fins to aid in its descent, which would in turn require a heavier cable to retrieve it and a more powerful winch.\nThe winch increases both cost and difficulties in handling the gear. To effectively exploit the sounding-lead principle, the instrument must have a very rapid thermal response. Otherwise, it cannot record vertical temperature changes accurately. This is desirable from another perspective as well. Any instrument lowered or raised at less than the maximum possible speed is influenced by horizontal temperature variations. This can be partially overcome by ensuring the instrument records only as it is lowered or raised. However, the only way to be certain the thermal element is functioning properly is to record most of both the upward and downward temperature changes.\n\nThe hydrographic instrument used in this work was a preliminary model called an \"oceanograph,\" built by Rossby and Lange at WHOI in 1934.\nand the temperature changes. Agreement between the two traces is proof that vertical and not horizontal gradients have been measured. Another major requirement is that the temperature record must be relatively free from the effects of vibration so that even slight temperature changes with depth can be observed, especially in the upper 50 feet of the water column. This necessity practically precluded the use of diving planes. Additionally, it again raised the question of whether or not the instrument should be constructed to record only the down trace, since vibration is most likely to occur during the raising. It was decided that such vibration as occurred was not serious enough to offset the advantage of having both traces recorded on the slide. Since then, however, there has been an increasing tendency.\nThe greatest weakness of the surface vessel BT discussed here is its tendency to take readings at high speeds, increasing vibration and making it difficult to interpret records. Vibration is a significant issue, and modifications may be required. The instrument must be used repeatedly from a relatively fast ship, making it almost impossible to have it record on deck. Insulated electric cables would never withstand use on a high-speed vessel. Furthermore, because there is a good chance that the wire may become fouled in the screws, resulting in the loss of the instrument, it should be inexpensive and easy to manufacture. Thus, a mechanical type of thermal element is almost a necessity.\n\nThese considerations and the tests carried out during the autumn of 1940 in the Eastern North Atlantic led to a simple, rugged design which has not been...\nA Bourdon-type thermal element, which is compensated by a bimetallic strip to take care of the difference in temperature between the water inside the instrument and that through which it is passing, actuates a pen arm that records on a smoked glass slide mounted rigidly on the pressure element. The pressure element is of the bellows type, having a stiff internal spring and an accurately machined internal guide rod. The effect of increasing external pressure is to shorten the length of the bellows. The speed of response of the thermal element is such that about 80 percent of the full temperature range can be achieved in less than 1 second.\n\nTemperature Element Pressure Element\nrecords vertical temperature gradients accurately enough for practical purposes when combined with a\nA good pressure element. A rough temperature calculation can be maintained, provided the surface temperature is observed with a reliable mercurial thermometer.\n\nEarly in the development of the BT, a basic decision had to be made. Should it record temperature against depth or, on the assumption that salinity is constant with depth, should it record the speed of sound? To have the instrument read directly in terms of the velocity of sound was the direct approach to the refraction problem, yet other considerations outweighed this one. Approximately 70 to 80 percent of the time, there exists near the surface a virtually isothermal layer which is stirred by convection and by the wind. However, this is not an isovelocity layer, because of the effect of pressure on the speed of sound. Thus, the proper performance of the instrument requires accounting for both temperature and pressure variations with depth.\nof  the  thermal  element  can  be  much  better  judged  in \nthe  absolute  accuracy  of  such  a  thermal  system  is  not \nnotably  great  unless  it  is  frequently  calil^rated,  it \nFigure  2.  Photograph  of  installation. \nRESTRICTED \nTHE  BATHYTHERMOGRAPH  FOR  StIBMARINES \nterms  of  temperature  than  in  terms  of  Aelocity.  Fur\u00ac \nthermore,  the  oceanographic  aspects  of  sound  trans\u00ac \nmission  are  much  more  easily  understood  in  terms  of \ntemperature.  As  a  residt  of  this  decision,  the  empha\u00ac \nsis  in  the  present  report  is  on  temperature  rather  than \non  changes  in  the  speed  of  sound.  At  the  same  time  it \nwas  decided  to  use  the  Fahrenheit  temperature  scale \nin  accordance  with  Navy  practice. \n13  THE  BATHYTHERMOGRAPH  FOR \nSUBMARINES \nDuring  the  course  of  the  development  of  the  sur\u00ac \nface  vessel  BT  it  became  evident  that  a  corresponding \ninstrument  for  submarines  woidd  have  several  prac\u00ac \nDuring the summer of 1941, in response to a request by the Commander of Submarines, Atlantic Fleet, a number of temperature-depth recorders were built at Woods Hole and tested in submarines both off New London and off Key West. Initially, the BT for submarines was thought of primarily as an acoustic instrument. That is, it would be used to predict the maximum range of the sonar equipment on the submarine, as well as the performance of her adversary\u2019s gear. However, early in the tests off Key West, it became evident that vertical temperature changes could be interpreted in terms of density with sufficient accuracy to be of considerable assistance to the diving officer in maintaining proper trim. Thus, a second use for the instrument arose.\nThe counter and weight in the blister tubing outside the conning tower holder are filled with xylene. The temperature is measured using a Bourdon tube stylus counter and weight. Figure 4 depicts the submarine bathythermograph diagram.\n\nThe best location for the thermal element on the submarine hull is still a matter to be settled by deliniite tests. Placing it high on the conning tower has been an acceptable compromise between a still higher position which would be better for acoustical purposes and a lower position which would reduce dicing. It is possible that two installations will be used later. Except for this issue, the initial design problem for the BT for submarines was not difficult. It involved building a sufficiently rugged and simple instrument.\nWhich thermal element would fit into the available space. Again, a Bourdon-tyrie thermal element was used with suitable compensation for temperature changes inside the submarine. Another Bourdon tube was used as a pressure element by connecting it with the pressure line leading to a depth gauge. The general features of the installation are shown diagrammatically in Figure 2.\n\nFrom the standpoint of submarine warfare, the density of seawater is relatively more sensitive to changes in salinity than is the speed of sound (see Section 2.3). Recently, there has been development of a so-called salinity-compensated BF for submarines. This measures temperature, salinity, and pressure, and computes and records liquid ballast change and the speed of sound against depth.\n\nChapter 2\nTHE DEVELOPMENT OF METHODS FOR PREDICTING\nTHE BEHAVIOR OF SUBMARINES IN THE SEA\n\n(Note: The text above has been cleaned to remove meaningless or unreadable content, introductions, notes, logistics information, publication information, or other content added by modern editors that obviously do not belong to the original text. No translation of ancient English or non-English languages into modern English was required as the text was already in modern English.)\nThe investigation of sound conditions leading to the development of the bathythermograph (BT) continued, quickly revealing the complex nature of sound transmission in seawater. Echo and listening ranges could be limited by various factors. Extensive fundamental research was necessary to translate the basic temperature-depth curve of the BT into a practical prediction of sonar conditions.\n\nWartime necessities demanded that research results be turned into practical information for the men on the ships as quickly as possible. Prediction methods have therefore been revised frequently as new research suggested the desirability of doing so.\nProper caution was exercised in accepting modifications to existing methods. Only one extensive revision of official procedure has been retired. However, the rapid developments in this field have resulted in some confusion, which, unfortunately, seemed justified by the needs of the moment.\n\nAside from manuals on the operation and maintenance of the Bl, official literature on the subject can be classified into two main groups:\n\n1. Prediction manuals. These are designed so that the on-board olxserver can make practical use of any particular bathy thermogram by determining within certain probable limits the range that can be obtained on a submarine. This information enables the olxserver to operate the shij) and sonar equipment according to the most efficient tactical usage for that particular range.\nA submariner obtains information similar to him on the best depth for evasion, probable ping and listening ranges, and the most efficient diving procedure.\n\n1. Charts. These include sonar charts showing average echo ranging conditions, average diving conditions (in the Submarine Supplements), and bottom sediment charts for shallow-water sonar work. Charts of average conditions are of less tactical value than a bathythermogram obtained at the time and place needed, because conditions are generally too variable to permit accurate enough predictions on the basis of averages. However, they provide a perspective unobtainable from a small number of bathythermograms and are therefore useful not only to the observer for determining how often BT lowerings should be made, but also for more important strategic purposes.\nIt is beyond the scope of the present work to discuss the Navy BT literature and its scientific origins in detail. However, a more limited discussion is warranted as frequent reference will be made throughout the volume to the official literature in connection with the oceanographic part of its background. The history and purpose of the prediction methods will therefore be described briefly. Where obvious improvements can be made, either by collection of more observations or by better use of existing data, these will be mentioned.\n\n2. PREDICTION MANUALS\nIn February 1941, a report was published summarizing what was then known about the refraction of sound in sea water and the oceanographic factors chiefly responsible. The present report is in part an expansion of the oceanographic section of this earlier report.\nThe study was based largely on experience gained during early transmission measurement periods. Since the notion that sound is refracted in sea water in accordance with geometrical optics principles was not generally accepted, much of the discussion in this early report focused on a simple refraction theory. The report was particularly concerned with demonstrating that the vertical temperature distribution alone provided a good means of calculating the refraction pattern. Such calculations were later simplified by the introduction of a refraction slide rule, and a collection of a large number of such calculations for common vertical temperature distributions has been published recently. Another contribution was the development of the sonic ray plotter.\nRecent studies of the transmission of standard RF.S I RICTEI methods for predicting sonar and diving conditions have shown that the clearly defined acoustic shadow zones, which are predicted on the basis of geometrical optics, are not always observed. Only in the case of sharp downward refraction does a marked acoustic shadow zone appear. The limitations of the simple refraction theory are not yet fully understood, and at the time of this writing, sound field measurements are still being actively secured.\n\nOn the other hand, the reduction in sound intensity below a sharp thermocline, the so-called layer effect in echo ranging, which is predicted by the simple theory, does in fact exist. Thus, no matter what the final result of the transmission studies may be, it is clear that under contemporary operating conditions, the layer effect is a significant factor.\nVertical temperature gradients, particularly marked ones, often limit submarine detection. The sensitivity of sonar equipment is increasing, and submarines are becoming more skilled in utilizing oceanographic factors in their favor. Success in subsurface warfare will increasingly depend on which side has a better understanding of the medium.\n\nAccording to current theories of antisubmarine and prosubmarine warfare, there are certain advantages to be gained by knowing the changes of maximum sonar range with depth. Additionally, it is generally agreed that our submarines can change depth more precisely and silently if the diving officer understands the changes in density in the superficial layers of the ocean.\n\nAlthough the scientific theory of sound transmission in the ocean is complex, it is well-established that sound travels faster in warmer water and slower in colder water. The refraction of sound waves at temperature gradients can significantly affect the range and accuracy of sonar systems. Understanding these oceanographic factors is crucial for both offensive and defensive submarine operations.\nThe problems in writing the manuals became apparent. In the first place, it had become clear that the refraction slide rule method of calculating acoustical ray diagrams was too ponderous and time-consuming to be of much practical value at sea. It was not enough to perform the relatively simple operation of determining the limits of the so-called shadow zone, as the intensity of sound near the outer limit of the shadow zone varied significantly, except in the case of strong refractions.\nThe direct sounding field Avas generally too low to return a detectable echo. It was necessary to go further and calculate the distribution of intensity Within the beam. This was a long task, generally requiring 2 hours' work or more by an experienced calculator, and it was hardly to be recommended as a standard Navy procedure. The alternative was a method of classifying BF slides according to the most significant features of their temperature structure, such as the depth of the mixed surface layer (known as layer depth in X-ray literature) and the strength of negative gradients near the surface and below the mixed layer. Then the probable echo range could be predicted according to simple rules for each type of temperature pattern.\n\nAny such method has both advantages and disadvantages. The vertical temperature structure of\nThe ocean is complex, and no simple scheme for classifying it will be accurate in all circumstances. The methods in the manuals reduce such errors to a relatively low percentage but do not entirely eliminate them. In fact, more careful scientific methods have thus far failed to show complete correlation between bathythermograms and observed ranges. The discrepancies are presumably due to a combination of several factors such as absorption and scattering of sound, and small and frequently changing variations in the refraction pattern that cannot be determined easily. These factors have not and perhaps never can be accurately evaluated.\n\nHowever, even if oceanographic variables were completely understood, it would be a mistake to suppose that maximum echo ranges could be forecast with great precision under practical circumstances.\nThere always remain unforeseeable factors, such as target aspect and speed, that may introduce variations in maximum range by up to plus or minus one-third of the prediction. With such large unavoidable errors in the predictions, it would be fruitless to complicate the system with small and relatively insignificant refinements in refraction classification. Moreover, a manual must take into account the fact that the predictable part of sonar performance is not always determined by water conditions. Indeed, it is difficult to form an estimate of how much of the time oceanographic factors are really limiting. If the antisubmarine vessel is a destroyer or destroyer escort and is not operating at too high a speed, if standard heavyweight sonar gear is being used, if the operator is skillful, and there is no electrical or mechanical interference.\nMechanical trouble, then in deep water, either the water or the temperature distribution may become limiting. Oceanographic factors may be limiting a small percentage of the time or most of the time depending on the ship, its equipment, sonar personnel, and type of duty.\n\nNon-oceanographic factors can be evaluated for any particular ship and any set of operating conditions by means of a few experiments. The current manual for the surface vessel BT (see reference 5) was intended primarily for destroyer escort class or larger ships, using standard heavyweight sonar equipment. The manual therefore evaluates problems of echo ranging as they apply to this particular type of vessel, with proper allowances for self-noise and the effect of heavy weather in reducing ranges. It assumes that the gear is operating properly.\nThe prediction manual for submarines, as referenced in [6], follows a similar basic plan as the manual for surface ships. Prediction methods vary, but the differences result from the unique characteristics and needs of submarines. Submarines have a much wider range of uses for the BT than surface vessels. One of the most important uses is predicting ballast adjustments for quiet diving with minimal lost time. From an acoustic standpoint, it is used to determine the least depth for evasion, ping ranges, and listening.\nSubmarines use acoustical predictions for surface ship ranges, and to a lesser extent, maximum echo ranges at periscope depth and various other depths for evasion. Each of these acoustical predictions is a separate problem where refraction plays a role but is modified by other non-oceanographic factors. In some respects, the submarine at periscope depth is in a more favorable position for echo ranging than a surface vessel. Self-noise can be reduced to a low level, and its deep projector and stability in heavy weather reduce echoing and pitching effects to a minimum. However, both the greatest range at which a submariner can obtain an echo from a surface vessel and the greatest range at which he can hear the pings of a surface vessel trying to echo-range off him are affected by the speed of the submarine.\nThe surface vessel and submarine encounter different listening range predictions. Maximum listening ranges must account for submarine and target ship speed, as well as wind force. A submariner's understanding of refraction conditions and utilization have been limited due to the temperature element being mounted on the conning tower, making it impossible to determine temperature structure in the upper 20 feet of water. Submariners lacked the knowledge to fully utilize short periscope depth ranges caused by pronounced temperature decreases in the upper few feet. The desire for great depth for increased evasion time results in most submarines going deep when attacked.\nNew installations providing a temperature element on the periscope shears will allow more accurate determination of refraction conditions and enlarge the choice of evasive tactics. Prediction methods will be improved in many small ways in further editions of the manuals. In many cases, the available information has not been as complete as desired. In time, this situation will be corrected, and the accuracy of prediction methods will be increased. There is great need for elaboration of acoustical methods in shallow water. It may well prove impossible to predict maximum echo and listening ranges in shallow water with any degree of precision, for it is too complex a subject to resolve itself easily into a few basic rules. However, there are tactical considerations such as selection of proper receiver settings and signal length.\nAnd manipulation of tilting beam can lead to great improvements in sonar performance. Predictions for echo ranging in deep water should also be improved, particularly in respect to ranges on a target at known depth. This becomes important with the advent of accurate depth-determining gear, since good predictions of range at the depth of the target will modify and improve the tactics of reattack. Far more important than these minor revisions of existing methods are the changes and additions that must be made to keep abreast of current Navy developments. New gear requires careful study to determine how oceanographic factors affect its operation. Within the short space of World War II, there were several major developments in sonar equipment, and one of these in particular, the tilting beam, has created new functions for the BT.\nWhich methods are more important than those for which it was originally intended. Submarine listening methods are expected to improve greatly.\n\nRESTRICTED: Methods for predicting sonar and diving conditions\n\nThis applies to the equipment itself and reduction of self-noise. In general, listening has not been studied nearly as thoroughly as echo ranging, and its full potentialities and the rules governing its use will not be developed for some time.\n\nNew tactics may also have oceanographic implications that are an important part of the statistical examination of their chances for success and may modify their use or determine whether or not they may be used in a particular situation. All such developments require changes in the existing manuals.\n\n22. Sonar charts\n\nEarly in the development of BT methods, only a few charts were available.\nFew ships were equipped with the instruments, and there was no possibility of making all necessary installations within less than a year or so. The need was apparent for some sort of information to aid sonar personnel in understanding the effects of oceanographic factors on echo ranging and in knowing approximately what kind of sound conditions might be expected in different parts of the oceans. The answer to this need was the sonar charts, which show average echo ranging conditions for all the oceans at different seasons of the year.\n\nSince their beginning, the charts have gone through several revisions and have changed in both their form and the purposes for which they are used. With the increase in the number of BT installations, ships are no longer dependent on charts for all of their information on sonar conditions. However, the charts remain valuable tools for navigators and researchers, providing essential data for planning sonar surveys and interpreting sonar data in various oceanic conditions.\nCharts have been incorporated in the prediction procedure and are used in conjunction with the BT to determine how often lowerings need to be made, indicate layer depth whenever tactical conditions prevent a deep lowering, and for various other purposes. They are especially applicable to submarine operations, though the Submarine Supplements discussed in Section 2.3 have replaced them with similar but more detailed information in certain strategic areas. Additionally, since they are the best available information on what kind of sonar conditions can be expected at any given place and time, it is expected that the charts may serve a purpose in planning naval operations.\n\nThe construction of these charts requires a nice balance between a purely statistical analysis of the available bathythermograms and general oceanographic information.\nThe data on winds is adequate, but the distribution of bathythermograms and oceanographic stations for any one month is most unsatisfactory. Even when observations from three months are combined, there are very large areas without a single observation. If the observations were evenly scattered, both geographically and with time, a purely statistical treatment might not be seriously misleading. However, in any given area, even as large as a 5-degree square, it often happens that the available data are mostly from a single month and not well distributed. The result is that it is still advisable to use a certain amount of art in drawing the contours, even in the case of the Northern Hemisphere oceans for which roughly 200,000 bathythermograms and oceanographic stations are now available. Except for\nIn the Southwest Pacific, there are less than 1,000 observations in all three Southern Hemisphere oceans combined. Figure 1 shows the positions where bathymetric data have been obtained. Surprisingly, general oceanographic knowledge is adequate for this particular purpose. The charts constructed before the bathymetric data were available in quantity differed only slightly from the newest editions as far as accuracy of oceanographic information is concerned.\n\nIn successive revisions, the sonar charts have gone through an evolution parallel to that of prediction manuals. In the beginning, they were based entirely on refraction, and the range contours on the charts represented average layer depth based on known wind and current systems. In later editions, other factors have been considered.\nThe charts have been expanded to include the periscope depth range chart and the assured range and layer depth chart. The first of these displays the average percentage of time that the periscope depth range is reduced to less than 1,500 yards due to unfavorable temperature gradients near the surface of the water or strong winds of force 7 or more on the Beaufort scale. The Beaufort scale, originally devised by Admiral Sir Francis Beaufort in 1805 based on how much canvas a man of war could carry under different winds, was later placed on a more objective footing by Dr. G.C. Simpson. His revised scale was accepted by the International Meteorological Committee in 1920. It is this revised Beaufort scale.\nFigure 1 displays the positions where latitude lines intersect. below is Figure 2, presenting the Beaufort scale in relation to wind measurements taken with an anemometer installed at a height of 33 feet.\n\nFigure 2. Beaufort scale compared to other velocity scales.\n\nThe assured range and layer depth chart demonstrates the average range on a submarine at its optimal depth for evading detection, which may be periscope depth or just below layer depth. The range contours on this chart indicate the average range as determined by temperature gradients when wind force is less than 7. In regions where strong winds significantly reduce the stirred range to less than 1,500 yards, the chart does not provide this information.\nThe percentage of this occurrence is indicated. This type of chart depends primarily on large-scale oceanographic features which can be judged rather well from a knowledge of the seasonal cycle. It will be improved considerably when more is known about the details of geographical variations in the seasonal thermal cycle. These two types of charts have been constructed for both winter and summer conditions in all oceans. When in the Northern Hemisphere, the sea level height is approximately 10 meters. The height is important, since when the air is stable (i.e., with colder air underlying warmer air), the wind velocity may vary greatly with altitude. Such a situation is common when the sea surface is much colder than the air, as on certain continental coasts in the summer time. Under such circumstances, the reading of an anemometer mounted on a tower may be affected.\nThe naval vessel's masthead is not a reliable indicator of wind force according to the Beaufort scale. The same months are used for December through February and summer as June through August. In Southern Hemisphere charts, the seasons are reversed. For the North Pacific and North Atlantic, there are also three smaller charts that show the monthly variation in average periscope depth, assured range, and layer depth. In a general way, sonar charts display the whole seasonal temperature cycle for these areas. Future sonar charts will be improved with the gradual acquisition of more BD' records. There are very few areas in the oceans that have a complete yearly cycle of BT observations, and there are very large areas where observations for only one season exist.\nMonthly records have been obtained. In such cases, it is necessary until more records have been obtained to base the charts almost entirely on general oceanographic knowledge, wind observations, and a scattering of hydrographic stations. The collection of useful records will also be accelerated by more accurate data accompanying the bathythermograms. Without the correct position, time, and date, a BT slide is useless for purposes of analysis. Many of them have been discarded because the positions were missing or obviously incorrect. Perhaps other errors not so obvious have escaped attention and have been responsible for some of the variability on the charts.\n\nIt has been apparent in the preceding discussion that sonar ranges are dependent not only on various purely oceanographic factors but also on winds, weather, and climate in general, these relationships\nwill be cliscus. This will be discussed in detail in the chapters that follow, although it will be seen that our knowledge about them is as yet incomplete.\n\n23. Submarine Supplements\nSubmarine Supplements to the Hydrographic Office's Stilling Directions for particular areas and seasons have been issued to provide submariners with local information about diving and sound conditions. Although their general function is somewhat similar to that of sonar charts, the scope is much broader. The Supplements contain charts of average diving and echo ranging conditions, but they also discuss the oceanography of the region in respect to effects of weather and seasonal climate, so that the usefulness of the charts is increased by providing real understanding of local conditions. Previous experience of submariners in the area is also made available.\nMethods for predicting sonar and diving conditions by including excerpts of action reports discussing the practical utilization of existing oceanographic conditions.\n\nThe first Submarine Supplement, covering the Bay of Biscay area, was issued by the Hydrographic Office in June 1943. It was followed shortly by a second one on late summer conditions in the Japanese Empire area. Their reception by submariners was favorable enough to justify plans for expanding the program and publishing Supplements for all areas of strategic importance.\n\nThe type of information in the different Supplements naturally varied somewhat, depending on the oceanography of particular regions. In regard to sonar conditions, the most important feature has been data on the best depths for avoiding detection by echo ranging activities, and this has been supplied in each Supplement.\nImplemented with material on assured ranges, maximum echo ranges at periscope depth, types of bottom in shallow water areas and their sonar significance, listening conditions, and local acoustic phenomena such as biological noise. Diving problems have been emphasized more than sonar conditions. Material on this subject has included ballast changes required for diving and cruising in the area and salinity corrections to BT data.\n\nThe Submarine Supplements have not been intended for immediate tactical use. Figures on average conditions and probable variations are poor substitutes for exploratory dives, although they are useful enough when an emergency prevents such dives from being made before beginning offensive or defensive action. On the other hand, an understanding in advance of conditions and a general knowledge of the area are essential.\nThe appropriate type of operations proves advantageous from both the tactical and strategic points. Strategy of larger scope, planning a submarine campaign according to the optimum balance between desired objectives and necessary risk, utilizes oceanography of the type discussed in the Supplements, which show the areas and seasons most favorable to submarine operation. These publications, such as sonar charts, have been something in the nature of an experiment. It has not been certain throughout their development what information was needed most, nor were the available observations so complete as might be desired. Consequently, the different Supplements have been variable in quality and manner of presentation, and revisions are needed to make them more comprehensive and more uniform in general style and content.\nAs in the case of prediction manuals, further developments in subsurface warfare will necessitate occasional revisions of the Supplements. Previously made statements about changes in response to modifications of sonar equipment apply especially to all these publications. It is also likely that submarines in the future may operate at greater depths than present. This would require extensive revision of all charts and considerable changes in both strategy and tactics.\n\n24. BOTTOM SEDIMENT CHARTS\n\nSubmarine warfare in coastal waters made it apparent early in World War II that there was great need for study of the problems of echo ranging in shallow water and the development of rules for both pro-submarine and anti-submarine forces. Accordingly, the production of bottom sediment charts was begun, which showed the distribution of different sediments.\nThis work began at a time when information on the acoustic qualities of bottom sediments was very incomplete. Indeed, the whole problem of echo ranging in shallow water is a difficult one that has not been solved in all its details. The different kinds of bottom shown on the first charts were chosen more or less arbitrarily. It was known that bottom reflection and scattering could significantly increase or decrease echo ranges in shallow water, and that in general, a smooth, hard bottom extended the range, while a rough bottom shortened it. However, the details of acoustic classification of these bottoms were not known, nor were the boundaries between them clear. A detailed geological map would obviously be too complex for this purpose.\nIn examining the effect of bottom structure on echo ranging, it's crucial to consider the composition of bottom sediments first. The texture of the sediments largely determines how much sound will be absorbed and how much will be reflected back into the water. Softer bottoms absorb more sound and reflect less, making it difficult for a soft mud bottom to return an echo from a submerged object.\n\nThe purpose at hand required grouping the various types of bottom that occur under the sea into a few general classes. The choices made were fortunate, and as experimental data have accumulated, only slight modifications to the range predictions have become necessary for the six major bottom types now in use.\n\nIn considering the effect of bottom structure on echo ranging, it's essential to take into account the composition of bottom sediments. The texture of the sediments primarily determines how much sound will be absorbed and how much will be reflected back into the water. Softer bottoms absorb more sound and reflect less, making it difficult for a soft mud bottom to return an echo from a submerged object.\n\nAs it turned out, the choices made were fortunate, and as experimental data have accumulated, only slight modifications to the range predictions have become necessary for the six major bottom types now in use.\nMarine echo ranges can be predicted based on refraction patterns in deep water. A sandy bottom may reflect nearly all sound, resulting in little correlation between refraction and range obtained. In bottom sediment charts, grain size, determined by mechanical analysis, was the criterion for estimating bottom relative firmness or softness. This classification has been reasonably satisfactory from the acoustical standpoint, except in the case of mud. Two mud deposits with the same particle size may behave differently regarding sound absorption, one absorbing it completely, the other not at all. It is suspected, although not proven, that mud texture alone is not an adequate criterion.\nwhich gives some extension by reflection contains considerable clay, which imparts firmness to the structure. Tests of the plasticity of critical deposits are needed to determine this theory. Once the problem has been solved by a proper combination of acoustical tests and laboratory analysis, the classification can be altered accordingly. If the percentage of clay in the samples proves to be the answer, many such areas could probably be located by geological inference and this information placed on the charts.\n\nThe construction of bottom sediment charts necessitated the synthesis of material from several sources \u2014 navigational charts, oceanographic surveys, acoustic tests, and general geological knowledge of how sediments are transported and how they are re-deposited.\n\nThe size limits were set arbitrarily as follows:\nMUD \u2014 90% smaller than 0.002 mm.\nSAND: 0.062 mm to 2.0 mm in size\nSAND: Less than 10% smaller than 0.062 mm and more than 90% smaller than 2.0 mm.\nSTONY: Rounded or angular pieces of rock, more than 2.0 mm and less than 10 cm in size, representing glacial drift or other transported material.\nROCK: Rocks larger than 10 cm or broken from rock ledges, or projecting rocks or rock ledges visible in bottom photographs.\nCORAL: Calcareous masses of coral, algae, or other lime-secreting organisms, as indicated by samples or bottom photographs.\nRelated to bottom topography. The best way to understand this is to review the history of the charts.\n\nPrior to the war, hundreds of bottom samples and cores in all types of sediments had been taken by the Scripps Institution of Oceanography and the Woods Hole Oceanographic Institution.\nThe Oceanographic Institute conducted work in submarine geology, analyzing most of the material mechanically. This provided substantial information for constructing charts for acoustical work in local areas. Where coverage by actual samples was incomplete, additional ones were taken. The first bottom charts on the east coast included the easterly end of Long Island Sound, Block Island Sound, the approaches to New York, and Massachusetts Bay. These were used for experimental sound ranging by the Columbia University Division of Water Research at the U.S. Navy Underwater Sound Laboratory in New London and for ambient noise surveys off New York and in Block Island Sound. Similar charts were made for the vicinity of San Diego and San Francisco on the west coast.\nFrancisco Bay and were used by the University of California Division of War Research at the U.S. Navy Radio and Sound Laboratory, San Diego, for acoustical tests of the bottom. During these charting programs, close contact was maintained between the east and west coast groups so that the classification of sediments and the methods of chart construction were comparable in every respect.\n\nAcoustical tests in areas such as the San Diego oiling, where bottom types varied widely in relatively short distances, required great care in demarcating bottom zones and keeping within the zones during tests. In some areas where abundant bottom samples showed sand, or sand and mud, dredging revealed the presence of scattered rock ledges, and in these areas the reverberation level was distinctly higher than in other zones where such ledges did not occur. Thus, it is important to accurately identify and distinguish between different bottom zones in order to ensure accurate and consistent acoustical test results.\nVery careful sampling was required for acoustical work on the bottom, and both dredge lines and bottom samples were needed along the course of proposed sound field runs. In rocky areas, dredging often proved slow and laborious. Photographs of the bottom taken with an underwater camera were found to be a better method. These photographs, examples of which are shown in Chapter 9, were quite adequate for the purpose when taken at closely spaced intervals. Restricted methods for predicting sonar and diving conditions revealed useful details of bottom topography that could not be determined by bottom samples.\n\nAs soon as the preliminary program of charting and acoustical tests in local areas had progressed far enough to provide a scientific basis for further work, a general charting program was begun. Outside the\nIn areas where samples were obtainable, it was necessary to depend primarily on bottom information collected during government hydrographic surveys, along with the small amount of material reported in various oceanographic investigations. The surveys varied greatly from place to place in detail and reliability, depending on the importance of the region to navigation and on the country that conducted the survey. In all these cases involving the transfer of information from navigational charts to charts of sound ranging conditions, judgment needed to be exercised on two counts: first, to attempt to compensate for lack of adequate information on the navigational charts by judging the situation according to what is known about particular areas that have been surveyed by more thorough methods; second, to simplify the charts by using in some cases a classification that\nThe functionally correct sound ranging, though not necessarily accurate geologically, is described in detail in a later chapter. Over several years, most important strategic areas have been charted, including the United States coast, the Philippines, the Japanese Islands, the east coast of India, French Indo-China, Malaya, the eastern side of the Bay of Bengal, parts of the East Indies, and selected areas off the European and African coasts. The locations of these charts are shown in Figure 3. Bottom sediment charts are used for range predictions and are incorporated in the classification schemes in the materials. They are therefore an important part of the general tactical considerations in the jetting of vessels and the operation.\nof sonar equipment to obtain maximum efficiency. They are equally important to seafarers in the latest project and can also be used in choosing favorable operating areas. It seems probable, however, that the full value of these charts will not be realized until work now underway has been completed. This will include not only general improvement of the charts along the lines already discussed, but also modifications of sonar equipment intended specifically to improve performance in shallow water.\n\nChapter 3\n\nTRANSMISSION OF SOUND IN SEAWATER\n\n3.1 Propagation of Sound Waves\n\nSound waves are propagated in a homogeneous medium and radiate outward from the source in straight lines. If the sound source is constructed to be directional, then most of the sound will be projected in the form of a conical beam with its axis perpendicular to the direction of propagation.\nUltra to the face of the projector, this situation is shown diagrammatically in Figure 1, where A, li, and G represent successful sound impinges (pings) which can be visualized as sections of the cone that constitute the highly directional and most intense part of the emitted sound. Sound of weaker intensity will be projected at greater angles, as indicated by dotted lines in the figure, and will return an echo from a target at close range, as indicated by the enlarged envelope of the sound impinge at A. But the greater the range, the smaller will be the angular width of the effective cone, which with standard Navy sonar gear is approximately 10 to 12 degrees wide at ranges greater than 800 yards.\n\n3.1.1 Factors Affecting Transmission\n\nBecause of divergence, the intensity of sound decreases with increasing distance from the sound source.\nWithin the sound pulse, the intensity decrease is inversely proportional to the square of the range, as the cross-sectional area of the beam increases and the amount of sound intercepted and reflected by a unit-size target decreases.\nThe intensity of the echo decreases as the inverse square of the range, combining transmission and reception losses. The total decrease in intensity between the outgoing pulse and the echo that comes back is proportional to the inverse fourth power of the range. For every tenfold increase in range, the intensity in the direct beam will be decreased to 1/1000th of its original value, and the echo intensity by the time it reaches the receiver will be reduced to 1/10,000th. Absorption of sound by water accelerates this decrease in sound intensity, particularly at long ranges. This explains why the sound of a ping at a range of 10,000 yards may be louder than an echo from a target at 1,000 yards, and why echo ranges are distinctly limited by the gear.\nmakes it clear that a very great increase in sound output would be required to produce a moderate increase in echo ranges. The strength of an echo depends on the size of the target as well as on range. Thus, a large vessel returns a stronger echo than a small one, and for a ship of any given size, the beam aspect presents a better target than bow or stern. These are a few of the simple properties of sound transmission in seawater.\n\nFigure 2. Diagrammatic drawing of outgoing ping and slowing echo.\n\nTransmission in a homogeneous medium. However, the sea is far from homogeneous and, moreover, in echo ranging the source of the sound is quite near the surface, which complicates the situation by reflecting and scattering sound. The physical characteristics of seawater\u2014its temperature and salinity, the number and distribution of suspended particles\u2014all affect sound transmission.\nand  size  of  the  particles  suspended  in  it,  and  the  dis\u00ac \nturbances  of  its  surface\u2014 vary  widely  from  place  to \nplace  and  from  time  to  time.  All  these  affect  trans\u00ac \nmission,  and  underwater  sound  is  therefore  sidDjcct \nnot  only  to  expected  divergence  and  absorption,  hut \nalso  to  \\arying  degrees  of  refraction,  reflection,  and \nscattering. \nReflection \nReflection  occurs  both  from  the  ocean  bottom  and \nfrom  the  underside  of  the  sea  surface.  If  these  surfaces \nare  smooth,  extension  of  range  may  result  through \nreinforcement  of  the  direct  sound  beam.  If  they  are \nrough,  sound  cvill  be  scattered  in  all  directions,  and \nthat  ]jart  which  is  returned  to  the  location  of  the \noriginal  sound  source,  thereby  interfering  with  echo \nrecognition,  is  known  as  reverberation.  The  bottom \neffects  arc  important  enough  to  he  regarded  as  the \ncontrolling  factor  in  echo  ranging  wherever  the \nThe depth of water is less than about 100 or 200 fathoms. Surface reflection and scattering are usually less significant in standard echo ranging. However, at short ranges (less than 1,000 yards), reverberation from the surface forms the principal background in echo ranging and may be the controlling factor in the detection of small objects when the sea is not calm.\n\nRefraction\n\nVariations in the temperature and salinity of sea water can profoundly affect sound transmission because they produce variation in the speed of sound as it travels from one point to another, and this in turn causes refraction of sound waves. It was shown in the introductory chapters how discovery of this phenomenon led to the development of the hydrothermograph [BT] and accompanying prediction methods as instruments of naval warfare. At this time.\nWorthwhile to discuss the principles of the simple refraction theory as it was first developed, since it provides an adequate framework for the essential facts on underwater sound transmission and the way maximum echo and listening ranges are affected by temperature gradients. It should be kept in mind, however, that while the theory is in approximate agreement with the most important observed results, subsequent experiments have shown it to be an incomplete explanation. Discussion of these later modifications of the refraction theory is beyond the scope of the present work but will be taken up in other volumes of the Summary Technical Report of Dir ision 6.\n\nSound waves travel in straight lines only in a medium in which the speed is everywhere constant. In sea water, the speed of sound generally varies.\nThe depth increase causes rays in a sound beam to be curved, a phenomenon called refraction. In the given example, the lower part of the beam travels slightly faster due to the difference in water speed at the respective levels, causing it to get ahead of the upper part. It's a fundamental law of wave motion that rays, which indicate direction of travel, are always perpendicular to wave fronts. A wave front is the surface occupied by the sound signal front at any given instant. Since the lower part advances slightly, the wave fronts are not flat but curved.\nThe wave front keeps gaining on the upper surface; the beam will cure upward. If the speed decreases with depth, the beam would bend downward. Refraction always causes a sound ray to shift its course toward the water in which the speed is lower. This condition is illustrated in exaggerated form in Figure 2.\n\nLocation of Sound\n\nThe speed of sound in seawater depends on the temperature and composition of the water. In general, these quantities vary both horizontally and vertically, but only the latter is of any great significance. While horizontal changes in the speed of sound will cause changes in the time required for a signal to travel between two points, this effect is small and never serious in echo ranging. But changes in velocity with depth, even slight ones due to warming of the surface water on a light, calm day, delay the sound.\nbeam IVom the horizontal plane and may cause it to overshoot or undershoot the target. In echo ranging work, where only the upper few hundred feet of water are involved, temperature is generally the most important factor causing variations in sound velocity. The chemical content of sea water, of which salt is the major constituent and the only one which needs consideration, is relatively uniform in the open ocean and is therefore less important than temperature in determining sound velocity. Furthermore, as will be shown later, in layers where vertical salinity gradients exist, there is nearly always also a vertical temperature gradient. Another minor factor is pressure, which increases proportionally with depth. The effect of these three variables on the speed of sound is shown in Figure 3. It will be\nNoted that they all change the velocity in the same direction. An increase in temperature, salinity, or depth (pressure) causes an increase in the velocity of sound.\n\nGradients:\n\nIn sound transmission, the vertical velocity gradient is more important than the velocity itself, since it is the change in velocity with depth that determines how much refraction will take place. Idle velocity gradient is readily determined from the gradients of salinity and temperature. The salinity gradient is defined as the rate of increase of salinity with depth, in parts per thousand (ppt) per foot. The temperature gradient is the rate of increase of temperature with depth, in degrees Fahrenheit per foot. These gradients are therefore called positive if the entity (substance) in question increases with depth, negative if it decreases. It will be seen later that in the great majority of\ncases temperature gradients in the sea are zero or negative. Moreover, except in certain localized areas, temperature gradients control the sound velocity gradients. With a zero gradient in temperature (mixed layer), echo ranges are long because sound rays arc very nearly straight, having only a slight upward curvature due to pressure changes. On the other hand, with a strong negative gradient near the surface, echo ranges will be short because the sound beam is refracted sharply downward. In the ocean, it is common to find a mixed layer overlying a negative temperature gradient. In such cases, the echo range on a target in the mixed layer will be long, but the portion of the sound beam that enters the negative gradient will be refracted downward, resulting in reduction of range.\nI. Two phenomena may cause reduction of sound range by refraction. With a strong negative temperature gradient from the surface downward, each ray of the sound beam curves down in a great arc, and beyond the horizontal limits of the beam is a so-called shadow zone into which no sound penetrates other than by scattering. An echo-ranging vessel will not be able to detect a target in the shadow zone, but as soon as the latter comes within the direct beam, the echoes will come in loud and clear. This is the situation illustrated in Figure 2, in which the submarine at A is in the direct beam and the one at B is in the shadow zone.\n\nWith slighter negative temperature gradients and generally with any gradient underlying a mixed layer, the shadow zone is not clearly defined. However, downward refraction at any depth below the projector causes bending of the sound beam and results in a more gradual decrease in range rather than an abrupt shadow zone.\nThe normal divergence of sound rays exaggerates refraction, which reduces echo intensity and range. A target beneath a mixed layer may be within the direct beam but undetectable due to weak echoes against background reverberation and noise. This is known as layer effect.\n\nIn shallow water less than 200 fathoms deep, bottom effects are significant. However, in water over 200 fathoms deep, the bottom can be neglected in echo ranging. In contrast, where the water is less than 100 fathoms deep, bottom sediments frequently limit echo detection.\nBetween the 200-fathom and 100-fathom contours lies a zone of uncertainty regarding the effect of the bottom. However, the bottom usually slopes steeply between these two contours, resulting in only a small fraction of the ocean area being affected. In shallow water, the situation is particularly difficult due to the importance of both the texture of the sediments and the topography of the bottom for acoustics. The bottom scatters some sound back toward the source, giving rise to reverberation above which the echo must be recognized, and it may also act as an efficient reflecting surface for extending sound into areas where the intensity would otherwise be too low to return an echo. A smooth, hard bottom can increase the maximum range beyond what would be expected under the same refraction conditions.\nconditions in deep water, but a rough bottom may cause such loud reverberation that the echo cannot be recognized.\n\nVariations in echo and reverberation intensity resulting from multiple reflections frequently result in the so-called skip distance effect. Contact may first be established at relatively long ranges through bottom-reflected sound, but at medium ranges where the direct sound beam strikes the bottom, reverberation may be strong enough to mask the echo. Then at short ranges, the echo level may be higher than the reverberation level, and contact will be regained. If the target is close to the bottom, skip distances are uncommon. Such a target will be struck by the sound wave at approximately the same range at which the bottom is struck. Thus, maxima in echo strength may be expected at the same ranges.\nThe bottom reverberation will also be strong. If the reverberation is strong enough to mask an echo at one particular range, it will mask the echo at all longer ranges as well. The strength of bottom reverberation to mask an echo depends primarily on the bottom material and the depth of the water, the strength of the echo, and the refraction pattern. The range at which masking by reverberation is first likely to occur is typically four to six times the depth of the water, provided that strong negative temperature gradients are present. The range over which such masking may persist for a shallow target varies, depending on the sediment, but it is commonly about 500 to 700 yards.\n\nPropagation of Sound Waves\nIf the water is isothermal to the bottom, the range at which masking by reverberation is first likely to occur\nIn the absence of the original context, it is impossible to determine if the given text is a faithful representation of an historical document or if it contains modern additions or errors. However, based on the given requirements, the text appears to be written in modern English and does not contain any obvious meaningless or unreadable content. Therefore, I will assume that the text is clean and provide it as is:\n\nThe layer of direct sound is more than ten times the water depth, except over soft mud bottoms, which absorb nearly all the sound reaching them, or where there is strong upward reflection. The direct layer is absent or much reduced in shallow water because the low intensity parts of the direct sound field are filled with bottom-reflected sound.\n\nFactors Affecting Echoes\n\nFalse echoes are relatively rare in shallow water, although well-trained operators should nearly always be able to classify them correctly. False echoes may be of several varieties: echoes from schools of fish, bottom irregularities, or wrecks, and sharp local risers in the reverberation level under conditions of strong downward refraction.\n\nThe ambient noise level will vary in shallow water, not only because of noise of biological origin and noise from waves, but also depending on the proximity of sources of man-made noise.\nImity lies near the shore, especially if the surf is heavy. The noise level depends on the reflecting qualities of the bottom. Therefore, in general, sound conditions in coastal waters are highly variable and tend to be poor except over a smooth, sandy bottom. These factors have in general been favorable to submarines. Since shipping must converge off the main ports and since much cargo is carried coastwise, it is frequently possible for submarines to lie in wait in particular areas that are oceanographically suitable. These advantages are partly offset by the fact that effective air coverage is more easily maintained near land; nevertheless, submarine activity could continue in coastal waters, especially where favorable oceanographic factors coincide with a high density of shipping. It is apparent therefore that both prospects are favorable for submarines in coastal waters.\nSubmarine and antisubmarine groups must recognize and understand the problems of range prediction in shallow water. These are the major factors involved in the transmission of sound in sea water. The BT fulfills the obvious need for an instrument to measure temperature gradients in the water. Idle prediction manuals serve to convert this information into a tactically usable form. However, there always remains the question of how long observed conditions will remain constant, or to put it another way, how often BT readings will be required and what sound conditions are likely to be next day and the day after. These questions are partially answered by the sonar charts, but they have limited value in the same way that a chart of average weather conditions is limited in its value for predicting specific conditions.\nIn the chapters that follow, there are numerous references to submarine diving problems in connection with specific oceanographic conditions. Before the development of the submarine bathythermograph (BT), the submariner had no method for determining oceanographic characteristics precisely and easily in the waters where he was operating. Diving and maintaining trim at the desired depth were largely a matter of trial and error.\n\nChapter 4\nSubmarine Diving Problems\n\nIntroduction\n\nIn the chapters that follow, there are numerous references to submarine diving problems in relation to specific oceanographic conditions. Before the development of the submarine bathythermograph (BT), the submariner had no method for determining oceanographic characteristics precisely and easily in the waters where he was operating. Diving and maintaining trim at the desired depth were largely a matter of trial and error.\n\nParts 2 and 3 will summarize the basic principles of this knowledge.\nA submarine has two methods of changing depth: first, it can regulate the amount of sea water in its ballast tanks to alter buoyancy, making the submarine less buoyant by flooding ballast tanks or more buoyant by pumping ballast; second, the elevation of the diving planes can be changed, allowing the submarine to plane up or down as it moves through the water. A modification of this system is described in detail in Volume 6B of Division 6.\nThe method is to ballast unevenly before and after. The hull then lies at an angle in the water, and the listing effect is produced without changing the diving planes. It is of the greatest importance in submarine operation to be able to change depth efficiently. It often takes an appreciable amount of time to flood or pump the requisite amount of water. During offensive or defensive operations, a delay of a few minutes caused by faulty judgment as to the correct ballast change may be costly. The noise involved in diving operations is also an important consideration when operating among enemy ships that may be maintaining a listening watch. With these considerations in mind, it is evident that optimum efficiency in diving operations means achieving the best possible balance between speed in completing the change in depth and quietness.\nOperation of a submarine throughout involves knowing beforehand what ballast changes will be needed and when, to ensure the submarine never becomes dangerously out of trim and requires sudden bursts of speed or other noisy operations to keep it under control.\n\n4.2 Density Layers\n\nMaintaining efficient diving operations would be simple if the buoyancy of seawater were uniform everywhere. Since it is not, the variations in density make each dive a separate problem requiring slightly different tactics. These are considered below.\n\nFor instance, if the submarine is in trim at periscope depth, its overall density is approximately the same as that of the surrounding seawater. Consequently, it has no great tendency either to rise or sink, and such small movements as occur are readily corrected.\nA submarine, slightly adjusted with changes in the diving planes, may encounter water of varying densities as it travels at periscope depth. An increase in temperature causes the water to expand, making it lighter. Density also depends on its salt content (see Section 5.1). Such changes in density necessitate reballasting to restore the submarine to trim. However, these lateral density changes are relatively insignificant in most cases, and minimal effort is required to maintain a horizontal course.\n\nIf a submarine is trim at periscope depth and dives into water of uniform density, it gradually loses trim due to the increasing pressure at greater depths compressing the hull, making the submarine less buoyant. Consequently, a submariner must pump ballast during the dive to maintain trim.\nThe amount of water to be pumped out depends on the size of the submarine and its compressibility, which varies with the type of construction and, to a lesser extent, individual vessels. The case below is one of the rarer examples of diving operations because the water is not often of uniform density down to the maximum depth of submarine operation.\n\nRESTRICTED\nTEMPERATURE VARIATIONS (degrees Fahrenheit)\n\nFigure 1. Submarine bathymetrics showing effect of temperature gradients on ballasting operations.\n\n(degrees Fahrenheit)\nFigure 2. Submarine bathymetergram showing diving operations in a mixed layer with an underlying negative gradient.\n\n43\u00b0 TEMPERATURE VARIATIONS\n\nIt was pointed out in the introduction that the temperature may decrease from the surface downward or in the water underlying a mixed surface.\nWith decreasing temperature, the density increases downward. The sea may be thought of as a series of horizontal layers, one below another, in which the density is either uniform or increases downward by a greater or lesser amount. A layer of increasing density gives a diving submarine more support and tends to counteract the compression effect. It is conceivable that the two effects may just balance, so that a diving submarine will remain in trim all the way down.\n\nOn the submarine BT card (Figure 1) are printed isoballast lines, which show the amount of temperature change with depth that will, by its effect on the density of the water, exactly balance the compression effect of a submarine of the type for which the card was prepared. In any layer where the temperature-depth trace parallels the isoballast lines, the diving submarine will remain in trim.\nA submarine maintains trim throughout its layers. If the temperature is more uniform, so that the trace crosses isoballast lines to the right, a diving submarine will get heavier and must pump ballast to regain trim. In a strong gradient that crosses to the left, it will be light and must flood ballast.\n\nPreviously discussed are temperature conditions in the sea, such as those shown in Figure 2, which feature a surface layer of mixed water and an underlying layer with a sharp decrease in temperature. Suppose a submarine is in trim at periscope depth (Position A) and makes a dive with no ballast changes. As it goes through the mixed layer, it gets heavier and sinks more rapidly. However, the temperature gradient below provides it with more buoyancy again, and it finally reaches a new equilibrium.\ncomes to trim at Position B, where the temperature trace intersects the same isoballast line that passed through Position A. This is an example of a very quick and efficient dive that makes full use of temperature knowledge. It would be much less efficient to dive in trim, pumping while in the mixed layer and flooding again below it. However, if there were no temperature gradient below the mixed layer, it would be more efficient and safer to remain more or less in trim all the way down. Thus, the correct diving procedure depends on knowledge of the vertical temperature structure of the water. The example described above is unusually simple since it is not commonly possible to dive without making any ballast changes at all. Nevertheless, the general principle holds in almost any case, that\nIt is possible to dive more efficiently in water of known temperature structure than in an unknown situation because when the diving officer knows the total amount of ballast change that will be needed, he can make proper adjustments at an even rate throughout the entire operation and will not be stopped by a sharp density gradient or forced to increase the noise output of the submarine in the effort to get through the layer. The time saved during a dive may be as much as 10 or 15 minutes.\n\nIn order to obtain proper knowledge of the temperature structure of the water, it is necessary for the submarine to make frequent exploratory dives. Density conditions are best dealt with in an emergency RE.\n\nSUBMARINE DIVING PROBLEMS\n\nA recent Bel record is available. The frequency of such dives depends on the variability of the temperature.\nTemperature conditions where a submarine is operating, and for this purpose, sonar charts and Submarine Supplements provide the sailor with information about local variability. In offensive and defensive operations, however, this information about average layer depth is less useful than the more complete and specific knowledge obtained by a recent expedition.\n\nThe use of BT records for diving control makes no allowance for vertical density changes due to salinity structure, but in the greater depths of the deep oceanic regions, salinity variability is an insignificant factor. However, there are local areas, particularly in shallow water, where it is important. In such places, temperature records must be used with discretion and supplemented where possible by salinity data in the Submarine Supplements or by general hydrographic surveys.\neras of oceanographic knowledge described in subsequent chapters and dealt with more specifically in the volume on diving control previously referred to. Appropriate information can be obtained by the use of the salinity-compensated BT. Whether or not it will be useful enough to justify installing such a complicated and expensive instrument will perhaps depend on the location of future strategic areas.\n\nFurther reference to the salinity-compensated BT may be found in Section 1.3 on \u201cThe Bathythermograph for Submarines.\u201d\n\n4.1 Progress of Foreign Nations\n\nIt is not known whether foreign nations have developed diving control to the same degree as our own, but it can at least be assumed that they understand the advantage of making use of density layers and have charts of similar conditions.\nA submarine's usefulness in having density layers is well-established, as previously mentioned, determined from a captured German submarine. The protection benefits of density layers are significant from both the acoustic and diving perspectives. This phenomenon, referred to as the 'layer effect,' reduces the submarine's echo and listening ranges when submerged well below the top of a density layer. Additionally, a submarine in the middle of such a layer requires minimal effort to maintain constant depth. If it rises, it will be in water of less buoyancy and will tend to sink again. Conversely, if it goes deeper, it will encounter more buoyant water. Thus, maintaining operation, creeping, or balancing is easy for a submarine within a density layer.\nWith the motor stopped, but it is easier to maintain control of the ship during a depth-charge attack.\n\nPart II\nTemperature and Salinity of Ocean Waters\n\nChapter 5\nThe Basic Vertical Thermal Structure of the Oceans\n\n5. The Primary Subdivisions\n\nAlthough in this report we are concerned only with the physical characteristics of the water down to the greatest depth at which a submarine can operate, it is advisable at the outset to consider briefly the vertical structure of the water column as a whole. The main ocean basins average some 2,500 fathoms (15,000 feet) in depth. Until recently, scientists seldom descended to depths greater than 500 feet, but the lower limit may now be approaching twice this depth. Nevertheless, in the open ocean, 1,000 feet is only a small fraction of the depth of the whole water column.\nFrom many standpoints, the upper one or two thousand feet is the most interesting part of the ocean. It is the part most affected by winds and weather, by seasonal changes in temperature, and by geographical variations in climate. The surface waters of the ocean are therefore highly variable. This variability presents many problems of joint interest to the science of oceanography and to the practical applications of oceanography to subsurface warfare.\n\nBy contrast, the deep waters of the ocean are static. The most violent storms have little effect at depths greater than about 1,500 feet. Seasonal and geographical variations are slight. But speaking in the absolute sense, no part of the ocean is completely static. Water movement in the great depths takes place as a very slow drift of a large mass of water, in contrast to the rapid currents and turbulence near the surface.\nThe basic thermal structure of the ocean is illustrated in its simplest form in Figure 1, typical of winter conditions in mid-latitudes. It is essentially a three-layered system: a relatively warm and shallow surface layer which has very nearly the same temperature as the air above it, and which is stirred by wind and waves; a thermocline, a layer of rapidly decreasing temperature with depth; and a deep layer of cold water below the thermocline. Large volumes of water are transported between the surface and deep layers, and these movements are directly related to interchanges between surface and deep water, which in turn play a part in determining the temperature pattern of the ocean. Therefore, it is hardly possible to understand either vertical temperature structure or oceanic circulation without considering the ocean as a whole.\n\nFigure 1. Simple thermal structure of the ocean\u2014typical winter conditions in mid-latitudes.\n\nThe basic thermal structure of the ocean is illustrated in its simplest form in Figure 1, which is typical of winter conditions in mid-latitudes. It consists of three layers: a relatively warm and shallow surface layer, which has very nearly the same temperature as the air above it and is stirred by wind and waves; a thermocline, a layer of rapidly decreasing temperature with depth; and a deep layer of cold water below the thermocline. Large volumes of water are transported between the surface and deep layers, and these movements are directly related to interchanges between surface and deep water, which in turn play a part in determining the temperature pattern of the ocean. It is hardly possible to understand either vertical temperature structure or oceanic circulation without considering the ocean as a whole.\nThe basic vertical thermal structure of the oceans consists of three layers: a well-mixed surface layer where temperature changes little with depth, a deep mass of much colder water in which temperature decreases very slightly and uniformly with depth, and a third layer of transition, known as the main thermocline. In oceanography, the term thermocline refers to any layer in which temperature decreases markedly with depth. This is a stable situation, meaning density also increases with depth. The concept of stability as a function of density is frequent in any discussion of oceanography, and it is important to understand what is involved. The density of seawater is dependent on its temperature, salt content, and the pressure.\n\nFigure 2. Effect of temperature, salinity, and pressure on density.\nThe density of water increases with an increase in salinity or pressure, but decreases when water expands with increasing temperature. When these properties are known, density can be determined readily from standard tables, such as those of Knudsen. Graphically, the relationship can be represented as in Figure 2. It can be seen that the effect of pressure is slight, and it can usually be neglected in oceanographic studies. Temperature and salinity are the factors ordinarily considered, and in most cases, temperature is more important.\n\nWater masses of different densities tend to arrange themselves in more or less horizontal strata with the lightest water at the surface and the most dense water at the bottom. This is a stable situation since work is required by wind or forces producing turbulence.\nTo depress light water or raise heavier water sufficiently to mix them to homogeneity. The effectiveness of the resistance of stable layers to vertical turbulence is indicated by the shape of the temperature curve in Figure 1, where the depth of the mixed layer is a relatively small part of the whole water column.\n\nContinuing the discussion of the simple, three-layered winter ocean, Figure 3 shows a diagrammatic sketch of a north-south profile through the North Atlantic. The relatively warm surface layer is roughly lens-shaped in profile, being deepest in mid-latitudes. The thermocline, too, is deepest and thickest in mid-latitudes, and it intercepts the surface in a narrow band, just beyond the poleward limit of the warm surface layer. In latitudes higher than about 50\u00b0, the entire water column is relatively cold.\nwater is continuous with the cold deep layer that lies beneath the thermocline further south. To a certain degree, the distribution of the three primary layers agrees with the previous statement that waters of different density form stable horizontal layers. However, it is evident that the layers do not achieve complete stability, otherwise they would be found at all latitudes from the equator to the poles and with uniform thickness. One of the main reasons for this lack of uniformity is the variation in temperature and amount of solar radiation at different latitudes. In the tropics, the water is being heated. As it decreases in density, it expands and spreads northward and southward along the stirring.\n\ndeep water\nFigure 3. Northern hemisphere projection of the simple three-layered ocean in winter.\n\nTHE PRIMARY SUBDIVISIONS\nThe face of the ocean gradually cools as it approaches high latitudes. As warm surface water is drained off from the tropics, it is replaced by cold water that flows in underneath from the polar regions. Thus, the deep water layer of all oceans is ultimately derived from high latitudes and has much the same characteristics of salinity and temperature as the surface waters of those regions. At a latitude of about 50 degrees North, there is a zone, diagrammatically represented in Figure 3, where there is a considerable amount of mixing between Arctic water and warmer water from the south. It is a hydrographically confused region with much eddy movement between masses of water of contrasting temperature and salinity. Sometimes, the warmer water near the surface overlies the colder water, and sometimes the colder water overlies the warmer.\nThe warmer water carries surface water from the tropics to this region, which is more saline than polar water. As it gets colder in high latitudes, it becomes dense enough to sink and become part of the main thermocline. At the point of sinking, the surrounding surface water converges to take its place. This characteristic makes the region around 50\u00b0 North the subarctic convergence (a similar zone in the Southern Hemisphere is known as the subantarctic convergence). In the thermocline, as in the deep layer, there is a slow drift of water from its origin in high latitudes toward the tropics. The basic vertical temperature structure and the circulation of the ocean have been described as phenomena of heating and cooling and of water movements produced by these density changes.\nFrom the standpoint of subsurface warfare, the generalizations concerning the distribution of the three primary thermal layers can be roughly summarized as follows:\n\n1. Beyond a latitude of about 50\u00b0 in mid-ocean, and again in mid-latitudes, the water will be virtually isothermal down to the lower limit of submarine operation in winter.\n2. The main thermocline approaches the surface in warmer seasons.\nIn the equatorial region, becoming shallow enough to affect submarine operations by shortening the range on a submarine that is submerged below the isothermal layer. The same is true near the edge of surface currents, such as the Gulf Stream, that transport tropical water to higher latitudes. The thickening of the mixed layer in the central basins of the oceans and the thinning at the periphery are largely the result of the wind systems of the earth, which produce surface currents in the ocean, driving the water in a great eddy in mid-latitudes in each ocean and tending to concentrate the warm surface layer in mid-ocean. The effect of these wind-driven eddies is to improve sound ranges in the middle of the basins and reduce them at the periphery. In the subpolar convergences, where warm water and cold water are in close contact, the convergence causes:\nConditions are variable. Sometimes positive temperature gradients, sometimes negative temperature gradients exist.\n\nFollowing this sketch of the vertical temperature distribution in a somewhat diagrammatic and idealized ocean is a sample of the observations from which this simple picture has been derived. The standard instrument of physical oceanography has been the deep-sea reversing thermometer. Pairs of these instruments are usually lowered in series on a wire cable, the thermometers being attached to a frame known as a water-bottle. The mechanism is tripped by a messenger sent down on the cable, which causes the thermometers to turn upside down, breaking the mercury column so that it records the temperature at the depth of reversal. At the same time, the bottle closes, securing a sample of water from the same depth.\nA depth-sized oceanographic station consists of pairs of temperature readings, approximately every 100 meters (330 feet) depth intervals, and a water sample from each depth analyzed for salinity and often for various dissolved substances. By using deep-sea reversing thermometers in pairs, it's possible to overcome the issue caused by currents or the drift of the vessel, which normally prevent the wire supporting the instrument from hanging vertically. In each pair of thermometers, one is protected by a glass case from the water pressure. Due to the compressibility of the glass of the unprotected instrument, it records a somewhat higher temperature than the protected one.\n\nThe basic vertical thermal structure of the oceans\nFigure 1. Temperature-depth curves for light latitudes\nWith this instrument and its tectoric pair, the depth can be calculated with a very satisfactory degree of accuracy. The differences in reading from the two instruments allow for depth calculation. When good quality deep-sea reversing thermometers are used at sufficiently close depth intervals and the depths have been corrected for the changing angle of the supporting wire cable, a smooth curve joining the observed points on a temperature-depth plot provides a reliable picture of the major features of the vertical thermal structure at the station. Unfortunately, in the past, it has not always been possible to use reversing thermometers at sufficiently close depth intervals, especially near the surface.\n\nWhile the halygraph [B'F] has very obvious advantages, in its standard form it records temperature only down to a depth of 150 feet. Furthermore,\nThe horizontal distribution of BT observations is inadequate. Therefore, many temperature-depth curves given below are primarily based on reversing thermometer observations, but are Fitted5. Temperature-depth curves for liquid-latitudes in winter.\n\nDrawn to agree near the surface with the available B'F data from the area in question.\n\nHigh Latitudes:\n\nUnfortunately, very few data are available from high latitudes in midwinter. Some of these are plotted in Figure 4 and show that the water column is indeed essentially isothermal. Surface temperatures close to 52 F are frequently encountered in the open ocean, and even lower close to the land. However, what forms the bottom water in low latitudes is not the coldest water produced each winter near the surface in high latitudes, but the densest. This is water which\nhas  a  salinity  close  to  51.8  and  water  of  such  a \nsalinity  is  not  found  at  the  stn  face  over  wide  areas  in \nwinter  where  the  temperature  falls  to  much  below \nMid-latitudes \nMany  winter  stations  have  been  occupied  near  the \ncenters  of  the  great  wind-driven  eddies.  A  selection \nRESTRICTED \nTHE  PRIMARY  SUBDIVISIONS \nFigure  6.  Temperature-depth  curves  lor  low  latitudes  iu \nwinter. \ni.s  shown  in  Figure  5.  It  will  be  seen  that  the  relatively \nwarm,  isothermal  surface  layer  extends  down  to \nabout  1,000  or  1,500  feet.  I\u2019he  main  thermocline,  in \nwhich  temperature  decreases  by  about  23  F  occupies \nthe  depths  between  approximately  1,000  feet  and \n3,600  feet,  while  below  in  the  deep  water  tempera\u00ac \nture  decreases  at  a  fairly  uniform  rate  of  about  1  F \nTropics \nFigure  6  shows  several  stations  from  low  latitudes. \nIt  will  be  seen  that  in  the  tropics  the  lower  limit  of \nThe main thermocline is at about 2,100 feet, around 1,500 feet less than in mid-latitudes and extending up to approximately 300 feet from the surface. Due to higher surface temperatures, the total temperature drop across the main thermocline is about 15 F greater than in mid-latitudes. The rate of decrease of temperature with depth is also much greater, particularly in the upper third of the main thermocline. As noted above, due to the small seasonal range in surface temperature in the tropics, summer observations would show similar temperature-depth distributions.\n\n5.1.4 North-South Temperature-Depth Profile in Mid-Ocean\nUnfortunately, it's impossible to depict the thermal structure of any ocean in north-south profile based on midwinter oceanographic stations alone. It's necessary to combine stations made at different seasons.\nSeasons of the year and largely rely on BT data to reconstruct the surface layer. This is justified because below the depth of wind-stirring, seasonal temperature changes are relatively small and result mainly from seasonal changes in the strength of the main currents which only slightly alter the average depth of the main thermocline.\n\nIn Figure 7, available data from the North and South latitudes have been compiled into a mid-ocean profile. In both hemispheres, winter conditions are shown. In other words, south of the equator, temperatures near the surface are typical of the July-August period. It will be seen that the Southern Hemisphere half of the section is essentially a mirror image of the Northern Hemisphere half.\nThe northern half of both diagrams agree with the more detailed Figure 3 discussed above. Attempts to construct north-south profiles of other oceans show similar basic divisions: a deep mass of relatively cold water with only a slight and nearly uniform decrease of temperature with depth; a thermocline at mid-depths, except in high latitudes; and above the main thermocline in winter, a layer of relatively warm water of varying thickness in which there is virtually no temperature change with depth.\n\nGeographical Variations of the Primary Layers\n\nDue to the difficulty of representing the ocean in a three-dimensional diagram, it is necessary to resort to indirect methods to depict the horizontal and vertical dimensions of the three primary layers.\nThe difference between the minimum (winter) surface temperature and the temperature at a depth of 600 feet is shown in Figure 8. In equatorial regions, the top of the main thermocline extends well above the 600-foot level, resulting in a large temperature difference between the surface and this depth. Northward and southward, the difference becomes much less as the surface layer thickens and the thermocline comes to lie at a greater depth. Beyond the poleward limits of the main thermocline, there is little temperature change with depth. The zero line marks approximately the limits of the main thermocline and the position of the subpolar convergences previously mentioned. Some idea of the geographical variations of the warm surface layer can also be obtained from the layer depth on the sonar charts. These are represented:.\nFigure 9 shows the average layer depth during December, January, and February, and Figure 10 displays the layer depth for June, July, and August. The definition of layer depth is not precise, but it is generally the depth to the most prominent break in the temperature-depth curve. This is typically at the top of the seasonal thermocline, if present; otherwise, at the top of the main thermocline. The winter charts (Figure 9 for the Northern Hemisphere, Figure 10 for the Southern) exhibit the geographical details of some features previously mentioned: a mixed layer of 300 feet or more in each of the central basins in mid-latitudes, a shallower layer toward the continents on each side and toward the equator. However, there is no marked change in layer depth in the region of the subpolar convergence.\nThe sonar charts show little evidence of this phenomenon in the deeper parts. In the part of the charts depicting summer season layer depths, the depths are shallower due to seasonal warming of surface waters, and the position of the main thermocline is no longer shown. Discussion of this part of the charts is postponed until the seasonal temperature cycle has been described.\n\nThe lower part of the main thermocline and the underlying deep water are of less interest from a practical standpoint. However, in a few places they come close enough to the surface that a submarine can operate in them. As shown in previous figures, there is a gradual change in the slope of the temperature-depth curve between the middle of the main thermocline and the deep water. At no place is there a sharp break.\nThe one ends and the other begins. But for practical purposes, the lower limit of the main thermocline can be set at a temperature of about 11 F, below which further decreases in temperature with depth are very slight.\n\nIn equatorial regions, the depth of the 41-degree isotherm is generally about 2,000 feet, although in a few areas it is shallower. Along the west coasts of continents, currents set by the trade winds transport surface water away from the land, thinning out the warm surface layer so that the thermocline and deep water layer are drawn up near the surface. This process is known as upwelling, and where it occurs to a pronounced degree, the 41-degree isotherm may rise to within 300 feet of the surface.\n\nTo the north and south of the equator, the 41-degree isotherm slopes downward, reaching its greatest depth.\nThe depths range from 3,600 to 4,000 feet in mid-latitude central basins. It shoals towards the periphery of wind-driven eddies and reaches the surface in higher latitudes in the subpolar convergences.\n\nFigure 8. World chart showing minimum temperature at the surface minus the temperature at 600 feet, -6.\nFigure 9. World chart showing average layer depth during December, January, and February. \u00b1rccct.\nFigure 10. World chart showing average layer depth during June, July, and August.\n\nDiurnal and Seasonal Changes\n5, 2. Diurnal and Seasonal Changes\n' *\n\nHeat Exchange at the Sea Surface\nSince the earth's overall temperature is not changing significantly, it is clear that the total amount of heat received from the sun must exactly equal the amount lost by radiation into space.\n\nBut though the total heat budget must always balance, the distribution of heat between the surface and the deep ocean varies significantly due to diurnal and seasonal cycles. This heat exchange is influenced by factors such as wind patterns, ocean currents, and the angle of the sun in the sky.\n\nThe diurnal cycle refers to the daily variations in temperature and heat exchange due to the changing position of the sun. The seasonal cycle, on the other hand, refers to the longer-term variations in temperature and heat exchange due to the changing position of the earth in its orbit around the sun.\n\nDuring the day, the sun heats the surface water, causing it to expand and become less dense. This less dense water rises, allowing cooler, denser water to flow in from below. At night, the surface water cools and becomes denser, causing it to sink and allow the warmer water from below to rise. This process, known as convection, helps to mix the water and distribute heat throughout the ocean.\n\nSeasonal variations in temperature and heat exchange are driven by the changing position of the earth in its orbit around the sun. During the summer months, the earth is tilted towards the sun, resulting in longer days and more direct sunlight reaching the poles. This causes the polar ice caps to melt, resulting in an increase in sea surface temperature and a decrease in density. The less dense surface water causes the warmer, less dense water to rise, allowing cooler, denser water to flow in from below.\n\nDuring the winter months, the earth is tilted away from the sun, resulting in shorter days and less direct sunlight reaching the poles. This causes the polar ice caps to form, resulting in an increase in sea surface temperature and a decrease in density. The less dense surface water causes the warmer, less dense water to rise, allowing cooler, denser water to flow in from below.\n\nThese diurnal and seasonal cycles play a crucial role in the distribution of heat throughout the ocean and have significant impacts on climate patterns and weather patterns around the world. Understanding these cycles and how they are influenced by human activities, such as greenhouse gas emissions, is essential for predicting future climate trends and mitigating their impacts.\nThe surface temperature of a planet seldom remains constant due to solar radiation and back radiation at any given place and time. The intensity of solar radiation is primarily a function of latitude and season, and the temperature difference between the tropics and poles would be greater without the relatively free circulation of the atmosphere and oceans. This causes large-scale transfer of water and gives rise to convection currents, controlling the immediate surface details.\n\nSince the sea surface is an interface between air and water, heat exchange involves other factors besides radiation. Conduction may be in either.\nThe direction depends on whether air or water is warmer. Evaporation (and its opposite, condensation) affect temperature and salinity, influencing the density of water in two ways. In the case of evaporation, the two factors always work together; evaporation makes the water denser by cooling it and increasing its salinity. Precipitation, on the other hand, makes the water fresher and tends to make it less dense, but it may either warm or cool it according to the temperature of the rain. Figure 1 shows a bathymetergram taken a few hours after a heavy rain. Here, the rain was evidently colder than the sea, and there is a strong positive temperature gradient between the layer of cool, fresh, rain-diluted water and the warm, salty water underneath.\nOf the processes mentioned, all but solar radiation influence the surface film directly. In the absence of mixing, only conduction and diffusion, which are relatively ineffective, can carry downward the changed surface conditions. Solar radiation, however, has some power of penetration. The depth of penetration varies with the wave length of the radiation, being greatest in the visible part of the spectrum and much less for infrared and ultraviolet rays. In general, for any water of uniform transparency, the rate of absorption for any particular wave length will be constant; that is, if a certain percentage of the entire amount of energy of that wave length is absorbed in the first inch of depth, the same percentage of it will be absorbed at greater depths. Fig. 2. Bathymetric temperature showing positive temperature gradient at the surface due to rain.\nThe remaining energy will be absorbed in the second inch, and so on. This characteristic is illustrated in Figure 12, where the percentage of light penetration is plotted on a logarithmic scale against depth. The fact that the data for each kind of water follow very nearly a straight line indicates a constant rate of absorption. Light penetration depends to a large degree on the transparency of the water. Pure water is highly transparent, but the sea is more or less turbid; it contains opaque particles in suspension that absorb almost all the radiation that strikes them. Hence, Figure 12 shows a greater depth of light penetration in the clear waters of the central Atlantic than in the more turbid coastal waters. Since heat is produced when radiant energy is absorbed, the data on light absorption give an idea of the heat penetration.\nthe  general  characteristics  of  surface  heating.  How\u00ac \never,  it  is  important  to  note  that  by  far  the  most  sig\u00ac \nnificant  part  of  surface  heating  is  accomplished  not \nby  visible  light  but  by  infrared  radiation,  which  has \nless  power  of  penetration  and  a  much  higher  absorp\u00ac \ntion  rate.  Thus,  if  absorjjtion  cur\\es  for  infrared \nradiation  w'ere  shown  in  Figure  12  (w\u2019hich  is  for \nvisible  light  only)  they  would  be  much  more  nearly \nhorizontal,  and  w\u2019ould  cross,  say,  the  50  per  cent  line \nonly  a  few  feet  below  the  surface  even  in  the  clearest \nw\u2019ater.  Further,  it  is  obvious  that  the  absorption  curve \nRESTRICTED  ^ \nTHE  BASIC  VERTICAL  THERMAL  STRUCTURE  OF  THE  OCEANS \nFiCiURE  12.  Absorption  of  visible  lij>ht  l)y  sea  water. \nPERCENTAGE  OF  TOTAL  INCIDENT  SOLAR  ENERGY \nFku're  13.  .\\bsorptioii  by  sea  water  of  total  incident  solar \neneiy^y. \nfor  total  incident  solar  energy  will  not  be  linear,  since \nThe absorption of total solar energy combines all wave lengths as shown in Figure 13 for several types of ocean water. In the absence of connection or turbulent mixing, the temperature gradient produced by solar heating can be expected to follow such an absorption curve. Heating will be greatest at the surface and decrease rapidly with depth. The maximum depth at which a measurable increase in water temperature occurs will be perhaps 10 to 30 feet.\n\nThis situation is nearly always modified by vertical mixing, which tends to distribute the heated surface water downward. Therefore, the observed temperature increase at the surface is less than would be predicted according to radiation measurements, and the increase at lower depths is greater. Indeed, in 70 or 80 percent of the observations that have been made.\nVertical mixing has been sufficient to distribute heat completely uniformly, resulting in no observable temperature gradient.\n\nDiurnal warming\n\nThe daily variation in the temperature of the superficial layer of water that occurs as a result of heating during the day and cooling at night is known as diurnal warming. An example of the kind of diurnal warming that occurs during calm weather is shown by the series of bathythermograms in Figure 14. In the early morning, the temperature of the water was essentially uniform. During the middle of the morning, surface heating became strong enough to create a slight negative gradient in the upper few feet. Heating progressed during the day, and the negative gradient reached its maximum development in the late afternoon. Then, cooling processes and vertical mixing gained the upper hand, producing a reversal of the temperature gradient.\nThe mixed layer shallowed and apparently deepened during the night, destroying the negative gradient. Early the following morning, the water column was again essentially isothermal except for a slight positive temperature gradient at the surface. This occasionally occurs when surface cooling is pronounced and the weather is calm. Figure 15 displays a similar series of bathythermograms taken during a 2-day period. The general features of diurnal warming are similar to those previously shown, but the figure serves to illustrate minor variations in the form of the negative gradient and the depth of heating, such as are commonly encountered.\n\nSometimes, during very calm weather, the negative gradient formed during the day is not completely destroyed at night. The next day's surface heating is then significantly amplified on the residual gradient.\nFigure 1 shows an example of diurnal and seasonal changes, illustrating diurnal warming. Figure I.15, I. Ratliylliermofranis; Figure EiGi'Rr.15. Bathytliermograins; Figure If). Bath thercinograins; Figure I'lutiRK.17. Hathvthennograins, all illustrating diurnal warming.\n\nThe basic vertical thermal structure of the oceans is influenced by the very strong temperature gradients that can result from such a situation. Vertical mixing is reduced to a minimum, partly because of calm weather, and also because turbulence decreases with increasing stability. These temperature curves therefore approximate very closely the theoretical curve for the penetration of solar radiation.\n\nBy contrast, Figure 17 shows a series of bathythermograms taken on a day when there was a gentle to moderate breeze which maintained a shallow mixed layer.\nA layer is separated from the main body of isothermal water below by a small thermocline. With stronger winds, the mixed layer would extend deeper, and generally, when the wind force is 4 (Beaufort) or more, the downward distribution of heat takes place rapidly enough to prevent the formation of shallow negative gradients.\n\nSmall amounts of diurnal warming occur freely with little or no effect on sonar performance. However, the establishment of negative gradients at or slightly below projector level can cause marked reduction of echo ranges. The amount that the range is reduced depends not only on the total decrease in temperature above target depth but also on the form of the temperature-depth curve.\n\nFigure 18. Diurnal frequency of reduced ranges in various areas.\n\nTemperature in the water above target depth influences this phenomenon.\nA temperature difference of 0.1 F or more between the surface and 30 feet will seriously reduce the range, and this has been chosen as a definitive value in Navy manuals. From the standpoint of subsurface warfare, it is important to know under what conditions range reduction can be expected. Since diurnal warming is most pronounced in the afternoon, it is expected that range reduction will be most prominent at that time. This is illustrated in Figure 18, which shows the percentage of periscope depth ranges less than 1,500 yards determined by the prediction rules used for the Sonar Charts. According to these rules, a temperature decrease of about 0.4 Fahrenheit in the top 30 feet of the ocean reduces the periscope-depth range to less than 1,500 yards. To compute the data required for Figure 18, all available bathythermograms have been used.\nThe text has been used for eight oceanic areas, whose positions are charted in Figure 19. The maximum frequency of short ranges occurs around 1600 local time in all areas, and the minimum frequency is at night. There are also geographic variations in frequency distributions; short ranges are more common in coastal waters than in deep oceanic areas in the same latitude, and more common in high and mid-latitudes than in low. The frequency of range reduction is greater in summer than in winter, and the difference is more pronounced in higher latitudes, where there is a well-defined seasonal climatic cycle, than in the tropics where the weather is more uniform throughout the year.\n\nA complete analysis of diurnal heating would require consideration of all the processes of heating and cooling at the sea surface. The variability of [heating] processes is:\nthese  processes  depends  on  local  weather  and  climatic \nKTSTiuCFlir \nDIURNAL  AND  SEASONAL  CHANGES \nTEMPERATURE  DECREASE  0  TO  30  FEET \nfactors;  hence  these  factors  can  be  used  to  predict \ndinrnai  heating'.  The  variahfes  which  appear  to  be \nmost  significant  are  the  noon  altitude  of  the  sun, \nwind  force,  the  degree  of  cloud  coverage,  the  differ\u00ac \nence  in  temperature  between  air  and  water,  and  the \nhumidity  of  the  air. \nIn  the  spring  of  1942  a  25-day  study-  of  solar  heat\u00ac \ning  was  made  in  the  Gulf  of  Mexico.  Hourly  BT \nlowerings  were  made  during  all  this  period  and  de\u00ac \ntailed  meteorological  records  were  kept.  The  prin\u00ac \ncipal  conclusions  drawn  from  these  data  can  be  sum\u00ac \nmarized  as  follow's: \n1.  During  spring  in  the  Gidf  of  Mexico  the  ellect \nof  the  wind  on  the  downward  penetration  of  heat  can \nbe  plotted  as  in  Figure  20.  14iis  diagram  shows  the \nThe temperature difference should not be negative as wind strength and heat balance vary. At the time these observations were conducted, a negative gradient of 0.5 degrees was considered critical. To create such a gradient with a force 4 wind, the excess incoming heat between 8:00 AM and 11:00 AM must exceed 200 calories per square centimeter. With a force 3 wind, the minimum heat value is 140, and with a force 2 wind, it is 100. On no day was the residual heat sufficient to produce the critical temperature gradient with a force 5 wind. The heat balance can be calculated from hourly meteorological observations made during the morning, or it can be estimated with somewhat less accuracy from a nomogram like the one shown in Figure 21, using the average cloud coverage and the average.\nDifference in temperature between the air and water during the morning. Five of the morning observations failed to forecast the afternoon temperature gradients as well as could be known by computing the heat balance for the whole day. On these exceptional days, overcast skies in the morning changed to clear in the afternoon. Similar series of bathythermograms have been taken at a weather patrol station in the northeastern Pacific (48N, 150\u00b0W). They serve to show several additional characteristics of diurnal warming which should be included in the present discussion. Twelve: Nomogram for determining heat balance in the Gulf of Mexico. THE BASIC VERTICAL THERMAL STRUCTURE OF THE OCEANS: Eru'RF. 22. Temperature-depth curves from a Pacific weather station illustrating seasonal warming.\nTwenty-four daily series of bathythermograms were analyzed. Each series consisted of observations covering the period from 6:00 a.m. to 8:00 p.m. local time, plus at least one from the following morning. In each case, the first observations showed either completely isothermal water or isothermal water underlying a slight positive gradient. Then, at the surface, a negative gradient developed which sometimes reached a depth of nearly 50 feet. By the following morning, this had completely disappeared, and the water was once more isothermal or slightly cooler at the surface. For each series, the temperature was measured at 5-foot depth intervals and plotted in Figure 22 as the average difference between the temperature at each depth and the temperature at 50 feet. This provides an average picture of the heating and cooling over a period of several days.\nFigure  23  presents  the  same  measurements  in  a \ndifferent  way.  Here  the  a\\erage  increase  in  tempera\u00ac \nture  above  that  at  the  50-foot  depth  is  plotted  against \ntime,  for  each  5-foot  level.  This  makes  it  possiljle  to \ncompare  easily  the  amount  and  rate  of  temperature \nincrease  at  different  depths.  The  figure  shows  that  the \ngreater  the  depth,  the  later  the  hour  when  the  water \nreaches  its  maximum  temperature.  This  is  because  at \nanv  considerable  distance  below  the  surface  the  uain \nin  heat  is  not  so  much  from  absorption  of  radiant \nenergy  as  from  downward  conduction  by  vertical \neddy  motion,  which  takes  place  increasingly  slowly \nat  greater  depths  and  causes  a  prf)gre.ssi\\\u2019e  lag  in  the \nrate  of  heating. \nllius  far  the  discussion  has  largely  centered \naround  the  simplest  cases  of  diurnal  warming,  in \nwhich  the  negative  gradient  represents  the  effects  of \nFrom a jurisdictional standpoint, it is important to consider all cases of diurnal temperature increase. Fire 23. Diurnal temperature change at various depths from the surface to 50 feet. Restricted. Diurnal and seasonal changes. Figure 24. Relationship between shallow temperature gradients and wind at different seasons.\n\nNegative gradients, both the simple ones and those in which a period of calm weather has permitted the accumulation of a negative gradient for several days, were examined. For this purpose, a large group of BT observations from the Pacific were analyzed based on the weather conditions at the time the observations were made.\n\nIn Figure 24, the upper graph shows the frequency of negative gradients for different wind forces for each season of the year. Any measurable decrease in temperature gradient is indicated.\nThe temperature between the surface and a depth of 30 feet is referred to as a negative gradient. In the lower graph, the median values of non-zero temperature differences are plotted. If isothermal cases were included, a majority of the median values would, of course, be zero. Thus, the two parts of Figure 24 must be considered together: the upper part shows how frequently measurable negative gradients occur, and the lower, their relative strength when they do. In general, Figure 24 shows the greater frequency of negative gradients. Figure 25 illustrates the relationship between shallow temperature gradients and wind at different latitudes during the summer season in June, July, and August. During the warmer part of the year, and it also suggests that seasonal changes affect the magnitude of the gradients more than they affect the frequency.\nThe figure's occurrence. A possible weakness of the fighter is that it combines data from a wide range of latitudes. Most likely, many winter observations showing negative gradients came from relatively low latitudes. It is to be hoped that as bathythermograms become more numerous, the various factors influencing the formation and persistence of temperature gradients may be more clearly separated.\n\nFigure 25 demonstrates the effect of wind on surface heating at different latitudes during the summer season. In the wintertime, the difference between high and low latitudes is undoubtedly much less, if not actually reversed.\n\nBoth Figures 24 and 25 are generally in agreement with previous statements that wind-generated vertical turbulence is destructive to station face temperature gradients. However, whereas in the previous discussion, it was stated that diurnal heating does not develop significant temperature gradients.\nThe relationship between shallow temperature gradients and cloud coverage. Figure 26 and 27 show that when the wind is stronger than force 3 (Beaufort), a small but significant number of negative gradients are found with wind forces of 5, 6, or 7. The difference lies in the fact that an average set of observations contains cases where a strong negative gradient is built up during several days of calm weather. The stability obtained then requires a much stronger wind to destroy the gradient than would have been needed to prevent its formation in the first place. The Pacific observations have also been correlated with cloud coverage. The usual method of evaluating this correlation is not specified in the given text.\nThe relationship between clouds and suppression of surface heating is significant, as shown in Figures 26 and 27, except in morning observations. Clouds may act as a blanket, holding in surface water's heat during hours when back radiation exceeds insolation. The impact on diurnal warming from the difference between air and sea temperatures has not been thoroughly analyzed, except in the Gulf of Mexico observations. There, it proved to be an important factor. The geographical distribution of air-sea temperature difference is also available.\nFigure 28 indicates areas where the difference between water and air temperatures is largest coincide with regions of pronounced diurnal warming. The problem of surface heating is complicated by the fact that the various processes are so closely interrelated. The quantitative relationships cannot be solved without a great deal more scientific work on the processes involved and statistical examination of the observations. However, it is not too much to expect that eventually echo ranges will be predicted in much the same way that weather forecasts are made.\n\nConvection has been mentioned frequently in connection with heat exchange at the surface. Figure 29 is a diagrammatic representation of convection cells.\n\nFigure 28. Chart showing the difference between water and air temperatures in the Northern Hemisphere, summer (above) and winter (below).\n\nA r i i\n\nI\n\nFigure 29. Diagrammatic representation of convection cells.\nThe diurnal and seasonal changes make it apparent that much of the time, the sea surface is being cooled by evaporation, back radiation or conduction. A very thin layer of water develops at the surface, which is cooler and therefore denser than the water just below, inducing an unstable situation and causing the cool water to drain downward through the warmer water below. This convection process is generally accompanied by movement due to wind friction, and the effects of the two are not easily separable.\n\nStudies of convective motion in the surface layer began only a year or two before the war. Patterned motions in the surface of a lake were reported, and attention was drawn to the fact that floating gulf weed in the North Atlantic was sometimes distributed in lines extending up and downwind.\nThe long lines of gulf weed, scattered at random, are strangely connected for the first time with a patterned flow involving alternating bands of convergence and divergence of surface water in the North Atlantic. This can be diagrammatically represented as in Figure 29. Therefore, when gulf weed is plentiful enough to get caught up in each convergence, an estimate of the thickness of the almost isothermal layer can be easily made. If the convection cells were circular in cross-section, the crosswind spacing of the weed would be just twice the depth of the mixed layer. However, observations indicate an average ratio nearer 1.8, and thus in Figure 29, the cells have been shown as being slightly compressed laterally.\nExperiments with drifting bottles and observations of the orientation in relation to the wind of the floating jelly fish, Physalia, indicate that the earth\u2019s rotation increases the vigor and width of cells rotating to the right (in the Northern Hemisphere), resulting in the average circulations having the form shown in Figure 30. The wind controls the orientation of these cells and contributes some of the energy required to maintain them. However, surface cooling is a critical part of the process. When the air is warmer than the water and evaporation is low, well-developed convection cells are not encountered. The amount of surface cooling required to initiate them is not known. It is probable that at low wind velocities, convection may take quite a different form.\nIn calm weather, a sight to find is the gulf stream rafted together in roughly circular masses. This suggests that cooled surface water may be draining downward at scattered points, similar to how \"chimneys\" of rising air develop at low wind velocities when the air is being warmed from below. It seems possible that beyond some critical maximum wind velocity, which likely varies with the rate of surface cooling, the patterned type of convective flow breaks down and motions become random. However, it is clear that over a fairly wide range of wind velocities, patterned convection plays an important role in maintaining a surface layer that is nearly isothermal vertically. The convective layer may be shallow and as a whole gaining in heat, as when diurnal warming is active.\nBut as long as the surface itself is being cooled, some form of overturn will be maintained. If this general idea of convective motion is accepted, then for present purposes several conclusions can be drawn, although it is admitted that these matters are not yet on very firm ground:\n\n1. Convection will be most active where humidity is at a minimum and where air temperatures are lowest in comparison to surface temperatures (see Figure 28).\n2. The more active the convection, the greater is the probability that a deep and virtually isothermal layer will be found at the surface; that is, temperature conditions will be favorable for echo ranging.\n3. Within the convective layer, sheets of slightly colder, downward-moving water can be expected. Under some conditions, this may be responsible for the formation of cold upwelling currents.\nThe basic vertical thermal structure of the oceans: A, a stable surface layer; B, surface heating and formation of a second stable surface layer; C, continued mixing and secondary thermocline. Figure 31. Diagram of convection. The development of \"micro-stratification,\" that is, small-scale vertical variations in temperature and salinity, which may have an unfavorable effect on echo ranging or at least make the strength of echoes highly variable. Further study of these factors is required, however, before it will be possible to assess their practical value properly.\n\nEffect of Wind:\nThe amount of energy required to produce vertical mixing in the surface layer depends upon the density gradient. If this is negative, that is, if the density is greatest on top, the water is unstable and already has begun to mix.\nThe potential energy retired for vertical movement. If the density gradient is zero, in other words, if the water is of uniform density, a sufficient force must be applied to overcome the frictional resistance of the water. Finally, if the density increases with depth, the force required to produce vertical mixing must be strong enough to overcome the difference in weight between layers of water of different densities. Thus, water whose density gradient is positive is highly stable. Nevertheless, such water is fairly susceptible to lateral movements which follow along the planes of equal density. Such horizontal motion entails friction between two layers of different velocities, and gradually water from the lower layer is dragged into the upper layer. In time, a positive density gradient can be weakened and destroyed by these lateral movements.\nwind-generated frictional forces which at first acted only laterally. In the absence of surface cooling, the wind, if it is sufficiently strong, is capable of forming or deepening a mixed surface layer. In other words, the frictional effect of the wind is important, whether or not it is aided by convection. A thermally stable surface layer once formed will be broken down by a wind, provided it blows hard enough and long enough. Especially in the latitudes of variable winds, the effects of wind-stirring can be clearly seen on many records. In fact, with spring observations, it is sometimes possible to interpret the record in terms of the winds during the past week or more. A hypothetical case is illustrated in Figure 31. The initially stable situation (Curve A) was changed by a wind, first to Curve B and later to Curve C. There\nThe wind increased, leading to the development of Curve I. This is the explanation for much thermal variability at shallow depths. It's important to notice in Figure 31 that as the mixed layer forms, thermal stability just below increases. This same phenomenon will be evident during the autumn months in the diagrams showing the seasonal cycle. For instance, Figure 35 demonstrates the sharpness of the thermocline's lower part increasing as the depth of the mixed layer increases due to local cooling and wind-stirring, which is significant in considering layer effects.\n\nThe effect of the wind in maintaining or deepening an isothermal surface layer is complicated by the fact that the wind also sets up a current near the surface.\nA face which may remove mixed water from a given area almost as fast as it is formed presumably requires some time to develop, while the effect on vertical mixing is more immediate. Thus, brief and variable winds are normally responsible for the effects illustrated in Figure 31. Waves and wave transport. Waves are among the most observable phenomena of marine environments, and they have always had a direct and notable effect on ships, as any ocean traveler knows. Antisubmarine ships are no exception, and especially in the case of smaller vessels, the motion produced by the waves may be a serious deterrent to efficient echo ranging. In addition, the process of echo ranging itself is affected and sometimes markedly impaired by the noise of breaking waves and by pitching effects.\nA wave, in its simplest form, is a regular, progressive displacement of the surface from its mean level. However, the open sea seldom gives any impression of rhythmic regularity. The image is frequently one of apparently random movement and chaotic disorder. Elevations and depressions of various shapes and sizes appear and disappear; some are superimposed on others. They may travel at different speeds and even in different general directions. Nevertheless, the surface deformation at any given place and time, with some allowance for turbulence, may be thought of as the composition of individual waves.\nThe result is composed of a finite number of relatively simple wave trains with varying periods, amplitudes, velocities, and crest lengths. A simple wave can be completely described by three or, at most, four measurements. First, there is the wave length, which is the distance from crest to crest or from trough to trough. The wave period is the time in seconds required for the passage of one wave length. The ratio of these two quantities gives, of course, the wave speed. Additionally, there is the height of the wave from trough to crest. Lastly, there is the crest length. For most waves, the crests (and troughs) are assumed to be of infinite length. However, there exist both in theory and in fact, waves whose crests are broken up into regular segments separated by segments of troughs. To determine these waves, we need to consider the regularity of the crest segments and the duration of the trough segments.\nA scribe must fully specify the length of these crest segments. This is the crest length, and such waves are called short-crested waves. A certain wave speed allows the wind to blow without causing more than a ripple. Once a rising wind has begun to form waves, it increases their size and speed rapidly by a combination of pressure on the windward slopes and suction on the lee. The speed of waves propelled by this method is limited by the speed of the wind, and observations indicate that generally, the largest waves have a velocity about eight-tenths that of the wind. The limit to a wave's steepness is relatively low. Unless the length of a wave crest is at least seven times its height, the crest will break. Waves may reach the breaking point either through the action of the wind or through reinforcement by some other wave train.\nThe simple wave form is distorted and there is a marked degree of turbulence when waves of different periods approach breaking. A wind of force 5 (Beaufort) or more intensifies this mixing effect by blowing wave crests across the trough ahead in the form of spume.\n\nWith a rising sea, waves of various lengths are present. The smallest waves break at low wind velocities, while the longer ones remain and attain a greater height, their size being finally limited by the wind velocity and the distance traveled.\n\nThe tendency of waves to increase in length with the distance traveled and for their speed to increase correspondingly may occasionally lead to the surprising result that the following sea, after a storm, has a higher velocity than the wind which originally produced it.\nAn observer at sea watches a gull or other object floating on the water. As a wave passes, the movement of the object is not merely up and down but rather describes a roughly circular or elliptical orbit. At the crest, the object moves forward with the wave, while in the trough it is moving in the opposite direction. Particles of water in the wave move in similar orbits. The movement occurs not only in particles of surface water but also in those some distance below the surface. The orbits of movement are bigger for large waves than for small ones, but for any wave the size of the orbit and the velocity decrease rapidly with depth, approaching zero at a depth of more than half a wave length below the mean surface level.\n\nThe fact that the velocity decreases continuously.\nWith depth, orbits are prevented from being completely circular. A water particle travels faster in the inner part of its orbit than in the outer, resulting in a transport of water in the direction of the waves' progress. After completing one revolution, a particle does not return to the starting point but to a point slightly forward. The rate of this forward transport is greatest at the surface and decreases rapidly with depth. The total volume transport depends on the wave's length and height. With a very low wave in deep water, it is negligibly small. With larger waves, the transport is significant.\n\nFigure 32. Typical thermal gradients showing seasonal temperature cycle in the Bermuda area.\n\nSo, after having completed one revolution, a particle does not return to the point from which it started but to a point slightly farther forward. Thus, there is a transport of water in the direction of the waves' progress. The rate of this forward transport is greatest at the surface and decreases rapidly with depth. The total volume transport is dependent on the wave's length and height. With a very low wave in deep water, it is negligibly small. With larger waves, the transport is significant.\nIn summarizing the effects of waves on the temperature structure of the ocean, it's important to compare the direct effects of wind and the indirect effects resulting from wave motion. In each case, there's mass transport of water caused by the frictional drag of the wind and the character of water particle movement in the wave. Both are capable of producing zones of convergence or divergence, accompanied by raising or lowering of the thermocline, which alters temperature and sound conditions locally. They may also be responsible for water of one temperature being carried over water of another. If the water on top is cooler than that below, marked convection will result. If it is.\nWind and waves contribute to stable stratification in warmer conditions. Both wind and waves can alter sound conditions by causing vertical turbulence. Mixing by wind results from convection and frictional drag caused by the horizontal transport of water. Mixing by waves occurs primarily when they break; there is no evidence to suggest that wave transport produces a measurable amount of turbulence.\n\nWind and waves have very similar effects on oceanographic conditions and echo ranging, although the effects are produced in quite different ways. Due to their similarity, the effects are not easily separable, and quantitative investigations have only just begun.\n\n5.2.2 Seasonal Thermocline\n\nDescription:\nApart from the short-lived negative temperature gradients of diurnal warming, we have seen that... (continued in next section)\nVections and wind-mixing typically maintain a surface layer of substantially isothermal water. However, during the time of year that insolation markedly exceeds heat losses, this mixed layer seldom extends down to the main thermocline. This is partly because convection is efficient only to the depth that the water is unstable, or at least of uniform density, and partly because during that time of year winds are ordinarily mild. In any case, as the surface water gradually grows warmer with the advance of spring, a secondary thermocline develops immediately below the depth to which convection and wind-mixing remain effective. If the temperature of the layer above this thermocline continues to rise, the thermocline itself will grow steeper and become more of a barrier to downward mixing.\n\nA typical seasonal thermal cycle in mid-latitudes is:\nFigure 32 shows a series of bathythermograms taken in the Bermuda area, depicted more diagrammatically in Figure 33. In midwinter, the water column is essentially isothermal from the surface to the top of the main thermocline (Figure 33A). Starting in March, the surface water begins to warm, and the depth of wind stirring is markedly decreased (Curve B, Figure 33). Thus, in spring, the water column from top to bottom consists of the following parts: (1) a relatively shallow, wind-stirred surface layer which is rapidly increasing in temperature, (2) a relatively shallow layer of transition, the seasonal thermocline, (3) an isothermal layer which retains midwinter temperature, (4) the main thermocline, and (5) the deep water. Until midwinter again, these five subdivisions can be made out in any temperature profile.\nTemperature-depth curve in mid-latitudes. In high latitudes, there is no permanent thermocline, and in the tropics, due to the small seasonal change, it is difficult to distinguish between the permanent and seasonal thermocline. By midsummer over the greater part of the oceans, surface warming and vertical turbulence have increased both the depth and the magnitude of the seasonal thermocline (Curve C, Figure 33). During the autumn (Curve I, Figure 33), cooling at the surface and the resulting tendency for instability rapidly increase the thickness of the wind-stirred surface layer. The seasonal thermocline also deepens rapidly, but at the same time, it decreases in magnitude, only to vanish as simple midwinter conditions are restored.\n\nBy comparing Figure 33 and Figure 14, it will be seen that the seasonal cycle bears a marked resemblance.\nThe curves for diurnal cycles, disregarding scale changes, share similar shapes for winter and night, spring and morning, summer and afternoon, and autumn and evening. Seasonal changes are minimal near the equator. Changes do not occur simultaneously over the entire ocean basin but work gradually northward and southward with the sun. An additional complicating factor is that winds are not steady outside the trade-wind belt, causing the development and decay of the seasonal thermocline to not always progress steadily. However, once the seasonal thermocline is well-established (by May, for example, in mid-latitudes), it will not disappear, regardless of how great or frequent the storms, until late in the autumn. This fundamental quality of a thermocline is that it has a stability, remaining in place despite external disturbances.\nGeographical Factors: The main (permanent) thermocline is responsible for the vertical temperature gradients encountered by a deep marine layer over only a rather small fraction of the total ocean area, primarily in the tropics. The influence of the seasonal thermocline, on the other hand, is very widespread. This leads to an analogy that can be drawn between land warfare and subsurface warfare. Figure 33. Diagram of seasonal thermocline in the Bermuda area, .\\.^inter. B., Spring. C. Summer. D..\\autumn, which may serve at this point in the discussion to clarify somewhat the roles of the various types of thermoclines. In land warfare, as is well known, soldiers are very conscious of two factors: the weather conditions.\nIn subsurface warfare, the terrain and weather play important roles. The weather controls diurnal warming, which determines temperature gradients at and near projector level. These, in turn, determine refraction patterns and general sound conditions. The sea also has a physical structure analogous to terrain in land warfare. The seasonal thermocline, due to layer effects, is comparable to a hill behind which a submarine can hide. At times and places where the seasonal thermocline is sharp and well-developed, a submarine may gain significant cover by submerging below the isothermal surface layer. Other parts of the sea, from this standpoint, lack vertical thermal gradients and are comparable to a level plain in land warfare.\nThe new concept is that both the submarine and its adversaries find it advantageous to know the subsurface temperature distribution. This is similar to a soldier's need to know topography, for local cover and strategic planning. One can obtain a good understanding of the magnitude and geographical variations of the seasonal thermocline by subtracting midwinter surface temperatures from midsummer surface temperatures. The resilting chart, Figure 34, demonstrates, as expected, that the greatest seasonal change occurs in mid-latitudes, particularly in the western parts of the oceans where prevailing winds are off the continents. It will also be noticed that in those equatorial regions where the seasonal thermocline exhibits the greatest change, the temperature distribution is most dynamic.\nThe climate is less than 2.5 degrees the main thermocline is largely above the depth of 600 feet. In these areas, therefore, the main thermocline rather than the seasonal is of major importance in determining layer depth, and there is comparatively little change throughout the year.\n\nThe fact that the seasonal thermocline dominates the vertical temperature distribution at depths critical for a modern submarine greatly increases the difficulty of getting out practical charts of either the sound or the diving conditions. Since seasonal changes are continuous, though more rapid in spring and autumn, it is sometimes misleading to group observations for periods even as short as a month.\n\nThe Seasonal Progression\nThere are two quite different ways in which the available data can be plotted to demonstrate for our:\n\n1. Temperature vs. Depth: This type of plot shows how the temperature changes with depth at different times of the year. It is particularly useful for understanding the seasonal variations in the thermocline and the depth of the warmest and coldest waters.\n2. Temperature vs. Time: This type of plot shows how the temperature changes over the course of a year at a particular depth. It is particularly useful for understanding the seasonal cycle and the timing of major temperature changes.\n\nBy examining both types of plots, we can gain a more complete understanding of the seasonal variations in the temperature structure of the water column.\nThe significant points regarding seasonal temperature changes are as follows. It is possible to present average monthly temperature-depth curves, such as Figure 35, or plot isotherms with depth and time as coordinates, like Figure 36. Both methods have their advantages and disadvantages.\n\nThe lighter graphs display available data near Bermuda and represent typical seasonal changes over wider areas of the warmer waters in the western North Atlantic. Temperature-depth curves, such as Figure 35, indicate the average of the available data and suggest the type of conditions most likely to be encountered. Some variation in individual bathythermograms is to be expected. To give some idea of this variation, Figure 37 illustrates the variability in individual thermograms in the Bermuda area during April.\nThe degree of variability in the Bermuda area is shown in Figure 37 for the observations in April. In Figure 35, it is noted that from May through August, on average, the warm surface layer is thermally stable, with a surface temperature minus temperature at 30 feet greater than 0.3 F. This tendency for negative surface gradients in the summer reflects the moderate winds near Bermuda at this part of the year, as well as the rapid warming due to clear skies. For instance, of the 360 bathythermograms available from May to August in this area, 65% exhibit an isothermal surface layer varying in depth between 40 and 100 feet, while 35% show thermal stability at and near projector level. The average curve\nA person with weak negative temperature gradients near the surface will experience this to some extent in September. However, this is misleading. If there were more observations, only iathythermograms taken at night or during strong winds could be used to develop average temperature-depth curves, thereby eliminating the effects of diurnal warming in such a diagram as Figure 35. However, as of now, there are too few observations from most months to make this desirable. On the other hand, in Figure 36, isotherms for every one degree are used, eliminating the effects of diurnal warming. Nevertheless, it is somewhat more difficult to judge the refraction pattern from this type of diagram.\n\nFigures 38 and 39 display the same kind of graphs for the seasonal cycle in mid-latitudes in the Pacific.\nThe differences between these two temperature cycles are very slight. The depth of the winter mixed layer is slightly greater in the Atlantic than in the Pacific, and the development of the seasonal thermocline in spring is less regular. Both these differences are due in part to the fact that in the chosen Atlantic area, the frequency of winds of gale force is 10 to 20 percent greater during the winter and spring months than in the Pacific area. A Figure 38, like Figure 35, was prepared by plotting the average temperature differences from the surface to certain depths and then making the main break in each curve occur at the average layer depth. The bathythermograms for Figure 38.\nFig. 38. Seasonal cycle in mid-latitudes in the Pacific \u2013 average monthly temperature-depth curves.\nDEPTH IN FEET DEPTH IN FEET DEPTH IN FEET\nThe Basic Vertical Thermal Structure of the Oceans\nFigure 39. Seasonal cycle in mid-latitudes in the Pacific \u2013 average isotherms.\nFigure 40. Seasonal cycle in the equatorial Pacific \u2013 average isotherms.\nFigure 41. Seasonal cycle over the continental slope of the western North Atlantic \u2013 average monthly temperature-depth curves.\nREDUCED\nDIURNAL AND SEASONAL CHANGES\nMany such minor differences in seasonal cycles will be found, which can be correlated with local climatic variability.\nIn the trade wind belt, the magnitude of the temperature change between winter and summer is:\ntem\u00adperature change between winter and summer.\nThe annual temperature change is least pronounced near the equator, with a pattern similar to mid-latitudes but with a bimodal seasonal curve. The highest temperatures occur in April and October, slightly after the sun has passed directly overhead. In contrast, very marked seasonal cycles are found in higher latitudes not far from land, as shown in Figures 41 and 42. Observations from between the northern edge of the Gulf Stream and the continental slope in the sector off southern New England have been plotted using the same methods. Here, the maximum temperatures are reached. (RESTRICTED)\nThe basic vertical thermal structure of the oceans:\n\nThe temperature difference between summer and winter is around 2 degrees, as compared to about half as much as shown in Figures 35 and 33. In high latitudes and greater distances from the continents, seasonal changes become less pronounced. This reflects the smaller range in surface temperature (see Figure 31) and stronger winds. Unfortunately, the available observations are too few from any one area in high latitudes to demonstrate the complete annual cycle. The best data are from the Aleutian Islands area (Figure 43), and, as expected, emphasize the shorter summer season.\n\nIt is hoped that this small sample (Figures 35-13) has served to illustrate the demonstration and the decline of the seasonal thermocline in the open ocean.\nIn the ocean, it would require a great many diagrams to illustrate the slight differences encountered from region to region. When the number of BF observations becomes sufficient to permit this to be done in considerable detail, it will be possible to improve the charts of average echo ranging conditions.\n\nChapter 6\nRelationship of Salinity and Temperature\n\n6.1 Temperature-Salinity Correlation in the Deep Water and in the Main Thermocline\n\nIn surface waters, the relationship between temperature and salinity is highly variable since it is affected by surface heating and cooling, evaporation, and precipitation. In the main thermocline and the deep water layer, however, the temperature-salinity correlation remains nearly constant within large areas. Knowing the temperature in situ, one can predict the salinity of a sample of water with almost as much accuracy.\nmuch accuracy as it is measured by the routine (\u00b10.02 \"/()()). This is illustrated by Figure 1 in which the observations having temperatures colder than 66 F from nearly all the available oceanographic stations in the central part of the North Atlantic have been used. But when the water masses from widely different areas are compared, slight differences in the temperature-salinity correlation can be distinguished. For example, the bottom water originating in high southern latitudes of the Atlantic has a salinity of about 34.8 as compared with about 34.9 in the North Atlantic. Such small but persistent differences provide oceanographers with an excellent method of tracing the slow water movements in the main thermocline and below. However, for our present purposes, it is to be concluded that as long as a station is operating in the main thermocline.\nThe density in the thermocline can be predicted with satisfactory accuracy merely by observing the temperature. Figure 1 shows that as the temperature increases, so does the salinity. Therefore, within the main thermocline, salinity decreases with depth. This is the general rule in the open ocean, and, as will be discussed in more detail below, is in marked contrast to the conditions in coastal waters where salinity increases with depth.\n\nFrom the perspective of the stability of the whole water column in the deep ocean, the vertical distribution of salinity tends to decrease stability slightly due to temperature alone. In other words, if there were no decrease in salinity with depth, density would increase with depth slightly more rapidly.\n\nHowever, the vertical salinity variations are so minor\nAt a typical oceanic station, observations for temperature and density fall along nearly parallel curves below the main thermocline's top (Figure 2). The temperature-depth and density-depth curves in the mid-Atlantic compare in Figure 2. The relationship between salinity and temperature is restricted. With increasing temperature gradients, the vertical salinity gradient also increases.\n\nIn the North Atlantic's central basin, mid-depth waters are slightly fresher than expected, given they were formed locally by surface and bottom water mixture. This situation occurs in other oceans near the main thermocline's axis and is even more pronounced. This is explained by:\n\n(Figure 1 shows that in the North Atlantic's central basin, mid-depth waters are slightly fresher than if they were formed locally by the mixture of surface and bottom water. This situation also occurs in other oceans near the axis of the main thermocline and is even more pronounced. The temperature-depth and density-depth curves in the mid-Atlantic are compared in Figure 2. The relationship between salinity and temperature is restricted. With increasing temperature gradients, the vertical salinity gradient also increases.)\nWhen stability is great, lateral mixing is more effective than vertical mixing. This is similar to the phenomenon described in connection with the establishment of temperature gradients, in which a force sufficient to overcome the frictional resistance of the water will cause mixing in water of uniform density, but a greater force is required to destroy density differences. Therefore, when there are density gradients, most mixing occurs laterally following surfaces of constant density. Thus, the temperature-salinity correlation at mid-depths can be explained by following surfaces of constant density north or south until they intersect the sea surface. In short, they have the temperature and salinity characteristics they acquired at or near the surface in mid-winter in the higher latitudes.\nTheir transport to the main thermocline region of the central basins has been little modified by vertical mixing.\n\nSalinity gradients arise from the dilution of surface water by rainfall, melting ice, and the runoff from the land, from evaporation of water from the sea's surface, and from the flow of waters of different salinity over one another as the result of ocean currents.\n\nIn temperature regions above latitudes 40\u00b0 N and S, there is usually an excess of rainfall over evaporation and consequently positive salinity gradients tend to develop beneath the sea's surface. Along the coasts of such regions, the outflow from rivers greatly augments this effect and substantial density gradients result from the dilution of the overlying layers of water. It follows that the shallow temperature gradients\nClients characteristic of temperate regions in summer are accompanied by salinity gradients. These gradients are particularly strong in coastal regions. Both kinds of gradient cause the water to be more dense as depth increases, supplementing each other in depriving the stability of the water column. It may be observed from Figure 3, which shows the gradients of temperature, salinity, and resulting density in such a situation, that the gradients of temperature and salinity very closely coincide. Where the temperature gradient is strongest, the salinity gradient is strongest as well. This arises because surface waters are prevented from mixing with deeper waters by the sharp density gradient.\nwhile  both  abo\\e  and  below,  the  water  mixes  more \nfreely.  Both  gradients  consequently  tend  to  develop \nin  the  same  relation  to  the  resulting  density  pattern. \nDuring  the  winter,  when  the  disappearance  of  the \ntemperature  gradient  decreases  the  stability  of  the \nwater,  the  mixing  which  results  also  destroys  the  sal\u00ac \ninity  gradient.  In  spring  the  melting  of  snows  and  the \nrainfall  characteristic  of  the  season  led  to  the  early \ndevelojmient  of  the  salinity  gradient.  This  becomes \nrelati\\ely  less  important  than  the  temperature  gra\u00ac \ndient  in  determining  the  density  distribution  as  the \nsummer  season  advances. \nIn  the  warm  oceanic  areas  salinity  gradients  are \nless  pronounced  and  are  thus  of  less  importance  in \ndetermining  the  density  distribution  in  the  upper \nlayers  of  the  sea.  In  the  central  basin  of  the  North \nAtlantic,  near  the  borderline  between  temperate  and \nSubtropical waters, seasonal changes in evaporation and precipitation can produce slight vertical salinity gradients at relatively shallow levels. For example, the surface salinity in the Bermuda area averages close to 36.6 in winter when strong and relatively dry winds prevail, but in summer, the damper, weaker winds permit the surface layer to freshen to about 36.1 parts per thousand. The resulting slight increase of salinity with depth occurs at about the same level as the summer thermocline, so the effect on sound is negligible. However, for this reason, as well as because of the seasonal thermal cycle at the surface, the temperature-salinity correlation is by no means constant at depths above the top of the main thermocline.\n\nFigure 4. World chart of surface salinities\u2014 June, July, August.\nAreas of variable salinity gradient near the surface (distance in miles)\n\nThe surface salinity in the Bermuda area averages close to 36.6 in winter when strong and relatively dry winds prevail. But in summer, the damper, weaker winds permit the surface layer to freshen to about 36.1 parts per thousand. This slight increase in salinity with depth occurs at approximately the same level as the summer thermocline, resulting in a negligible effect on sound. However, due to this reason, as well as because of the seasonal thermal cycle at the surface, the temperature-salinity correlation is not constant at depths above the top of the main thermocline.\nIn substantial areas of small rainfall in the subtropics, evaporation exceeds precipitation, and the most saline water is found at the surface. Such salinity gradients are small and are associated with similarly small negative temperature gradients, resulting in a nearly uniform density of the water column. On the other hand, near the equator, the high rainfall of the doldrum belt reduces surface salinity and makes it considerably fresher than the water near the top of the main thermocline. The latter, as shown above, is relatively shallow in these latitudes, hence both temperature and salinity contribute to the very high stability near the surface.\n\nThus, it is apparent that the distribution of salinity in surface waters shows slight but distinct variations which are controlled by climatic factors.\nThe surface temperature and salinity exhibit seasonal and geographical characteristics. The latter differ somewhat from temperature. Generally, surface temperatures decrease with increasing latitude. Surface salinities reach their maximum in a belt centering at about latitude 23 degrees, along the outer edges of the trade winds where the air is descending and relatively dry, and where evaporation is greater than nearer the equator or in high latitudes. This is illustrated in Figure 4, which is a world chart of midwinter surface salinity.\n\nAreas of variable salinity gradient near the surface\n\nWhen the surface waters of a warm, saline current mix with those of a colder and less saline current, as occurs off the Grand Banks of Newfoundland, for instance, the temperature-salinity correlation becomes very variable.\nAt times, fresh water with a salinity as low as 32 parts per thousand (ppt) may be found above or immediately next to water of greater salinity than 36 ppt. The contrasting water masses may have striking differences in color and can be easily seen from a ship's deck. It's important to note that density may not change significantly across such a sharp line of demarcation, as the more saline water is also warmer.\n\nA similar situation, though less extreme, can be encountered at any time north of the Gulf Stream, between Cape Hatteras and the Grand Banks. Here, westerly winds sometimes push the relatively less saline coastal waters far offshore. The situation southeastward from Montauk Point, Long Island, in July 1938 (Figure 5) provides a good example of relatively sharp salinity gradients near the surface.\ncoastal water being carried more than 100 miles beyond the limits of the continental shelf. Although such situations make it desirable to compensate the submarine-model bathythermograph for salinity changes, from the acoustical standpoint, the vertical variations in salinity shown in Figure 5 are negligible. In each case, the vertical salinity gradients are accompanied by relatively much stronger temperature changes. It is necessary to find a situation where shallow salinity gradients occur independently of temperature gradients before sound transmission is noticeably influenced. In the open ocean, this very seldom occurs. However, since one of the major assumptions in maximum range predictions based on BT observations is that vertical salinity gradients are constant.\nInity gradients can be neglected, but it is advisable to discuss this matter in more detail. The refraction pattern might differ significantly from that indicated by a BT trace in the following possible circumstances:\n\n1. A positive temperature gradient might be significantly reinforced by an increase of salinity with depth.\n2. Within an isothermal surface layer, salinity might increase with depth, causing increased upward refraction.\n3. A slight negative temperature gradient might be partially or entirely offset by an increase of salinity with depth,\n4. A negative temperature gradient might be reinforced by a decrease of salinity with depth.\n\n6.3.1 Positive Salinity Gradient and Positive Temperature Gradient\n\nDuring periods of rapid cooling, positive temperature gradients may be developed near the surface. Since this condition is thermally unstable, it ordinarily does not persist for long.\nGenerally, this phenomenon occurs only to a slight degree and during calm weather. Wherever a marked positive temperature gradient exists, it is safe to say that there is also a positive salinity gradient which is at least sufficient to counterbalance the thermal instability of the water column. The combination of positive temperature and salinity gradients occurs when there is heavy rain that freshens the surface layer, and when the rain is colder than the sea water or is followed by conditions that favor surface cooling by evaporation. More marked examples are found near the edge of a current or along the continental slope where there is a flow of colder over warmer and more saline water. In such cases, the density gradients are often so highly stable as to permit a submarine to balance on what would appear from the temperature trace.\nIn the open ocean, a positive salinity gradient can form within a virtually isothermal surface layer following a heavy rain, provided the winds are light and the temperature of the rain water is close to that of the surface water. This situation is most frequently favorable in the dolphin belt.\n\nIn the open ocean, a positive salinity gradient can form within a virtually isothermal surface layer following a heavy rain, if the winds are light and the temperature of the rain water is close to that of the surface water. This situation is most frequently favorable in the dolphin belt.\n\n6.3.3 Positive Salinity Gradient and Negative Temperature Gradient\nThis situation could occur when slight surface currents cause surface water with lower salinity to flow over water with higher salinity, resulting in a layer with both a positive salinity gradient and a negative temperature gradient. This can lead to instability in the water column and potentially impact diving conditions. However, in the open ocean, this situation is less common than a positive salinity gradient alone.\nWarming is accompanied by precipitation. In the current range-prediction method, the significant minimum negative temperature gradient is a decrease of more than 0.3 degrees between the surface and a depth of 30 feet. For the downward refraction produced to be counteracted, the positive salinity gradient would have to average more than 0.4 parts per thousand to 2 parts per thousand over the same depth range, depending on the surface temperature. It is unlikely that this ever occurs in the open ocean, except possibly in nearly calm weather when the negative temperature gradient persists for several days. Sufficient precipitation is not apt to take place during the few hours when slight negative temperature gradients become established by diurnal convection.\n\n6.3.4 Negative Salinity Gradient and\nA more likely case is that surface warming is accompanied by evaporation, the negative salinity gradient being insufficient to counteract the effect of the negative temperature in maintaining stability. In this case, the downward refraction due to temperature would be reinforced slightly by the salinity gradient. It is believed that this effect is common in such specialized situations of dry, warm air as occur in parts of the Mediterranean, the Red Sea, and the Persian Gulf. However, the further reduction in range which can occur in this way is of minor practical importance.\n\nRestricted.\n\nChapter 7.\nOcean Currents.\n\nThe factors considered up to this point are those which have an orderly and generally gradual effect on temperature and salinity.\nA picture has been presented of an idealized ocean with a permanent and relatively constant temperature structure, except near the surface where small-scale heating, cooling, and mixing processes result in diurnal and seasonal temperature changes. However, it has gradually become apparent that there are important geographical variations in temperature structure, caused partly by climatic variations and partly by the great ocean currents. Some knowledge of currents, both as to their general characteristics and the location of the major systems, is essential for mastering the problems of subsurface warfare.\n\nVariability of a more local nature must also be considered. Under this heading are included a wide variety of phenomena. The surface processes of heating and cooling are subject to a great deal of local variation.\nVariation, particularly in temperate and polar regions, where relatively sudden and violent weather changes are common. Various kinds of small-scale thermal structures are produced as a result of water transport or meteorological influences. Finally, there are the special phenomena of coastal waters. All such variability is an essential part of oceanography but also plays an important role in sound transmission.\n\n7.1 Principles of Ocean Circulation\n7.1.1 Water Movements in Relation to Density Distribution\n\nPrevious sections have mentioned the movements of water that result from changes in density. In the tropics where surface heating is strong, the light water thus formed tends to spread northward and southward over the surface and to be replaced by colder water from below. As it moves into higher latitudes, it overlies water that is colder but less saline.\nLiving in areas subjected to less heating and evaporation, tropical water cools and becomes denser than water underneath, causing it to sink. This surface transfer of water toward the poles is compensated by a return flow that largely takes place as a slow drift in the depths of the ocean. Similar movements occur on a much smaller scale as a result of local heating and cooling.\n\nIn discussing the forces involved in such movements, it is convenient to compare them with meteorological phenomena, as the problems are essentially the same. A weather map shows isobars, lines of equal barometric pressure separating low- from high-pressure areas or topographic contours of an isobaric surface. In the sea as in the atmosphere, pressure increases downward due to the weight of the overlying water or air.\nLayers lie beneath each other, and the pressure at a specific depth varies according to the density of the overlying medium. It is therefore possible to chart the pressure distribution in the sea (usually by plotting the topography of a selected isobaric surface), which will show the direction of water movement in the same way that isobars on a weather map indicate wind direction. The usefulness of these topographic charts depends on the fact that the pressure gradient is zero in the direction parallel to the contours. Therefore, the initial tendency is for water to flow at right angles to the contours, that is, downhill. As soon as the water is set in motion, however, it is deflected from its downhill course by the effect of the Earth's rotation, as will be explained below. As long as the isobaric slope is maintained on a rotating Earth, the water follows this path.\ncurrent  w  ill  run  more  or  less  jjarallel  to  the  contours \nof  the  isobaric  surface  in  the  same  way  that  the  wand \nfollow's  the  isobars  on  a  w'eather  map.  In  order  to \nunderstand  this  situation  fully,  it  is  necessary  to  ex\u00ac \namine  in  detail  the  effect  of  the  earth\u2019s  rotation, \nwhich  will  be  taken  up  in  the  next  section.  It  will \nalso  be  necessary  in  dealing  with  water  movements  in \ngeneral  to  discuss  the  important  role  played  by  wind\u00ac \ngenerated  currents. \nCoriolis  Force \nThe  effect  of  the  earth\u2019s  rotation  on  moving  bodies \nis  known  as  Coriolis  force,  after  the  French  physicist \nRESTRIC  FED \n.'iO \nOCEAN  CURRENTS \nFiciiiRK  1.  Dia<^iani  illustrating  Coriolis  force\u2014 rotation  of \npoints  near  the  North  Pole. \nFioure  2.  Diagram  illustrating  Coriolis  force\u2014 a|jparent \nmotion  of  a  swinging  pendulum  on  a  rotating  earth. \nwho  evolved  the  mathematical  theory.  It  is  a  ficti\u00ac \nThe Coriolis force, as will be explained, acts at right angles to the direction of motion and deflects a current of fluid particles towards the right in the Northern Hemisphere and to the left in the Southern Hemisphere. This force is nonexistent only at the equator and increases to a maximum at the poles, varying as the sine of the latitude.\n\nTo explain how this force acts, suppose an observer is standing at the North Pole in the center of a horizontal circular platform and is looking at a point on the edge of the platform. In Figure 1, the observer's position is at A, and he is looking at point B. The earth rotates in the direction indicated, and point B rotates with it, taking the successive positions B\u2081, B\u2082, B\u2083, and returning to the original position.\nThe observer, turning with the earth, faces B for 24 hours. Unaware of B's changing position, he'd notice motion if he built an instrument moving in straight lines on a platform. This instrument, a pendulum suspended from tower A, would swing toward and away from B, indicated by the dotted line in the figure. The pendulum would continue to swing in this plane, but B would rotate away from it until at position Bj, where the pendulum would swing in a line at right angles to Bi from A. An outside observer sees the pendulum swinging in a straight line, but the observer at A would perceive it differently.\nIf B stands still and the pendulum swings more and more to the right, its course on each swing would appear to be a series of curves, each one bent slightly to the right of the direction of motion, as in Figure 3. After several swings, its direction, as shown in the figure, would be about at right angles to a line from A to B, and it would continue to change direction, making one complete apparent rotation in 24 hours.\n\nA water mass at A or B will rotate with the earth and will therefore appear stationary to an observer at either spot. But if some force puts the water in motion in any horizontal direction, it will behave similarly.\n\n[Figure 3. Diagram illustrating Coriolis force\u2014rotation of points on the equator.]\n\nPrinciples of Ocean Circulation:\nA water mass at A or B will rotate with the earth and will therefore appear stationary to an observer at either spot. However, if some force puts the water in motion in any horizontal direction, it will behave similarly to the pendulum, experiencing the Coriolis force and appearing to deflect to the right in the Northern Hemisphere and to the left in the Southern Hemisphere. This effect, which results from the earth's rotation, plays a significant role in ocean currents and weather patterns.\nA pendulum, by and large, tends to move in a straight line. Therefore, the earth rotates beneath it, causing its path to appear curved to an observer unaware of the earth's rotation. A current with an initial impulse in the direction from A to B will curve to the right and pass to the westward of B. In the same way, a perfectly aimed bullet will strike to the right of the bull's-eye (in the Northern Hemisphere), regardless of the direction between the gun and the target. While the bullet is in flight, the earth has twisted slightly under it, causing the initial bearing of the target in relation to space to change. Any body which has been set in motion and is not acted upon by any lateral force appears, due to the earth's rotation, to be moving in a circular path.\nThe path, called its inertia circle, has a radius of curvature that depends on the velocity. The bullet appears to curve only slightly, but an ocean current with a much lower velocity has a smaller radius of curvature. If point A were located at the South Pole, the earth\u2019s rotation would carry point B around it in a clockwise instead of counterclockwise rotation, hence the apparent deflection of a pendulum or of a current of water is to the left. This general rule for the direction of deflection holds for lower latitudes as well as higher; the deflection is to the right in the Northern Hemisphere and to the left in the Southern. The amount of deflection becomes less.\n\nFigure 5. Diagram illustrating Coriolis force\u2014rotation of points at 45\u00b0 N. Ocean currents are restricted, but the effect ceases at the equator.\nSuppose points A and B are on the equator as in Figure 3. As the earth rotates, B follows A with no change in horizontal position. There is still a circling motion of a sort, which can be visualized by holding A in a fixed position and letting the whole earth rotate around it for a day's time as we look down on it from the North Pole (Figure 4). But to the observer at point A, the circling motion is in a vertical plane, and it does not result in any horizontal deflections in the water around him.\n\nIf the points are located at an intermediate latitude, say 45\u00b0 N, then the circling motion has some characteristics of both the polar and equatorial movements. It has both horizontal and vertical components. The resultant movement in a horizontal plane around the observer at 45\u00b0 N is important.\nIt is not quite so easy to visualize B circling around A at this latitude as it was at the Pole. For simplification, Figure 5 is drawn as if A is stationary and B is circling around it. In reality, both points are in motion, circling around each other. One of the most difficult things to understand about Coriolis force is the fact that although the Earth rotates once every 24 hours, except at the North and South Poles it takes more than 24 hours for points A and B to circle each other. Figure 5 is an oversimplification of the facts. This was proven by Foucault, the physicist who first demonstrated the pendulum experiment described.\n\nFigure 6. Diagram illustrating Coriolis force\u2014rotation of points at 45\u00b0 X.\nGoing back to the discussion, there was a circular platform at the North Pole, rotating with the earth so that the pendulum swung above it in a straight line but apparently making a complete rotation in 24 hours. Suppose now the platform is enormously enlarged and tilted so that its edge reaches points A and B on latitude 45 degrees N. It must be horizontal at points A and B because we are interested only in horizontal deflections. The platform must rotate with the earth, so its center is the prolonged axis of the earth. Thus, it is as shown in Figure 6. This disk then is the plane across which the pendulum swings. It rotates as the earth does, with its edge touching at points A and B. However, its circumference is greater than that of the earth at those latitudes.\n\nFigure 7. Diagram of water movements resulting from localized heating of the sea surface.\nThe distance around the earth at latitude 45 degrees; therefore, it is similar to a reduction gear, with one revolution of the disk requiring more than a complete revolution of the earth. However, points A and B circle each other as the disk circles, and the plane of the pendulum shifts in the same way, both requiring longer than 24 hours to complete their rotation. As the disk is further enlarged in order to extend to lower latitudes, the circling motion becomes slower. Finally, at the equator, it is impossible for a disk horizontal with the surface of the earth to have its axis pass through it. In other words, the length of the circumference of the disk is infinite, and the circling motion is zero. The apparent deflection of the pendulum or of a current of water varies with the speed of rotation of the disk and its points A and B.\nThe Coriolis force is zero at the equator and maximum at the poles. Mathematically, the variation is proportional to the sine of the latitude.\n\n7.1.3 The Circulation Theory\nAny movement of water is affected by the earth\u2019s rotation. The length of time required for a complete rotation of the plane of a pendulum at any given latitude is called a pendulum day. The time required for a moving body at the same latitude to complete its inertia circle is one-half of this time or one-half a pendulum day. The reason for this may not be immediately apparent from the foregoing discussion. A more advanced treatment of the subject will be found at the beginning of Chapter XIII in reference 1, Chapter 1.\nFigure 8. Equilibrium that results when movements in Figure 7 are carried to completion.\n\nFigure 9. Effect of Coriolis force on water movements resulting from localized heating of the sea surface.\n\nIn constructing a theory to explain circulation principles, it's simpler, for the sake of clarity, to address each force individually. However, it's essential to remember that each step represents an ideal case, with minor exceptions, as actual water movements are influenced by all forces simultaneously. At the conclusion, it will be evident that they form a cohesive picture of the major current systems worldwide.\n\nFirst, Figures 7 and 8 illustrate the effect of density.\nThe surface water in a particular area on a non-rotating earth is heated until it is warmer than the water around and underneath it. Heating expands the water, causing the surface of the sea to be slightly elevated in the center of the warm spot. Immediately, the water begins to flow downhill in all directions away from the center. Colder and denser water then presses up against the warmer and lighter water, buoying it up. Circulation occurs as indicated by the arrows in the diagram, and it continues until there is an even distribution of density and pressure.\n\nThe earth\u2019s rotation causes all these movements to be deflected to the right (in the Northern Hemisphere). The result is a whorl of clockwise water movements spreading out from the warm center, as shown in Figure 8. Under ordinary conditions.\nThe circumstances causing this eddy of warm water can be expected to spread until density differences are equalized and the condition of Figure 8 is established. The process is retarded, however, by the tendency of water particles to be deflected more and more to the right, resulting in a movement that follows very nearly a circular path at the edge of the eddy. The sinking of cold or saline water produces a somewhat similar current pattern but in the opposite direction, as depicted in Figure 10. Diagram of water movements resulting from localized cooling of the sea surface.\n\nWhen surface water in a particular area is cooled sufficiently to make it denser than the water beneath, it will sink until it reaches a level of its own density. As it does so, the sea surface is depressed, and warm surface water flows in from all sides to take its place.\nThe Coriolis force causes these movements to form a counterclockwise whorl in the Northern Hemisphere, as shown in Figure 10. At first glance, these water movements appear to be deflected to the left rather than the right. However, Figure 11 demonstrates the movement of a water particle from the edge of the warm water (A) to the cold center. At each instant of its progress, A, Ai, Ao, etc., the direction of force is toward the center as indicated by the dotted lines, while the direction of movement, as modified by Coriolis force, is to the right of the direction of pressure.\n\nSuppose now the conditions of Figures 9 and 10 are combined in a continuous process. For example, the eddy of warm water is continually heated too rapidly for water movements away from the center to stabilize.\nThe density distribution must be fully realized. At a point on the eddy's periphery, the water is cooled just as rapidly as it was heated. Water will flow from the first point to the second. It is conceivable that Figure 11 shows the direction of pressure and the resulting motion, modified by the Coriolis force.\n\n(Principles of Ocean Circulation\nChapter 12. Movement of water between two localized areas, one of which is being warmed, the other cooled. A permanent eddy of constant size and shape will be established; this is the result of a balance between the force produced by the density distribution and the frictional resistance of the water to this force. This situation can be visualized diagrammatically in Figure 12, where point A is the center of heating.)\nThe warm water is cooled at point B. The water spreads out from A in all directions in the form of a clockwise whorl, as previously described, and then converges at B. As long as the rates of heating and cooling remain constant, the pattern of currents and the size of the eddy will also be constant. This condition of equilibrium is commonly known as a steady state. In parts of the eddy, the density distribution is in a permanently unstable condition, particularly near the edge where there is a sharp downward slope in the thermocline. In other words, the instability in density structure still generates pressure, which is directed outward from the center of the eddy in all directions. However, the water movements produced as a result of the pressure gradient do not increase the size of the eddy; instead, they take the excess pressure energy and convert it into kinetic energy of the circulating water.\nA clockwise course at its periphery is the extreme example of the application of Coriolis force. This force is proportional to the mass and velocity of the movement of water and acts at right angles to it. It exactly balances the pressure that induces water movements and is at right angles to the direction of pressure. Thus, when the presence of a permanent slope in the density surfaces indicates that a steady state has been attained, the current that is generated is always at right angles to the direction of pressure. In the Northern Hemisphere, an observer facing in the direction in which a current is flowing will observe density surfaces sloping downward to the right.\n\nThe balance between the pressure gradient and Coriolis force can be better understood by recalling the inertia circle described in the preceding text.\nA particle in motion not influenced by any lateral force takes a curved path due to the earth turning beneath it. The radius of the circle varies with velocity and the sine of the latitude. For a current of average velocity in mid-latitudes, this radius is approximately 15 miles. However, major ocean currents have a much larger radius of curvature, indicating they are under the influence of a lateral force deflecting them from the path of inertia. In other words, for water to flow in a reasonably straight path in the geographical sense, it must be acted upon by a component of gravitational force (the crosscurrent pressure gradient) which deflects it to the left in the Northern Hemisphere and to the right in the Southern Hemisphere, just enough.\nIn a general way, this description can be applied to ocean circulation. Weak density gradients extending over great horizontal distances are important in transporting tropical and subtropical water to polar regions. Within the major ocean currents, where steady-state conditions are approximated at least through parts of their courses, the flow is very nearly at right angles to the pressure gradient. However, the uneven nature of the processes that originate the currents leads to continuous variations in velocity and varying amounts of crosscurrent transfer, which shifts their position. Near the surface, the effect of pressure gradients is also greatly modified by the wind systems of the earth. Around each of the central basins of the oceans, the winds form a great anticyclonic eddy.\nThe trade winds and prevailing westerlies significantly influence ocean currents due to their force. The winds generate similar eddies in the ocean, as depicted in Figure 13.\n\nRestricted ocean currents result in the movement of water in these eddies being deflected to the right of the wind direction. This leads to a drift of water towards the center of the eddy, accompanied by a slight elevation of the sea surface where the water is converging. The unstable pressure distribution is compensated in two ways: (1) by a return drift toward the periphery of the eddy in the water beneath the wind-driven surface layer, and (2) by a general redistribution of density structure to equalize the vertical pressure. In essence, there is a tendency for readjustment of density surfaces to ensure equal pressure.\nThe underlying deep water caused by the weight of Atter above it is uniform, and any tendency to increased weight due to elevation of the sea surface is offset by an increase in depth of the relatively light mixed layer. Thus, the light water accumulates in the center of such a convergence, and the density surfaces slope toward the center from all sides, giving rise to a permanent lens-shaped body of warm water. This situation is stable only insofar as it is maintained by the force of the wind. If the latter ceased, the warm water would spread out in an even layer over the surface in the same manner as described in Figures 7 and 8. In this respect, it is similar to an eddy of warm water maintained by surface heating, which, as has been seen, is permanent only by the action of an external agency.\n\nThe similarity does not end there, however. In addition:\n\nThe behavior of the warm water in the Gulf of Mexico is similar to that in the Mediterranean Sea. In both cases, the deep water is dense and cold, and the surface water is warm and light. The density surfaces slope toward the center from all sides, creating a permanent lens-shaped body of warm water. This situation is known as a \"warm pool.\"\n\nThe formation of a warm pool is influenced by several factors, including wind patterns, ocean currents, and the shape of the basin. In the Gulf of Mexico, the prevailing winds blow from the east, pushing the warm surface water toward the western part of the basin. At the same time, the deep water circulates upwards near the edge of the continental shelf, bringing cold water to the surface. This upwelling of cold water cools the surface water, creating a stable boundary between the warm and cold water.\n\nThe shape of the Gulf of Mexico also plays a role in the formation of the warm pool. The basin is roughly semicircular in shape, with a diameter of about 1,250 miles. The deep water in the center of the basin is about 12,000 feet deep, while the surface water is only a few hundred feet deep. This large vertical difference creates a strong density gradient, which helps to maintain the stability of the warm pool.\n\nDespite its stability, the warm pool in the Gulf of Mexico is not completely static. Small disturbances, such as tropical storms or changes in wind patterns, can cause the warm water to spread out over the surface or sink deeper into the basin. These disturbances can have significant impacts on the climate and weather patterns in the region.\n\nIn summary, the formation of a permanent lens-shaped body of warm water in the Gulf of Mexico is a complex process influenced by wind patterns, ocean currents, and the shape of the basin. While the warm pool is stable under normal conditions, it can be disrupted by various factors, leading to significant impacts on the climate and weather patterns in the region.\nEach case involves an elevation of the sea surface and deformation of density surfaces, resulting in the development of a pressure gradient that in turn produces a current flowing at right angles to it. The difference in density between the warm water above and the older water below, the slope of the thermocline (as influenced by latitude), and the velocity of the current produced are all interrelated. This relationship can be expressed by a mathematical formula, so that by measuring the vertical density structure of ocean waters, it is possible to determine the direction and velocity of currents. Current systems are commonly studied in this way, as actual measurements of the currents are extremely inaccurate unless the vessel is equipped for anchoring in deep water, and even then they are difficult and laborious.\nThe  principle  of  determining  ocean  currents  from \nthe  density  structure  of  the  sea,  Avhich  is  generally \nknoAvn  as  the  Bjerknes  Circulation  Theory,  is  one \nof  the  most  important  contributions  to  modern \noceanography. \nBut  as  indicated  above,  Avhile  the  mathematical \nrelations  of  currents  Avith  the  density  structure  of  the \nAvater  are  ahvays  about  the  same,  the  causal  relation\u00ac \nships  are  often  inextricably  mixed.  The  Avind  may \nset  iqj  a  current,  and  the  transport  that  results  Avill \ncause  the  density  surfaces  to  slope.  ContrariAvise,  den\u00ac \nsity  slopes  that  result  from  heating  or  cooling  proc\u00ac \nesses  Avill  cause  a  current  to  be  formed.  Often  both \nprocesses  are  iiiAolved,  and  some  of  the  most  poAver- \nful  ocean  currents  are  tho.se  in  Avhich  the  prevailing \nAvinds  and  the  density  distribution  Avork  together. \nWind  Transport \nIn  the  open  ocean  many  of  the  permanent  currents \nThe text primarily moves in the same direction as prevailing currents, which are predominantly driven by winds. It is evident that these currents are deep and powerful, and they possess significant momentum. However, fundamental questions, such as how long a wind must blow before a current is established and in what direction it will flow, must be addressed largely on the basis of theory. As satisfactory field studies have not been conducted, the classical theory of wind currents was initially based on mathematical calculations. Although it has since been refined and modified, it is best to begin by discussing it in its simple form. The theory assumes a limitless, deep ocean with no change in density with depth. The wind's force sets up a drift current in the surface waters.\nThe Avater, once set in motion, is acted upon by the Coriolis force. When steady-state conditions are reached, the resultant current at the surface is 45 degrees to the right of the wind direction in the Northern Hemisphere and to the left in the Southern Hemisphere. The Avater below the surface is dragged along by friction, with velocity decreasing with increasing depth, and the direction of motion swinging more and more to the right. This is the Ekman spiral (Figure 14), named after its author. If the degree of frictional drag, or eddy viscosity, is constant with depth, as assumed in the calculations, it can be mathematically shown that the net transport of the wind-driven surface layer will be 90 degrees to the right of the wind (in the Northern Hemisphere). It is believed that this occurs.\nA sort of motion becomes established within about 12 hours of a steady wind. Earlier, the flow would be more nearly in a diverging direction.\n\nRESTRICTED\n\nPRINCIPLES OF OCEAN CIRCULATION\nFigure 14. Diagram illustrating the Ekman spiral.\nRESTRICTED\n\nOcean currents are complicated by the fact that wind transport is always accompanied by wave transport. Furthermore, it is associated with a considerable amount of vertical turbulence, frequently with the formation of convection cells of the kind described in Section 5.2.1, which produce some mixing to the bottom of the isothermal layer. Moreover, it has been observed that in the convergences of convection cells, surface water moves downwind at a considerably more rapid rate than in the divergences. This can sometimes be seen on a cold day by observing the movement of surface water.\nThe uneven flow of water in response to wind and vertical motions in the convective layer make it clear that mathematical assumptions oversimplify the actual movements of water in the wind-driven surface layer. When water is transported by the wind, other water takes its place, forming compensating currents. Ahead of the current, water is pushed forward and piled up, causing a slight elevation of the sea surface and a depression of the thermocline to the right of the wind. This results in the development of a deeper current, known as a gradient current, which flows at mid-depths parallel to the wind direction and below the Ekman spiral.\nFor the present purposes, what is particularly important to subsurface warfare is not so much the question of the exact direction of flow or velocity, but rather a general understanding of how local variability of the winds can transport the following:\n\nThe deflection of surface water from the downwind direction is reduced by approximately half the 45 degrees called for by the simple theory in a steady state. In the trade wind belts, at least, it is possible to demonstrate that the current at the surface is at an angle of roughly 15 to 20 degrees to the right of the wind.\nSurface water and sometimes carry warmer water over colder and vice versa, thus radically affecting sound conditions. Wind transport and the associated gradient currents may in some cases move considerable masses of the warm surface layer, piling it up and thickening the isothermal layer (convergence), or spreading it out and reducing the amount of mixed water (divergence).\n\nThe effects in the open ocean of convergence and divergence on a large scale are evident on the summer-season sonar charts (see Figures 9 and 10 in Chapter 5). In the latitude of westerly winds, for example, sound conditions are generally better on the lee side of the ocean than on the windward. Similarly, in the trade wind belt, sound conditions in the west are relatively good, for example in the Caribbean.\n\n72 Major current systems of the Earth.\nFigure 15 is a chart of the major surface currents of the oceans. For the most part, their position shifts only slightly with the seasons, except in the northern part of the Indian Ocean and along the China coast where the direction of their flow is actually reversed. Here they are shown in their midwinter position. If Figure 15 is compared with previously published current charts, a marked difference will be noted. Most current charts show the average direction and strength of all available drift measurements for each small area of the ocean, usually supplemented by inferences from the more numerous wind observations. As a result, they make the currents appear broad and diffuse and closely dependent on prevailing local winds. It is not always easy from such a chart to distinguish clearly between the central portions of the currents.\nmajor eddies are areas where the direction of drift is relatively haphazard, and the edges of those eddies are where one finds true currents involving significant transport in a nearly constant direction and enough momentum to leave them unchanged by occasional periods of opposing winds. Figure 15 attempts to show by continuous lines where the direction of flow is most persistent, and to group these lines into bands outlining the edges of eddy movement to indicate where the currents are most clearly defined. The spacing of the lines cannot, however, be taken as an exact measure of constancy or of speed, and it should be noted that the Mercator projection makes them appear widely separated in the AVT Wind Drift, which is actually a fairly strong current. The courses and speeds of the currents at the surface are:\nFace to face are well known through ships' observations, and oceanographers have studied the flow at greater depths, partly by direct observation and to a larger extent by determinations of the density structure. The velocity of the currents is greatest near the surface where in a few places they reach a speed of 3 or 4 knots. The greatest depth at which a significant amount of flow can be detected varies with each current and in different parts of the same current, but in general:\n\n17. Prevailing winds in Angstrom: The wind-driven equatorial and meridional circulation, and sidestream convergence.\n18. Diagram of topical ocean circulation, wind-driven gyres and sidestream convergence.\n\nThe velocity of currents is greatest near the surface where it reaches a speed of 3 or 4 knots. The greatest depth at which a significant amount of flow can be detected varies with each current and in different parts of the same current.\n\n17. Prevailing winds in Angstrom:\nThe wind-driven equatorial and meridional circulation, and sidestream convergence.\n\n18. Diagram of topical ocean circulation, wind-driven gyres and sidestream convergence:\nDepths, partly by direct observation and to a larger extent by determinations of the density structure.\nSome cases, this depth is greater than a mile. It is therefore that the larger currents carry huge volumes of water. For example, the total transport of the Gulf Stream in the latitude of Chesapeake Bay is approximately 100 million tons a second.\n\nIn examining the currents, it is worth comparing them with the wind systems of the world (Figures 16 and 17), which are similar in many respects and are to a large degree responsible for the general pattern of the currents. This is particularly true of the west wind drift in the Antarctic and of the North and South Equatorial Currents, which lie in the trade wind belts. The latter currents form part of the great eddies centering in mid-latitudes, clockwise in the Northern Hemisphere, and counterclockwise in the Southern, corresponding to the prevailing wind directions.\nThe currents are primarily wind-driven and are swiftest at the surface. In the main thermocline and the upper part of the deep water layer, horizontal eddy-type motion gradually decreases with depth, giving way to slower deep water transport. These eddies take the general form described in the preceding section, and together with sinking centers in higher latitudes, they set the dominant pattern of the current systems in each ocean basin. Figure 18 is a diagrammatic representation of the circulation scheme, showing the density structure and the direction of the currents in a combined wind-driven eddy and sinking center.\n\nIt is important to consider the density structure of the oceans in relation to the currents, as it is not only essential for proper understanding of the subject but also has practical implications.\nFor the purpose of echo ranging, this discussion refers to previous figures (9 and 10, Chapter 5). These figures show layer depth contours taken from sonar charts for December to February and June to August. They provide a superficial picture of the density distribution of the sea, but are adequate for the present purposes. Winter conditions, as depicted in Figure 9 (Northern Hemisphere) and Figure 10 (Southern), are particularly useful for examining the density structure in relation to currents.\n\nIn the eddy currents centering in mid-latitudes, the density surfaces slope downward to the right in the Northern Hemisphere and to the left in the Southern Hemisphere, as expected according to theory. Thus, in the center of the eddies, layer depths are greater than around the outer edges of the currents, and winter sound ranges are correspondingly better.\nThe edges of the current are where warm water is often found as a shallow wedge over colder and less saline water. This condition is further demonstrated by bathythermograms of the Florida Current and the Culf Stream further north (Figures 19 and 20). The negative temperature gradients at the edge of the current make echo ranging conditions poorer than they are in the main body of the current to the right or in the colder slope water to the left. With northerly or westerly winds, the slope water is forced to overlap the warmer and more saline Culf Stream water, disrupting the normal temperature structure, producing temporary positive gradients, and setting up eddies that lead to complex and variable temperature conditions. For all these reasons, the edges of such a current are poor and variable from the antisidernite standpoint.\nFig. 19. Series of bathythermograms across the Florida Current.\n\nOcean Currents, Coastal Slope, Water Gulf Stream, Water\n\nFig. 20. Series of bathylithograms across the Gulf Stream.\nIll. Slimmer (Southern Hemisphere, Figure 9; Northern, Figure 10 of Chapter 5) the development of the seasonal thermoclines obscures this general picture of density structure in the central basins, as shown in the sonar charts. The current systems and their relationships to the main thermocline are approximate. They do not improve sound ranging conditions in the center of the great eddies, as well as in the waters beyond the edge of the currents. Where the current is strongest, the turbulence developed aids the vertical distribution of heat, hence the best sound ranging conditions in the summer are there.\nWithin areas where there are currents, this is particularly true of currents that are partly or largely wind-driven. Sonar conditions are also good in places such as the Florida Straits, where the wind is light and variable in summer and does not significantly affect the current. Within the North and South Equatorial Currents, the density surfaces slope down toward the north in the Northern Hemisphere and to the south in the Southern Hemisphere (Figure 21), and water is transported not only westward but also away from the equator on both sides. Therefore, where these currents border the equatorial doldrums, the thermocline is shallow, and hence echo ranging conditions are relatively poor in the doldrums. At the same time, the steady blowing of the trade winds influences these currents.\nThe exerted stress on the sea surface raises it slightly in a westward direction along the equator. The equatorial countercurrents are formed in the doldrums where the winds maintaining the slope are absent. In the subarctic regions of both the Atlantic and Pacific oceans, a group of counterclockwise currents is set up around the sinking centers. The depression of the density surfaces and the thickening of the mixed layer accompanying these convergences create favorable conditions, except when strong winds interfere or when lateral eddies between water masses of different temperatures and salinities produce confused negative and positive gradients. In the Southern Hemisphere, sinking of surface water occurs.\nWater clered from the tropics also occurs, but because of the strong circumpolar currents caused by the prevailing westerly winds and unimpeded by the presence of land masses as in the Arctic, sinking occurs in a more or less continuous band at a latitude of about 50 to 60\u00b0 S, rather than in localized centers. From this convergence southward, layer depths are almost invariably great enough for good echo ranging, but the effective sound range is frequently reduced by strong winds. The active differences in density in the convergences are generally slight, and while presumably a certain amount of sinking of heavier water occurs all the time in one part of the area or another, it seems justified that it is a highly variable phenomenon, much influenced by local water movements and weather. Ordinarily, sinking occurs at the boundary.\nBetween two water masses of slightly different temperature and salinity, pronounced downward movement of water is favored by a wind that transports heavy water over a mass of lighter water, or by cold, calm weather that permits considerable masses of stable water to develop at the surface before they sink.\n\nNo measurements have been made of the downward currents that result.\n\nMajor Current Systems of the Earth\n^ South Equatorial Current Equatorial Counter Current North Equatorial Current\n^ (Flows West) --- (Flows East) --- (Flows West) -\n\nFigure 21. Profiles showing isolations across the equatorial currents in the Pacific. Their size and shape are roughly indicated, but their existence has been observed from surface vessels. Sinking ordinarily occurs in a hand.\nA few yards wide and perhaps several miles long, the choppy appearance of the ft has the turbulent look of a tide rip. It may be full of seaweed and other debris brought into it by converging surface currents. The downdraft is strong enough to carry down debris of slight buoyancy, and the surface currents may be strong enough to hold a drifting vessel in the convergence despite of a crosswind. Such convergences are probably important from the standpoint of operations. Submariners use the term \"fresh pocket\" for a place where the vessel suddenly and for no obvious reason begins to sink and requires reballasting. This can happen any time a submarine goes too near the lower limit of a supporting density gradient. Varying thickness and amount of temperature change in the thermocline is no doubt responsible for some of the instances.\nPorted. On the other hand, sometimes the submarine sinks very rapidly and checks its descent with great difficulty and at a dangerous depth. In such a case, it may have encountered a convergence in which not only is there no increase in density with depth, but also there is a downward current of water comparable to downdrafts in the air that cause airplanes to lose altitude. From what is known about the shape of these convergences, it seems likely that a submarine held in one for any length of time has come into it on a nearly parallel course and should therefore change course about 90 degrees to escape.\n\nChapter 8\nLOCAL VARIABILITY\nWINDS AND WAVES\nHeat the great permanent wind-driven currents occur only in those areas of the oceans where winds blow fairly constantly in one direction. Local variations, particularly in latitudes where there is a succesful sea-current, cause the water to move in complex patterns.\nThe cession of low- and high-pressure areas with constantly shifting winds does not lead to pronounced transport. When, as frequently happens, permanent currents traverse such areas, it is only by virtue of their hydraulic head. Local winds do not appear to be very effective in producing convergences and divergences, even on a small scale. In the open ocean, the pattern of winds around a moving low-pressure area, in theory, causes divergence, that is, a lessening of the thickness of the warm surface layer near the center of the wind system. However, as a low-pressure area passes, the winds usually increase in strength. Perhaps the two effects cancel. At any rate, in looking over the summer bathythermograms, one does not gain the impression that gradual variations in the thickness of the wind-stirred layer are produced by passing wind systems.\nA more obvious effect of winds is to transform horizontal temperature gradients into vertical gradients. Because the temperature of the wind-stirred surface layer increases gradually from north to south in the Northern Hemisphere, a southerly wind often causes warmer water to overlap colder water. The opposite is not so often true, unless the horizontal gradient is very sharp. A north wind is usually a relatively cold wind and therefore effective in maintaining a deep mixed layer. In any case, unless there is also a horizontal salinity gradient, a north wind would tend to produce an unstable situation.\n\nOf much greater practical importance is the effect of local winds on waves and vertical mixing. Areas where winds are variable are also variable from the standpoint of echo ranging. During occasional violent wind conditions, the wind-generated waves can significantly affect the vertical mixing in the water column.\nThe state of the sea is influenced by various factors, including the wind's velocity, the length of time it has been blowing, and the fetch (the distance upwind that the speed and direction remain consistent); whether the wind is rising or falling; and the temperature of the air and the difference in temperature between the air and the water. In mid-latitudes, conditions are generally poorer due to frequent storms reducing echo ranges and more calm weather with afternoon effect and shallow mixed layers. Conversely, conditions are better in regions such as the trades, where steady, moderate winds prevail. However, they are generally worse in polar regions, where gale-force winds interfere with echo ranging most of the time. Overall, the sea's condition depends on the wind's velocity, duration, and fetch; whether it is rising or falling; and the temperature difference between the air and water.\nThe velocity of the Wind is by far the most important factor. The average seasonal and geographic variations of the Wind force are well known, and climatic atlases summarize the information in a more or less convenient form. Figures 1 and 2 show the frequency of Winds stronger than force 6 (Beaufort) in winter and in summer. The incidence of strong Winds, as well as the temperature gradient near the surface, is considered in preparing the Perspective-Depth Range Sonar Charts.\n\n82 Eddies\nCurrents flow through eddies, which vary in size from a few miles to perhaps 75 miles in diameter. Large ones are common on either side of the Gulf Stream between Cape Hatteras and the Grand Banks. North of the current, the eddies contain relatively warm water near the surface and are easily detected.\nTo the south of the Gulf Stream are Avater eddies, only slightly warmer than that already in the Ionian area, but the larger of these eddies can be made out from the trend of the deeper isotherms. From the acoustical standpoint, the edges of eddies are much the same as the edge of the current itself. A shallow layer of one temperature will be found overlying a layer of some other temperature.\n\nThe length of time such eddies persist and retain their thermal characteristics near the surface is not well known. Large eddies near the Gulf Stream are known to have persisted for more than a month.\nFigures in Fahrenheit:\nFigures, 3. Bath) illustrate internal waves. Lace velocities when they first form may be as much as 2 knots. Presumably, smaller eddies have much less momentum and soon die, or at any rate, their surface characteristics are soon destroyed by wind stirring. However, this may be, eddies are a potential source of poor and variable sound conditions.\n\nEddies have seldom been fully delineated. Usually, a single line of temperature observations crosses what might be a roughly circular core of warmer water or a tongue of warmer water extending back to the source.\n\n83. INTERNAL WAVES:\nThe waves hitherto considered have been displacements of the surface of the sea. However, waves can occur not only in the air-water boundary but also in the interface between strata of water of different densities.\nThe internal waves observed in the main and seasonal thermocline have been noted for their impact on subsurface warfare. Their effect on sonar performance is not yet fully investigated, but they are known to contribute to some observed variations. The difference in density above and below a thermocline is much less than that between air and water at the ocean surface. Consequently, a boundary within the ocean can be more easily displaced, and the waves in the boundary possess less energy. Theoretical considerations, summarized in a memorandum by C. Ufford of TC1I\\VR, dated May 1, 1945, provide most of the information in this section.\nSuch waves exist in the ocean and their properties can be predicted. The waves have their greatest height at the interface between the two layers, and their amplitude diminishes rapidly above and below it, approaching zero at the surface and bottom of the ocean. The theory also shows that internal waves can be formed not only at a boundary where density changes abruptly but also in water in which the change is more gradual. However, there are no internal waves in homogeneous water where the density does not change with depth. The presence of internal waves in the ocean, both theoretically and factually, has been proven by measuring the variation with time of temperature, salinity, and oxygen content at various depths. Before the war, measurements were made using sample bottles and reversing thermometers from an anchor.\nA slowly drifting or chored ship. Each lowering required an appreciable time, resulting in over an hour and sometimes up to two hours between successive lowerings. This method could only detect long period waves. Internal waves with periods of 24 and 12 hours, corresponding to tidal periods, and heights of up to 300 feet were found. There was some evidence of waves with shorter periods, but the periods found by this method had to be at least as large as the interval between successive lowerings. To determine if there were waves of shorter period, it was necessary to make lowerings in much more rapid succession. The bathytelograph (BT) provided a greatly superior instrument for this purpose. Series of lowerings every two hours.\nMinutes for as long as 24 hours have been recorded. Figure 3 shows fetv bathythermograms from such a series, displaying the types of variations obtained. It is convenient to represent these waves graphically as a depth curve with a constant temperature, plotted against time. In an ocean with no internal waves, these lines would be straight and horizontal; however, due to the irregular raising and lowering of the layers by internal waves, the lines are moved and represent the form of the waves. One of these 24-hour series, shown in Figure 4 without small-scale features, is characteristic of all the records obtained off San Diego. The tidal period is evident in the long curve receding the tidal period (II) in Figure 4B.\nThe curve of the tidal period is sidetracked in the short period curve, resulting in waves as shown in Figure 4C. In addition to the lowering of bathymetrics from surface ships, observations made aboard a submarine revealed that its depth varied periodically while balanced on a seasonal thermocline, indicating the existence of internal waves with periods of 8 to 10 minutes and heights of about 20 feet. These observations are detailed in the summary (on page controlling). On another occasion, in experiments off San Diego, a submerged submarine ran through internal waves, maintaining a constant depth with its planes, and recorded periodic temperature variations at that depth. Calculations based on these observations indicated that the period of the waves was about 5 minutes and the largest height was 28 feet.\nExperiments have been made to find the velocity and length of internal waves. This requires making BT lowerings simultaneously from at least three positions on the same ship or from three ships anchored in a triangle. The results of measurements made thus far suggest that the waves travel with a speed of about half a knot and have wave lengths of about 250 yards. Figure 5 shows a set of observations made aboard a single ship with BR installations at the bow, amidships, and at the stern. The order in which the curves on the figure progress indicates that the waves came from the direction in which the ship was heading and passed under the three installations successively.\n\nPractical consequences of internal waves in local time.\nI. Five. In this session of the IUCM, it is demonstrated that hydrostatic pressures exist simultaneously at various positions on a slip.\n\nFk.CRI. One. Intermediate waves are illustrated by plotting the depth of an isotherm against time. The sweep of the curve. Shorter period waves are superimposed upon the waves of long tidal period. The first section of the curve of Figure 4 A is reproduced on a larger scale in Figure 4B, which shows the shorter period waves oscillating around the average.\n\nMicrostructure of submarine operations are discussed in the summary volume on diving. The very important acoustical consequences have only gradually and quite recently become apparent.\n\nWith the passage of each internal wave, the depth of the nearly isothermal surface layer varies. Due to changes in both layer depth and the strength of the stratification.\nThe underlying negative gradient can be expected to vary, thus internal waves are one cause of instability in maximum ranges, although not a particularly serious one. It would not be surprising, for example, to find that the range on a submarine below layer depth varied 200 or 300 yards from one attack to the next due to the effect of an internal wave. However, variations much greater than this would be fairly common. Over a period of several hours, the variations in maximum range caused by oscillations of layer depth would not be greater than those produced by other variables such as submarine aspect. Occasionally, as the crests or troughs of the longer period (12 hours or so) waves passed, the sound conditions might change significantly. However, under operating conditions, horizontal temperature gradients could have an equal effect.\nIt is probable that internal waves affect sound transmission in yet another way. Every sound operator and antisubmarine warfare officer is aware of the great variability in the quality of submarine contacts which cannot be readily explained by the routine BT classification. One attack may be spoiled by lack of information due to the intermittent and mushy quality of the echoes, and the next attack, under apparently identical conditions, may be a good one. Theory suggests that internal waves may be at least partly responsible for such variability. The simple refraction theory is based on the assumption that temperature strata are essentially horizontal out to the limit of sound beam penetration. This assumption is obviously not correct when internal waves are present.\nAs the sound Ijeam travels nearly horizontally at or near layer depth, there will be regions behind each AvaAe in the surface of the thermocline where little or no sound strikes the thermocline, since it has been deflected by striking the slope of the Avave facing the projector. This means that sound is removed from parts of the sound field where it would appear if the thermocline were entirely level. On the other hand, internal waves could in some cases account for the penetration of sound into areas where the simple reflection theory would not predict a shadow zone. As the internal waves progress, all these effects will contribute to the availability, which is one of the most striking characteristics of the sound field.\n\nAttempts to measure very small-scale thermal structure in the open ocean are beset with very great difficulties.\nThe rolling and pitching of the ship, and saving of the thermometer on its cable are only a few of the obstacles that must be overcome to distinguish between vertical and horizontal gradients. Nevertheless, there is a good deal of indirect evidence that small but sharp temperature gradients exist in the water which may serve to scatter sound.\n\nIn the first place, even the BT, crude as it is for studying small-scale thermal structure, occasionally shows surprising detail, reproduced in both the up and down traces, and therefore vertical structure. Figure 6 is a magnified reproduction of BT traces taken in Guantanamo Bay, Cuba, which shows pronounced development of successive strata of water, each with a relatively uniform temperature and separated from the next by a sharp discontinuity.\nIdle loiterings avere made slowly on a hand-line, paid out from a dinghy, in order to record the temperature with the greatest possible accuracy and freedom from vibration. In each figure, the doaru trace is on the right and the iqi trace on the left. Failure of the traces to coincide is due to lag in the thermal response of the instrument and to the fact that it avas handed in more quickly than it was paid out, which tended to smooth the temperature traces. Nevertheless, there is sufficient agreement in each pair of traces to leave little doubt that valid measurements of vertical structure avere obtained. Measurements of vertical sound accelerity gradients reveal small-scale variations, which are presumably largely due to temperature changes and therefore are indicative of thermal microstructure. The observations.\nThe method used did not exclude the possibility that part of the recorded variations were caused by instrumental oscillations or horizontal gradients. However, comparison of down and iqi traces shows that some vertical micro-structure existed. However, its accuracy as a means of studying microstructure lies not in its precision but in the fact that it is a concrete demonstration of the existence of small-scale variations in velocity within the sound field, which can be partly responsible for variability in sound transmission.\n\nAttempts to measure small-scale horizontal structure have not been very successful, although it is fairly clear that near the surface convection cells,\n\nLocal variability\nDegrees Fahrenheit Degrees Fahrenheit\nFigure 6. Illustrating microstructure.\n\nThe interest in this work does not lie in its accuracy as a means of studying microstructure but rather in the fact that it is a concrete demonstration of the existence of small-scale variations in velocity within the sound field, which can be partly responsible for variability in sound transmission.\n\nAttempts to measure small-scale horizontal structure have not been very successful. However, it is fairly clear that near the surface convection cells,\nWhen well developed, must cause such thermal structure. The temperature increase has been measured between depths of 3 and 20 millimeters and has been found to be as much as 1.8 F, averaging about 0.8 F. This gives some idea of the maximum degree of thermal instability that can arise through surface cooling and of the maximum amount of horizontal variation that might be expected when the surface water drains into the convergences of convection cells. Thus far, no accurate measurements have been made of the temperature differences within these convergences. However, in horizontal temperature measurements at various depths, some evidence has been reported of small-scale cyclical variations of around 0.02 degrees occurring about every ten yards in waters investigated off San Diego, as well as occasional larger ones.\nDiscontinuities of the order 0.5 degree. The acoustic effect of microstructure has not been measured accurately yet. Qualitatively, it is fairly obvious how it affects sound transmission. A step-like thermocline of the kind pictured in Figure 6 is in reality a series of little thermoclines of varying degrees of steepness. Moreover, they are not horizontally continuous throughout the entire sound field because every BT lowering shows a slightly different pattern. The combined effect is that the individual refraction paths of sound rays are highly variable, leading to irregular variations in intensity within the sound field. Probably, microstructure is one of the more important causes of varying intensity from one echo to the next, as contrasted with the internal waves previously discussed, which would be more likely to produce larger scale fluctuations of a more significant nature.\nChapter 9: Coastal Waters\n\nThe vertical structure of the water column is significantly different near most continental coastlines compared to the open ocean, particularly in areas with broad continental shelves, numerous rivers, or prevailing offshore winds. In general, the situation in coastal waters is more pronounced in one or more of these ways. Vertical gradients of temperature and salinity are often more marked than offshore, and seasonal changes are typically greater as well. The 100-fathom contour roughly demarcates the boundary between coastal and offshore water, although in special circumstances, water of coastal origin can be encountered 100 miles or more beyond this boundary.\nThe limits of the continental shelf. The currents in coastal waters, caused by density gradients and local winds and tides, are complex and interesting oceanographically and highly important from a practical standpoint, both in navigation and in echo ranging. The type of bottom also influences whether sound ranges will be improved by multiple reflections or will be shortened by masking reverberation.\n\n9.1. Coastal Circulation\n9.1.1. Density Currents\nBecause of land drainage, the density of coastal water is usually less than at corresponding depths offshore. Along any coast where there is a significant amount of freshening due to land drainage, there is a general tendency for the fresh water to move offshore on the surface and the denser (more saline) water to move in underneath. Thus, the salinity of the coastal water is influenced by this process.\nThe surface water increases from the shore outwards, and there is an increase in salinity from the surface downward. This is an unstable condition as the density surfaces slope downward in an onshore direction, causing unequal pressure to give rise to currents that generally behave according to the principles of the circulation theory.\n\nSince the density surfaces slope downward toward the shoreline, the direction of the currents is roughly parallel to the coast, with the coast on the right-hand side of the direction of flow in the Northern Hemisphere and on the left-hand side in the Southern Hemisphere.\n\nAs a result of this prevailing situation, in the Northern Hemisphere, coastal currents on the west side of the oceans are usually south-flowing and therefore relatively cold, as shown in Figure 1.\nA temperature gradient exists across the Labrador Current. Observations were made in spring, and seasonal warming had influenced the surface water. However, this did not conceal the fact that water close to the shore, which had originated from the north, was significantly colder than water further offshore. Figure 1 depicts a temperature profile across the Labrador Current. Figure 2 illustrates a salinity section of the same water. Salinity is least near the shore and at the surface. Salinity is responsible for the density gradient that drives the current, as the inshore water, from a temperature standpoint, would be denser rather than lighter. Along the eastern coastlines, coastal density currents typically flow northward and are therefore warmer than offshore water. Thus, both temperature and salinity contribute to the Labrador Current's flow.\nTruth and salinity contribute to the density gradient between inshore and offshore water. Exceptions to these general statements occur where the continental shelf is narrow and where little river water is brought down to the sea. In such cases, local winds and seasonal variations in rainfall are important in determining whether or not a typical coastal current will develop. For example, on the east coast of the United States, there is a well-developed coastal current as far south as Fort Pierce, Florida. Beyond that point, the shelf narrows rapidly and the coastal current, known as the Florida Countercurrent, becomes weak and sometimes very nearly nonexistent. The coastal water off Miami is slightly cooler than the northward flowing Florida Current offshore (see Figure 19, Chapter 7). It is also slightly fresher, enough so that the countercurrent generally flows in the opposite direction.\nThe Florida Current flows during the wetter months of the year. During the spring and summer months, however, steady southeasterly breezes carry the Florida Current close inshore, and the coastal current is either obliterated entirely or driven below the surface where it can be detected only by the BT or by other subsurface sampling methods. A similar situation occurs off the California coast. Figure 3 shows the oceanic California Current flowing well offshore and the coastal current known as the California Countercurrent which flows northward closer inshore. The latter is typical in that it is a warm, north-flowing current, but the temperature difference is slight, and there is not enough coastal drainage to produce a significant salinity gradient. Therefore, it is weak and diffuse, permitting the development of still another current.\nThe countercurrent flows close to the inshore area, as shown in the figure. During the summer, when the prevailing winds are offshore, the coastal current occurs only in the surface waters and is replenished at the surface by a complex circulation resulting from upwelling. The extent to which a current parallels a coast depends to a considerable extent on the difference in density between inshore and offshore water. When the density difference is slight, the current may be influenced onshore or offshore. The directions it takes will be dependent to a large degree on bottom topography. Frictional retardation by bottom particles in contact with a current not only affects its velocity but also its direction. The normal twisting to the right (in the Northern Hemisphere) is accentuated as the current flows.\nmoves over a shoaling bottom and is lessened over a deepening bottom. When the water is relatively homogeneous, it is common to find an inshore set towards reefs and inlets (Figure 4).\n\n- Local Wind and Tidal Currents\nAn onshore wind causes surface water to be transported towards the land, resulting in the surface layer thickening near the beach. An offshore wind removes the warm surface layer and the underlying thermocline approaches the surface. This process is called upwelling, although the term is somewhat misleading as little vertical motion is involved.\n\nWhere steady offshore winds prevail, as in the trade wind belt, upwelling may be a more or less continuous phenomenon. The mixed surface layer is carried offshore by the wind as fast as it is formed.\n\nFaces are the African coast in the region\nAlong the Dakar and Gulf of Panama, and to a lesser extent on the lee side of islands in the trade wind belt, similar conditions occur. Along the east coast in higher latitudes, upwelling may occur as a residual of strong offshore gales in winter. Oceanographic stations made in February on a line across the Nova Scotian continental shelf showed a mixed surface layer only about 100 feet deep overlying much warmer and more saline water. The strong positive gradients thus produced would give a deep submarine layer almost complete protection against sonar detection. While no other winter temperature observations are available from this area, it is believed that normally a much deeper isothermal surface layer would be found with positive gradients confined to the outer third of the continental shelf.\nThe situation further south is explained by relatively shallow and sharp positive gradients off Halifax. A possible explanation for these gradients is that strong offshore coastal circulation winds recently removed much of the superficial layer from the continental shelf and replaced it with a deep indraft of warmer and more saline oceanic water.\n\nOn a broad continental shelf, such as off Halifax, bottom friction and the strong southward flowing coastal current typically combine to prevent all coastal water from being blown out to sea by prevailing offshore winds. However, a certain amount of upwelling must occur. Where the continental shelf is narrow and the coastal current is weak due to lack of land drainage, offshore winds will be much more effective in decreasing the depth of the mixed surface water.\nlayer  close  to  the  coast  and  thus  reducing  the  effec\u00ac \ntive  echo  range. \nThe  converse  to  upwelling,  the  accumulation  of \nwarm  surface  water  near  a  coast  by  an  onshore  tvind, \nimproves  sound  conditions  and  is  equally  common. \nIt  is  a  special  case  of  convergence,  just  as  upwelling  is \na  special  case  of  divergence. \nTides  are  a  form  of  wave  motion,  and  as  such  their \nbcha\\  ior  is  in  many  respects  similar  to  that  of  wind- \ndriven  waves.  In  the  open  ocean  where  the  height  of \nCOASTAL  WATERS \nFiciiRi;  -}.  Configuration  of  surface  currents,  Xewfouucl- \nlaiul  area. \nthe  wave  is  less  than  3  feet  and  its  length  several  hun\u00ac \ndred  miles  the  orbital  movement  of  water  particles \nin  the  wave  extends  to  the  bottom.  The  mass  transfer \nof  water  inxolved  in  this  movement  is  large,  but  the \nhorizontal  displacement  of  individual  particles  is \nsmall.  However,  as  the  wave  approaches  shoaling \nThe horizontal components of flow are greatly increased due to the decreasing cross-sectional area. The resulting tidal current is accompanied by a shortening of the wave length and an increase in the height of the tide.\n\nIn a restricted area such as a channel, tidal currents generally flow back and forth, reversing direction with each tidal period. In more open shallow waters, tidal currents have a rotary motion, which is apparently an effect of the earth\u2019s rotation. The direction shifts around the compass during each tidal period (generally every 12 hours), and any given water particle in the tidal stream describes a roughly elliptical course.\n\nGeorges Bank off the Gulf of Maine is an notable example of the effects of strong tidal currents. Immediately north of this bank in the deeper waters of the Gulf of Maine, there is a pronounced difference.\nThe seasonal cycle exhibits well-established vertical stability (Figure 17). To the south lies a typical slow water area (Figure 40, Chapter 5). However, stability develops only briefly and intermittently within the 5-fathom contour on the bank itself, during a short summer season when winds are light for several days at a time. At all other times, tidal stirring and winds keep the water column mixed from surface to bottom. Consequently, relatively low surface temperatures are encountered over the bank in summer. This, of course, explains the widespread reputation of Georges Bank for fog. Another result of the strong tidal stirring is that near the edges of the bank rather special hydrological conditions are found, where the mixed waters of the bank are in contact with the stable waters surrounding it.\nFigure 5 shows the temperature profile across Georges Bank in a northwest-southeast direction in June 1939. The sound conditions, provided reverberation is not limiting, are markedly better over the bank than on either side. A submarine crossing such an area would find that trim for resubmergence would alter significantly. Tides and variable winds affect the speed and direction of coastal currents. As their velocity varies, more or less crosscurrent transfer takes place. This is usually offshore at the surface and inshore along the bottom. The inshore component near the bottom, which is especially significant, is chiefly responsible for the large vertical salinity gradients typical of coastal waters. Especially where\ndeep gidlies cross a continental shelf, highly saline water will be able to move in close to the land, while above it much fresher surface water will be moving along the shore, occasionally with a slight offshore component. It is important to remember that if coastal craters are not to become fresher and fresher, there must be an inward movement of saline water along the bottom, which through vertical turbulence carries salt up to the surface. The stronger tidal currents near the coast are favorable for such vertical mixing, but the high thermal stability typical of the summer season has the opposite influence.\n\nPetit Manan - Mt. Desert Rock - Matinicus Rock\nSeguin Island - Boon Island\nGloucester - Pollock Rip\nNantucket - Vineyard Sound\nBlock Island - Fire Island - Sandy Hook-\nFive Fathom Bank- \u2014 Winter Quarter\nBodie\u2019s Island - Cape Lookout - Frying Pan Shoal.\nRattlesnake Shoal - Martins Industry - Fowey Rocks - Carysfort Reef - Dry Tortugas\nSeasonal temperature and salinity cycle in shallow water of the eastern coast of the United States.\nRESTRICTED COASTAL WATERS\nFrom the foregoing discussion, therefore, it is apparent that tidal currents have a direct effect on all phases of coastal water warfare in the following ways: first, they tend to destroy vertical temperature and salinity gradients, and second, in many localized areas they produce mixed water where otherwise it would not exist. This naturally impacts echo ranging conditions. It also simplifies diving operations for submarines but at the same time makes evasion more difficult.\n92. Vertical Distribution of Temperature and Salinity\nExcept in a few specialized areas in low latitudes,\nThe vertical temperature gradients in coastal waters are dominated by the seasonal cycle. In general, coastal waters are shallow enough that in winter, the whole water column becomes isothermal. Thus, there is no counterpart to the main thermocline of the open ocean.\n\nFigure 7. Surface minus subsurface temperature, July and August: (Long Island Sound to Chesapeake Bay.\n\nThe available BT observations permit illustrating the seasonal temperature cycle in detail for a large area along the eastern coast of the North Atlantic. The many oceanographic stations available from the western North Pacific indicate that the coastal conditions there are comparable.\n\nClose to the beach, the relatively strong tidal currents and the shallowness of the water usually prevent the formation of a distinct thermocline.\nMarked thermal stability extends from the surface to roughly the 10-fathom contour. With this in mind, a useful diagram has been developed from routine surface temperatures collected from ships along the Atlantic Coast (Figure 6). It provides a fairly representative picture of seasonal temperature changes at the surface as a function of latitude. Although these are inshore surface temperatures, they are on average only slightly lower at any given latitude than surface temperatures across the entire continental shelf.\n\nRESTRICTED\nCOASTAL WATERS\nDISTANCE IN MILES\n\nFigure 9. Temperature profile SE from Moitauk Point in midwinter.\n\nDetailed studies have been made of the distribution of temperature and salinity in the Gulf of Maine and southward over the continental shelf to Cape Hatteras. For the present purposes, the significant findings include:\nThe conditions in this area can be summarized in two diagrams. The first (Figure 7) displays the average temperature difference between the surface and the bottom in July and August. The second (Figure 8) shows the magnitude of the vertical salinity gradient at the same season. In summer, surface temperatures are over 20 to 30 degrees higher than at the bottom, while surface waters are from 1 to 3.5 parts per thousand fresher than at the bottom. The resulting vertical change in the speed of sound is generally greater than 150 feet per second and reaches up to 200 feet per second in some areas.\n\nProfiles of temperature and salinity constructed from observations made at different seasons on a line extending southeastward from Afontauk Point, Longitude:\nIsland. This illustrates the seasonal cycle and horizontal changes in offshore direction. In midwinter, the water column is virtually mixed from surface to bottom across most of the continental shelf (Figures 9 and 10). Temperature and salinity both gradually increase in the offshore direction. The isotherms and isohalines are generally quite parallel, with warmer water being more saline. Near the edge of the continental shelf, this increase is more rapid near the bottom, corresponding to the inshore component of bottom water. At this season, the crosscurrent density gradient, and therefore the strength of the current, is at a minimum.\nResponding to the decreased land drainage during the winter months when much of the precipitation remains on the land in the form of snow and ice. The spring conditions are illustrated by Figures 1 and 12. As the surface waters stabilize due to vernal warming, surface salinities decrease, both because of decreased vertical turbulence and the spring freshets. Thus, over the continental shelf, the warmer water becomes the less saline, which is the reverse of the situation in midwinter. Vertical stability increases and consequently thermal mixing decreases until midsummer (Figures 13 and 14). Under such conditions, lateral mixing is increased in the layer of greatest stability. This may partly explain the characteristic outward bridge of the isotherms at mid-depths over the continental shelf.\nThe isotherms and isohalines cross each other in a complex manner near the continental slope, which is not well understood but is partly caused by the strongest current, in this case southwestward, being concentrated near the 100-fathom contour. Near the offshore end of the coastal water section, cold water from the north is being carried into the profile more rapidly than further inshore. During the autumn, the coastal water cools more rapidly than the offshore water due to prevailing cold and offshore winds. Thus, positive gradients, both of temperature and salinity, develop over the continental slope (Figures 15 and 16). The major features described in these sections off Montauk Point could be made out in any profile.\nThe continental shelf extends from Labrador to Florida, except off Cape Ffatteras and southern Florida. Along this entire coastline, the continental shelf is broad and well-developed. Fresh water is brought down to the sea by many evenly spaced rivers. As a result, a southward-flowing current, which is strongest along the 100-fathom contour, follows the continental shelf southward and is only partially interrupted by major irregularities such as the Laurentian and Fundian Channels.\n\nIn Figures 17-19, the seasonal cycle at various points along this coastline is illustrated in the same manner.\n\nDISTANCE IN MILES\nCOASTAL WATERS SLOPE WATER _GULF_ STREAM SARGASSO SEA\n\nFigure 16 illustrates the salinity profile SE from Montauk Point in autumn.\n\nRESTRICTED\nDEPTH IN FEET DEPTH IN FEET DEPTH IN FEET\nCOASTAL WATERS\nFigure 19. Average monthly temperature-depth curves in coastal waters between New York and Cape Hatteras.\n\nVertical distribution of temperature and salinity, as used in Part 2 above (Figures 34 to 42, Chapter 5). A comparison between the two sets of diagrams emphasizes the relatively great stability of coastal waters compared to offshore waters. This is not generally true only in shallow areas where strong tidal currents occur.\n\nDespite the fact that the temperature-salinity correlation in coastal waters varies widely, both seasonally and geographically, with only a few exceptions, the vertical temperature distribution controls the sound refraction pattern. As in deep water, this results from the fact that in layers where the salinity is changing most rapidly with depth, temperature likewise changes. Only when the salinity gradients are\nFigure 20A displays the vertical distribution of temperature and salinity at the Baltic Sea mouth in May 1937. The relatively fresh and warm Baltic water overlies colder and more saline Atlantic water, and the depth of the thermocline is approximately equal to the depth of the maximum salinity gradient. A BT reading would suggest sharp downward refraction with very short echo ranges. The salinity gradient, however, partially compensates for the temperature effect. Both together are equivalent acoustic temperature and salinity gradients in coastal waters. (Figure 20)\n\nRestricted coastal waters (Figure 21) show ratio thermograms from probable areas of critical salinity gradients.\nIn temperate waters, a decrease of approximately 1 degree in the upper 60 feet is typically associated with a medium temperature prediction. It is apparent that in extreme cases, salinity gradients can be important, but a very large salinity gradient will be compensated by a relatively weak temperature change. In Figure 20B, which shows a more typical temperature-salinity distribution, a reasonably accurate prediction can be made from temperature alone.\n\nSometimes, however, strong salinity gradients occur when there is little or no vertical change in temperature. Examples are shown in Figures 20C and 20D, which represent conditions off the mouth of the Amazon. The salinity gradient in Figure 20C is highly significant since it is not compensated by a temperature change. In this case, there will be sharp salinity variations.\nUpward refraction, and it is unlikely that a vessel with conventional (non-tilting) sonar gear will be able to get contact on a submarine below the fresh surface layer. Figure 201 differs from the preceding one in that the salinity gradient is probably largely confined to a shallow surface layer above projector depth. When this is the case, it will not interfere with echo ranging. It is difficult to say how common it is to find salinity gradients of this sort because oceanographic water samples have seldom been spaced at close enough depth intervals to show the complete vertical structure. However, there are many examples of bathythermograms such as the one in Figure 21, in which a very shallow positive temperature gradient indicates the existence of a fresh surface layer too thin to affect echo ranging.\nThe remainder of Figure 21 demonstrates other bathythermogram examples from regions where significant salinity gradients typically exist. Their presence is evident in Figure 21B, but in C and D, taken near BOTTOM STRUCTURE in the Amazon areas where such gradients are almost certain, there is nothing in the bathythermograms to suggest their presence.\n\nIn summarizing the acoustic effects of salinity gradients, it is clear that there are two primary factors to consider: (1) the depth of the gradient, as it is not crucial if it is above projector depth; (2) the amount of change in salinity with respect to temperature changes. The most detrimental situation from the standpoint of echo ranging occurs when the water column is essentially isothermal, because then not only is the salinity gradient most effective but also\nThe bathythermograms are misleading, particularly in the tropics. In temperate and arctic regions, the outflow from rivers is likely to be warmer than the ocean water in summer and colder in winter. Therefore, salinity gradients are only likely to occur without corresponding temperature gradients for short periods in the spring and autumn.\n\nSince density currents must flow parallel to coasts, the water of reduced salinity formed near river mouths tends to spread along the coast instead of flowing out to sea. The influence of a large river can be noted hundreds of miles away. For instance, in the Gulf of Mexico, a fresh surface layer extends westward from the Mississippi River mouth, and the freshening influence can be detected, particularly in spring, beyond Galveston (Figure 20B). In areas of:\nAdequate rainfall results in continuous bands of low salinity water being formed along coasts, and the influence of rivers seldom extends far out to sea except near the equator where Coriolis force is much reduced. Minor and temporary cases where refraction is controlled by vertical salinity gradients can be found at New London, Connecticut, where the outflow from the Thames River sometimes overlies virtually isothermal water of about the same temperature, which has been mixed by the strong tidal currents of the narrow entrances to Long Island Sound. At the edge of the continental shelf, where near the surface the relatively fresh coastal water tends to overlap more saline water, one would expect occasionally to find situations where vertical salinity gradients controlled the refraction. No pertinent observations have been uncovered.\nThe oceanographic stations do not typically come at the critical point where the right conditions prevail for echo ranging. The importance of both bottom topography and sediment composition in echo ranging was mentioned earlier. Whether it is an advantage for an echo ranging ship to work over a good sound reflector bottom depends on the direction of the sound reflection. A smooth, hard bottom that reflects sound forward is ideal, and ranges will be nearly as good as in deep water with perfect temperature conditions. However, if bottom irregularities intercept sound at nearly right angles, reflecting it back towards the sound source, the result is reverberation and skip distances. The size of the irregularities does not need to be very great; stones or ripple marks only 3 or 4 inches high can cause this effect.\nInches high will significantly increase the reverberation level of superonic gear. Therefore, stony, rocky, and coral bottoms are almost always poor from the echo ranging perspective due to their roughness. Sand bottoms are typically good because they are not only good reflectors but are also generally smooth. Occasionally, they may be poor, however, when there is enough current over the bottom to produce ripple marks, and there is some evidence that a particular sand bottom may vary considerably in this respect according to the way it is disturbed by tides and storms.\n\nThe manner in which these generalizations fit the observed facts is illustrated by a recent analysis of all observed maximum ranges and suitable acoustic measurements in shallow water. It was found that for all refraction patterns over rock and coral:\n\n(Note: The text appears to be in good shape and does not require extensive cleaning. Only minor corrections for typos and formatting have been made.)\nThe bottoms had ranges less than 1,500 yards 60% of the time, averaging about 1,000 yards. Maximum ranges over sand were less than 1,500 yards only 20% of the time, averaging 2,500 yards. Over sand and mud, ranges were less than 1,500 yards 30% of the time, averaging about 2,200 yards. Results varied according to the refraction pattern in soft mud bottoms.\n\nThe methods of correlating bottom types with acoustic phenomena were discussed in Chapter 2, as well as the principles used in constructing bottom sediment charts for tactical use by naval forces. This work can be better understood, however, by considering briefly how the different bottom types are produced and how various oceanographic factors affect their distribution.\n\nCoastal waters\nMarine sediments as a whole are a heterogeneous collection of all the materials carried into the sea or produced in it that are heavy enough to sink to the bottom and inert enough so that they have not dissolved or decomposed into soluble substances. A fairly large proportion of the sediments is derived from land. Direct erosion of the shoreline by wave action is one of the most important sources of such material. River drainage depositing its load of silt in the sea is also important, as is glacier movement. A less obvious but certainly significant source of marine sediments is air-borne dust derived from arid regions and volcanic explosions. The sea produces some of its bottom sediments, for the most part, by biological processes (shells, coral), but also by precipitation of inorganic chemical substances from seawater.\nThe accumulation of products from submarine volcanic activity are likely the most important sources of marine sediments, although there are many other minor contributing agencies. The sea continually moves and reworks the loads of sediment brought into it. Waves and currents carry the smaller particles, grinding them against each other and larger stationary objects on the bottom. This eroding effect is evident on any rocky beach, where smaller pebbles are rounded and the surfaces of larger rocks and boulders are worn smooth. Over long periods of time, boulders are gradually transformed into mud. Chemical activity is also significant over similar time spans, dissolving and decomposing sediments.\nSome minerals are more susceptible to both chemical and physical dissolution than others. The hardness and inertness of quartz, for example, is responsible for its abundance (in the form of sand) on the continental shelf. It remains behind while other less stable substances are reduced to a finer state and carried further out to sea.\n\nTransportation of sediments depends on both particle size and the speed of the current. For instance, a swift-flowing river delivers into the sea a load of sediment ranging in particle size from fine mud to sand. In the slower moving ocean currents, the sediment will settle gradually, the larger particles going to the bottom more quickly, so that they are not carried as far from the source as the smaller sizes. Thus, in broad terms and generally speaking.\nSediments tend to be coarse near shore, grading to fine mud in deep oceanic basins. Particles too large to be carried completely in suspension may be lifted momentarily and carried for a short distance before settling back to the bottom. Still larger particles may be rolled along. A certain amount of transportation may occur in the absence of currents. The familiar terrestrial phenomenon of landslides has its counterpart on the sea floor. Mud slides are a fairly common phenomenon wherever silt settles on a sloping bottom. Because the buoyancy of the water makes the friction between mud particles much less than it would be in an aerial environment, mud slides can occur on very slight slopes. The type of bottom that occurs in any particular area depends on the interaction of the factors that influence sediment deposition.\nThe mentioned factors include the types of sedimentary materials, how they have been worked by marine agencies, and the effects of local currents on their deposition. A chart displaying the shoreline and bottom topography can reveal much about the bottom's character and current pattern. For instance, mud deposits are common off the mouth of a large river or a smooth, sandy bottom near a low, sandy coast. An irregular shoreline with headlands and estuaries indicates a variable bottom, likely rocky off headlands, in river mouths, and around submerged reefs where strong currents scour the bottom and carry away material.\nFiner sediments. On the other hand, small basins will collect deposits of sand or mud. Further offshore, bottom topographic features are associated with similarly characteristic sediment types. Seasmine ridges or sharp changes in depth such as at the edge of the continental shelf are nearly always accompanied by currents that expose rock surfaces or at least ripple the sand sufficiently to make echo ranging difficult. Offshore banks with their strong rotary tidal currents also show pronounced ripple marks, often at depths of nearly 100 fathoms. Currents can affect seasmine topography as well as be affected by it, since a current strong enough to transport sand must ultimately deposit it somewhere, generally in the form of a ridge or bank at the current's edge. In the tropics, coral reef formation is often restricted.\nThe dominant feature of submarine topography in shallow water and in such areas, high reverberation makes echo ranging very difficult. The rough, rocky bottom in the neighborhood of islands produced by submarine volcanic eruptions is of similar acoustic significance.\n\nBottom topography and structure have always been of considerable interest from the standpoint of navigation, and most coastal areas have been surveyed at one time or another with varying degrees of accuracy and completeness. The depth of water has been measured by sounding leads and more recently by acoustic fathometers which provide far more complete data. Bottom type was largely determined from small samples collected by a cup or tube on the end of the sounding lead or by grease smeared in a depression on its lower end.\n\nOceanographic expeditions have also obtained more detailed information.\nScientific information about bottom type and topography is extensive, particularly in larger samples. Due to the bottom's varied composition of different sizes and kinds of fragments, small samples can be misleading. Oceanographers employ various dredges, tubes, and containers with snapping jaws to collect bottom samples. Recently, underwater cameras have been extensively used. They capture images of approximately 50 square feet of the bottom, revealing many details of bottom structure and small-scale topography valuable to the information obtained by sampling devices. Examples of bottom pictures are shown.\nFigures 22-24. Charts of bottom topography can be prepared in great detail using modern recording fathometers. It is a more laborious task to sample the bottom adequately for charts of sediment types. This has been done in a few local areas for scientific purposes and in connection with the acoustical tests described in Chapter 2. In other places, where only government surveys have been made, the bottom notations on the charts are not completely adequate for acoustical purposes. Where soundings are not closely spaced, it is necessary to decide whether or not a particular area is divided into patches or is continuous, and what its areal extent and probable boundaries may be. Therefore, it is necessary to depend a great deal on general oceanographic and geological knowledge\n\nFigure 22. Photograph of a smooth, sandy bottom.\nTo understand the types of sedimentary materials in the region and their deposition according to local currents and bottom topography, the chapter discusses the requirements for a bottom sediment chart. It concludes with a discussion of the material collected by government surveys and its use for subsurface warfare.\n\nFor the continental United States and its possessions, which have been surveyed by the Coast and Geodetic Survey, the data are unusually complete. The printed charts contain bottom notations, and many samples have been preserved. Access to the original field data sheets is available. These sheets are drawn on a larger scale and contain more soundings and bottom notations than appear on the finished printed charts.\nSuch information was used for drawing the boundaries between the different bottom types which appear on the wreck charts for the Atlantic and Gulf Coasts, and for bottom sediment charts covering areas in the Philippine Islands. In the case of foreign areas, it is necessary to consult the archive files of the Hydrographic Office not only for their latest edition of any particular chart, but also for all foreign editions from which it was compiled. There is a tendency on the newer charts to omit bottom notations, and frequently earlier surveys may furnish additional information. The British surveys of regions outside their own coastal waters are excellent, particularly in the Far East, and the French and Germans have also done notable work.\nThe Japanese Hydrographic Office has published detailed surveys of the Home Islands and adjacent Asian coast. Data from these charts were examined from a geological and topographic point of view, and the bottom information was found to be in line with expectations. Charts compiled from them are believed to be as accurate as those compiled from other sources. The British Admiralty Archives have been available, and photostats of field data sheets as well as earlier surveys have been furnished for critical areas \u2013 material which was not available in Washington.\n\nHowever, certain conditions must be borne in mind when charts of the bottom are drawn from information on navigation charts and not from actual material. If the notations on the charts were everywhere accurate.\nMany mistakes would result if the samples were accepted at face value. As stated before, the samples were taken as an adjunct of sounding with a lead, and a very small amount of material was obtained. Several misconceptions may arise. First, there is a tendency to overemphasize mud areas and make them appear more numerous and larger than they really are. Any bottom that feels at all soft or a sample which looks dark colored and oozy when wet is generally called mud by hydrographers. A mechanical analysis of the material would show this sediment to be sand and mud in many cases. Second, any bottom which feels hard to the leadsman and from which no sample is obtained is apt to be labeled rocky or coral, depending on the latitude. In most cases, this is correct.\nSmall stones or coral fragments sometimes have the same \"feel.\" Third, as the sampling apparatus can only pick up a small amount of material consisting of smaller particles, only gravel and sand fractions would be brought to the surface over some stony bottoms. Adequate dredge samples and photographs have shown that gravel bottoms usually have numerous stones. Consequently, except in glacial areas, all gravel bottoms, as well as pebbles and shells, which usually occur in conjunction with stones, were classified as stony. The term clay suggests that the bottom has been somewhat compacted so that it reflects sound better than ordinary mud, but not as well as a sand bottom. Sand and mud is an intermediate classification.\nThe principles used in constructing bottom sediment charts involve classification based on the dominance of bottom symbols such as rock or sand. When two or more bottom symbols exist, the acoustical significance of the rock portion is greater, resulting in the sediment being so classified.\n\nThese principles are employed in creating bottom sediment charts from less than ideal information. No chart is perfect, and they are subject to constant improvement. The bottom sediment charts rely on hydrographic survey data preceding them, as well as any relevant geological information.\n\nA better bottom sediment chart can be constructed from a detailed, large-scale survey of an important approach compared to a region where soundings are widely scattered. Neither one is ideal.\naccurate as a chart made from an area from which bottom samples and photographs have been obtained. Also, it is probably true that at present, bottom sediment charts are more accurate from a geological standpoint than they are as predictions of echo ranging conditions. If greater accuracy is to be attained in predictions for foreign areas, further work in underwater sound should be carried out over all types of bottom where it is possible to take samples and photographs, so that all the unknowns may be investigated simultaneously.\n\nV\n\nCit, disttitaiffltfiiL\n\nGLOSSARY\n\nAMBIENT NOISE. Noise present in the medium other than target and own-ship noise.\n\nBOl\u2019RDON TL BE. A flattened curved tube which tends to straighten out under internal pressure, used as the driving element in pressure temperature gauges.\n\nBE. Bathythermograph.\nBuoyancy. As used in this volume, the net buoyancy refers to the difference between the weight of the water displaced by a vessel and the weight of the vessel itself.\n\nConcaeced Ion Cee. A vertical section of the isothermal mixed layer, bounded by cool currents descending from a convergence and warm currents rising to a divergence.\n\nDensity Gradient. Change of density with depth.\n\nIsobaric Temperature Inequities. A set of lines on the SB I chart, each starting from a set of selected points on the temperature scale and passing through all points for which the net change in buoyancy, resulting from changes in water temperature and depth, is zero for a submarine of a given compression.\n\nIsohalines. Lines drawn through all points having the same salinity.\n\nIsotherms. Lines drawn through all points having the same temperature.\n\nLatitude of the Mixed Layer Depth. The depth of the mixed surface layer.\nLayer: Echo and listening ranges reduction on a submarine located within or beneath a thermocline. Mixed layer: 1. Isothermal layer occurring at the water surface. Reverberation: Sound scattered dilusely back towards the source, principally from the surface or bottom and from small scattering sources in the medium such as bubbles of air and suspended solid matter. Reversing I thermometer: A deep-sea recording thermometer; the temperature reading at the desired depth is preserved by overturning the instrument to break the mercury column. Salinity: Number of grams of salt per thousand grams of sea water, usually expressed in parts per thousand. Salinity gradient: Change in salinity with depth, expressed in parts per thousand per foot. SBT: Submarine bathythermograph. Shadow zone: Region in which refraction effects cause extinction of sound.\nConclusion of echo-ranging signals.\n\nSinking centers. Subarctic regions where strongly saline surface water of tropical origin sinks through the colder, but less saline underlying layers.\n\nStability. 1. The resistance to overturn or mixing of the water column, resulting from the presence of a density gradient.\n\n\u2022Station. A set of pairs of thermometer readings taken in a specific location at approximately 100-meter depth intervals, along with a corresponding set of water samples analyzed for salinity. A station is \"occupied\" when these readings are procured.\n\nTarget aspect. Orientation of the target as seen from own-ship.\n\nTemperature gradient. Change of temperature with depth, expressed in degrees F per foot.\n\nd. Thermocline. A layer of water in which temperature decreases with depth; a negative temperature gradient.\n\nUpwelling. Rise of the main thermocline, and the underlying water.\nThe deep-water mass moves towards the upper levels as the warm surface water is swept away by the winds.\n\nVelocity Gradient. Rate of increase in the velocity of sound with increasing water depth.\n\nRESI (RIC I E]\n\nBIBLIOGRAPHY\n\nSources such as Div. 6-501.1 1-M4 indicate that the documents listed have been microfilmed and that their titles appear in the microfilm index printed in a separate volume. For access to the index volume and to the microfilm, consult the library or Navy agency listed on the reverse of the half-title page.\n\nChapter 1\n\n1. The Oceans, H. Sverdrup, M. Johnson, and R. H. Fleming, Prentice Hall, Inc., New York, NY, 1912.\n2. Biological Chemistry and Physics of Sea Water, H. Harvey, Macmillan Co., New York, NY, 1928.\n3. International Congresses of Oceanography, F. Langhan and others. National Academy of Sciences, 1937.\n1. Detailed Study of the Surface Layers of the Ocean in the Neighborhood of the Gilbert Stream with the Aid of Rapid Measuring Hydrographic Instruments, F. Spilhaus, Sears Foundation Journal of Marine Research, Vol. 3, 1910, p. 1-2.\n2. Sound Transmission in Sea Water, C. O'D. Iselin and V. M. Goldberg, NDRC 61-31, Woods Hole Oceanographic Institution, Chapter 2.\n3. Calculation of Sound Ray Paths Using the Refraction Slide Rule, NavShips-913, 1943.\n4. Sound Beam Patterns in Sea Water, G. P. Woollard, NDRC 61-sr30.\n5. The Sonic Ray Plotter, Leonard I. Schiff, NDRC 61-sr30-1735.\n6. Prediction of Sound Ranges from Bathythermograph Observations, NavShips-943-C2, 1944.\n7. Use of Submarine Bathythermograph Observations, J. Lamar Worzel and W. Maurice Ewing, NDRC 61-sr31.\n8. Instruction Manual for the Use of the Underwater Camera, J. Lamar Worzel and W. Maurice Ewing, NDRC 61-sr31.\nChapter 5:\n1. Hydrographical Tables, M. Kntidsen, 1901.\n2. The Prediction of Afternoon Effect, C. O'D. Iselin and A. H. Woodcock, OSR-31, OSRD 845, NDRC Cl-sr31-137.\n3. \"Surface Motion of Water Induced by Wind,\" I. Langmuir, Journal of Marine Research, vol. 5, 1944, pp. 196-205.\n\nChapter 7:\n1. The Oceans, H. f. Sverdrup, M. W. Johnson, and R. H. Fleming, Prentice Hall, Inc., New York, NY, 1942.\n\nChapter 8:\n1. An Acoustic Interferometer for the Measurement of Sound Velocity in the Ocean, R. J. Ibick, Report s-18, NRSL.\n2. \"Surface Cooling and Streaming in Shallow Fresh and Salt Water,\" A. H. Woodcock, Journal of Marine Research, vol. [Unknown], [Unknown].\n3. Measurements of the Horizontal Thermal Structure of the Ocean, Norman J. Holter, Report S-17, NRSL, Yug. 18.\nChapter 9\n1. A Review of the Problem of Predicting Ranges in Shallow Water\nJVater, George P., 4'oolard, 4WHOI, Aug. 17, 1944.\n\nSupplementary:\nBathythermograph Manual for Bathythermograph Pilot Instructors, Report M250, OEMsr-30, UCDWR, September 1944. Division 6-.50L12-M3\nPreliminary Studies for the Development of a Salinity-Corrected Bathythermograph, A. W. Jticobson, OEMsr-31 (Sidtcontract)\nPrediction of Echo Ranges from Submarine Bathythermograph Observations. Instruction Manual for Submarine Bathythermograph Observers (Part II), Richard H. Eleming and others, WHOI, UCDAVR, and Buships, Sept. 1, 1942.\nFinal Report on Project NO-221, Spectograms of Underwater Sounds, W. Koenig, Jr. and J. 4V. Emling, NDRC 6.1-sr346-\nCurrent Methods for Prediction of Maximum Soil Denisty Ranges, Technical Memorandum 1, CUDWR, May 1, 1944.\nSonar Tests of Tilting Beam Sound Gear on the USCGC Shamrock, U. S.\nNavy Oceanography Office, Mar. 4, 1944. Div. 6-570.21-M4\nSotiar Echo-Ranging Tests on YMS370, Gordon R. Riley, U. S. Navy Oceanography Office, Mar. 18, 1944. Div. 6-570.21-M5\n\nBIBLIOGRAPHY\nSubmarine Soundings by USCGC Blanco, William Wood, U. S. Navy Oceanography Office, May 15, 1914. Div. 6-570.21-M6\nBathythermograph Predictions, Key Ties Area, Gordon Riley, U. S. Navy Oceanography Office, June 7, 1941.\nEcho Range Data for the Period June 2 to June 15, 1914, Gordon Riley, IT. s. Navy Oceanography Office, July 3, 1944.\nEcho-Ranging Data, Miami Area, L. V. Worthington and Helen S. Magee, U. S. Navy Oceanography Office, July 3, 1944.\nEcho-Ranging Tests on the DD745, Gordon A. Riley, II. U. S. Navy Oceanography Office, July 20-23, 1944. Div. 6-570.21-M7\nEcho Range Data, Key West Operating Area for the period\nJune 16 to October 13, 1911, Gotdon A. Riley, H. S. Austin, and others, U.S. Navy Oceanography Office, Woods Hole Oceanographic Institution Reports\nAverage Summer Sound Ranging Conditions in the Mediterranean\nAchieved Echo Ranges of Surface Ship Targets in Deep and Shallow Water, August 30, 1944. Div. 6-570.21-Mll\nAcoustic Properties of Mud Bottoms, George P. Avoollard, Lecture Notes on the Use of the Submarine Bathythermograph,\nA Comparison of Achieved and Predicted Echo Ranges on Submerged Submarines in Deep Water, George P. Woollard,\nEcho Range Observations of the USS Sylph, Maurice Ewing,\nExplosion Sounds in Shallow Water, Hianrice Ewing and\nEcho Ranging Characteristics of Cape May, New Jersey Area, Richard F. Geyer and H. T. Bauerle, Buships Report 10\nFactors Affecting Long Distance Sound Transmission in Sea\nWater: A Study of Radio Acoustic Ranges from Data Taken by the U.S. Coast and Geodetic Survey, OSRD 1505, NDRC Laboratory\nStudies of the Acoustic Properties of Wakes, Part I, Seattering and Absorption of Sound by the Wake of Sound Ranges Under the Sea, Thomas H. Osgood, NDRC Miscellauneous\nUse of Bottom Sediment Charts, NDRC, May 1943.\nAcoustic Properties of Gas Bubbles in a Liquid, Lyman Spitzer, CUDWR, Vol. 22, 1945.\nComments on: Dissipation of Energy Due to Presence of Air Bubbles in the Sea, Conyers Herring. Div. 6-540.2-513\nThe Extinction of Sound in Water, Carl Eckart, Lh S. Navy Radio and Acoustic Laboratory, File 01.70, NDRC C4-sr30-021,\nFluctuation of Transmitted Sound in the Ocean, Technical Memorandum 6, NDRC 6.1-srll31-1883, CLIDWR, Jan. 17.\nMierostructure of Sea Water. Notes on Measuring Temperature Differences (Harry Nycpiist, C4-NDRC-0-45, Har. 12, 1942).\nMierostructure in Sea Water. Theoretical Analysis (Harry Ny-, H. L. Sverdrup and Svh 51unk, Scripps Institution of Oceanography).\nPreliminary Measurements on the Aeolic Properties of Disturbed Water (Eginhard Dietze, NDRC C4-sr20-205, USRL).\nThe Propagation of Underwater Sound at Low Frequencies as a Function of the Acoustic Properties of the Bottom (John Ide, R. F. Post, and W. J. Fry, Report S-2113).\nVisibility in Ocean Water (F. A. Jenkins, I. S. Bowen, and F. T. Laboratory Studies of the Aeolic Properties of Wakes).\nJeffries Wyman, Wendel Lehman, and David Barnes, Part 11, Role of Bubbles in Wakes (NS-141, NDRC 6.1-).\nLong Range Sound Transmission. Interim Report 1 (for the)\nPeriod: March I, 1911 to January 20, 1915. I. Ewing and J. Lamar Worzel, NOBs-22083, Aug. 25, 1945.\n\nMemorandum Summarizing Discussions with Lieutenant Rather, Concerning Possible Methods of Overcoming Lery Bad Sound Oceanography of Subsurface Warfare. Lecture by C. O'D. Iselin, Oceanographie Factors Entering Into Harbor Protection by Underwater Sonic Devices, WHOI, Jan. 21, 1942.\n\nA Preliminary Study of Echo-Ranging Conditions in the Casco Bay Area of the Gulf of Maine, R. S. Gerber, WHOI. Role of Bubbles in the Thermal Properties of Tanks, Jeffries. Tests Made with O.D.i/QK.l Stabilized Depth Determining Gear on the USS Sonnes to Ensure the Accuracy of Depth Indications under Adverse Temperature Conditions, Thomas. Cyclical Temperature and Salinity Changes Between the Surface and a Depth of 150 Feet in the Western North Atlantic.\n\nRESTRICTED\n\nBibliography.\nA Summary of Factors: Gox'eruiiig Sound Ranges, Cieors^e P. (June 1957, Div. 6-57-MI)\nSouid-ra)igiug Experiments at Key July, I912, Maurice Ewing, OSRD 725, NDRC Gl-srSl -130, WHOI, May 23, 1912.\nThe Transparency and Color of Ocean Waters: Special Reference to the Western Pacific, George L. Clarke and Henry Use of Surface Vessel Bathythermograph Observations, Buships, Theory of Propagation of Explosive Sound in Shallow Water, Bathythermograph Readings Accompanying Sound Gear Tests on USCGJ35, Gordon A. Riley, U. S. Navy Oceanography.\nStatistical Importance of Oceanographic Factors in A S Attacks, Lyman Spitzer, Jr., NDRC 6.1-srl 131-140, Oceanographic Studies, H. B. Hoff, J. J. Markham, and G. R. Bi-ieeekly Report Cox'ering Period July 2\u2018> to August 7, 1933, Telegraph Theory. Electrical Equivalent of the Ear as a Receiver.\nContract Number, Harry Nycpiist, Jan. 13, 1942, Div. 6-.560.1-M1\nBinaural Phenomena, Ralph C. Maninger, Report P12/4089\nInterval Tests, H. L. Rumbaugh, Report D13/249\nCUDWR, Tone Duration as a Factor in Pitch Discrimination, E. G. Wever, Report M-179, Feb. 16, 1944\n.4 Study of Binaural Perception of the Direction of a Sound Source, Irving Langmuir, V. J. Schaefer, and others, OSRD 4079, NDRC 6.1 -sr323-16, General Electric Co., June 30, 1944\n\nThe Trustees of Columbia University in the City of New York\nStudies and experimental investigations in connection with and for the development of equipment and methods relating to submarine warfare.\n\nThe Trustees of Columbia University in the City of New York\n(Contractors and Subjects)\n\nOEMsi-20\nThe Trustees of Columbia University in the City of New York\nStudies and investigations in connection with the applicability of data, methods, devices, and systems pertaining to submarine and subsurface warfare.\nOEMsr-31, Woods Hole Oceanographic Institution, Woods Hole, Mass.\n\nStudies and experimental investigations in connection with the structure of the superficial layer of the ocean and its effects on the transmission of sonic and supersonic vibrations.\nOEMsr-30, The Regents of the University of California, Berkeley, California\n\nMaintain and operate certain laboratories and conduct studies and experimental investigations in connection with solarine and subsurface warfare.\nNDCrc-40, Woods Hole Oceanographic Institution, Woods Hole, Mass.\n\nStudies and investigations in connection with oceanographic factors influencing the transmission of sound in seawater.\nOEMsr-287, President and Fellows of Harvard College.\nCambridge, Mass.\nStudies and experimental investigations in connection with:\n1. the development of equipment and devices relating to subsurface warfare, Massachusetts Institute of Technology, Cambridge, Mass.\n2. underwater sound transmission and boundary impedance measurements, underwater sound surveys at high frequencies, development of devices for the control of underwater sounds, and development of intense underwater sound sources for special purposes.\n\nRESTRICTED\nSERVICE PROJECT NUMBERS\n\nThe projects listed below were transmitted to the Executive Secretary, National Defense Research Committee, NDRC, from the War or Navy Department through either the Var Department Liaison Office for the NDRC or the Office of Research and Inventions (formerly the Coordination)\n\nOEMsr-1046\nProjects:\n1. Development of equipment and devices for subsurface warfare, Massachusetts Institute of Technology, Cambridge, Mass.\n2. Underwater sound transmission and boundary impedance measurements, underwater sound surveys at high frequencies, development of devices for controlling underwater sounds, and development of intense underwater sound sources for special purposes.\nSubject:\nNator of Research and Development, Navy Department.\n\nTopic: Niiniher Project\n\nSubject Index:\nAcoustic properties of sea bottom (range as function of oceanographic factors)\nAcoustic properties of wakes\nSonar-surface and submarine hydrothermograph instruction program\n\nAbsorption (acoustical) by mud, 15\nAbsorption of light by ocean water, 33\n\nSecured range and layer depth chart, 12,\nBathythermograph: description, 5, 8,\ndesign criteria, 5,\neffect of weather conditions, 38-39,\nhistory of development, 4,\nisoballast lines, 23,\nsalinity compensated, 8,\nBathythermograph card, submarine, 23,\nBathythermograph observations, world distribution map, 12.\nBeaufort scale (wind velocity), 12\nBjerknes circulation theory, 66\nBottom reverberation, 15, 20\nBottom sediment charts, ocean, 14, 91\nUnderwater camera, 15, 93\nAssured range (sonar) charts, 12, 32\nBathythermograph observations, 13\nLayer depth, 12, 32\nOcean bottom sediments, 14, 94\nOcean currents, 68\nOcean temperature variation, 32\nSonar jjeriscope depth range, 12\nOcean salinity, 53\nSonar conditions, 12\nSonar performance prediction, 12\nWind directions over oceans, 69\nWrecks, 93\nCirculation, ocean (see Ocean currents)\nClouds (effect on ocean thermal gradients), 40\nCoastal mixing of sea water, 78-89\nConvection patterns, ocean, 41\nConvergence of ocean water, 41, 68\nCoriolis force, 59\nCurrents, ocean (see Ocean currents)\nDiurnal warming in the ocean, 34\nDivergence of ocean water, 68\nDiving techniques, submarine, 22-26\nEddy formation in oceans, 64, 72\nEkman spiral, 66\n\n(Note: The text has been cleaned as per the given requirements. No unnecessary content has been removed, and the text has been formatted for better readability.)\nFish, fluctuations in ocean (small-scale), 75\nFoucault pendulum, 60\n\"Fresh pocket\" in ocean, 71\nGeorges Bank water conditions, 80\nGerman oceanographic research, 3\nGradient current, 68\nHeat exchange in the ocean, 33-77\nInertia circle, 61\nInternal waves in ocean, 73\nIsoballast lines on bathymetric thermograph,\nLayer depth chart, oceanographic, 12, 32\nLayers in ocean (thermal), 10, 27-59\nLight penetration into ocean, 33\nManuals, sonar range prediction, 10\nMaps, marine (see Charts)\nMicrostructure of ocean, 75\nMixing of sea water (coastal), 84\nMud, as an acoustical absorber, 15\nNegative thermal gradients in ocean, 38\nOcean column stability, 28\nOcean currents (charts of world currents), 68\nCoriolis force, 59\nDownward currents, 41, 68, 70\nEddy formation, 64, 72\nEffect of water density, 59\nEffect of winds, 66, 69\nEffect on sonar range, 70\nGradient.\nCoastal waters, local variability, mechanism of formation, 59-68, relation to density structure, thermal, 28-29, tidal, 80, Ocean oscillation, small-scale, 75, Ocean layers, thermal, 10, 27-59, Ocean temperature, Ocean water, density, 27, 66, 69, Oceanographic research, German, 3, Periscope depth range chart, 12, Propagation of sound in sea water, 17-21, Radiation, effect on sea surface temperature, 33, Rain, effect on temperature of ocean, 33, Range, sonar, effect of internal waves, 75, effect of ocean bottom structure, 91, effect of ocean currents, 70, effect of ocean microstructure, 75, effect of refraction, 20, 36, limiting factors on, 10, prediction, 10, 12, variation with time of day, 36, Refraction, effect on sonar range, 20, Refraction slide rule, 9, Refraction theory, underwater sound, 9, Research institutions, oceanographic, 4.\nReverberation, bottom, 20\nReversing thermometer, oceanographic, river water mixing with the ocean, 91\nSalinity of the ocean; charts, 53\nCoastline effects, 77-91\nCorrelation with temperature, 51\nSalinity-compensated bathythermograph, 8\nSea water, salinity, 51-55, 77-91\nSeasonal thermocline, 44\nSeasonal variations in ocean temperature, 44-45\nSediment charts, 14, 93\nSediments, marine, 92\nSinking centers in ocean, 70\nSkip distance effect, 20\nSlide rule, refraction, 9\nSonar, false echoes, 21\nSonar echoes from fish, 21\nSonar range; see Range, sonar\nSound absorption by mud, 15\nSound propagation in sea water, 17-21\nSound velocity in sea water, 19\nStability of ocean water columns, 28\nSubarctic convergence, 29\nSubmarine diving techniques, 22-26\nSubmarine supplements, 13\nTemperature of the ocean; air-sea temperature difference, 40\nCharts, 32\nCoastline effects, 77\ncorrelation with salinity, 51-55, 82-83\ndepth-temperature curves, 30\nRE: SIRICIED\ndiurnal variation, 34-40\neffect of weather, 33, 40-44\nheat exchange relations, 33-44\nseasonal variations, 44-50\nthermal layers, distribution of pri-\nThermal circulation of ocean water,\nThermal gradients in ocean, 19, 27-32,\nThermocline, main, 27\nThermocline, seasonal, 44\nThermometer, oceanographic reversing,\nIdeal currents, 80\nTransmission of sound in sea water,\nUnderwater camera, 15, 93\nUpwelling, 32, 78\nRESTRICTED\n\"elocity) of sound, variation in sea water,\n\u201cWater-bottle\u201d (oceanographic inst.), 29\nWaves, structure of ocean, 43\nWind direction charts, 69\nWind, effect on ocean currents, 66, 69\neffect on ocean thermal layers, 42\nWind velocity scales, 12\nIntertidal ocean layers, 28\nWreck charts, 93", "source_dataset": "Internet_Archive", "source_dataset_detailed": "Internet_Archive_LibOfCong"},
{"language": "eng", "scanningcenter": "capitolhill", "contributor": "The Library of Congress", "date": "1946", "subject": ["Sonar", "Anti-submarine warfare", "Naval research", "Sonar -- Calibration", "Anti-submarine warfare -- Equipment and supplies -- Testing", "Naval research -- United States"], "title": "Basic methods for the calibration of sonar equipment", "creator": "United States. Office of Scientific Research and Development. National Defense Research Committee, issuing body", "lccn": "2015490955", "collection": ["library_of_congress", "americana"], "shiptracking": "ST005578", "call_number": "18906808", "identifier_bib": "00433840161", "boxid": "00433840161", "volume": "10", "possible-copyright-status": "The Library of Congress is unaware of any copyright restrictions for this item.", "description": ["Title on half-title page: Summary technical report of the National Defense Research Committee", "\"Manuscript and illustrations for this volume were prepared for publication by the Summary Reports Group of the Columbia University Division of War Research under contract OEMsr-1131 with the Office of Scientific Research and Development. This volume was printed and bound by the Columbia University Press\"--Unnumbered page ii", "LC Science, Business & Technology copy no. 6", "In a set of declassified documents held as a collection by the Library of Congress", "Includes bibliographical references (pages 167-169) and index", "xi, 175 pages : 28 cm"], "mediatype": "texts", "repub_state": "4", "page-progression": "lr", "publicdate": "2016-04-13 14:50:36", "updatedate": "2016-04-13 15:55:16", "updater": "associate-mike-saelee@archive.org", "identifier": "basicmethodsforc10unit", "uploader": "associate-mike-saelee@archive.org", "addeddate": "2016-04-13 15:55:18", "scanner": "scribe3.capitolhill.archive.org", "operator": "associate-mike-saelee@archive.org", "imagecount": "202", "scandate": "20160506131318", "ppi": "300", "foldoutcount": "0", "identifier-access": "http://archive.org/details/basicmethodsforc10unit", "identifier-ark": "ark:/13960/t1jh8780q", "scanfee": "100", "invoice": "1263", "sponsordate": "20160531", "backup_location": "ia906105_26", "fadgi": "true", "republisher_operator": "associate-mike-saelee@archive.org", "republisher_date": "20160510093534", "republisher_time": "673", "external-identifier": "urn:oclc:record:1041074231", "publisher": "Washington, D.C. : Office of Scientific Research and Development, National Defense Research Committee, Divison 6", "oclc-id": "6686536", "associated-names": "United States. Office of Scientific Research and Development. National Defense Research Committee, issuing body", "ocr_module_version": "0.0.21", "ocr_converted": "abbyy-to-hocr 1.1.37", "page_number_confidence": "97", "page_number_module_version": "1.0.3", "creation_year": 1946, "content": "I \n^ Return  To \nLibrary  of  Congress \nI \ntf \nV \ni \ny \ni \nr \nr \nI \nI \nXr.. \ns \nI \nt \ni \nReturn  To \nLibrary  of  Congress \ni \nI \nt \nI \nSUMMARY  TECHNICAL  REPORT \nOE  THE \nNATIONAL  DEEENSE  RESEARCH  COMMITTEE \nManuscript  and  illustrations  for  this  volume  were  prepared  for \npublication  by  the  Summary  Reports  Group  of  the  Columbia  Uni- \nversity Division  of  War  Research  under  contract  OEMsr-1 131  with \nthe  Office  of  Scientific  Research  and  Development.  This  volume \nwas  printed  and  bound  by  the  Columbia  University  Press. \nDistribution  of  the  Summary  Technical  Report  of  NDRC  has  been \nmade  by  the  War  and  Navy  Departments.  Inquiries  concerning  the \navailability  and  distribution  of  the  Summary  Technical  Report \nvolumes  and  microfilmed  and  other  reference  material  should  be \naddressed  to  the  War  Department  Library,  Room  lA-522,  The \nPentagon,  Washington  25,  D.  C.,  or  to  the  Office  of  Naval  Research, \nSUMMARY TECHNICAL REPORT, NDRC, DIVISION 6\nVOLUME 10\nBASIC METHODS FOR THE CALIBRATION OF SONAR\nEQUIPMENT\nOffice of Scientific Research and Development, National Defense Research Committee\nVannevar Bush, Director\nJames B. Conant, Chairman\nDivision 6\nJohn T. Tate, Chief\nWashington, D.C., 1946\n\nNational Defense Research Committee\nJames B. Conant, Chairman\nRichard C. Tolman, Vice Chairman\nRoger Adams, Army Representative\nFrank B. Jewett, Navy Representative\nKarl T. Compton, Commissioner of Patents\nIrvin Stewart, Executive Secretary\n\nArmy representatives in order of service:\nMaj. Gen. G. V. Strong\nCol. L. A. Denson\nMaj. Gen. R. C. Moore\nCol. P. R. Faymonville\nMaj. Gen. C. C. Williams\nBrig. Gen. E. A. Regnier\nBrig. Gen. W. A. Wood, Jr.\nCol. M. M. Irvine\nCol. E. A. Routheau\n\nNavy representatives in order of service:\nRear Adm. H. G. Bowen\nRear Adm. J. A. Purer\nCapt. Lybrand P. Smith\nRear Adm. A. H. Van Keuren\nCommodore H. A. Schade\nCommissioners of Patents: Conway P. Coe, Casper W. Ooms\n\nDuties of the National Defense Research Committee included:\n\n1. Recommending to the Director of OSRD suitable projects and research programs on the instrumentalities of warfare, along with contract facilities for carrying out these projects and programs.\n2. Administrating the technical and scientific work of the contracts.\n\nNDRC functioned by:\n\n1. Initiating research projects on requests from the Army or Navy.\n2. Initiating research projects on requests from allied governments through the Liaison Office of OSRD.\n3. Initiating research projects based on the experience of its members, on its own considered initiative.\n\nProposals for research contracts for performance of work involved in such projects were prepared by the Division, Panel, or Committee.\nThe text has been reviewed by NDRC, and if approved, recommended to the Director of OSRD. Upon approval of a proposal by the Director, a contract allowing maximum flexibility for scientific effort was arranged. The business aspects of the contract, including matters such as materials, clearances, vouchers, patents, priorities, legal matters, and administration of patent matters, were handled by the Executive Secretary of OSRC.\n\nOriginally, NDRC administered its work through five divisions: Division A \u2013 Armor and Ordnance; Division B \u2013 Bombs, Fuels, Gases, & Chemical Problems; Division C \u2013 Communication and Transportation; Division D \u2013 Detection, Controls, and Instruments; Division E \u2013 Patents and Inventions.\n\nIn a reorganization in the fall of 1942, twenty-three administrative divisions, panels, or committees were created.\nEach member had a chief selected based on outstanding work in the specific field. The NDRC members became a reviewing and advisory group to the Director of OSRD. The final organization was as follows:\n\nDivision 1 \u2014 Ballistic Research\nDivision 2 \u2014 Effects of Impact and Explosion\nDivision 3 \u2014 Rocket Ordnance\nDivision 4 \u2014 Ordnance Accessories\nDivision 5 \u2014 New Missiles\nDivision 6 \u2014 Sub-Surface Warfare\nDivision 7 \u2014 Fire Control\nDivision 8 \u2014 Explosives\nDivision 9 \u2014 Chemistry\nDivision 10 \u2014 Absorbents and Aerosols\nDivision 11 \u2014 Chemical Engineering\nDivision 12 \u2014 Transportation\nDivision 13 \u2014 Electrical Communication\nDivision 14 \u2014 Radar\nDivision 15 \u2014 Radio Coordination\nDivision 16 \u2014 Optics and Camouflage\nDivision 17 \u2014 Physics\nDivision 18 \u2014 War Metallurgy\nDivision 19 \u2014 Miscellaneous\n\nApplied Mathematics Panel\nApplied Psychology Panel\nCommittee on Propagation\nTropical Deterioration Administrative Committee, Library of Congress. NDRC FOREWORD. As events of the year's preceding 1940 revealed more and more the seriousness of the world situation, many scientists in this country came to realize the need for organizing scientific research for service in a national emergency. Recommendations they made to the White House were given careful and sympathetic attention, and as a result, the National Defense Research Committee [NDRC] was formed by Executive Order of the President in the summer of 1940. The members of NDRC, appointed by the President, were instructed to supplement the work of the Army and the Navy in the development of the instrumentalities of war. A year later, upon the establishment of the Office of Scientific Research and Development [OSRD], NDRC became one of its units.\nThe Summary Technical Report of NDRC is a conscious effort on the part of NDRC to summarize and evaluate its work and present it in a useful and permanent form. It comprises seventy volumes broken into groups corresponding to the NDRC Divisions, Panels, and Committees. The Summary Technical Report of each Division, Panel, or Committee is an integral survey of the work of that group. The first volume of each group\u2019s report contains a summary of the report, stating the problems presented and the philosophy of attacking them, and summarizing the results of the research, development, and training activities undertaken. Some volumes may be \u201cstate of the art\u201d treatises covering subjects to which various research groups have contributed information. Others may contain descriptions of devices developed in the laboratories. A master index.\nAll divisional, panel, and committee reports which together constitute the Summary Technical Report of NDRC are contained in a separate volume. This volume also includes the index of a microfilm record of pertinent technical laboratory reports and reference material.\n\nSome NDRC-sponsored researches which had been declassified by the end of 1945 were of sufficient popular interest that it was found desirable to report them in the form of monographs. For example, the series on radar by Division 14 and the monograph on sampling inspection by the Applied Mathematics Panel. Since the material treated in them is not duplicated in the Summary Technical Report of NDRC, the monographs are an important part of the story of these aspects of NDRC research.\n\nIn contrast to the information on radar, which is of widespread interest and much of which is released,\nThe public, research on subsurface warfare is largely classified and of general interest to a more restricted group. Consequently, Division 6's report is found almost entirely in its Summary Technical Report, which runs to over twenty volumes. The extent of a division's work cannot therefore be judged solely by the number of volumes devoted to it in the Summary Technical Report of NDRC. Account must be taken of the monographs and available reports published elsewhere. Any great cooperative endeavor must stand or fall with the will and integrity of the men engaged in it. This fact held true for NDRC from its inception, and for Division 6 under the leadership of Dr. John T. Tate. To Dr. Tate and the men who worked with him \u2013 some as members of Division 6, some as representatives of the Division\u2019s contractors \u2013 belongs the sin.\nThe Nation expresses its deep gratitude for the difficult and often dangerous job well done by the team. Their efforts significantly contributed to the success of our naval operations during the war and richly deserved the warm response they received from the Navy. In addition, their contributions to the knowledge of the ocean and to the art of oceanographic research will undoubtedly speed up peacetime investigations in this field and bring rich benefits to all mankind.\n\nThe Summary Technical Report of Division 6, prepared under the direction of the Division Chief and authorized by him for publication, presents the methods and results of widely varied research and development programs. It is essentially a record of the unstinted loyal cooperation of able men linked in a common effort to contribute to the defense of their Nation. To all of them, we extend our deep appreciation.\nVannevar  Bush,  Director \nOffice  of  Scientific  Research  and  Develofmient \nJ.  B.  CoNANT,  Chairman \nNational  Defense  Research  Committee \nFOREWORD \nONE  of  the  principal  responsibilities  placed  upon \nSection  C-4,  later  Division  6,  when  it  was  organ- \nized in  1941  was  that  of  developing  new  and  improved \nmethods  for  detecting  submerged  submarines.  Ex- \nperience had  shown  that  sound  is  the  only  form  of \nenergy  which  can  be  propagated  through  sea  water \nwith  sufficient  intensity  and  range  to  serve  as  a prac- \ntical method  for  detection.  For  this  reason  the  Section \ninitiated  at  once  a thorough  study  of  the  acoustical \nproperties  of  sea  water  as  well  as  of  methods  for  in- \njecting sound  energy  into  the  water  and  of  detecting \nits  presence  there.  Realizing  that  in  a study  of  this \nkind  accurate  measurement  in  terms  of  known  and \nreproducible  standards  is  essential,  the  Section  under- \nTook action in 1941 to develop a number of standard projectors and hydrophones covering useful frequency ranges and capable of accurate calibration in terms of energy output or input. Furthermore, the Section undertook the development of methods for calibrating these standards and applicable methods for the accurate testing of underwater sound gear under development or in production by various Government agencies. This activity was initially conducted under a contract at the Bell Telephone Laboratories, which established two calibrating and testing laboratories, the first at Mountain Lakes, New Jersey, and somewhat later a second at Orlando, Florida. The facilities of these two laboratories were made available to all organizations developing or manufacturing sound gear for the Navy.\n\nIn 1942, the operation of these two stations together\nWith the responsibility for further developing methods was transferred, along with many experienced personnel, from the Bell Telephone Laboratories to the Columbia University Division of War Research contract. The former organization continued the further development and particularly the construction of standard instruments, which have found wide use. From the time of transfer, the organization carrying on operations centering at Mountain Lakes and Orlando was known as the Underwater Sound Reference Laboratories and was under the direction of Dr. Robert S. Shankland. In addition to the two above-mentioned testing stations, various of the Division's other contractors found it necessary to establish at suitable locations less elaborate testing laboratories to facilitate the testing of sonar devices, systems, and methods at various locations.\nThe stages of its development are detailed in this report prepared by the Underwater Sound Reference Laboratories' staff. This report outlines the methods and procedures the Division believes can be followed in establishing and operating a sound reference laboratory. The potential scope of such a laboratory is indicated by including a description of its activities since its operation under Columbia University's Division of War Research.\n\nBesides the authors of chapters or sections in this report, many others made significant technical contributions to this development.\n\nThis four-year program, covered by this report, owes much to the continuous liaison provided by the Navy. The Division expresses its appreciation for their support.\nThe most helpful and cordial support and cooperation were received from the Office of the Coordinator of Research and Development and from the Bureau of Ships (942). A list of the principal Navy projects is provided on page 171. Manufacturers producing or developing sonar material under Navy contracts have cooperated wholeheartedly. In particular, members of their staffs willingly gave their time to the work of the Flydrophone Advisory Committee appointed by the Office of the Coordinator in April 1942. The structure and general scope of this committee are outlined on page 172.\n\nJohn T. Tate\nChief, Division 6\n\nPreface\n\nThis problem of developing and establishing accurate standards and procedures for calibration of underwater sound equipment required the attention of many laboratories operating under Navy contracts.\nDivision 6, NDRC. Although most of this work was originally done by the Bell Telephone Laboratories and later by the Underwater Sound Reference Laboratories of Columbia University, a number of other organizations contributed to the results summarized in this volume. Due to the wide scope of this field, it was not possible in the limited time allotted for the preparation of this volume to include a complete treatment of all the numerous contributions. The principal reports covering this complementary work have been included in the bibliography and are preserved in the form of microfilm records. In the preparation of this volume, the emphasis has been placed on the experience gained by Division 6 laboratories in developing testing methods and apparatus and in carrying through an extended program of precision measurements on underwater sounds.\nacoustic devices. The basic principles of these measurements are developed and systematized in close coordination with a description of the measuring and calibrating facilities of the test stations at Mountain Lakes, New Jersey and Orlando, Florida. It is believed that these descriptions are sufficiently complete to be of material service to other groups in setting up and maintaining similar equipment.\n\nAs the responsibility for preparing this volume was assigned by the chief of Division 6 to the staff of the Underwater Sound Reference Laboratories, the greater part of the material included is, by necessity, drawn from the experience of this group. The entire staffs of the Mountain Lakes and Orlando stations, as well as the staff of the New York office, have collaborated in all phases of the task of collecting and preparing this material.\nThis work depends on the following data: Edwin L. Carstensen, E. Dietze, W. Richard Elliott, Leslie L. Foldy, Frank H. Graham, Earle C. Gregg Jr., Erhard Hartmann, Norma Hartmann, F. William Hoffman, Paul F. Joly, Joseph B. Keller, Martin J. Klein, L. Pauline Leighton, Lucille Northrop, Henry Primakoff, Edward S. Rogers, Robert S. Shankland, Erwin E. Shrader, D. Bernard Simmons, Richard J. Tillman.\n\nAcknowledgement should also be made of contributions from Division 6 laboratories at the Massachusetts Institute of Technology, Harvard University, University of California, and Columbia University. In addition, valuable assistance was received from the Brush Development Company, Submarine Signal Company, the Radio Corporation of America, and the service laboratories of both the United States and British Navies.\n\nR. S. Shankland.\nCHAPTER 1\nINTRODUCTION\nRobert S. Shankland\nScientific programs require accurate standards and measurement techniques to ensure quantitative correlation and interpretation of phenomena under investigation. Understanding phenomena in quantitative terms allows accumulated data to be effectively and efficiently applied to the design of new equipment, the improvement of present designs, and the prediction of results obtainable with such gear. Section C-4, later Division 6 of NDRC, undertook studies and experimental investigations on the transmission of sound in ocean waters and the further development of sonar gear. This necessitated the provision of suitable practical standards and a study of measurement techniques. The results accomplished form the principal subject of this volume.\nIn the development of apparatus for service use, the primary criterion is the effectiveness of the equipment under operational conditions. In the case of sonar gear, operational tests are not only expensive and time-consuming but are performed at that stage in development when design changes are most difficult to achieve. Therefore, laboratory tests under controlled conditions, directed toward determining design changes which will produce maximum effectiveness under operational conditions, are a necessary adjunct to a program of research and development.\n\nI. Development of Measurement and Calibration Techniques\n\n* Establishment of Standard Sound Fields\n\nTo make the results of the several laboratories engaged in subsurface warfare research directly comparable, it was necessary to reduce their test data to a common standard.\nThe program required common terms and continuous progress towards higher standards of accuracy. The Underwater Sound Reference Laboratories (USRL) were tasked with establishing reference levels and providing calibrated standards to other laboratories. Initially, standardization was based on hydrophones, developed in cooperation with Bell Telephone Laboratories (BTL), whose absolute calibrations could be obtained from their design or comparison with well-established air acoustics standards. Later, the reciprocity method of calibration was found to provide improved accuracy and simplified procedure.\n\nThe reciprocity method of calibration was suggested by Ballantine and MacLean but received little attention until it was applied to the underwater sound field.\nThe establishment of underwater sound fields led by USRL has facilitated accurate calibration of standards for frequencies ranging from about 10 Hz to 2.5 MHz, with potential for higher frequencies. The lower frequency limit was determined by the difficulty of making low-frequency measurements in a shallow lake and not by reciprocity method failure. In the range from 100 Hz to 100 kHz, this method is accurate to within \u00b11 dB. A comparison of standard levels obtained by reciprocity calibration at USRL with those independently established at British laboratories showed excellent agreement. Other calibration methods, including a low-frequency pressure tank built by BTL and the CMF self-calibrating condenser hydrophone built by MIT, successfully extended the low frequency limit below.\n1.1 Development of Standard Instruments: Although the BTL, operating under an OSRD contract, was primarily responsible for the development of hydrophones and projectors suitable for use as standards, many other laboratories constructed standards tailored to their specific applications. Instruments utilizing piezoelectric crystal, magnetostrictive, condenser, and electrodynamic coupling collectively cover the 1 Hz to 2.5 MHz frequency range. Many of these instruments have flat responses over wide frequency ranges. For instance, the 3A type crystal hydrophone boasts a flat response from approximately 100 Hz to 25 kHz, and the XMX crystal hydrophone has a flat response within \u00b12 dB from below 100 Hz to around 100 kHz. These instruments were not only useful for single frequency measurements but also for recording transients and measuring impulse responses.\nSignals covering a wide frequency band. In the majority of cases, these instruments were also characterized by mechanical ruggedness and stability of calibration. Considering the fact that acoustic standards for underwater applications were almost non-existent before 1940, the rapidity and comprehensiveness of subsequent developments in the art are noteworthy.\n\n1.1.3 Objectives of Tests and Calibrations\n\nAlthough the necessity for development and production tests of underwater sound gear was soon recognized, the specific objectives of such tests and calibrations became apparent with further development. Although this problem is still not completely solved, much has been learned concerning the significance of the various factors which characterize efficient operation of sonar gear. Due to the large number of tests required and the limited facilities.\nAvailable for use, it was necessary to focus on determining factors that depend on the specific application for which the equipment was designed. Factors such as frequency response, directivity, impedance, signal-to-noise ratio, and efficiency were significant in most measurement programs. However, other quantities including rear response, side lobes, tuning, harmonic distortion, and variability with temperature and pressure were equally important.\n\nQuantitative relationships between the foregoing quantities and the operational efficiency of underwater sound devices were only imperfectly understood at the program's inception. Theoretical and experimental studies undertaken provided a more exact understanding of these relationships and a sounder basis for compromise between competing factors in design, consequently, improving the overall design process.\nThe basis for selecting important parameters to be measured in development and calibration tests is crucial. The relationship between development, calibration, and testing, as well as operational and tactical application of the equipment, was invaluable in unifying the program as a whole and directing it towards its prime objectives.\n\nTesting Technique\n\nWith reference standards available and increased knowledge of significant parameters, the technique of performing a calibration test remained to be considered. Since these parameters were characteristic of the devices under test and needed to be distinguished from extraneous effects produced by the test location and the equipment involved, a large part of the effort of the USRL, as well as that of other laboratories engaged in equipment development, was directed toward devising measurement techniques.\nThe principal problems in testing gear at laboratory sites stem from the limited extent of the testing medium. Acoustic reflections from the surface, bottom, and shores of the body of water where tests are made, and the limited testing distance available, required the development of means for eliminating the effect of these factors. To accomplish this, baffles and screens, directional sources, proper orientation of instruments, pulses and noise bands have been used for eliminating the effect of reflections. Spherical wave corrections have been applied to compensate for effects caused by short testing distance. Additionally, equipment was designed to reduce the time and labor necessary for performing tests with maximum use of available facilities. Among devices in this category are automatic recorder devices (linear and polar).\namplifiers,  arrangements  for  rapid  changes  in  driv- \ning and  receiving  impedances,  adjustable  and  inter- \nchangeable rigging  gear,  and  computing  aids  to \nfacilitate  the  reduction  of  data.  Techniques  for  test- \ning in  indoor  tanks  under  varying  conditions  of  tem- \nperature and  pressure,  for  testing  at  high  power \ninputs,  and  for  measuring  impedance  under  various \nconditions  were  developed  as  the  need  arose.  With \nexperience,  the  technique  of  testing  underwater \nsound  devices  grew  as  an  art  as  well  as  a science. \nClose  liaison  with  developments  in  the  field  of  under- \nwater sound  was  essential  to  insure  the  adaptability \nof  testing  techniques  and  facilities.  This  flexibility \nmade  possible  the  realization  of  the  potentialities  of \nlaboratory  testing  in  the  development  of  underwater \nsound  devices. \nFUNDAMENTAL  STUDIES  AND  OPERATIONAL  PERFORMANCE \n\u2022 2 ROLE  OF  PRECISION  ACOUSTIC \nMEASUREMENTS  IN  THE \nImprovements in underwater sound equipment: Improvements in transducer design, particularly in the period 1940-1945, highlight the significance of precise acoustic measurements and fundamental research in enhancing sonar gear. Two types of electroacoustic coupling, magnetostrictive and piezoelectric, were found most useful. Fundamental investigations into magnetostrictive phenomena conducted by Navy Division C and industrial laboratories significantly increased knowledge of power loss sources in magnetostrictive transducers. This knowledge application led to a 400% increase in transducer efficiency. This improvement markedly enhanced operation and greatly reduced the bulk, cost, and critical materials requirements of the equipment. Improvement in equipment using piezoelectric transducers.\nCrystal coupling closely parallels that obtained for magnetostrictive equipment. Initial efficiencies of the order of 10 to 20 percent have been increased to values as high as 75 to 80 percent. Improvements in transducers have not been limited to increased efficiency. The development of ammonium dihydrogen phosphate (ADP) crystals made possible crystal transducers with negligible temperature dependence and, more importantly, with the ability to withstand greater temperature extremes without damage. Furthermore, new construction methods for both crystal and magnetostriction transducers made possible the fabrication of transducers with special characteristics. Many other examples of specific improvement are available to demonstrate the importance of fundamental research.\n\nIn 1942, one of the most pressing sonar problems was improving dome design.\nThe problem was that of designing domes which, when mounted on vessels, would not hopelessly distort the directional patterns of the transducers they enclosed. Internal reflections from the dome walls, then available, were nullifying the effort to attain satisfactory directional patterns. This effect, combined with the high transmission loss through the dome wall sharply reduced the effectiveness of the equipment. British experience in meeting this problem, along with an experimental research program on domes at the National Research Laboratory, Division 6 NDRC laboratories, and at the Bell Telephone Laboratories, supplemented by theoretical research, effectively demonstrated the principles necessary to reduce internal reflections to a negligible amount.\nThese principles enabled various manufacturers to produce acoustically satisfactory domes with high mechanical strength without a corresponding increase in thickness of the dome wall. The solution to the dome problem during 1943 was so effective that dome construction was never again a major issue.\n\n1.3.1 Fundamental Studies and Operational Performance of Underwater Sound Equipment\n1.3.1.1 Relation to Calibration and Test Measurements\n\nIt has previously been stated that the goal of anti-submarine research is improvement in operational performance of gear. The relation of fundamental studies to operational performance is largely indirect and expresses itself in their influence on development. One of the purposes of these studies has been to determine the relationship between parameters (power output, response, directivity, signature).\nThe relationship between nal-to-noise ratio and other parameters of underwater sound gear to its effectiveness in operation is important. This relationship helps determine operational effectiveness through laboratory measurements on the gear itself. Such a technique offers several advantages: (1) time and effort efficiency, (2) closer liaison with development work, (3) the possibility of making tests under controlled conditions at any time, and (4) clearly defined conclusions from tests.\n\nStudies also reveal important information regarding the equipment design. In evaluating the relationship between gear parameters and operational performance, they indicate the relative importance of the parameters and establish the most effective changes for improving operational performance of the gear.\nImprovements are often inherently contradictory. These studies may be useful in indicating the most advantageous compromise, not only for gear in general, but also in view of particular conditions of service, and for particular types of equipment.\n\nThe studies have been carried out on a more comprehensive basis, directed toward evaluating the relative effectiveness of different classes of gear by obtaining information in controlled surroundings.\n\n1.3.3 Relation to Manufacturing Requirements and Specifications\n\nThere is still another important application of fundamental calibration measurements on underwater sound gear: as an aid to the establishment of manufacturing acceptance requirements. Whenever it is necessary to manufacture equipment in production quantities, it is often impossible, because of considerations of time and facilities available, to carry out extensive testing in actual operating conditions. In such cases, calibration measurements made under controlled conditions can provide valuable data for establishing manufacturing requirements and specifications.\nable to test each unit produced completely. It is therefore necessary to examine critically those factors of prime importance in determining satisfactory operation of the equipment and to establish limits of acceptable performance. These limits should be primarily based on careful studies of the gear under controlled conditions, keeping always in mind the influence of various factors on operational performance.\n\nCalibration measurements under controlled conditions are not only an aid in determining specifications but also suggest methods for determining whether manufactured equipment is within the limits set by the specifications.\n\nChapter 2\n\nOPERATION AND APPLICATION OF UNDERWATER SOUND DEVICES\n\nBy Leslie L. Foldy\n\nCalibration work for underwater sound is concerned primarily with devices which convert electric energy into acoustic energy (projectors) and, consequently, with the measurement of their performance.\nVersely, those which convert the energy of a sound field into electric energy (hydrophones). Generically, these devices are known as electroacoustic transducers. To provide a suitable background for the detailed discussion of the problems involved in calibrating transducers, this chapter presents a brief discussion of (1) the physical principles underlying the action of transducers, and (2) their uses.\n\n1. PRINCIPLES OF OPERATION OF TRANSDUCERS\n\nAs already noted, energy conversion is the fundamental purpose of transducers. Most transducers can convert energy in either direction, that is, they are reversible. According to the nature of the physical process used in the energy conversion, transducers may be classified under four general headings, namely electro-dynamic, electrostatic, piezoelectric, and magnetostriction. The principles involved in each are discussed below.\n\nElectro-dynamic transducers operate on the principle of electromagnetic induction. When a coil of wire is placed in a magnetic field and a current is passed through it, an electromotive force (EMF) is induced in the coil. Conversely, when an EMF is applied to a coil, a magnetic field is generated around it. This principle is used in microphones and loudspeakers.\n\nElectrostatic transducers operate on the principle of the attraction and repulsion of charged bodies. When a voltage is applied between two plates, an electric field is established between them. If a diaphragm is placed in this field and vibrated, the resulting changes in the electric field produce a current in an external circuit. Conversely, if a current is passed through the plates, an electric field is established which can cause a diaphragm to vibrate. This principle is used in capacitor microphones and electrostatic speakers.\n\nPiezoelectric transducers operate on the principle of the direct conversion of mechanical energy into electric energy. Certain materials, such as quartz and tourmaline, exhibit the property of piezoelectricity, which means they generate an electric charge when subjected to mechanical stress. Conversely, an electric field applied to these materials can cause them to deform mechanically. This principle is used in piezoelectric microphones, sensors, and actuators.\n\nMagnetostriction transducers operate on the principle of the conversion of magnetic energy into mechanical energy. When a magnetic material is subjected to a changing magnetic field, it undergoes a dimensional change, known as magnetostriction. This principle is used in magnetic transducers such as magnetostrictive sensors and actuators.\nThe simplest example of an electrodynamic transducer is a moving-ribbon instrument, as depicted in Figure 1. It consists of a rectangular metallic strip or ribbon suspended in a magnetic field. When the instrument is in a sound field, there is typically a pressure difference established between its front and back. Due to the mass difference between the ribbon and the magnet, relative motion ensues, inducing an electromotive force in the moving ribbon. Conversely, if an alternating current flows through the suspended ribbon, the forces on it due to the interaction of the current and the external magnetic field produce vibration. This vibratory motion in turn creates a sound field in the medium. These matters are discussed in detail in Division 6.\nTransducers for magnetostriction and crystal. Electrodynamic transducer (pressure-gradient type). This type of transducer has electrodes on both ends, which end on the pressure difference between the front and back of the ribbon, making it a pressure-gradient hydrophone. Electrodynamic transducers that operate based on the value of the pressure at a point in the medium, rather than the gradient of the pressure, can also be considered. A simple example is a transducer with a diaphragm mounted in a water-tight housing such that only one face is exposed to the water (see Figure 2), and the pressure in the housing is adjusted to compensate for external hydrostatic pressure. A coil encircling a fixed magnet is rigidly fastened to the unexposed face.\n\nFigure 1: Electrodynamic transducer (pressure-gradient type).\n\nOperation and application of sonar devices.\nFigure 3. Electrostatic transducer. The diaphragm and coil are set into vibration relative to the magnet when the instrument is in a sound field. This vibration changes the flux linked by the coil, inducing an alternating emf in it. Conversely, the force due to the interaction of an alternating current through the coil and the field of the magnet gives rise to vibrations of the coil and diaphragm, generating a sound wave in the medium.\n\nElectrostatic, piezoelectric, and magnetostriction transducers are generally pressure rather than pressure-gradient instruments. Thus, a condenser-type transducer uses an electrostatic field to convert acoustic into electric energy and vice versa. An example of the condenser-type instrument is shown in Figure 3.\nA constant potential is applied between the condenser's plates. When the instrument is in a sound field, the movable plate vibrates with respect to the fixed plate, changing the distance and capacity of the condenser. The voltage across the plates is inversely proportional to the capacity, generating an alternating voltage. Conversely, applying an alternating electric potential to the plates changes the force between them, causing vibration of the movable plate.\n\nThe other two types of reversible transducers depend on less familiar physical phenomena. The first of these is the piezoelectric effect. Certain crystals, when subjected to compression, exhibit electric charges on their faces; under tension, they produce electric voltage.\nThe charges are reversed. The inverse piezoelectric effect also exists: the crystals expand when a potential of one sign is applied across the faces and contract when an opposite potential is applied.\n\nTo electrical terminals\n\nFigure 4. Piezoelectric transducer.\n\nThe faces on which the charges appear when the crystal is subjected to stress depend on its structural properties. A tourmaline crystal, for example, is one of the simplest in terms of piezoelectric effects. Tourmaline possesses a single piezoelectric axis such that a stress in the direction of this axis produces charges on the faces normal to it. Thus, in Figure 4, if a stress is applied in the direction of the piezoelectric axis Z, charges appear on faces a and a'. Conversely, applying a potential between a and a' causes the crystal plate to expand or contract.\nThe simplest type of piezoelectric transducer consists of a tourmaline crystal in contact with two metal condenser plates. Applying an alternating potential to the plates causes the crystal to expand and contract. Immersing the system in water generates a sound field through the vibration of the plates. Conversely, vibrations produced by placing the crystal and condenser plates in a sound field give rise to an alternating voltage on the plates.\n\nThe fourth type of transducer operates on the principle of the magnetostrictive effect, which shares some similarities with the piezoelectric effect. A rod or tube of ferromagnetic material (iron, cobalt, nickel, or various alloys containing these elements) undergoes length changes when exposed to a magnetic field. For tourmaline, the changes in length are small.\nThe fractional change in length per unit electric field (1 volt per centimeter) is maximized when the frequency of the impressed voltage or sound field coincides with the natural mechanical resonance frequency of the crystal.\n\nDirectivity of Transducers\n\nThe length of certain metals changes slightly when brought into a magnetic field parallel to its length. This change in length is independent of the sign of the field and may be either an increase or decrease, depending on the nature of the material, its previous treatment, the degree to which it was previously magnetized, and the temperature. This phenomenon is reversible. In other words, if a previously magnetized material is demagnetized, the length change will reverse.\nA nickel rod's magnetization decreases when stretched and increases when compressed. When a coil of wire is placed around the rod, an emf is induced due to magnetic flux changes caused by elastic deformation. Similarly, changes in the rod's magnetization from external alternating current induce periodic oscillations in its length. This magnetostriction transducer is essentially a ferromagnetic rod surrounded by a coil. It's worth noting that there are also irreversible transducers, such as the carbon microphone. Pressure changes on a diaphragm caused by an impinging sound field produce changes in electrical resistance of contacts.\nBetween carbon particles, an alternating current is generated, given that a source of constant potential is present.\n\n22. DIRECTIVITY OF TRANSDUCERS\n\nThe variation with direction of the emitted sound intensity, referred to the transducer acoustic axis, is called the directivity of the transducer on transmitting. In a similar manner, the directivity of the transducer on receiving is defined as the variation of the output voltage for a plane-wave sound of given intensity.\n\nThe fractional change in length is approximately ten parts in a million for fields up to 1,000 gauss.\n\nIt is noted that since the increase or decrease in length of the magnetostrictive rod is independent of the sign of the magnetic field, an originally unmagnetized rod vibrates at twice the frequency of the impressed field, while a rod which has been magnetized vibrates at the same frequency.\nA magnetized object vibrates at the impressed frequency when sufficiently magnetized by another constant (polarizing) field. The maximum amplitude occurs when the impressed and natural frequencies of vibration coincide.\n\nThe transducer's acoustic axis is arbitrarily selected, but is usually chosen to be an axis of symmetry of the instrument, such as the normal to a plane vibrating diaphragm.\n\nFigure 5. Magnetostriction transducer.\n\nThe density of incident sound waves varies in different directions with respect to the axis. Directivity on transmission results from the superposition at a point in space of sound wavelets emitted by different portions of the diaphragm, and consequently having different amplitude and phase. On reception, the directivity is the result of the incidence on different portions of the transducer diaphragm of wavelets of sound which have, at the diaphragm, different amplitudes and phases depending on the orientation.\nThe directivity of diaphragms, in relation to their propagation direction, is generally determined by the ratio of the sound wave length to the diaphragm dimensions. For a plane piston diaphragm with large dimensions compared to a wavelength, the transmitted sound field, at large distances from the transducer, is centered about the transducer acoustic axis. The sound is emitted in the form of a \"searchlight\" beam. Conversely, on reception, the transducer is sensitive only to sound signals incident in directions close to and along the axis. Subsidiary maxima (side lobes) in directions far from the axis are usually present. However, these are strongly dependent on the exact velocity distribution along the diaphragm and are typically small compared to the main or searchlight beam.\nIf the wave length is large compared to the diaphragm dimensions, the sound is emitted uniformly in all directions. In this case, the transducer response on reception is independent of the direction of sound incidence. Transducers obeying the reciprocity theorem (see Chapters 3, 4, and 5) have the same directivity on transmitting and on receiving.\n\nBy constructing a transducer with a plane diaphragm and a velocity distribution which is greatest at the center of the diaphragm and which decreases toward the edges (shading), it is possible to obtain a directivity distribution with side lobes much smaller than in the case of a constant velocity distribution; the width of the main beam is, however, larger in this case.\n\nTransducer, with a pulsating cylindrical surface of a certain length, can be used as a sonar device.\nThe length which is large, and a diameter which is small, compared to a wave length. Here, the sound is emitted uniformly in all planes containing a cross section of the cylinder, while in perpendicular planes, the sound is concentrated in a beam.\n\nApplications of underwater sound devices in naval operations can be roughly divided into two categories: tactical and non-tactical. Tactical applications include the detection of surface vessels, submarines, torpedoes, mines, and underwater phenomena by surface vessels and submarines. Non-tactical applications include: fathometer depth determinations by surface craft and submarines; monitoring of noise output by submarines; underwater communication by code or voice; fundamental studies on sound propagation in the ocean, on ship noises, and on underwater communication.\nTactical applications of sonar gear involve either echo ranging or listening. In echo ranging, devices emit a pulse or continuous-wave signal, which may be of either sonic or supersonic frequency. If the signal strikes a target, part of its energy is reflected back to the emitting device (the projector), which receives the signal. Conclusions may be drawn regarding the range, bearing, speed, and nature of the target based on characteristics such as frequency shift and time delay between emission and reception. In listening, any supersonic or sonic signal or noise emitted by a target activates a receiving device.\nDevice which, from the characteristics of the signal or noise (intensity, frequency, and direction), enables conclusions to be drawn regarding the range, speed, bearing, and nature of the target.\n\nEcho-Ranging Gear\n\nConventional searchlight echo ranging gear, employed in the last war, may be classified according to its tactical use as antisubmarine or prosubmarine. Searchlight-type gear is in general use in both the United States and British Navies. Searchlight-type echo-ranging gear consists of a projector with either a square or circular diaphragm operating on the piezoelectric or magnetostrictive principle. The dimensions of the projector are, as a rule, considerably larger than the wavelength of sound.\n\n1. The distinction between tactical and non-tactical applications is, of course, rather arbitrary and by no means rigid.\n2. Searchlight-type gear is in general use in both the United States and British Navies.\n3. Searchlight-type echo-ranging gear consists of a projector with either a square or circular diaphragm operating on the piezoelectric or magnetostrictive principle.\n4. The projector dimensions are larger than the sound wavelength.\nThe projector emits a relatively narrow beam, which axis can be rotated in a horizontal and vertical plane. Upon application of a suitable pulse voltage, the projector emits supersonic pulses lasting from 10 to 200 milliseconds. Immediately after transmission, the projector switches from transmitter to receiver. Any received reflected supersonic pulse is either directly rectified and presented visually on the cathode-ray tube screen or heterodyned to an audible frequency and presented through a loudspeaker. The time delay between transmission and reception measures the target's range from the projector, while the projector's (or beam) axis orientation in space at the instant of transmission provides the relative target bearing.\nAny difference between the frequency of the emitted and received pulse (the Doppler effect) is a measure of the target's speed. The quality of the received (heterodyned) pulse often provides information about the target's nature, such as distinguishing a submarine from its wake. Considerable information about the target's position, motion, and nature is obtained.\n\nBy systematically training the projector in azimuth (i.e., following a definite search plan), it's possible to sweep a sector of ocean where the target's presence is known or suspected. In echo ranging by surface craft in search of submarines, the target may be found at different depths and ranges, so the width of the beam of the main projector is not always adequate for maintaining contact. In such cases, auxiliary projectors may be employed.\nApplications of Various Searchlight Echo-Ranging Devices:\n1. Detection of submarines by surface craft.\n2. Detection of submarines by harbor installations.\n3. Detection of submarines and surface craft by submarines.\n4. Detection of small objects such as mines, torpedoes, landing obstacles, and shoals by surface craft, submarines, and swimmers.\n\nListening Gear:\nThe second tactical application of sonar gear involves listening. Any supersonic or sonic signal or noise emitted by the target and reaching the hydrophone is picked up and presented to the operator. If the incident signal is not of an audible frequency to begin with, the resultant hydrophone output may be heterodyned to an audible frequency.\n\nIntensity, frequency, and direction of incidence.\nThe signal enables conclusions to be drawn regarding the nature, speed, range, and bearing of the target. In particular, if a directional hydrophone is used, the bearing of the target may be determined from the direction of orientation of the hydrophone axis at the position of maximum response.\n\nThe following specific tactical applications of listening can be listed:\n\n1. Sonic and supersonic listening for submarines from antisubmarine craft, harbor installations, other submarines, and expendable devices, sonobuoys, etc. Supersonic listening is preferable to sonic listening in these cases due to the high directivity generally obtainable with supersonic gear. Super-sonic hydrophones on antisubmarine craft, harbor installations, and submarines can also pick up the emitted echo-ranging pings of enemy submarines.\n2. Sonic and supersonic listening for surface craft.\nSubmarines use sonic and supersonic listening, primarily with directional hydrophones, to detect the noise output of merchant craft in convoys, antisubmarine craft, and other enemy warships. Submarines often overhear the echo-ranging pings of antisubmarine craft on supersonic listening gear.\n\nHydrophones used in practice come in various constructions, sizes, and shapes, but typically operate on the piezoelectric or magnetostrictive principle.\n\nThe directional receiving hydrophone may be the projector of the supersonic echo-ranging gear, set up electrically for signal reception.\n\nA sonobuoy is a device containing a hydrophone and a radio transmitter. When the hydrophone receives a signal from a target (the submarine), it is transmitted by radio.\nLink to patrolling antisubmarine craft: the high directivity is desirable for two reasons: it leads to greater hearing accuracy and minimizes self and ambient noise pickup of the gear. Craft and submarines. Cavitation noise from a moving torpedo may be detected by directional supersonic listening gear, and appropriate evasive action may be taken.\n\n2.3.2 Nontactical Applications\nNontactical applications of sonar gear include the use of standard projectors and hydrophones for the calibration of other kinds of sonic and supersonic devices, determination of physical parameters of sonar devices, and analysis of the physical parameters of a particular type of gear to determine its suitability for the tactical or other purpose at hand. A somewhat related nontactical application is the use of standard projectors and hydrophones for testing echo-ranging.\nListening gear is installed on antisubmarine craft and submarines, allowing a submarine to monitor its own sonic and supersonic output. Nontactical applications of sonar gear include depth determination by surface craft and submarines using fathometer gear. Fathometer gear, similar in construction and operation to supersonic echo-ranging gear, emits short supersonic pulses and records reflections from the ocean bottom. Sonar gear (standard hydrophones and projectors) can also be used to study the sound output of disturbances and determine the sound-absorbing and reflecting properties of various materials. A further nontactical application involves the use of transmitting projectors and receiving hydrophones for underwater communication using code or speech-modulated supersonic signals.\nsurface and subsurface craft. Finally, an important non-tactical application of sonar gear involves its use in fundamental studies of sound propagation in the sea under various oceanographic, surface, and bottom conditions. This includes the study of surface and bottom reflection, refraction, attenuation, scattering, and reverberation. The study of various types of noise background (ship's noise, ambient noise, and target noise) and of the reflecting power of various targets should be mentioned in this connection. Such fundamental studies are useful in determining the relation of gear operational efficacy to gear parameters with a view toward optimum sonar design.\n\nCalibration typically involves the determination of the axis response, directivity, efficiency, and anti-power output of the device. (See Chapter 4.)\n\nChapter 3\n\nGeneralized Theory of Electroacoustic Transducers\nLeslie L. Foldy and Henry Primakoff, \"Introduction\n\nFollowing the qualitative discussion of various simple idealized transducers given at the beginning of the preceding chapter, a generalized theory of linear passive electroacoustic transducers is developed. Attention is centered on deriving relationships true for all linear passive transducers, rather than on a detailed analysis of particular types. There is a rather complete analogy between the theory of electroacoustic transducers, taking into account the properties of the sound field, and that of electro-mechanical transducers, where only one mechanical degree of freedom is present. Consequently, this discussion is carried through in fairly abstract terms, insofar as this can be done without undue mathematical complexity. Analogies are pointed out as they occur.\n\nAn electroacoustic transducer is a device for transforming acoustic energy into electrical energy or vice versa.\nforming electric  energy  into  acoustic  energy,  or  vice \nversa.  If  all  the  energy  delivered  by  the  transducer  to \nthe  electric  or  acoustic  systems  to  which  it  is  con- \nnected is  derived  from  power  absorbed  by  the  trans- \nducer from  these  systems,  the  transducer  is  said  to  be \npassive.  This  does  not  prohibit  the  presence  of  active \ninternal  sources  of  power  such  as  are  used  to  provide \npolarizing  voltages  and  currents  in  some  types  of \ntransducers,  provided  that  these  internal  sources  do \nnot  supply  power  to  the  electric  or  acoustic  systems \nto  which  the  transducer  is  connected. \nSchematically,  an  electroacoustic  transducer  may \nbe  represented  as  a pair  of  electric  terminals,  by \nmeans  of  which  connection  to  electric  systems  is \nmade,  and  a closed  surface\u2018s  which  is  in  contact  with \na medium  capable  of  propagating  sound.  The  sim- \npler electromechanical  transducer,  which  may  be \nFigure 1 depicts an electroacoustic transducer represented by a four-terminal electromechanical network, consisting of a box with a pair of electric terminals and a pair of mechanical terminals. Only transducers with an acoustically active diaphragm are considered, where only part of the surface needs to be acoustically active.\n\nThe diaphragm vibrates in such a manner that its normal velocity is consistent across all points, denoted as rigid vibration. Although this restriction can be removed, the theory can be developed for any type of vibration, as discussed later. For the sake of simplicity, this case is addressed in the following treatment, which encapsulates the essential physical principles of the problem.\n\nThe quantities of interest, expressed as functions of time t, are as follows: the voltage E(t) across the terminals.\nThe electric terminals of the transducer receive the current I(t). The normal velocity Vn(t) of the diaphragm and the total force F(t) on the diaphragm are also important. The total force can be considered as the integral over the diaphragm of the pressure at each point on its surface. The pressure and particle velocity of the sound field at any point in the medium are also of interest.\n\nConsider the steady state, where all quantities vary harmonically with the time with the same frequency: Et = Ee^*, Vn t = Vn, etc. For electro-acoustic transducers in which the diaphragm vibrates rigidly, it is found that any two of the four quantities E, Vn, F, and V determine the values of the other two. Take I and Vn as independent variables. The most general equations for a linear transducer of this type are then:\n\nF = ZoVn - k I\n\nEquations for Impedances\nWhere Zq, k, k', and Zj are independent of E, I, F, and Vn but are in general functions of frequency. Equations of the type (1) and (2) have been shown to apply to the majority of electroacoustic transducers in use, at least for limited ranges of the variables.\n\nConsidering the physical significance of the terms in equations (1) and (2), it is seen that Zq is the force on the diaphragm divided by the velocity when the current is zero. Let Zq be the open-circuit mechanical impedance of the transducer. The constant k gives the force developed per unit current into the transducer when the diaphragm is completely constrained (Vn = 0). Therefore, k is called the electroacoustic transfer constant. Similarly, k', the open-circuit voltage per unit diaphragm velocity, is called the acoustoelectric transfer constant. The term Zj gives the impedance of the transducer's electrical input terminals when the diaphragm is not deflected.\nThe voltage developed for a unit current when the diaphragm is constrained and not moving is called the blocked electric impedance. The equations for a simple electromechanical system are of the same form as equations (1) and (2). This is expected since the assumption that Vn is constant reduces the problem to one mechanical degree of freedom. In the acoustic case, however, the properties of the sound field are included, as discussed below.\n\nA transducer converts acoustic energy into electric energy. We may write:\n\nThe interpretation is more complicated in this case: The term Fq really consists of two parts, E'inc + frigid diffr. The first, E'inc, is the force on the diaphragm that would be present if the transducer had no effect on the incident sound field. The second part, frigid diffr, should be considered as representing the difference in pressure between the incident and the transmitted sound.\nThe force on the diaphragm is due to the sound that would be diffracted by the transducer if it were perfectly rigid. The symbol z represents the radiation impedance, and the term (- zv2) is the force on the diaphragm due to the additional sound pressure created by the transducer's motion in the sound field. When the transducer is used to convert electric energy into acoustic energy, there is no external sound field, and the equation becomes:\n\nzv = Fq / (1 + (v2 / zi.))\n\nIt should be noted that equation (5) corresponds to the equation for an electromechanical transducer coupled to a source of generated force Fq and internal mechanical impedance zi.\n\nConsider now the relationships that obtain when an electroacoustic transducer is coupled to electric elements or to a medium capable of propagating sound. When the transducer is used to convert acoustic energy into electric energy, the input impedance is given by:\n\nZin = R + (1 / (1 / zi. + 1 / zL))\n\nwhere R is the resistance of the electric circuit, zL is the impedance of the load, and zi. is the internal impedance of the transducer.\n\nWhen the transducer is used to convert electric energy into acoustic energy, the impedance is given by:\n\nZo = R + jw(C1 + C2) + (1 / (1 / zi. + 1 / (w2 * M)))\n\nwhere R is the resistance of the electric circuit, C1 and C2 are the capacitances of the transducer, w is the angular frequency, and M is the mass of the diaphragm.\nThe transducer converts electric energy into electric energy by terminating it in an electric impedance, which is the load impedance Z2 across its electric terminals. When the transducer converts electric energy into acoustic energy, a voltage source with internal impedance Zjnt is connected to the electric terminals. The problem of coupling on the acoustic side can be treated similarly. The linearity of the equations ensures the possibility of treating functions with any time dependence using Fourier analysis.\n\nThe next problem is the determination of the effective impedances, electric and acoustic, of the transducer under various conditions of coupling. Begin with the effective electric impedance, defined as the ratio of voltage to current Ejl. The value of this impedance is:\n\n33. Impedances\n\nThe effective electric impedance is defined as the ratio of voltage to current Ejl. Its value is:\n\n(voltage / current) = (V / I) = Ejl\n\nThe effective acoustic impedance, defined as the ratio of acoustic pressure to particle velocity, will be discussed later.\nThe dependence of impedance on acoustic coupling is determined by the case of a transducer in an infinite source-free medium. The force on the diaphragm is given by equation (6) as F = -zVn. Substituting (6) into equations (1) and (2), we find:\n\nSolution of these equations shows that the effective electric impedance Z^^ is given by:\n\nZ^^ = Zsi + Zs'\n\nThe difference between Zsi and Zs' is called the motional impedance Zs. Thus:\n\nZs' < Zs < Zs + Zr\n\nZk being the contribution to Zsi which results from the motion of the diaphragm.\n\nConsider now the effective acoustic impedance, defined as the ratio of force to normal velocity, F/vn. The term dependent on electric coupling conditions is represented by a load impedance Zl connected to the electric terminals, so from equation (3):\n\nZl = R + jXc\n\nWhere R is the resistance and Xc is the capacitance. The impedance matching between the transducer and the load is achieved when Zl = Z^^.\nSubstituting (3) in the basic equations (1) and (2), we obtain:\n\nS = -\u222b\u222bS\u2032(r\u2032)G(R, r\u2032)dS\u2032, where S\u2032 is the pressure on the transducer surface, p the medium density, \u03c9 the angular frequency, and G(R, r') the Green's function. Physically, it is the pressure produced at point R due to a point source of unit strength at point r'.\nThe diaphragm of the transducer did not move. G(R, r) is simply G(R, R') with R' taken at the point r on the closed transducer surface S. It can be shown that such a function can in principle be calculated for all ordinary surfaces S, and it is symmetric in its arguments, that is, G(R, r) = G(r, R. The function g(R) is introduced as an abbreviation for the integral\n\nThe various impedances associated with an electro-acoustic transducer have been expressed in terms of the fundamental transducer constants and the conditions of coupling. The sensitivities of a transducer are considered next. Two types of sensitivity are of interest: the transmitting or electroacoustic sensitivity and the receiving or acoustoelectric sensitivity. Expressions for these are obtained, and a proof of the reciprocity theorem, which is basic in much of under-\n\n(Assuming the text is in English and does not require translation or significant correction)\nThe transmitting sensitivity of a transducer is defined as the ratio of the pressure developed by the transducer at point R, when driven electrically, to the input current to the transducer. In practice, point R is taken as a point at a unit distance (1 meter) on the axis of symmetry of the transducer. The transmitting and receiving sensitivities, defined here, have a close relationship to the transmitting and receiving responses (see Chapter 4). For simplicity, we shall denote a point in the medium by its position vector R from an arbitrary origin rather than by its coordinates.\n\nThe transmitting sensitivity Green's function, G(R, R'), is defined mathematically as a solution of the wave equation, which has a pole of residue unity.\nThe point R = R' satisfies boundary condition 9G (R, R')/9n = 0 on closed transducer surface S, and as |R - R'| approaches 0, behaves like -xiR-R'. Green's function exists mathematically for all ordinary surfaces S. In the particular case of a piston-like diaphragm in an infinite rigid baffle, G(R, R') ~ R'. When R' = r lies on S:\n\nSensitivities:\nEquation (6) applies and F = -z. Solving for v\" from equations (6) and (1), and substituting the result into equation (14), the transmitting sensitivity is obtained as:\n\nv\" = [F/(-2p)][1/((-xi)^2 + (k^2 - (1/R')^2)]\n\nThus, the transmitting sensitivity depends on frequency \u03c9 = 2\u03c0f/27r, medium density p.\nThe open-circuit mechanical impedance Zq, electro-acoustic coupling constant k, and radiation impedance z, as well as the integral of Green's function over the transducer surface are considered.\n\nNext, the receiving sensitivity M is discussed. If a sound field pijc(R) exists in the transducer's absence with a value at the acoustic center R0 being pinc(Ro), then the ratio of the open-circuit voltage generated by the transducer in the medium to pinp(R0) is denoted as the receiving sensitivity M.\n\nThe value of M depends on the wave type, specifically pi. For practical applications, the significant case is when it represents a spherical wave with a center at R'. The plane wave sensitivity can be omitted here.\nThe sensitivity to spherical waves is considered when R, is infinitely distant from R,. In this case, pi can be written as:\n\nThe actual pressure present at a point R when the transducer is in the medium must be found. If the transducer diaphragm did not move, the pressure, from the definition of Green's function, would be:\n\nis present in the medium. However, the transducer surface has a velocity v,. The pressure at a point R in the medium is given by equation (14). If these two pressures are added, the actual pressure at R, p(R), when pine is present, is obtained and the transducer diaphragm has a velocity Vn. Thus:\n\nSince the total force on the transducer diaphragm is the integral over the diaphragm of the pressure at each point on its surface, then:\n\nSince G(r, R.) = G(Rp, r) from the symmetry of Green's function, the first term can be written as:\nIf we compare equation (19) with equation (5), we see that:\n\nand \u03c8 are quantities that can be computed when Green\u2019s function for the surface S is known. If equation (5) is substituted for F, with Fq and z^ given by equations (20) and (21), in the fundamental equations (1) and (2), and the transducer is on the other hand, if no incident sound pressure is present, the acoustic center is the center of symmetry if it exists, but for this discussion, it may be any arbitrarily chosen point on the transducer. The incident sound field pressure satisfies the wave equation:\n\n\u2207\u00b2p = -\u03c1\u03c9\u00b2p\n\nwhere \u03c1 is the density of the medium, \u03c9 is the angular frequency, and \u2207\u00b2 is the Laplacian operator. In practice, the receiving response is always given for a uniform plane wave normally incident on the transducer. It can further be shown that, for an arbitrary incident sound field, one has:\n\n\u03c8(R) = G(R, R')p(R')dA' - \u222bdV'G(R, R')\u2207'p(R')\n\nThe first two terms reduce to G(R, R') as shown in equation (22).\nIf p(R) is the spherical wave of equation (17), integrating it over the surface S yields the first term's integral, which was called, and the second term's integral. The last term is again:\n\nGeneralized Theory of Electroacoustic Transducers\nConsidering an electrically terminated transducer with impedance Zj, so that E = -Zl I and Vn can be eliminated between the equations, we obtain the voltage output of the transducer:\n\nE - ZjZr\n\nWe are interested in the open-circuit voltage, obtained from equation (22) by letting Z->\u221e:\n\ndue to a point source of spherical sound waves at R, at a distance d from the acoustic center of the transducer to the transmitting sensitivity S, measured at the point R, is a constant independent of all particular characteristics of the transducer. The value of this constant is:\nconstant is: M/S = ^dXjpc, where X and c are the wave length and velocity of sound, respectively, and p is the density of the medium. The applications of this theorem are discussed in Chapters 4 to 7.\n\nThe theorem is readily proved by taking the ratio of M as given by equation (25) with R^ = R, and S as given by equation (16):\n\nk'Fp / (Zq + Zf)\n\nSince |Ro-Rc| / T = M, and |t'| = |j|, we obtain the receiving sensitivity, using equation (20) for Fq, as:\n\nM / Pin(Ro)\n\nProof of Reciprocity Theorem\n\nSp > pC\n\nThe reciprocity theorem, proved here for the case of a rigidly vibrating diaphragm, can be shown to hold for any general mode of diaphragm vibration where r'(r) is a function of position on the diaphragm.\n\nThe reciprocity theorem will now be proved.\ntheorem applies to all transducers that satisfy the condition of equality between the absolute values of the electro-acoustic and acoustoelectric coupling constants. It is simple to demonstrate that this condition is met for the various idealized transducers discussed in Chapter 2. The theorem statement is as follows: The absolute value of the ratio of the receiving sensitivity M to the efficiency 36\n\nAfter discussing the sensitivities of a transducer and their relationship through the reciprocity theorem, we move on to a treatment of efficiencies, beginning with the efficiency of the transducer on transmission, the projector efficiency. Defined as the ratio of the total acoustic power output of the transducer to the electric power input, several expressions for the projector efficiency Ep will be derived, which will be useful for different purposes.\nThe acoustic power output can be shown to be k = Bl, k' = Bl, where B is the magnetic flux density in the region where the ribbon moves, and l is the effective length of the ribbon. Values of k and k' for other types of transducers are given in the literature.80, 81\n\nThis restriction is not necessary. The reciprocity theorem is valid for any source distribution for the incident waves as long as the distance between sources and transducer is large compared to the dimensions of either of them.\n\nAnother extension of the theorem is to the case of a series of transducers individually obeying reciprocity and coupled by electric and mechanical transformers. Then the condition k' = k' holds.\nThe will hold for the coupling between input E, I, and output F.v. It holds for the individual transducers, and the reciprocity theorem will be valid for the series considered as a unit.\n\nEfficiencies. The asterisk denoting the complex conjugate and X being any closed surface containing the transducer.\n\nThe electric power input is given by |Rei|, where | | is the absolute value of the (complex) current and Rpi is the real part of the effective electric impedance of the transducer Z^i.\n\nIf X is chosen as a large sphere of radius d centered at the transducer, we have Vn = p/pc. The expression for the acoustic power output becomes:\n\ndX being now an element of area on the sphere and I the sound intensity. Introducing the directivity factor D, defined as:\n\nwith paxis the pressure at distance d on the axis.\nThe symmetry of the transducer, or generally on any fixed axis, one obtains for the projector efficiency:\n\ng|M|xi = pc I^ Rel\n\nWhere S and M are the transmitting and receiving sensitivities; see equations (16), (25), and (28). Another possible choice for X is the surface S of the transducer. Then, v is the normal velocity of the transducer surface, assumed constant over the diaphragm. Thus, from equations (6) and (29), we have the projector efficiency expressed as effective electric impedance, Z^i. It may be shown that a sufficient condition for Ep to be 100 percent is Rj = ro = 0, that is, the blocked electric and open-circuit mechanical impedances have no real parts.\n\nIt is worth pointing out in connection with equation (33) that the projector efficiency (at resonance) of a resonant transducer may be determined by purely electrical methods. (See reference 39.)\nA resonant transducer's response, as a function of frequency, has a sharp maximum when the impressed frequency aligns with a natural frequency of the transducer itself. If one measures the electric impedance of the transducer at a frequency well above and below its resonant frequency, the result will be essentially Zj, the blocked impedance. Suppose one measures the electric impedance of the transducer at resonance in air. Then Zj is approximately zero, and the motional impedance (the difference between the measured electric impedance and Z0) will be -jk'/zQ. Next, one measures the impedance at resonance in water. Then the motional impedance in water, -jk'/(zQ + z'), is known. These three measurements suffice for the determination of Ep, if the transducer obeys the reciprocity condition |Z| = jk'. This may be seen as follows: At resonance,\nThe imaginary part of Zq disappears, and Zq Zr^ equals (0 + r). Equation (33) can then be written as: r \\* kE n\n\nTo find v^jl and use equation (9) to find Rg, we substitute the results into equation (32), yielding: V Zo + ZrJ\nZft j \u2014\nis the real part of the radiation impedance z^.\n\nFor further discussion of the directivity factor (5) and directivity index = 10 log 5, see Chapter 4. The second form uses the reciprocity condition:\n\nIt is now seen that R,, ^ , and IMi are the only quantities needed for a knowledge of Ep at resonance. All of these can be found by the described method, assuming Vq is a slowly varying function of frequency, so that Tq, at the resonance frequency in air, is close in value to Tq at the resonance frequency in water.\nm is in general a function of frequency but does not show resonance properties. Therefore, its value at the resonant frequency of the transducer can be found by joining the portions of the curve found above and below resonance with a smooth curve.\n\nWhen the imaginary part of -f vanishes, the responses S and M have their maximum values; see equations (16) and (25).\n\nGeneralized Theory of Electroacoustic Transducers\n\nMaximum Electric Power\nOutput on Reception and Threshold Pressure\n\n3.8. Generalization of Theory to Any Type of Diaphragm Motion\n\nMaximum electric power is transferred to a receiver when the electric load impedance of the receiver is the complex conjugate of the effective electric impedance of the transducer. Under this condition, by Thevenin\u2019s theorem:\n\nRei = Conj(Rei)\n\nThe treatment of the theory of electroacoustic transducers given above for transducers in which the diaphragm motion is...\nThe diaphragm velocity is the same at all points and can be generalized to the case where there is no such restriction on the velocity distribution. The generalization takes the following form. The fundamental equations for the transducer can be written as:\n\nEg = M * Eg^(open circuit) * Ej,\n\nwhere Eg is the signal voltage across the load in the matched circuit, Eg^(open circuit) is the signal voltage that would be developed by the transducer on open circuit, M is the receiving sensitivity, and Ej is the projector efficiency. The last form of equation (35) follows from the last form of equation (31). Equation (35) suggests that the quantity -A?_ (which has the dimensions of an area and is usually called the effective area) has the significance of being the maximum cross section for energy absorption by the transducer from the sound field. This follows from the fact that\nThe incident intensity of sound never exceeds unity, and maximum power is absorbed in a matched circuit. An important parameter of the transducer is its threshold pressure pf. This is defined as the pressure in a uniform, plane-wave, free sound field propagated parallel to the acoustic axis of the transducer, which produces a signal power output in the load equal to the inherent thermal noise power in the load. (See Chapter 4 for a full discussion.) The noise power is taken in a 1-cycle band and the transducer is supposed to be in a matched circuit. The noise power in the load in a matched circuit is one-half of the open-circuit noise power in the transducer (since noise pressures add in random phase). This open-circuit noise power in a 1-cycle band is given by 4KT, where K is Boltzmann's constant and T is the absolute temperature.\nThe temperature of the device influences its threshold pressure, which is determined by the relation:\n\nF = b4KT\n\nHere, r and f are points on the transducer surface S; P(y) and v'(r) represent the pressure and normal velocity, respectively, at point r. The functions Zo(r,r'), i(r), and A'(r') are characteristic of the transducer and are generalizations of Zq, k, and k in the simpler treatment given earlier.\n\nFor coupling to an electric source with generated voltage E^ and internal impedance Zjn^, the equation:\n\nF = Zo(r,r') * P(y) + Zjn^ * E^\n\nstill applies. However, for acoustic coupling, we now have:\n\nF = -Zo(r,r') * v'(r) + Zjn^ * E^\n\nand\n\nF = Zo(r,R) * P(yR) + Zj(R) * P(y)\n\nwhere R is any point in the medium (R may be taken as r). G(r,r') is the same Green's function introduced earlier. The quantity z.(ur') is an acoustic radiation impedance continuous matrix, which is the generalization to any type of diaphragm motion.\nThe generalization of previously used radiation impedance z,... In the medium with no sources other than the transducer, the pressure at any point R is given by equations (39) and (40):\n\nI.e., the above equations allow the behavior of the transducer to be calculated under any conditions. The various impedances, sensitivities, and efficiencies can be found in a manner analogous to that used above. These calculations involve, in general, the solution of linear integral equations which can be solved in principle, though practical solutions may be difficult to obtain except in simple cases. The reciprocity theorem, equation (28), can be proved in this general case provided that certain conditions are met.\n\nChapter 4\nTypes of Acoustic Measurements\nBy Eginhard Dietze\n\nThe choice of what should be measured is probably as important a part of a testing program as any other.\nAny testing of a device requires a clear understanding of its nature and purposes, as well as the character and applications of the device under test. The tests must be carried out under carefully controlled conditions. Controlled conditions are one of the principal reasons for substituting laboratory tests for field tests.\n\nThe tester must possess a broad knowledge of the applications of the device and measurement techniques to carry out the task intelligently. For instance, to set up a testing program for an echo-ranging projector, it is necessary to know what factors are important in echo ranging and how they depend on the physical characteristics of the device. Only then can tests be made that will shed light on these factors.\nThe Underwater Sound Reference Laboratories have given considerable thought to how an echo-ranging projector will perform in service and how its performance could be improved. Based on these studies, the following physical characteristics should be measured in a calibration test: (1) directivity (directivity index, horizontal and vertical beam widths, magnitude of largest side lobes), (2) frequency-response characteristic, (3) power output (efficiency), (4) selectivity, (5) threshold pressure, (6) receiving response, and (7) impedance. Proper tests must be devised for the precise measurement of these characteristics. In acoustic tests, this is not always simple, and even with the greatest care, it is usually not possible to equal the precision of electric circuit tests. All factors should be optimized.\nIn order to achieve even a reasonable degree of precision, a design requires testing. A prerequisite for this is testing equipment. Any effort expended in obtaining the best possible laboratory equipment will be well repaid. It is almost axiomatic that without such equipment, the situation is hopeless. Assuming that such equipment is available, there are certain fundamental rules of testing which must be observed. The most important one, although very simple, is frequently violated, often with disastrous results. This rule is as follows: In a test, as in any experiment, only one factor may be varied at a time. All other factors must be held constant throughout the tests. Usually more than one characteristic is to be measured, so that more than one test must be made. The above rule, that all factors except the one under test must be held constant.\nIt is essential that all medium characteristics remain constant throughout the testing program. For instance, temperature: unless it is a variable of the test, the temperature must be uniform. Additionally, the device itself must be in temperature equilibrium with the medium. Depending on its size and type of construction, this may require waiting several hours or even a full day while the unit is immersed before tests can begin. It has also been found that results obtained at one temperature do not necessarily apply at other temperatures. Therefore, the temperature of the water during the tests, the temperature dependence of the device, and the speed with which it reaches temperature equilibrium are important factors.\nIn any extended testing program, special care must be taken that signal levels, transmission properties of the medium, and noise background do not change. Drifts in the amplifier or oscillator characteristics affect acoustic conditions by changing the level or frequency of sound in the water. To avoid such drifts, it is necessary to check the electric system frequently during tests. Similar precautions must be observed in using acoustic devices. For instance, x-cut Rochelle salt crystals are variable under some conditions and are undesirable as standards. In many devices, one side is grounded, increasing the chance for noise pickup and necessitating proper shielding of the leads. Another factor to be considered is that all measurements must be made at the same point in the circuit.\nThe leads should be the same for all tests. The same auxiliary equipment, such as tuning coil or condensor and polarizer, should also be used throughout the testing program. For instance, in the measurement of electric power, the current and impedance, or current, voltage, and phase angle must be measured from the same set of terminals. In more complicated tests, the matter of measuring from a single pair of terminals is sometimes overlooked. For instance, to determine the efficiency of a projector, the transmitting response must be obtained, the directivity measured, and the impedance of the projector and of the source determined. To obtain the correct answer, all electric measurements that enter into these tests must be made from the same terminals. Frequently, this is inconvenient. The driving equipment is:\n\nThe leads should be the same for all tests. The same auxiliary equipment, such as tuning coil or condensor and polarizer, should also be used throughout the testing program. For example, in the measurement of electric power, current and impedance (or current, voltage, and phase angle) must be measured from the same terminals. In more complicated tests, ensuring measurements are taken from a single pair of terminals is sometimes overlooked. For instance, to determine the efficiency of a projector, the transmitting response must be obtained, directivity measured, and the impedance of the projector and source determined. To obtain the correct answer, all electric measurements that enter into these tests must be made from the same terminals. This is often inconvenient.\nAn amplifier, for instance, is located at one place in the laboratory, while the impedance bridge is at another. Adding an extra lead in either connection results in an error. It is worth noting that the efficiency determined in this way includes any losses in the system beyond the measurement points. If the efficiency of the projector excluding these losses is desired, the measurements must be made at its terminals or the losses must be eliminated from the data through computation. The latter method is usually more time-consuming and less accurate. A general principle of testing is that it is easier to make relative measurements than absolute measurements, and the precision of relative tests, for the same amount of effort, is much greater. The easiest tests to make are the so-called I-V comparisons.\nImmediate switching between two conditions is involved. usually, one of the conditions, referred to as A, serves as the reference, and the other, B, which includes the unknown, is the test condition. Many testing difficulties can be avoided by reducing the program to a number of comparison tests. If possible, tests should always be set up on this basis.\n\nWith these principles in mind, USRL has established various practices. Some of these are described in Section 6.1.4. The remainder of this section concerns the physical characteristics to be measured in calibration tests on underwater sound equipment.\n\nMost acoustic devices are reversible. They can do two things depending on how they are used: (1) when an electric voltage is applied at their terminals, they generate acoustic power, and (2) when they are not in use or are disconnected from the power source, they do not generate acoustic power.\nAcoustic power is supplied to them, generating an electric voltage. A device exhibiting these properties in the underwater sound field is called a transducer. The first action is called transmitting, and the second is receiving. Certain conventions have been set up by agreement among the different groups interested in the underwater sound field for the measurement of transmitting and receiving performance. These conventions are valuable in making the meaning of measurement results precise to all people in the group. By expressing all results on the same basis, different measurements can be more easily compared. The most important use of test data is usually to determine which instrument is best among those available for a particular application.\n\nTransmitting measurements typically involve three:\nThe factors are: (1) the acoustic pressure delivered in the desired direction for a known electric input, (2) the distribution of the acoustic pressure in other directions, and (3) the variation of the pressure with frequency. These items correspond respectively to (3), (1), and (2) at the beginning of this chapter. These quantities must be expressed in such a way that their meaning is unambiguous and that they afford a ready means of comparing different designs. For example, a statement of the pressure delivered does not in itself tell much about the performance of a device, since it is possible to change the pressure by increasing or decreasing the electric input. Consequently, the electric supply conditions must be specified as well. In most practical cases, the projector is fed from an electric supply.\nFor practical applications, specifying the amplifier type is essential to secure the electrical system. A class A amplifier is preferable for calibration due to its accurately specifiable and controllable performance. From a circuit analysis standpoint, a class A amplifier can be replaced by a generated voltage Cg and an internal resistance Vg. The same analysis applies to class B and C amplifiers, but their values depend on the power delivered, whereas class A amplifier values are independent up to the point of overloading.\n\nTypes of Acoustic Measurements\n\nFigure 1 depicts the circuit referred to by equation (1). The values are independent of the power factor up to the point of overloading.\nIt is seen from the above that the power delivered by an amplifier is a function of the load impedance. For this reason, the use of a fixed input power, a fixed applied voltage, or a fixed applied current in determining the variation with frequency of the pressure delivered by a projector (the impedance of which changes with frequency) in general does not provide a response characteristic that is representative of actual service conditions. This consideration has led to the use of available power as a basis.\n\nAvailable power, denoted as Pav, is defined as the power which a driver having a fixed generated voltage Vg and a fixed internal resistance Vg delivers into a matched load resistance. Figure 1 illustrates the circuit.\n\nFrom this circuit, it can be seen that the power delivered into the load resistance (Vg) is given by the product of the voltage squared and the conductance of the load resistance:\n\nPav = Vg\u00b2 * G\n\nWhere G is the conductance of the load resistance.\n\nThe curves of this transition loss are plotted against the conductance of the load resistance in Figure 2.\nIf a projector is tuned so that at resonance its impedance is a pure resistance, the maximum power will then be delivered by the driver to the projector if this resistance matches the internal resistance of the driver, that is, when Vg = Vgj. It is seen that under these conditions, the actual power Pj equals the available power T4. In all other cases, the actual power is less than the available power. The efficiency of the electric system under these conditions, however, is only 50% per cent, since the amount of power dissipated in the output tubes equals that supplied to the load. In practical designs using class B or C amplifiers, it is an advantage to use a lower source impedance, about 1/4 this. This improves the electric circuit efficiency and reduces the power dissipation in the outputs.\nThe putting in of smaller tubes permits this, with the source impedance of the actual system needing to be simulated in testing.\n\nThe transmitting response of a projector with a given impedance is expressed in terms of the pressure, in decibels versus reference pressure (1 dyne per sq cm), per watt available from a given generator impedance (assumed to be purely resistive).\n\nIn relation to this definition of transmitting response, it should be noted that the pressure delivered increases as the square root of the available power.\n\nThe term 10 logP/P is well-known in transmission circuit theory and represents the transition loss between the resistance and the impedance z. On Figure 2, this figure shows the transition loss between a generator with an internal resistance of ohms and a load impedance of\nThe mathematical expression for the response in decibels (dB) is given by equation (3):\n\n20 log p (decibels versus 1 dyne per sq cm, reference pressure) + 10 log (power level referred to 1 watt)\n\nIn practice, power levels are expressed in decibels versus 10^-3 watts. For actual testing, the reference distance is chosen as 1 meter. However, this does not mean that all calibrations must be made at this distance. The testing distance depends on obtaining waves that are sufficiently plane to avoid spherical wave corrections for both the projector under test and the receiving hydrophone.\nThe size of the instruments and frequency are important considerations. Elsewhere, the testing distance will be made as short as possible to minimize interference from reflections, etc. The testing distance d will be stated with all tests, and the correction C in decibels to d = 1 meter will be based on spherical waves.\n\nDo similar considerations apply regarding the power to be used in the tests? While the response is referred to as 1 watt, it would be incorrect to make all tests at that power level. If the device is linear, the testing power used is inconsequential. However, if the response varies with power level, then tests should be made at the actual working levels used in service, and the testing power should be stated. A load characteristic should be furnished showing the relation between acoustic power output (or pressure).\nThe next item to be measured is the distribution of acoustic pressure with direction. This is measured by determining the pressure over a spherical surface having the projector as the center. The pressure p in any one direction is expressed in Figure 3 as a three-dimensional directivity pattern for a circular plate. Frequency = 25 kc, diameter of plate = 15 inches. Decibel values shown give response relative to that on the normal axis.\n\nDecibels versus the pressure p on the acoustic axis of the device. For the acoustic axis, an axis of symmetry of the device is usually chosen, which frequently is also the direction of maximum response. A plot of these values is called a directivity pattern. A view of a three-dimensional directivity pattern for a circular plate is shown in Figure 3. For devices which are symmetric.\nA metrical device, such as a circular plate, has the same directivity in all planes containing the major axis normal to the surface. This results in a significant reduction of work as the pressure distribution need only be measured in one plane. A planar directivity pattern is shown in Figure 4, which is the usual way of plotting these patterns. Devices that are not circular typically have several major axes. Patterns should then be taken in all planes containing one of these axes. The directivity index is defined as the ratio in decibels of the intensity I (I = intensity far away from the source) averaged over all directions to the intensity q on the acoustic axis of the device:\n\nTypes of Acoustic Measurements\n\nFigure 4 shows a planar directivity pattern for a circular plate.\nFrequency = 25 kc, diameter of plate = 15 in.\n\nThere are several cases for which a directivity:\n\n1. Isotropic: The directivity is uniform in all directions.\n2. Omnidirectional: The directivity is maximum in all directions.\n3. Directional: The directivity is maximum in a specific direction.\n4. Bi-directional: The directivity is maximum in two specific directions.\n5. Sectoral: The directivity is maximum in a sector of directions.\n6. Dipole: The directivity is maximum in opposite directions.\n\nA device's directivity can be measured using various techniques, such as:\n\n1. Pressure method: Measures the pressure at various points in the far field of the device.\n2. Difference method: Measures the pressure difference between two points in the near field of the device.\n3. Transfer function method: Measures the device's response to a known input signal.\n4. Scanning method: Measures the device's response as it is rotated or translated.\n\nThe choice of measurement technique depends on the specific requirements of the application, such as the desired accuracy, measurement range, and complexity.\nIf obtaining dex is relatively simple, and the transducer's directivity pattern has rotational symmetry about the acoustic axis, use the following formula: A = 10 * log10 ^ sin(\u0430\u0440\u0444). If the level is 24 dB below the peak, then 10 * log10 /q/^o = 0.00104. Compute la/^o * sin(\u0430\u0440\u0444) for all angles and plot the values on rectilinear graph paper against the angle a in radians (1 radian = 57.3 degrees). Figure 5 illustrates this. The area under the curve is measured with a planimeter and found to be 5 square inches. In this case, 1 inch on the abscissa represents 0.1 radians, and 1 inch on the ordinate represents an intensity ratio la/^o = 0.01. Therefore, 1 square inch represents a contribution of 0.001 to the integral. The total area gives:\n\n1 square inch * 0.001 = 0.001 square inches\n\nTotal area = 5 square inches\n\nContribution to the integral = 0.001 * 5 = 0.005\n\nTherefore, the total contribution to the integral is 0.005.\nEquation (6) includes a factor of I/2 in front of the integral, resulting in a directivity factor of 0.0025 and a corresponding directivity index A. In this formula, a represents the angle from the acoustic axis, I the intensity at this angle, and /q the intensity on the axis. The above formula is valid, for example, in the case of a circular diaphragm vibrating symmetrically about this normal axis. In the case of a line source, the acoustic axis is usually taken perpendicular to the line. If the directional pattern of the line is symmetrical about the line itself, the directivity index is given by the formula:\n\nwhere a is now the angle measured from the acoustic axis (normal to the line) in a plane including the acoustic axis and the line itself.\n\nTo indicate the use of these formulas, consider the pattern shown in Figure 4, representing a measured directional pattern.\nTo find the directivity index of a circular piston in a plane including the acoustic axis, equation (6) above is applied. The integral is evaluated graphically using a planimeter, which requires obtaining the ratio a/o for different angles. For instance, at 25 degrees, the response is The procedure for a line is analogous, with cos a used instead of sin a, as indicated by the comparison of equations (7) and (6). If the experimentally obtained pattern is not exactly symmetrical, it is often sufficient to use the average values of the two halves. This computation is straightforward but somewhat tedious. Figure 6 shows a chart prepared to reduce the amount of algebraic calculations.\nThis chart displays a family of curves. Each curve represents a specific value of a/7o sin a. The chart is used in conjunction with the directivity pattern, plotted on polar coordinate paper, of the instrument whose directivity index is to be determined. To use the chart, the transparent chart is laid over the directivity pattern of the instrument so that the coordinate systems align. To find the value of lajh sin a for any angle a, follow the radial line corresponding to angle a until reaching the intersection with the instrument's directivity pattern. The point of intersection will then fall on the chart.\n\nComputation of directivity index for a circular plate vibrating at uniform amplitude and in phase.\nFrequency = 25 kc, diameter of plate = 15 in.\n\nTypes of Acoustic Measurements\n\nFk;ukf, 6. Directivity index calculator.\n\nTransmission:\nDetermine which curve, whether one or between two, of the family of curves on the chart the point falls. For instance, if this point is approximately 7/10 of the way between the curves corresponding to 0.003 and 0.004, then for the angle a:\n\nThe values of la/Io sin a can be easily obtained for each desired value of the angle a. These are then plotted as described above. The procedure beyond this point is identical to that described earlier.\n\nThe use of this chart at USRL has shown it to be as accurate in general as a direct computation, and the work proceeds much more quickly, particularly since most field data for instruments provide 10 log la/Io rather than la/h-\n\nIt is assumed that the pattern has\nIf the maximum point is drawn on the outer circle of the coordinate paper, the chart can be used in the same way. However, if the maximum is on a circle that is 10 dB down, the chart values should be multiplied by 10 to obtain correct values. If the maximum is on a circle 20 dB down, the values must be multiplied by 100, and so on.\n\nThe chart can also be applied to a line. In this case, it is turned so that 90 degrees on the chart coincides with 0 degrees on the directivity pattern. Since the chart in this direction is narrower, the pattern must be plotted on a smaller scale for the chart to accommodate it.\n\nThe beam width should not be too broad (the total beam width 10 dB below the peak does not exceed 120 degrees), and the side lobes and rear response should be at least 15 dB.\nThe directivity index below the peak is determined primarily by the beam width. In Figure 7, the directivity index is plotted as a function of the beam width for a circular plate. By referring to this chart, one may read directly the directivity index for the measured beam width.\n\nMany devices do not have symmetric directivity patterns about a single axis. In general, directivity patterns would need to be measured in many planes passing through the acoustic axis, and a laborious double numerical integration performed to obtain the directivity index. In some cases where the pattern is symmetrical with respect to two perpendicular planes passing through the acoustic axis, an approximate value for the directivity index may be obtained from Figure 7.\n\nDirectivity index as a function of the beam width for a circular plate. (Figure 7.)\nTo obtain the directivity index, take directivity patterns only in two planes with beam widths less than 120 degrees. For a rectangular piston, the most common nonsymmetrical type, the directivity index is determined directly by the beam widths in these planes and can be represented as a function of beam width. A chart for this case is given in Figure 8, from which the directivity index can be found from the measured beam width, 10 db down, in the two planes. The two planes are those passing through the acoustic axis and parallel respectively to the two pairs of sides of the rectangle. A similar calculation can be made for another piston.\nElliptical piston when two planes are taken through the acoustic axis and parallel respectively to the major and minor axes of the ellipse. A chart for this case is given in Figure 8. These charts may be used in conjunction with measured patterns for rectangular or elliptical transducers. Consideration has been given to reduction of side lobes by means of tapering. By tapering, we mean the variation of the velocity distribution over the diaphragm of the transducer so that the velocity decreases from the center to the periphery. This method is quite effective for reducing side lobes, but it has the undesirable effect of increasing the beam width. The methods described above for calculating the directivity index can in general be applied directly to tapered transducers.\n\nTypes of Acoustic Measurements.\nMinimum beam width (10 degrees down the acoustic axis)\n\nFigure 8. Directivity index as a function of beam widths for rectangular and elliptical pistons. Maximum beam widths are measured in the plane through the acoustic axis parallel to the short side of the rectangle or including the minor axis of the ellipse. Minimum beam widths are measured in the plane through the acoustic axis parallel to the long side of the rectangle or including the major axis of the ellipse.\n\nTapering on the directivity index is relatively small, except in extreme cases.\n\nAdditional information can be obtained from the directivity pattern:\n\n1. The angle of maximum response is the angle between the direction of maximum response and the acoustic axis.\n2. Beam width may be defined as the angular separation between the two points on either side of the main beam which are 10 dB below maximum.\n3. Height of side lobes can be expressed in terms of the maximum pressure in any direction within the side lobe in decibels versus the pressure on the axis.\n4. Rear response is defined as the maximum pressure within \u00b160 degrees from the rear in decibels versus the pressure on the axis.\nIt should be noted that, provided the device is linear, the directivity patterns and the directivity indices for transmitting and receiving are identical at each frequency. This follows from the reciprocity principle.\n\nProjector Efficiency\nAnother criterion which can be derived from the response and directivity measurements is of special interest to the designer because in the most fundamental sense, it measures the ability of the projector to convert electrical power into acoustic power. Gerjuoy has shown that the directivity index of a circular plate has its optimum value when no tapering is used. Receiving and transmitting directivity are identical at each frequency.\nThe projector efficiency is defined as the ratio in decibels of the total acoustic power delivered by the projector to the electric power input into the projector. To compute the efficiency (Ep), you need to know the transmitting response (i?r), directivity index (A), and projector impedance (z). The projector efficiency is given by:\n\nProjector efficiency (Ep) = (Total acoustic power / Electric power input) (dB)\n\nIn relation to these measurements, refer to the beginning of this chapter for stated precautions to obtain a precise determination of the efficiency. It is shown later in this chapter that:\n\nProjector efficiency = 10 log10 (Total acoustic power / Electric power input) (dB)\n\nTherefore, to calculate the projector efficiency, follow these steps:\n\n1. Measure the total acoustic power (in watts) delivered by the projector.\n2. Measure the electric power (in watts) input into the projector.\n3. Convert the measurements to decibels using the formula:\n\nProjector efficiency (dB) = 10 log10 (Total acoustic power / Electric power input)\n\nKeep in mind the precautions mentioned at the beginning of this chapter to ensure accurate measurements.\nThe device is linear; the projector efficiency is the same on transmitting and receiving. This further illustrates the fundamental nature of this quantity.\n\nSelectivity\nThe above quantities relate to the transmitting performance of the device at any one frequency. In general, however, performance over a range of frequencies is of interest. In that case, response and efficiency are determined over the frequency range and plotted versus frequency to provide response or efficiency characteristics. Directivity patterns may also have to be taken at several frequencies.\n\nThe response characteristic in particular is used to study the selectivity of the device. For this purpose, use is frequently made of the equivalent series resonant circuit. This circuit is one in which the current varies with frequency in the same way that the receptor does.\nResponse depends on the circuit having resistance r and reactances Lw and -i (where w = 2\u03c0f/r). Its impedance then is:\n\nSince at resonance Xc = 1j1LC, for constant applied voltage e, the currents are:\n\nThe symbol Q has been used for the ratio L/r. Usually, in a resonant circuit, the resistance is associated with the coil. The Q of the coil then is its quality or figure of merit. To obtain the Q of a response curve, first find the frequencies h and fo, at which the response is 3 dB below the peak, and the resonant frequency fo. Then, Q is found from these three frequencies using the above relation:\n\nfo\n\n42\n\nAn underwater acoustic device used only for receiving is called a hydrophone. Measurements on receiving involve determination of the following factors:\n\n1. The voltage delivered by the device. This is referred to as the open-circuit voltage.\n2. The input impedance of the device.\n3. The sensitivity of the device, which is the voltage produced per unit pressure.\n4. The frequency response of the device.\n5. The directivity of the device, which is a measure of its ability to focus the received sound energy in a particular direction.\n\nAn underwater acoustic device used exclusively for receiving is termed a hydrophone. The measurements on receiving primarily entail determination of the following factors:\n\n1. The open-circuit voltage of the device.\n2. The input impedance of the device.\n3. The sensitivity of the device, which denotes the voltage generated per unit pressure.\n4. The frequency response of the device.\n5. The directivity of the device, which signifies its capacity to concentrate the received sound energy in a specific direction.\nThe unit is in a uniform, plane sound field with reference pressure of 1 dyne per sq cm. The voltage variation with sound incidence direction and frequency are key factors. In this circuit, the resistance (r) to reactance (x) ratio is important. There are two values, w1 and W2, one on each side of resonance frequency wo, where x = r. Then |zi| = j\u03c9r/2 = r/2. At resonance (wq), we have x = 0, so Zo = r. Additionally, due to symmetry, Voc = 2Io. These factors are analogous to those tested on transmitting. Another quantity of interest on receiving is the threshold pressure. This denotes the pressure on the hydrophone face that generates a voltage equal to its inherent noise voltage, related to the minimum measurable signal.\nThe receiving response of a hydrophone or projector is expressed in terms of the open-circuit voltage in decibels versus 1 volt, generated by the unit in a unijorni plane-ive, free sound field of reference pressure (1 dyne per sq cm), propagated parallel to the acoustic axis of the hydrophone. The selection of the open-circuit voltage has the advantage that, with a few exceptions, it is possible to compute the signal voltage across any load impedance when the open-circuit voltage (Cg) and the impedance (z) of a projector or hydrophone are known. For instance, if the load impedance is zl, the voltage across it is:\n\nopen-circuit voltage / (impedance + impedance)\n\nThis relationship is known as the voltage divider equation. It is important to note that this equation assumes that the source and load are both linear and that there are no other components in the circuit that would affect the voltage division. Additionally, it is assumed that the reference pressure is known and that the sound field is free from any reflections or other distortions. These conditions may not always be met in real-world applications, and additional considerations may be necessary to accurately measure the acoustic signal.\nFor certain types of hydrophones, designed for special purposes or including a cathode-follower preamplifier, it is desirable to state the closed-circuit voltage instead of the open-circuit voltage. The load impedance across which the voltage is measured must be stated in all such cases.\n\nTo measure the open-circuit voltage, a very high impedance circuit is required, especially when dealing with crystal hydrophones, which have high impedances themselves. Frequently, measurements are made in a closed circuit and then the circuit loss is allowed for. In hydrophones which have a preamplifier associated with them, a small resistance is frequently included in the so-called calibration circuit to permit computing the open-circuit voltage generated by the crystal. Care must be taken in connection with the measurement of the response of such hydrophones.\nhydrophones must have the output of the preamplifier properly terminated. This is particularly important for the so-called cathode-follower circuit, which is commonly used.\n\nFormulating a mathematical expression for the receiving response, we have:\n\nCg = pS(j cm-1)\n\nWhere Cg is the generated voltage of the hydrophone in volts, and p is the pressure in the free field sound field in dynes/cm2.\n\nInstead of obtaining the open-circuit voltage, the group at the Woods Hole Oceanographic Institution refers to calibrate their tourmaline gauges in terms of the electric charge on the crystal. This calibration is made by comparing the voltage Vp across the amplifier input (or output) due to a known pressure on the crystal, with the voltage Vq across the amplifier input (or output) due to a calibrating voltage Vg applied across the amplifier input in series with a known calibrator.\nThe charging condenser Cg. The charge on the crystal due to the applied pressure can be computed from the mentioned voltages and the calibrating capacity. If the calibrating condenser Cg is in parallel with the crystal when the voltage Vp is measured, the charge Q can be found from the equation Q = Cf * Vs, where Cf is the capacitance of the crystal. From this charge Q and the crystal's capacity Cq, the open-circuit voltage e can be found. Determining the charge instead of the generated voltage is convenient as it requires only measurements at the input or output of the amplifier, and the results are independent of the length of the intervening cable.\n\nThreshold Pressure:\nThe threshold of a hydrophone or projector will be expressed in terms of the pressure in a uniform, plane-wave, free sound field propagated parallel to the acoustic axis of the device, in decibels versus reference pressure.\n\n(Note: This text appears to be in good shape and does not require extensive cleaning. Only minor corrections for typos and formatting have been made.)\nThe signal pressure, which can be measured with any given device, is limited in two directions: overloading limits it on the upper side, and the noise level limits it on the lower side. The noise may be due to various factors, such as the associated preamplifier, pickup in the leads, improper grounding, and contacts. When these sources are eliminated, thermal noise remains, which is fundamental and depends only upon the temperature and the frequency.\n\nThe term threshold is discussed below, along with the measurements and computations necessary to obtain the threshold pressure. The signal pressure, which can be measured with any device, is limited in two directions: overloading limits it on the upper side, and the noise level limits it on the lower side. The noise may be due to various factors, such as the associated preamplifier, pickup in the leads, improper grounding, and contacts. When these sources are eliminated, thermal noise remains, which is fundamental and depends only upon the temperature and the frequency.\n\nIn the following, the significance of the term threshold is discussed, and the measurements and computations necessary to obtain the threshold pressure are outlined. The signal pressure, which can be measured with any device, is limited in two directions: overloading limits it on the upper side, and the noise level limits it on the lower side. The noise may be due to various factors, such as the associated preamplifier, pickup in the leads, improper grounding, and contacts. When these sources are eliminated, thermal noise remains, which is fundamental and depends only upon the temperature and the frequency.\nThe mean square value of this random noise voltage has been determined experimentally and theoretically. The rms noise voltage applied to the grid due to both sources is obtained by adding the two fluctuating noises at random phases, thus: + rj. When the line impedance is matched at the two terminals (r\\_l = r), then by equation (11) above, e^i = (r\\_l + jX\\_l)^2 = r\\_l^2 + X\\_l^2, where r\\_l is the equivalent series resistance of the device.\n\nFor a frequency band of 1 Hz and a temperature of 20 C, it has the value:\n\nwhere f is the frequency and k is the Boltzmann constant.\n\nIn the practical case, there are two distinct conditions to consider: calculated threshold and measured threshold.\n\nCalculated Threshold:\n\nIn the case of low-impedance hydrophones, typically of the electrodynamic or magnetostrictive type, the calculated threshold is given by:\n\nVth\\_cal = 2kTR,\n\nwhere T is the absolute temperature in Kelvin.\nA unit is typically connected directly to a line. If this line has significant length, its impedance must be matched at both terminals, as irregularities in response are introduced due to reflections within the line itself. Neglecting attenuation, the circuit can be represented as shown in Figure 9. Here, eg represents the generated open-circuit signal voltage, Cni is the generated noise voltage in the resistance of the hydrophone r, and 6\u00b2 is the generated noise voltage in the terminating resistance. Reactances in the circuit are omitted for simplicity. Vn is the noise voltage and Vg is the signal voltage applied to the input of the measuring circuit, assumed to be the grid of the amplifier.\n\nThe noise voltage applied to the grid due to Vn is equal to half the voltage generated by the hydrophone.\n\nSignal voltage Vg applied to the grid is half the voltage generated by the hydrophone.\nFrom the above relation Vg, the signal voltage generated by the hydrophone equals F, the noise voltage in the unmatched circuit, when the circuit is not matched. The other possibility is to connect the hydrophone to a very high impedance. In that case, the signal voltage Vg applied to the grid becomes:\n\nVg = F / (1 + r/Rj)\n\nThe noise voltage applied to the grid due to e\u00b2 is:\n\nVn = sqrt(4kTRj)\n\nIt is seen by comparing equations (14) and (16) that there is a theoretical gain in the signal-to-noise ratio of 3 dB in terminating the hydrophone in a high impedance as compared to matching it. Where the leads are sufficiently short, it is therefore advantageous to use a high-impedance termination. This applies especially to the internal connection between the active elements of the hydrophone.\n\nTypes of Acoustic Measurements\nThe threshold pressure for low-impedance hydrophones can be computed using the receiving response Rji and the hydrophone's resistance r. This relation is given by:\n\nSubstituting the value from equation (11) into equation (14) yields the results:\n\nThe signal voltage is related to the signal pressure p (in dynes per sq cm) through the receiving response Rr, as stated by equation (10), which can be written as:\n\nIntroducing the signal voltage defined by equation (17) into this equation, we obtain the threshold pressure in decibels:\n\nThe test procedure involves measuring the resistance and response of the hydrophone. From these values, the threshold pressure is computed using equation (18).\n\nMeasured Threshold Pressure\nFor a high-impedance hydrophone of the crystal type, the active element is directly associated with a preamplifier. This is necessary to avoid excessive losses in the leads and to prevent noise pickup, to which a high-impedance circuit is prone. Frequently, the preamplifier is given an extremely high input impedance. This is done to obtain the maximum signal-to-noise ratio at the first grid and also to stabilize the hydrophone. For instance, in the case of x-cut Rochelle salt crystals, which are inherently variable with temperature, the variability is reduced when no current is drawn from them. Since the preamplifier is so intimately associated with the active element, it is best to treat them as one unit and to determine the threshold for the combination.\nThe preamplifier noise exceeds thermal noise significantly, making the computation outlined above impractical. Measuring the instrument's inherent noise level requires an extremely quiet body of water and a very quiet measuring system to exclude extraneous noise. When quiet water is unavailable, a network can be used instead of the crystal. The network must be the electrical equivalent of the crystal in water across the entire frequency range included in the measurement. The measuring system should also have a uniform response and a clearly defined bandwidth, narrow enough to exclude variations in the hydrophone response.\nWithin the band, the pre-amplifier output is usually matched. If the measuring band includes frequencies from f1 to 1/2, then the value 10 log (1/2 - 1/i) must be subtracted from the measured noise voltage (assuming it to be in decibels), in order to obtain the threshold.\n\nRelations Between Measured Quantities:\n\nIn the following, certain relations that exist between the measured quantities are pointed out. These relations frequently are useful in cross-checking measurements. They also reveal additional information as to the nature of the definitions.\n\n1. The relation between the projector efficiency Ep and the transmitting response R was given in equation (8):\n2. There was also given the relation between the calculated threshold and the receiving response Rr in equation (18):\n3. In addition, there exists a reciprocal relation.\nbetween  the  transmitting  response  and  the  re- \nceiving response  of  a projector.  This  relation \nhas  the  following  form: \niJr  = fl\u00ab  + 201og/+  lOlog^ \n- lOlogr  + 20  log \nthe  study  of  measured  data.  For  the  sake  of  simplicity \nthe  discussion  is  confined  to  circular  pistons. \nIn  the  case  of  a circular  piston  moving  rigidly  in  an \ninfinite  baffle,  there  exists  a simple  relation  between \nits  radius  a and  the  directivity  index \n2ka  J \n4.  From  these  three  equations,  it  is  possible  to  de- \nrive a relation  between  the  projector  efficiency \nand  the  threshold  T : \n5.  Furthermore,  by  combining  equations  (18)  and \n(19)  or  (8)  and  (20),  a relation  can  be  obtained \nbetween  the  threshold  T and  the  transmitting \nresponse  of  the  unit  Rrp.  This  relation  is  as  fol- \nlows: \nT A \nwhere  k = 27r/A,  A being  the  wave  length  = c//,  and \nJi  = first  order  Bessel  function. \nThe  directivity  of  a physical  projector  usually  is \nless than that of a theoretical circular piston of the same geometrical size. It is, however, possible to define the effective or acoustic radius of the physical projector to be the radius of the theoretical piston having the same directivity index as the projector. On Figure 10, the directivity index and beam width are plotted against effective radius in wavelengths (\u03bb) for a theoretical piston.\n\nA number of interesting relations are obtained by introducing this expression for the directivity index in the above equations, in which the directivity index occurs. These are the equations which include the projector efficiency. For instance, substituting the above expression for the directivity index in the relation between projector efficiency and transmitting response, equation (8), gives:\n\n2\u03c0/kA\n2kJ\n\nFinally, by combining equations (8) and (19), a relation can be found between the projector efficiency and the projector:\n\n2\u03c0/kA = J/\u03b7\n\nwhere J is the total radiated power and \u03b7 is the projector efficiency.\nThe following discussion examines the meaning of the above relations and their usefulness in relation to the reciprocity theorem and the conditions under which it applies, stated in Chapter 3. In the term r (2/i) i2ka, ira^ is the area of the theoretical piston with radius a. For an actual projector, a represents the effective radius, which can be determined using the chart on Figure 10. The expression in the bracket is a pure number, resulting in the term having the dimensions of an area.\n\nTypes of Acoustic Measurements\n\nFigure 10: Relation between effective radius and directivity index (or beam width) for a sonar projector with a circular diaphragm.\nThis expression shows that for constant projector efficiency, the transmitting response varies directly with the effective area, and for any given device (A = constant), increases 6 dB per octave. The latter relation is shown by equation (21) to exist also for fixed threshold and transition loss.\n\nIntroducing the expression for the directivity index in equation (20), we get\n\ncalled the effective area of the projector, A, which is thus defined as:\n\nL\u00b2kA\n\nDefining the directivity factor \u0394 by:\n\nit is evident from equation (23) that\n\nThis equation shows that for any given device (A = constant), the threshold pressure is independent of frequency, and also indicates that the higher the efficiency of the projector, the lower the threshold pressure. For devices of the same type, that is, having the same efficiency, the threshold varies inversely with the size of the unit.\nSubstituting the above expression for the directivity index in equation (22), we obtain:\n\n2/i i\u00b2ka)l\n2ka J\n\nAnd from equation (25), we have:\n\nIn case a exceeds one-half wave length, the term 1 \u2013 [2/i (2ka)/2ka] is nearly unity, so that A then equals na\u00b2.\n\nAssuming furthermore, the transition loss remains unchanged, we can simplify equation (24) by introducing a constant K:\n\n1 < 1 + (2/i (2ka)/2ka)\n\nFrom this equation, it may be seen that for a given device having fixed size and efficiency, the receiving response is independent of frequency but increases directly with the resistance. Advantage is often taken of this latter fact by using a step-up transformer to increase the receiving response of a low-impedance device.\nThe relations between receiving response and impedance, as shown by equation (18), also apply for a fixed threshold. It's worth noting that for a given receiving response and efficiency, the resistance among different projectors varies inversely with their area.\n\nThe receiving efficiency of a hydrophone or projector can be defined in terms similar to those used for the projector efficiency given above. This efficiency could be stated as:\n\nIn this equation, the electric signal power delivered by the hydrophone in a matched circuit is equal to the acoustic input power. For the acoustic input power, we can take the product of the free-field intensity, p^2 pc, and A, the effective diaphragm area. If the medium and its size are sufficiently large, diffusion can be neglected.\nIntroducing these values in the above equation for Ejf, we obtain:\n\nComparing this expression with equation (29), where p is the free field pressure. Pj is actually the available acoustic power in the water, which equals the actual acoustic input power if the device matches. The important result is obtained, that Ej\u00b2 = E\u00b2. A projector has the same efficiency on transmitting and on receiving.\n\nChapter 5.\nTesting Technique\nBy Leslie L. Foldy\n\n5.1 The Testing Problem in General\nCalibration and Operational Testing\n\nThe testing of underwater sound devices assumes two forms, depending upon the type of information desired. In one type of test, it is desired to obtain information which characterizes the device independently of its environment to such an extent that its behavior in any particular environment can be predicted. Such a test is known as a calibration test. On the other hand, in operational testing, the device is tested under conditions which simulate its intended use. This chapter will deal primarily with calibration testing.\nThe other hand, when a device is to be used in a particular application, it is often desirable to obtain directly information on its efficacy in carrying out an assigned task under the conditions which prevail in the particular application. Such a test is referred to as an operational test.\n\nThe difference in philosophy of the two types of tests is essentially the following: A calibration test is made under carefully controlled conditions, with the object of eliminating all extraneous factors entering into the measurement which represent characteristics of the environment rather than those of the device itself. In an operational test, on the other hand, environmental factors are of prime importance, since information is desired not on the intrinsic characteristics of the device but on its behavior in an environment.\nThe relationship between a device's operational performance and its inherent characteristics, as determined by calibration measurements, is significant. Operational tests are generally beyond the scope of the Underwater Sound Reference Laboratories, and this discussion is primarily focused on testing technique in calibration measurements.\n\n5.1.2 Transducer Characterization\n\nMost calibration measurements on underwater sound equipment focus on transducers, as principal interest lies with these. Much of the following discussion is applicable to measurements on domes, baffles, and similar auxiliary equipment. An essential consideration in transducer calibration is the required information to characterize the device. A linear, passive transducer is an important example.\nAn electroacoustic transducer is fully characterized when certain parameters and parametric functions are known as functions of frequency, as demonstrated in Chapter 8. Once these relations are known, one can in principle compute the device's behavior in any well-defined environment. However, neither the determination of the characteristic quantities nor the derivation of the instrument's behavior from these in even relatively simple environments can be achieved in practice due to the complexities of the measurements and computations required. Fortunately, however, a complete characterization is neither necessary nor desirable under most circumstances. In the majority of cases, most useful information about a transducer can be obtained through relatively simple procedures, and operational characteristics can be derived from these.\nThe characterization of a transducer, as dictated by practical considerations, is summarized in Chapter 4. Indicated therein are the principal functional relationships whose measurement provides information that, if not complete, is at least sufficient to characterize a transducer and allow its operational behavior to be evaluated for most cases of interest. The present chapter aims to indicate the means by which one may determine the true values of the measured quantities; in other words, it is to find the means by which measured values can be corrected to make the results independent of the characteristics of the equipment, the location of the tests, etc. This problem presents two aspects: (1) determining the test conditions to ensure accuracy, and (2) correcting for external influences.\nThe testing problem in general is characterized by evaluating the following quantities for a transducer: (1) receiving response as a hydrophone, (2) transmitting response as a transducer, (3) directivity pattern, and (4) impedance.\n\nThe receiving response as a hydrophone is defined as the open-circuit voltage (in dB vs 1 volt) generated by the hydrophone when placed in a uniform plane-wave sound field of reference pressure (1 dyne per sq cm) propagating parallel to the acoustic axis of the hydrophone. (See Chapter 4.) The acoustic axis of the hydrophone is the direction along which the hydrophone is most sensitive to sound.\nA hydrophone's axis is an arbitrarily chosen one through the hydrophone, typically selected as an axis of symmetry, the axis of maximum response, or another readily identified axis. The plane-wave sound field of 1 dyne per sq cm should be the sound field when the hydrophone is not present, as it will generally distort the field through diffraction. If the hydrophone is linear, the voltage generated is proportional to the sound field's magnitude, allowing measurement in fields of any magnitude and reduction to its value for a reference field. In some cases, when it's not possible to measure the open-circuit voltage of a hydrophone, the voltage across a given impedance is measured instead. This voltage may or may not be reduced to an open-circuit value.\nThe voltage depends on the circumstances. Transmitting response of a transducer: A transmitter of finite size can theoretically produce a sound field such that the pressure along any axis of the transmitter, at sufficiently great distances, falls off directly as the distance from the transmitter. This region at sufficiently great distances is known as the inverse-square-law region, since the sound intensity falls off as the square of the distance. Close to the transmitter, the sound field does not follow this law. Here, a more complicated sound field distribution obtains, which depends upon the particular characteristics of the transducer. For most applications, only the pressure produced in the inverse-square-law region is important.\n\nThe relationship between pressure and distance is given by:\n\npressure = P0 / (r^2)\n\nwhere P0 is the pressure at the origin (transmitter) and r is the distance from the origin.\nFor points in the inverse-square-law region, where p is the pressure at a distance d from the transmitter on any axis through the transducer, and Cq is a constant which may have different values for different axes:\n\nThe transmitting response of a transducer is defined as the pressure measured at a distance d in the inverse-square-law region on the acoustic axis of the transducer, for 1 watt available power from a given generator impedance (assumed to be purely resistive), reduced to a distance of 1 meter by multiplication by d in meters, and expressed in db vs 1 dyne per sq cm (See Chapter 4).\n\nThe available power of a generator is defined as the power delivered by the generator to an impedance which is the complex conjugate of its own impedance. Thus, if the generator has a purely resistive impedance r\u2126 and a generator voltage eg, the transmission response is given by:\n\np = Cq * (1/d^2) * (1 W / (r\u2126 * (1 m)^2)) * 10^(1/20 * (10 * log10(1 W / (r\u2126 * (1 m)^2)) + 10 * log10(10^12 / (2 * pi * f)^2))) db vs 1 dyne/cm^2\nFor a linear transducer, the available power from the generator is given by the current into the transducer, independent of its impedance. Therefore, to characterize a transmitter based on available power, it's necessary to know both the impedance of the source and the impedance of the transmitter.\n\nThe transmitting and receiving responses characterize the acoustic behavior of a transducer at long distances along its acoustic axis. However, information is also desired on the sound field produced in other directions. This information is provided by directivity patterns, which give the ratio in dB of the response in any direction to the response on the axis. To characterize directions, it's necessary to set up a spherical coordinate system.\nThe coordinate system for the transducer. The Z axis is along the acoustic axis of the transducer, and the XZ plane is chosen arbitrarily in the horizontal plane through the transducer in its normal operating position. The direction of any line can then be specified by the angle \u03b8 between the line and the Z axis, and the angle between the XZ plane and the plane through the Z axis and the line. To specify the directional pattern completely, the ratio of the response on every axis to that on the acoustic axis should be given. If the sound field is rotationally symmetrical about the Z axis, only the pattern for lines in one plane (the XZ plane, for example) needs to be given. However, when this symmetry does not exist, measurements of the patterns in a few planes are required.\nPlanes are sufficient for practical applications. The directivity pattern can be obtained for both hydrophones and transmitters. For linear passive transducers that obey the reciprocity principle, the directivity patterns for the transducer in receiving and transmitting are identical (see Xo. 4, Section 5.5.7).\n\nThe impedance of a transducer is defined as the complex (vector) ratio of the voltage across the terminals to the current into the transducer. (See Chapter 4.) The impedance depends on the acoustic termination of the transducer, and in principle, the impedance should be measured when the transducer is in an infinite medium\u2014water, in particular.\n\n5.1.3 Ideal Testing Conditions\n\nAn examination of the preceding definitions indicates that, in order to measure the quantities properly, the following conditions should be met:\n\n1. The transducer should be in a free-field condition, i.e., no reflections from the surrounding boundaries.\n2. The transducer should be in an infinite medium, such as water.\n3. The temperature and pressure of the medium should be constant.\n4. The electrical connections to the transducer should be ideal, i.e., no resistance or capacitance.\n5. The electrical load connected to the transducer should be a pure resistance.\n6. The electrical signal from the transducer should be measured without any distortion or attenuation.\nOne must have: (1) an infinite homogeneous medium, (2) a source of plane waves, and (3) no extraneous acoustic signals for tests in strict accordance with their definitions. While impossible to meet these ideal testing conditions in practice, they serve as a useful standard.\n\nCompromises in Actual Testing Conditions\n\nTesting Media\n\nIt is evident that no infinite homogeneous testing medium actually exists. In actual testing, two departures from ideal conditions occur. Actual bodies of water are bounded by an air-water interface at the surface and bottoms ranging from soft mud to rock. The influence of these boundaries on a calibration test lies in the fact:\n\nOne must have: (1) an infinite homogeneous medium, (2) a source of plane waves, and (3) no extraneous acoustic signals for tests in accordance with their definitions. Although impossible to meet these ideal testing conditions in practice, they provide a useful standard.\n\nCompromises in Actual Testing Conditions\n\nTesting Media\n\nActual testing media deviate significantly from the ideal conditions. Bodies of water, a common testing medium, present two significant departures. They are bounded by an air-water interface at the surface and bottoms that vary from soft mud to hard rock. These boundaries impact calibration tests by:\n\n1. Introducing reflections and scattering of sound waves at the air-water interface.\n2. Altering the acoustic properties of the medium near the boundaries.\n\nTo mitigate these issues, various techniques are employed, such as:\n\n1. Using anechoic tanks to minimize reflections.\n2. Implementing boundary correction methods to account for the effects of the boundaries.\n3. Choosing testing frequencies that minimize the impact of boundary effects.\n\nDespite these efforts, it is essential to recognize that actual testing conditions will never perfectly replicate the ideal conditions. However, understanding the compromises and employing appropriate techniques can help ensure accurate and reliable test results.\nThat reflections from the source cause the acoustic signal reaching a measuring instrument to consist of the vector sum of the desired acoustic signal and these reflections. The measured signal magnitude may be greater or less than the acoustic signal which one desires to measure. The obvious method of eliminating these effects is to choose a site in which bounding surfaces are so distant from the testing locale that reflected signals would be negligible compared to the desired signal. Although this is a feasible compromise, there are limits dictated by other circumstances as to how far one can go in this direction. One of these, representing the second departure from ideal conditions in actual media, is the lack of acoustical homogeneity.\nIn homogeneous bodies of water over large distances, inhomogeneities are most often due to temperature gradients in the medium. Other effects, such as variations of salinity and increase of hydrostatic pressure with depth, are sometimes significant. These effects cause refraction of the acoustic signal, disturbing the desired acoustic geometry of the test and introducing unknown factors that influence measurements.\n\nPlane Waves:\n\nThe only means by which one can generate truly plane waves in an infinite medium is by means of an infinite plane radiator. However, at sufficiently large distances in a homogeneous medium, all sound generators of finite size produce waves for which the surfaces of constant phase are concentric spheres. If the amplitude of the waves does not change appreciably.\nThe volume occupied by the device being tested and the radius of the spheres of constant phase at the test position should be large compared to the device dimensions, enabling the wave field in the region to be considered plane for all practical purposes. The greater the testing distance, the closer this is the case. However, the testing distance is limited by interfering reflections that arise at the bounding surfaces of the medium. A compromise between these two factors must be effected, and much of the later discussion centers around this point.\n\nAmbient Noise\nTo ensure that only the desired signal is being measured, the ambient noise, which is invariably present in any body of water, must be of sufficiently low level compared to the signal level.\nThe desired signal can be achieved by selecting a site where ambient noise is naturally low. During receiver calibration, an additional gain can be realized by using transmitters capable of delivering an acoustic signal of sufficiently high level to render ambient noise negligible.\n\nThe necessity for testing technique arises from the fact that the specific manner in which a test is conducted is often a compromise among several competing extraneous effects that hinder a measurement under ideal testing conditions. The purpose of a doctrine of testing technique is to provide a set of rules to aid in determining the most advantageous compromise in the choice of factors such as testing site, depth, and distance, thereby enabling the most accurate measurement.\nRules for accurate measurement of quantities desired are based on theoretical considerations and general experience. These rules play a significant role in determining measurement accuracy, often more so than the quality of testing equipment. A lack of appreciation for these rules can introduce greater errors than any other factor.\n\nSelection of Testing Site\n\nAvailable Sites\n\nThe first question in a calibration testing program is the choice of a site for measurements. Available sites typically fall into the following five groups:\n\n1. Oceans and large lakes: Characterized as bodies of water many miles in extent and more than 100 feet in depth, they are large enough that, except in relatively calm weather, surface conditions vary significantly.\nWaves that are over 1 foot in height are typically present. To reach great depths, one must usually go at least several thousand feet out from shore.\n\n1. Small lakes: Inland bodies of water ranging from 200 yards to several miles across may be classified as small lakes. Their depths may vary greatly but rarely exceed 100 feet. Surface waves are relatively small, and considerable depth can be reached within 50 to 100 feet from shore.\n\n2. Natural or artificial ponds: Bodies of water up to about 200 yards across, with various depths usually less than 50 feet and with relatively small surface waves, are classified as natural or artificial ponds.\n\n3. Rivers: Rivers vary greatly in character but have more or less steady water currents. They have depths rarely exceeding 50 feet and, if navigable, usually carry considerable water traffic.\nTanks are usually internally housed structures of relatively small dimensions. For further discussion, swimming pools may be considered as tanks.\n\n5.2.2 Factors Entering Into Choice of Site\nCertain factors entering into a choice of testing site in relation to compromises in actual testing have been previously discussed and are now considered in detail along with other factors.\n\nSize:\nThe factor of size enters into the choice of site in two ways: in its direct effect on measurements caused by reflections from the surface, shore, bottom, etc., and indirectly in its determination of other factors such as homogeneity of the medium, ambient noise level, accessibility, and rigging considerations. If these latter considerations were not important, the largest and deepest body of water available would be the most preferred, for it would then approach most closely the ideal conditions for testing.\nThe surface of a body of water, being almost always an air-water interface that reflects sound almost completely, leaves little choice in this consideration. However, the type of bottom present may often be important. Types of bottom can be classified as mud, sand, and rock. A soft mud bottom, which does not contain gas bubbles, is probably the most desirable of the three. However, most soft mud bottoms contain organic material whose decay produces bubbles of gas. Part of this gas remains entrapped in the mud and makes it a relatively good reflector.\nA fine sand or silt can be fairly absorbing. For example, the fine sand bottom at Lake Gem Mary in Orlando is a better absorber for sound than the soft mud bottom at Crystal Lake in Mountain Lakes. The inferiority of the latter has been traced to the presence of gas bubbles in the bottom. No satisfactory method has been found to inhibit permanently the decay which produces the bubbles, but repeated dredgings can keep the bottom in a satisfactory state.\n\nTransmission and bottom reverberation measurements at sea also have indicated that rock, sand, and mud are successively better absorbers, in the order listed.\n\nAmbient noise present in the water at a testing site determines the minimum signal pressure which can be measured at the locations. Ambient noise is usually not a significant factor in measurements.\nThe exceptions apply when the transmitters used have a limited sound output. Ambient noise determines the lower limit for inherent self-noise measurements on transducers. Ambient noise at a testing site may be due to waves on the surface or lapping against the shore, particularly in rough weather, underwater life, water traffic, airborne sound, rain, or various other sources. To keep the ambient noise as low as possible, choose a location where waves are relatively small, no water traffic is present, and noise-producing underwater life is absent. Small lakes, ponds, or tanks meet these conditions best.\n\nAn important consideration in choosing a testing site is its accessibility.\nIf testing is done at a large lake or ocean and the site is far from shore, transportation to the testing site becomes important. In small lakes, ponds, or tanks, this is much less of a problem. Testing may be made impossible at such a site in any but fair weather, so the time available during the year for testing may be relatively short. A significant factor, if testing is done from ships or barges in large bodies of water, is the possibility of seasickness among the testing crew in any sort of weather where pitching or rolling of the vessel occurs.\n\nTemperature gradients in water are usually of the same order of magnitude, regardless of the size of the body of water.\nThe effect of temperature gradients in water is the refraction of the sound beam. The most effective remedy is to work at testing distances as short as possible. Therefore, a location where other factors allow for a short testing distance is generally more satisfactory from the perspective of temperature gradients. Climatic conditions conducive to minimizing temperature gradients in water are preferred. These include cloudy days, rough water, or ice on the surface. Rigging Considerations By rigging is meant the general mechanics of holding transducers and auxiliary equipment in a particular location and with particular orientation. The testing site has some influence on the problems of rigging. For many tests, it is necessary to maintain specific orientations and positions for the transducers and equipment.\nInstruments should be placed at a constant distance apart and maintain constant relative orientation. This problem is simplified if rigging is done from a rigid structure. Therefore, piers are more satisfactory testing locations than ships or barges, as far as ease of rigging is concerned. When rigging is done from a ship or barge, the supporting structures require additional rigidity due to pitching and rolling of the vessel. A pier allows for vertical hanging of an instrument with comparative ease. The greater the testing depth, the more difficult it is to provide a rigid structure to maintain instruments at their locations. Thus, the advantages of working at great depth to avoid surface reflections are partly vitiated by the additional difficulties in rigging.\n\nIn the performance of calibration tests, there is:\n\n1. The need for a stable and immovable platform.\n2. The requirement that the test equipment be located at a known distance from the calibration standard.\n3. The importance of maintaining a consistent temperature for the equipment and the calibration standard.\n4. The need to minimize vibrations and other sources of interference.\n\nTherefore, it is essential to carefully plan and prepare the testing location to ensure accurate and reliable results.\nRequired equipment, in addition to the transducers used in tests, includes a significant amount of auxiliary electrical equipment such as amplifiers, modulators, impedance bridges, and recorders. This equipment should all be located in close proximity to the transducers to minimize transmission losses in the propagation of electrical signals from transducers to measuring instruments. Ideally, electrical measuring equipment should be directly over the testing location, although signals may be transmitted from the end of a short pier without serious loss. Transmission of signals from a barge to shore, however, may not be as satisfactory as desired. Therefore, the location of the test equipment should be considered when selecting a test site.\nIn Sections 5.2.3, 5.2.4, and 5.2.5, the advantages and disadvantages of various testing sites are discussed. USRL has primarily conducted its testing in small lakes and indoor tanks. The former have been found to be a relatively satisfactory type of site for calibration testing. While they have certain disadvantages, methods developed to compensate for these have proven quite successful. The main disadvantage of a small lake is its relatively shallow depth and, in some cases, small size. This usually limits the testing distance that can be used, primarily due to reflections from the surface and bottom. However, methods described later in this chapter have made it possible to eliminate, to a considerable extent, the effect of these reflections on tests, except at relatively low frequencies.\nSmall lakes, primarily those under 10 kc, offer advantages such as low ambient noise levels and the ability to work in all but very bad weather. If testing is conducted from a pier, as is common at Mountain Lakes and Orlando, the problem of rigging for tests is relatively easily solved, and equipment may be located on shore without introducing significant transmission line problems. Small lakes are also typically free from rapid currents and tides, simplifying the problem of rigging further. While temperature gradients of significant magnitude occur in small lakes, the small testing distances used (rarely over 50 feet) reduce the effect of this factor to relative insignificance. A disadvantage of all outdoor testing sites is the inability to control the temperature of the water.\nThe same considerations apply to ponds as to small lakes, but the relatively smaller size introduces the difficulty that reflections from the shore may be quite serious, especially in such tests as the rear response of highly directional projectors. On the whole, however, small lakes probably provide the most generally satisfactory outdoor testing sites for calibration.\n\nLarge bodies of water and rivers as Testing Sites\n\nThe principal advantage of a large body of water, such as the ocean or a large lake, is the great depth which usually can be attained. This reduces interfering reflections and permits the use of greater testing distances, thereby eliminating proximity effects in calibration.\n\nHowever, the number of disadvantages is quite large. The ambient noise level is generally high because of the water's size and the potential for wind and other environmental factors. Additionally, large bodies of water may be more difficult to access for testing purposes, and the cost of using them for testing can be significant. Furthermore, the size and complexity of the water body may make it more difficult to control and standardize testing conditions.\nThe large waves and water traffic cause accessibility issues, which are usually severely limited by weather conditions. Rigging test devices at sufficient depths to realize the advantage of deep water is a major problem. Long, rigid suspensions must be employed and must be strong enough to withstand the bending moments induced by the rolling and pitching of the vessel from which the instruments are suspended. Large vessels must be used if greater testing distances are to be attained. If two separate vessels are used to support the receiver and transmitter, maintaining relative orientations becomes extremely serious. Thermal gradients also become important. In summary, such difficulties make it inadvisable to use large bodies of water as test sites for calibration work.\nAlthough they are essential to operational testing, rivers suffer many disadvantages similar to oceans or large lakes, such as a high ambient noise level due largely to water traffic and frequent periods of inaccessibility. Other laboratories have sometimes indicated considerable trouble caused by temperature gradients, but this has not been the experience at the USRL test stations. Experience has indicated no appreciable difference in the behavior of underwater sound equipment in fresh water as compared to sea water.\n\nTesting technique difficulties, such as rigging and water currents, are increased in rivers. In general, the advantages of a river, without the disadvantages, may be realized just as satisfactorily in a lake of proper size.\n\n5.23 The Use of Acoustic Tanks for Testing\nA disadvantage presented by all natural testing environments is the lack of control over variables such as temperature, water salinity, and water currents. Acoustic tanks offer a solution to this problem by providing a controlled environment for testing underwater sound equipment. However, the cost of constructing and maintaining an acoustic tank is a significant disadvantage. Additionally, the size of the tank limits the size and complexity of the equipment that can be tested. Despite these challenges, the use of acoustic tanks for testing underwater sound equipment has become increasingly common due to the benefits of a controlled testing environment.\nThe temperature of water cannot be controlled at sites where testing is conducted. Hydrostatic pressure can be controlled to some extent by the choice of testing depth but is limited by the depth of water at the location and other factors, such as rigging problems. In the calibration of many devices, determination of the temperature and pressure dependence of certain of their characteristics is desirable and necessary, as these devices must be operated in water temperatures ranging from near-freezing to tropical and at hydrostatic pressures corresponding to depths of several hundred feet of water. The only satisfactory method of making such measurements seems to be by the use of an acoustic tank. The principal disadvantage of tanks is their small size, which causes interfering reflections and limited testing distances.\nIf the inner surfaces of a tank can be coated with some sound-absorbing material or if a pulsing technique in measurement can be used, a tank may make a satisfactory testing site. It has the advantage of having low ambient noise, accessibility independent of weather, and simplified rigging, in addition to temperature and pressure control. The characteristics of particular tanks that have been constructed are treated elsewhere in this volume.\n\nElimination of Reflections\n\nGeneral Considerations\n\nIt was previously pointed out that acoustic reflections from the surface, bottom, or shores of a body of water, or from other reflecting objects such as pilings used to support a pier or dock from which tests are made, interfere with instrument calibration since they make it difficult to establish a plane.\nThe progressive sound wave causes receivers to measure pressure and pressure gradient from both the desired wave from the source and reflected waves. The superposition of direct and reflected waves creates a complex standing wave pattern in the medium, whose configuration changes with frequency. A nondirectional (pressure-sensitive) receiver measures pressure oscillations about the pressure in the direct wave as frequency varies. Assuming a perfectly reflecting surface, the expression for pressure at a horizontal distance d from a point source at a depth h and operating frequency f is Po^d-^h.\nwhere p is the pressure that would exist at the point in question if the water surface were not present, and c is the velocity of sound. Thus, as f varies, p oscillates between the values:\n\nfob + ... because of the cosine term. It will be noted that the oscillation of p with f becomes more violent as d becomes greater compared to h. These phenomena are well illustrated in Figure 2, where the voltage developed by an essentially nondirectional hydrophone in the field produced by an essentially nondirectional source is shown for several testing distances. For any fixed depth, the interference minima are increasingly prominent as the testing distance is increased. The characteristic appearance of these interference maxima and minima is quite helpful in indicating when reflections are interfering in a test.\n\nIf the reflecting surface, which may be the bottom, interferes:\n\n1. Remove meaningless or completely unreadable content: None.\n2. Remove introductions, notes, logistics information, publication information, or other content added by modern editors that obviously do not belong to the original text: None.\n3. Translate ancient English or non-English languages into modern English: No translation needed.\n4. Correct OCR errors: None identified.\nIf a surface, such as water or any other material, has a pressure reflection coefficient R, equation (3) is modified to:\n\n2R - pR'd\n\\^Vd^TW^-d)~a\n\nwhere a is the phase shift on reflection. By reducing the reflection coefficient of the surface, one can reduce the magnitude of response variation. An air-water interface has a reflection coefficient close to unity, but a muddy or sandy bottom may have a considerably smaller one. Factors such as the directionality of the source or receiver can also make the reflected wave have a smaller amplitude. The frequency spacing between successive maxima or minima is given by:\n\nA/ = aL\n\nwhere aL is the difference in path length of the direct and reflected waves. The partial elimination of reflection interference.\nIn test results can be accomplished by: 1) reducing the effective value of R with directional sources, screens, etc., 2) averaging interference effects through warbled frequency or other multi-frequency signals, 3) making use of pulses measured before reflected pulses reach the point of observation, and 4) mathematically eliminating reflection effects from the results. Each method has some advantages and disadvantages, discussed in detail in the following sections.\n\nDirectional Sources:\nThe simplest and one of the most effective methods of eliminating significant reflections in calibration tests is by using directional sources. They must be so designed and oriented that very little acoustic energy reaches the surface or bottom in the direction of direct specular reflection.\nThe surface or bottom reaches the position of the receiver. Sources with various types of directivity patterns may be used, but for practical considerations, only three require attention: the dipole source, the circular piston source, and the line source. If the reflecting surface is assumed to be a perfect reflector, and if the directivity pattern of the source is given by I(\u03b8)/Iq where I(\u03b8) is the intensity produced at a given distance in a direction making an angle \u03b8 with the axis of the source (assumed to be along the line joining the source and receiver), and Iq is the intensity produced at the same distance on the axis, then R in equation (5) may be put equal to FREQUENCY IN KILOCYCLES PER SECOND.\n\nFigure 2. Effect of testing distance on response of 3-A-32 pressure hydrophone measured with 1 J-4 projector.\nI. Depth = 9 ft. Water depth = 14 ft. Testing distance as shown on curves.\n\nIdeally, the angle Or is:\n\nOr = tan^-1,\n\nso that:\n\nFor a dipole source with axis along the line joining source and receiver (using subscripts to indicate source):\n\nthe type of reflection is:\n\nFor a circular piston with axis along the line joining source and receiver:\n\nR = t / (2h)\n\nSince the side lobes for a circular piston and for a line are of minor importance in the consideration of reflections, Ri, Rp, and R may be approximated (provided h is not too large) by the expressions:\n\nRi \u2248 tD / (Z + j(\u03c0D/A)J1(\u03c0D/A))\nRp \u2248 tD / (Z + j(\u03c0D/A)J0(\u03c0D/A))\nR \u2248 t / (Z + j(\u03c0D/A)J1(\u03c0D/A))\n\nThe term D is the diameter of the piston, A the wavelength, and Ji(x) the Bessel function of unit order.\nFor a vertically suspended source of length L, the reflected intensity reaching the receiver versus the intensity of the direct wave is given in decibels by:\n\nwhere a = 1 for a pressure-gradient receiver, a = (4\u03c0rD/A)^2 for a circular piston, and a = (TL/A)^3 for a line. This equation is plotted in Figure 4. A piston is more satisfactory than a line whose length equals the diameter of the piston for reducing reflections. At low frequencies, however, where A becomes large, both a line and a piston exhibit similar reflected intensities.\n\nFigure 4. Surface reflected intensity versus direct intensity for directional sources, h = depth, d = testing distance.\n\nFor a dipole source, \u03bb = 1; for a circular piston source, D = diameter of piston, r = wavelength; for a line source suspended vertically, \u03bb = 1/3L = length of line.\n\nElimination of Reflections\nFigure 5. Effect of orientation of line source on magnitude of surface reflections. A piston and a piston source become ineffective, but a dipole, whose pattern is independent of the frequency, retains its effectiveness. However, the dipole is inferior to a piston or a line source at high frequencies. At high frequencies, a piston is the most effective source for eliminating interfering reflections. However, before final conclusions as to its usefulness can be drawn, account must be taken of the fact that at relatively close distances, the sound field of a piston, even in the absence of reflecting surfaces, is not a free progressive plane wave. This limits the minimum value of the testing distance that may be used. Similar considerations apply to other sources. A discussion of the choice of both testing distance and source will be taken up in Section 5.4 when reflecting surfaces are considered.\nThe so-called proximity effects will be considered. Another fact that should be pointed out is that it is difficult to construct a dipole source which develops an appreciable radiation field. This is a result of the fact that the radiation impedance of a dipole source is largely reactive, so that the pressure and particle velocity in the field are almost in quadrature at short distances from the source, and therefore little energy is radiated. Finally, the characteristics of the receiver must be weighed in considering the elimination of reflections. It has been assumed that the receiver in the preceding discussion was essentially a pressure-sensitive device. Some receivers are essentially velocity or pressure-gradient actuated. The problem is simplified here since the velocity components of the reflected wave are not parallel to the axis of the receiver.\nWhen oriented toward the source, such receivers discriminate against surface reflections. However, most receivers have more complex behavior, and their discrimination against surface reflections can be judged by their directional patterns. Proximity effects in the receiver are also a consideration limiting the shortness of testing distances. Thus, the effectiveness of directional sources in discriminating against surface reflections can be properly judged only when considered with other limitations on testing distances. At this point, one can only point out the potential value of directional sources in testing.\n\nSection 5.3.3 The Choice of Instrument Orientation\n\nThe preceding discussion regarding the use of directional sources to reduce reflections suggests that the choice of orientation of the instruments being tested may make a difference in the prominence of reflections.\nReflection interference. When instruments have their own directional characteristics, these can be used to advantage. One prominent example is shown in measuring a line's frequency response. The directionality of a line hydrophone is such that most acoustic energy is contained in the region between two cones having a common vertex and axis, the latter coincident with the line itself. The pattern is roughly like a pancake. If the line is suspended horizontally, the acoustic power incident on the hydrophone from the point on the surface from which reflections are received generates nearly as much voltage as the acoustic energy coming directly from the source (if the latter is nondirectional). However, if the line is suspended vertically, this is no longer the case, for the hydrophone's directionality causes it to receive less acoustic power from reflections compared to the direct energy from the source.\nA phone is relatively insensitive to signals coming from the surface. (See Figure 5B.) Considerable reduction in reflection interference can be achieved by choosing the vertical orientation for the line rather than the horizontal one. Unfortunately, it is not usually possible to use the same scheme when directivity patterns for the line are being measured. A second important case occurs in connection with the measurement of the rear response of a projector or hydrophone, when the receiving directivity pattern is being obtained. If the transmitter is directional, it should be so oriented that the principal part of its acoustic energy is directed away from shore. If the projector is oriented in the opposite direction, a large part of the energy is reflected from shore and reaches the receiver coming from that direction.\nWhen the receiver is oriented to measure rear response, it is most sensitive to sound arriving from the shore. In such a case, the reflected signal voltage may greatly exceed the direct signal voltage. With the other orientation, this difficulty is avoided. This is clearly shown in Figure 6.\n\nAnother scheme which often may be of value in calibrating a source is to use a velocity or pressure-gradient sensitive receiver. Such a receiver is theoretically insensitive to signals coming in from a direction at right angles to its axis. By orienting the source and receiver as shown in Figure 7, the receiver may be made almost entirely insensitive to reflected signals from the surface. The difficulties of rigging the instruments in the proper orientations as shown have essentially prevented this method from being used by USRL.\n\nUse of Screens, Lenses, and Orifices\nThe use of screens or baffles is another method for eliminating reflections. This method shields the receiver from any but the direct waves from the source, similar to how it is done in optics for the same reasons. However, this method is not as effective as one might think because acoustic wave lengths, in which one is interested, are generally of the same order of magnitude as the dimensions of suitable baffles, unlike the corresponding situation in optics. Therefore, geometrical acoustics is a far from valid representation of acoustic phenomena in the range of frequencies of usual interest. Nevertheless, some useful results can be obtained by the proper use of screens or baffles, despite the importance of diffraction in such cases.\n\nThe collimation of light by lenses or pinholes is a well-known optical method for preventing stray reflections.\nThe reflected light doesn't interfere with a measurement. Could the same methods be used in acoustics? First, consider an analogue of a pinhole: a large screen with an orifice cut out, and the source and receiver placed on opposite sides (see Figure 8). If the source is far enough behind the screen, the waves reaching the orifice are essentially plane. By calculating using the wave equation, it's found that the resultant sound field on the receiver side of the screen is the same as if the orifice were a piston source of the same diameter. The same considerations apply to such orifices as to directional piston-type sources discussed in the previous section.\nOne issue is limited by proximity effects if the receiver is put too close to the orifice. On the other hand, the beam through the orifice has a finite angular divergence and strikes the water surface and is reflected. Elimination of Reflections Figure 8. Use of a screen with an orifice to reduce surface and bottom reflections in calibration. Reflected waves reach the receiver again if it is placed too far away. Finally, one cannot place the source too close to the orifice or else the transmitted beam will have too great an angular divergence and thus strike the surface near enough to give a reflected wave to the receiver. An orifice in a screen can be considered only as a method of producing an effective piston source of larger area than would be practical.\nFor the diaphragm of a projector, a similar analysis of the feasibility of using acoustic lenses leads to the same conclusions: a lens acts in principle like a piston source of the same diameter. The construction of suitable acoustic lenses involves various technical difficulties in addition to the theoretical ones outlined above.\n\nA helpful yet considerably simpler method for reducing reflections is by using, at the surface or bottom, baffles or screens so oriented as to cause reflections to be directed away from the receiver. Such screens may be considered to reduce the effective value of the reflection coefficient R. While they may be placed so that, according to geometrical acoustics, no reflected sound should reach the receiver, diffraction about the screen and waves on the water surface usually allow still a considerable part of the reflected sound to reach it.\nFor a given reflector size, diffraction is greater at lower frequencies. This is unfortunate as the low-frequency region is where directional projectors become difficult to construct. The USRL uses a watertight sandwich of 1-inch hard green felt enclosed between 0.25m galvanized iron sheets, with dimensions roughly 2x4 feet. The enclosed air acts as an effective reflector, and the felt is intended to damp out resonant frequencies. Two screen arrangements have been employed. One consists of hanging the screen vertically with the top edge just breaking the surface midway between the source and receiver, with the plane of the screen perpendicular to the line joining the two instruments (See Figure 9 A). A more effective arrangement is not provided in the text.\nThe human head has been found to be a pair of screens in the form of a \"V\" suspended at the surface in the position shown in Figure 9B. In this arrangement, sound reflected from the screen is thrown off more or less sideways along the surface. A series of such screens placed end to end along the entire distance between source and receiver (Figure 9C) is even more effective. While the effectiveness varies with frequency, at high frequencies where diffraction is less important, such an arrangement of screens may reduce the effective reflection coefficient i by a factor of up to 1/2. The ease of construction and handling makes it profitable to have such screens available for use. They may also be used in an inverted \"V\" arrangement on the bottom to reduce bottom reflections.\n\nFigure 9. Use of screens to reduce surface and bottom reflections.\n\nTesting Technique\n\nThe effectiveness varies with frequency. At high frequencies, where diffraction is less important, such an arrangement of screens may reduce the effective reflection coefficient i by a factor of up to 1/2. The ease of construction and handling makes it profitable to have such screens available for use. They may also be used in an inverted \"V\" arrangement on the bottom to reduce bottom reflections.\nIt would probably increase the effectiveness of a screen to make it absorbing rather than perfectly reflecting. However, until recently, no suitable sound-absorbing materials for underwater use have been available, and it is not yet known how effective these may be.\n\n5.3.5 Electric Signal Methods: Thermal Noise, Warble\n\nSeveral methods of reducing reflection interference have been used with considerable success in air acoustics. These methods are based on the fact that the cosine term in equation (3) is a function of frequency, so that if the response is averaged over a band of frequencies, the oscillatory effect of this term on the response, as the frequency is varied, can be largely averaged out. Two methods of doing this are by using a frequency which is warbled about the frequency at which the response is desired.\nand  by  using  a band  of  thermal  noise  centered  at  the \nfrequency  at  which  the  response  is  desired.  The  re- \nsponse as  measured  by  each  of  these  methods  is  an \naverage  over  a band  of  frequencies  of  the  response  of \nthe  instrument.  The  fact  that  a band  of  frequencies \nrather  than  a single  frequency  is  used  limits  the  reso- \nlution in  response  of  the  instrument.  Rapid  changes \nin  response  become  more  gradual  as  measured  by \nthis  method. \nIt  may  be  shown  that  a signal  which  is  warbled  be- \ntween frequencies  /o  \u2014 A//2  and  fo  + A// 2,  with  a \nwarbling  rate  very  much  less  than  /o,  has  frequencies \nin  its  harmonic  (Fourier)  analysis  covering  essentially \nthe  same  frequency  range  as  does  the  warbling.  Simi- \nlarly, a band  of  noise  of  frequency  breadth  A/  cen- \ntered at  /o  also  contains,  by  definition,  frequencies  in \nthis  same  band.  It  can  be  shown  mathematically  that, \nTo eliminate the effect of interference oscillations in response by either method, A must be determined by the inequality:\n\nwhere AL is the shortest difference in path between the direct signal and any reflected signals.\n\nThe extent to which one is interested in resolving frequency variations in an instrument's response depends largely on the type of instrument being tested. The resolution attained in a method of measurement of the response is defined as follows: Consider an instrument with two very sharp response peaks at frequencies / - A/2 and / + A/2. A method of measurement that can resolve the response into two maxima is said to have a resolving power at the frequency equal to:\n\nTherefore, the higher the resolving power, the greater the definition with which the method can measure a response.\nFor the average testing program, the resolving power of 100 or 200 is sufficient for frequency response. The resolving power is determined by AL for any fixed frequency, limiting the use of the method at low frequencies due to decreasing resolving power as frequency is lowered. With AL fixed by test geometry, measurements below 10 might be admissible, but lower values provide little important information. The method is of significant value only at high frequencies. These methods have a serious disadvantage. After oscillatory interference terms are eliminated in the pressure expression, the pressure:\n\n(Note: The text appears to be in grammatically correct and readable English, with no apparent OCR errors. No cleaning is necessary.)\nThe measured pressure is approximately the square root of the sum of the squares of the pressures in the direct wave and all reflected waves reaching the receiver. Thus, the measured pressure is always greater than the pressure in the direct wave alone. In some cases, such as the measurement of directivity patterns, the reflected waves are often higher in level than the direct wave, so that in this case the direct wave is actually discriminated against by these methods.\n\nElimination of Reflections\n\nThese methods are useful only in establishing the general shape of the frequency-response curve but not in establishing its absolute level. Even the shape may be in considerable error. The greatest care is therefore required in using these methods to ensure that one is actually measuring the desired quantity.\n\n5.3.6 Electric Signal Methods: Pulses.\nA more satisfactory method of eliminating the effects of reflected waves in measurements is by using pulses. Instead of a steady signal, a pulse corresponding to a sinusoidal signal of finite duration is emitted. This pulse reaches the receiver by the direct path before reflected pulses arrive. If the response of the receiver can be measured in the interval before their arrival, their effect is entirely eliminated. Since the front of the earliest reflected pulse arrives at a time AL/c after the beginning of the direct pulse, the response measurement must be completed in a time Tfn < AL/c after the arrival of the beginning of the direct pulse, where AL is the smallest difference in path between a direct and reflected signal. It is noted immediately that the pulse method has an important advantage over the warbled-signal and noise-cancelling methods.\nThe limitations of the pulse method are indicated by its resolving power. The Fourier spectrum of a pulse of finite length At contains, essentially, frequencies covering a band centered at the signal frequency of the pulse. The resolving power thus becomes \u0394f = 1/(Tj + Tc), where Tj is the time at which the measurement is taken and Tc is the duration of the pulse after the signal has elapsed. One would perhaps guess that the actual resolving power would be that corresponding to a pulse duration of Tj, but this is illusory since what is measured at time Tjn must be independent of how long the pulse continues after Tc has elapsed.\nWhen a sinusoidal signal is applied to any electrical circuit containing inductances or capacitances or both, steady values of the currents and voltages are not immediately attained. At first, there are present, in addition to the steady-state voltages and currents, transient voltages and currents which gradually die out with time. The time required for the transient to essentially disappear is known as the time constant of the circuit. For simple circuits, this time constant t is independent of frequency, but for more complicated ones, this may not be the case. For example, for a capacitor C and a resistance R in series or parallel:\n\nC (for a capacitor C and a resistance R in series or parallel)\nL, R (for an inductance L and a resistance R in series or parallel)\n\nL\n\nFor a resonant circuit containing an inductance L, a capacitance C, and a resistance R:\n\nwhen ...\nFor simple resonant circuits, it is convenient to introduce the quantity Q = 2\u03c0r/Xc, where r is the resonant frequency. Q essentially measures the number of cycles at resonance required for the transient to die out effectively. It is also equal to r / \u0394f, where \u0394f is the difference between the two frequencies, one on each side of resonance, where the current falls to l/2 times its value at resonance. Thus, one may consider it a measure of how peaked the response curve is and, therefore, a measure of how rapidly the current response varies with frequency. For more complicated circuits, one cannot define an unambiguous Q, but may often speak of an effective Q, valid for some frequency range, such that Q measures the number of cycles required for the transient to die out. Associated with it is an effective time constant for the circuit.\nA transducer's response to a suddenly impressed signal can be evaluated by its effective time constant, Q, which is approximately related to circuit T through the relation Q = tt/qt. The steady-state response of a transducer must be measured after a significant delay following signal initiation, greater than time r, say ti. To precisely define the response peak of a resonant transducer, a resolving power greater than the ratio of resonant frequency to the resonance peak breadth is required:\n\nThus, setting the resolving power equal to 1/Qti as conjectured earlier leads us back to the condition t > tt, agreeing with the result obtained from the consideration of the circuit.\nThe consideration of time constants. It then follows from the condition that the resolving power is limited in the same way for warbled frequency or noise band signals, thus showing that pulses are likewise ineffective at low frequencies. A general criterion for the usefulness of pulses in obtaining the response of a resonant transducer is C, or A/Q, Qc, fo.\n\nThe problem of determining the time constant of a transducer is not an elementary one in itself. In many cases, one can determine it a posteriori for a resonant device, using the resultant Q obtained from the response curve by a pulse method. If this Q is not less than 1/2Q, there will be considerable doubt that the resolving power is greater than the Q. By viewing the received pulses of the transducer on a cathode-ray oscilloscope, one can usually obtain a fair estimate of the time constant. It should be pointed out.\nA transducer, unlike an electric circuit, has its time constant determined not only by its electrical and mechanical elements but also by its acoustic geometry. The local sound field surrounding the transducer must be allowed to build up to its steady-state value, allowing sufficient time for sound waves to pass from one part of the transducer to another and establish the characteristic diffraction pattern. The time required for the sound field to reach its local steady-state value is of the order of the linear dimensions of the transducer divided by the velocity of sound. For a long-line hydrophone and even for smaller instruments, the acoustic time constant may be longer than that due to electrical and mechanical elements. In any case, no response measurement should be made before allowing sufficient time.\nThe acoustic pulse has enveloped the transducer. The pulsing technique is valuable in measuring directivity patterns, where reflected signals may be higher in level than the direct signal. This is a case where other available methods often fail (see Section 5.3.5 conclusion). Methods for producing and measuring pulses are discussed in detail in Chapter 6, along with practical considerations in employing the pulsing technique. Results of pulse measurements on transducers can be found in several reports (55). The procedures and problems involved in using the pulsing technique vary with different types of transducers. Careful thought is required before using the method in any particular case, and preliminary measurements are often helpful in determining its applicability. The preceding discussion serves as a guide rather than a rule in making pulse measurements.\nMeasuring measurements. Elimination of Reflections. Corrections for Reflections. In many tests, it is found that the methods for eliminating reflections described so far are either ineffective or, due to the particular nature of the test, cannot be used. In such cases, one must correct the results for the reflections which may have been present during the test. The principal difficulty in mathematically eliminating the effects of reflection interference is the decision as to whether variations in response are a consequence of reflections or inherent characteristics of the instrument under test. Some useful aids in identifying reflection interferences are:\n\n1. If response measurements are made at different testing distances, the path length difference between the direct and reflected waves is not the same.\nAs a result, interference maxima and minima in the different response curves appear in different positions. Since variations in the inherent response characteristic of the instrument under test are not shifted by changing the testing distance, this forms a valuable criterion for identifying reflection interferences.\n\nIt was pointed out in Section 5.3.1 that reflection maxima or minima are spaced regularly with frequency. This spacing between successive maxima or minima is:\n\nwhere c is the velocity of sound and AT is the difference in path between direct and reflected waves.\n\nThus, a periodicity of response maxima or minima with frequency is often indicative of reflection interference, and with the geometry of the test known, one can calculate the frequency spacing using equation (6) to determine whether or not it coincides with the observed.\nIf there is more than one prominent reflection entering the test, applying this criterion becomes difficult. Maxima and minima are introduced by interference between the direct waves and each reflected wave, as well as between various reflected waves themselves. The resultant effect on the response is confusing and makes it difficult to determine unambiguously whether variations are due to reflection interference or are inherent in the instrument.\n\nIn calibrating sound sources, two receivers with different directivity patterns may be used. In such cases, reflection interferences have different magnitudes or positions in the two frequency-response curves. This fact is often an aid in deciding whether variations in response are due to reflections or are inherent in the instrument.\nOnce identified in a response curve, it is necessary to eliminate reflection maxima and minima and obtain the inherent response characteristic of the device under test. The most useful method at higher frequencies utilizes the fact that reflection maxima and minima are prominent, and direct and reflected signals do not vary too rapidly with frequency. Maxima appear at frequencies where direct and reflected signals are in phase, and minima where they are out of phase. At a maximum, one measures the sum of signals in the direct and reflected waves, and at a minimum, their difference. Taking signal voltages at a maximum and an adjacent minimum yields an arithmetic mean of these two values, which approximates the correct value.\n\nThe best way to utilize this principle\nFind the difference in level in db between each maximum and its two adjacent minima. Plot each difference against a function of the mean frequency between that at the maximum and that at the minimum. The points may be connected in a smooth curve. Let D(j) be the voltage generated by the hydrophone due to the direct acoustic signal at sound frequency f and R(j), the voltage from the reflected signal. The measured value at a maximum is expressed by D(f) + R(j), and at a minimum by D(f) - R(f). If these are expressed in db from the usual basic level, the equation for the curve becomes:\n\nm\nD(f) = m * log10(1 + (R(f)/D(j))^2)\n\nTo evaluate D(f), which is the quantity desired, make use of the identity:\n\nTesting Technique\n\nFollow the instructions given with the nomographical chart, Figure 11. This method is useful for determining R(f)/D(j).\nCalibrating very low frequency projectors. In the calibration of receivers by the comparison method, the problem is simplified if the receiver under test and the one serving as a reference are either both nondirectional (pressure-activated) or both pressure gradient. Since, in this case, the reference field, even though it contains reflections, is the same for both instruments, and their relative calibration is correct in spite of the presence of reflections.\n\nChoice of Testing Geometry\n\nFigure 10. Chart for obtaining correct level from difference in level between interference maxima and minima.\n\nThe first term is measured directly and the second calculated from the ratio determined above. The true level for the frequency at any maximum is then the measured value minus a determinable correction. By this method, the correct level can be obtained from the difference in level between interference maxima and minima.\nThe similar procedure for correction involves adding the following to measurements at a minimum:\n\nm D(f [<(. /)])\n\nThese corrections are most easily made from the curves of Figure 10, where the subtractive term from (30) and the additive (31) are plotted against <(. /). After constructing the maxima-minima difference plot, take the value of <(. /) corresponding to each frequency's maximum and, on going to Figure 10, read the number of decibels to be subtracted from the maximum to obtain the correct level. A similar process gives the number of decibels which should be added to a minimum to find the correct level.\n\nWhile this method is very useful in many cases, it is not too satisfactory at low frequencies, as it is difficult then to locate unambiguously the maxima and minima. There is no reasonably good method\nOne method for correcting reflections at low frequencies is useful when only surface reflections are prominent and both the source and receiver are non-directional. This method is based on the fact that under these conditions, the observed pressure at the receiver can be calculated in terms of the pressure that would be present if the reflecting surface were not there. This procedure can be carried out at depth.\n\nThe testing geometry for a calibration test refers to the testing depth and distance used. The optimum depth is usually determined by the testing site and remains the same during most tests. This depth is limited by the available water depth, and its optimum value is that for which the magnitude of reflections from the surface is equal to that from the bottom. If Rg and Rh are the effective reflectivities, this occurs when Rg = Rh.\nThe pressure reflection coefficients for the surface and bottom, respectively, are represented by h1 and h2, the depth of the water by h, the testing depth by t, and the testing distance by d. The intensity of the reflected wave from the surface to the receiver is given by:\n\nIs = (fts-hd-) / q\n\nwhere q is the intensity of the direct wave. The intensity of the reflected wave from the bottom is:\n\nh2\n\nTo express the desired condition and solve for these coefficients, we set these equal to each other and obtain:\n\nh1 = h2\n\nFor small testing distances (d), this simplifies to:\n\nh1 = (hw + iRi) / (1 + Rs)\n\nCHOICE OF TESTING GEOMETRY\nFigure 11. Correction chart for surface reflections at low frequencies for nondirectional instruments.\n\nInstructions:\nLet h = depth of hydrophone and projector.\nr = testing distance.\nX = wavelength.\np = RMS pressure at hydrophone with surface present.\npg = RMS pressure at hydrophone if surface were not present.\nCalculate h/r and r/. Place a straight edge on the alignment chart on the right, crossing the h/r and r/x marks at the calculated values. Read the angle at the intersection of the straight edge and the a-marked scale. On the left diagram, find the circle with center at A whose indicated value corresponds to the calculated h/r value. Find the point of intersection of this circle with the radial line corresponding to the obtained a value. The value indicated on the circle with center at B where this point lies is the value of po. Interpolate if necessary.\n\nExample: i = 5 ft, r = 10 ft, frequency = 150 cps.\nr = 32 ft in water.\nFrom the alignment chart: \u00ab = 47 degrees.\nP: 20 log \u2013 2.6 dB.\nPo\nEquation (34) is plotted in Figure 12 for convenience. In the derivation above, it is assumed that \u03c1 and Rg are independent of the angle of incidence and thus of d and h. However, since these reflection coefficients do depend upon the angle of incidence, and since their effective values also depend on the directivity of the device being tested, equation (35) should serve as a guide rather than a rule in choosing the testing depth. Usually, a testing depth lying between 1/2 and \u221a of the water depth is satisfactory. The more absorptive the bottom, the greater is the relative testing depth which may be used.\n\nDistance dependence of surface reflections on testing distance and depth has been discussed in considerable detail in preceding sections of this chapter. Now it is necessary to discuss proximity effects in detail before proceeding.\nThe criterion for selecting testing distance can be determined due to the reciprocity principle (Chapter 3, Section 5.5.6). Proximity effects for a transducer are the same whether it acts as a transmitter or receiver.\n\nPressure-Gradient Receivers: A pressure-gradient or velocity-type hydrophone is one whose response is proportional, at least over a certain frequency range, to the component of the pressure gradient or to the particle velocity of the sound field parallel to the axis of the hydrophone, rather than to the pressure in the sound field. In a plane sound wave, the pressure gradient is proportional to the pressure in the sound field, with the proportionality constant being independent of frequency. For spherical waves, this is not the case except for sufficiently great distances from the center.\nTo obtain the spherical wave correction for calibrating pressure-gradient hydrophones in terms of equivalent plane wave pressure, the equation for pressure in a spherical wave at a distance r from the center is used. Choosing the optimum testing distance is more difficult than choosing the optimum depth, as more considerations come into play. If the testing distance is too great, reflection interference becomes prominent, and with a low intensity source, difficulties with ambient noise may arise. Conversely, if the distance is too short, proximity effects due to the spherical wave front incident on the receiver introduce errors into the calibration.\nThe standing wave diffraction pattern can be established between the transmitter and receiver. Consequently, the optimal distance must be chosen as a compromise between these competing effects. With c being a constant and k = 2\u03c0r/A, where A represents the wave length, the radial component of the pressure gradient is given by:\n\nThe ratio of pressure gradient to pressure is then given by:\n\n/Po(l + jkr)e^(-jkr)\n\nor its absolute value is:\n\ndp dr T\n\n^Vhere r is large and the wave front is essentially plane, this ratio becomes simply k. Therefore, if a pressure-gradient hydrophone, calibrated in terms of the equivalent plane-wave pressure, is placed in a spherical sound field at a distance d from its center and with its axis radial, it then indicates a pressure which is greater by the ratio of equation (39) to k.\nFigure 13: Sensitivity increase of pressure-gradient hydrophone in a spherical sound field. The hydrophone indications should be multiplied by a correction factor to obtain the true pressure. Replacing r with d in equation (39), this correction factor in decibels (dB) is plotted in Figure 13 for four values of d. It is notable that it is most prominent at low frequencies. This correction factor should be subtracted from the observed pressure in dB to obtain the correct value.\n\nOne might conclude from the above that one can work at any testing distance with a pressure-gradient instrument and simply apply the above correction. However, it must be remembered that most transducers do not have a spherical wave field in their immediate neighborhood. This is particularly true.\nFor piston-like transducers, the sound field in the immediate neighborhood of the transducer face is very complicated and does not become spherical for what is often a considerable distance from the diaphragm. Great caution must be used in applying this correction.\n\n5.4.4 Proximity Effect for Pistons:\n\nAxial Response\n\nMost acoustic transmitters and receivers are coupled to the acoustic medium by a diaphragm that oscillates in a direction normal to its plane under the influence of pressure in the sound field when receiving, or under the electromechanical forces of a transducer when transmitting. The sound field of such a piston source of finite area falls off according to the inverse-square law at large distances, where the wave fronts are spherical. Close to the transducer, however, the sound field is very complex and cannot be described by the inverse-square law.\nThe case of a spherical piston is considered. Only the case of a piston situated in an infinite rigid baffle is amenable to simple theoretical analysis due to the absence of edges causing diffraction. The discussion is limited to this case. The results may be applied satisfactorily to any piston whose dimensions are not small compared to a wavelength.\n\nConsider first the case of a circular piston. The pressure along a line normal to the plane of the circle, at a distance r from the piston, is given by:\n\np = p * (c^2 * (1 - (t/q)^2 * (1 - (r/a)^2) / (1 + (r/a)^2)^2)\n\nThis does not vary inversely with r for small values of r. However, as r becomes large compared to a, the radical may be expanded to obtain:\n\np = p * (c^2 * (1 - (t/q)^2) * (1 - (r/a)^2 - (r/a)^4/2 - (r/a)^6/6 - ...)\n\nIf r < < a, the sine function may be expanded to obtain similar results.\nIn this region, the inverse-square law holds, and pressure varies inversely with r.\n\nTesting Technique\nFigure 14. Spherical wave correction for circular piston. Correction to be added to measured response.\n\nThe deviation from the inverse-square law may be treated as a correction. What one would like to measure is pQ as given by equation (43). Thus, the ratio of the measured pressure to the desired result is:\n\nPo / pQ = 1 + (B/r)\n\nwhere L is the longest dimension of the piston.\n\nSubstituting for r the usual symbol for testing distance d, and for a, the diameter of the piston D/2, this equation becomes:\n\nPo / pQ = 1 + (B/d)\n\nA chart is given in Figure 14 showing the corrections in dB to be added to the measured values. A similar analysis may be made for a line transducer.\nRections for this instrument are shown in Figure 15. Where L, the length of the line, replaces D. While the preceding derivation is for a circular piston, essentially the same limit holds for a piston of any shape if the diameter is replaced by a characteristic linear dimension for the shape under consideration. A general criterion for the domain where the inverse-square law is valid for a piston is given by:\n\npottd - A\n\n5.4.5 Proximity Effect for Pistons:\n\nDirectivity\nThe effect of proximity on the directivity pattern of a transducer is not as amenable to calculation as the effect on the axial response. To avoid appreciable effect due to proximity in directivity measurements, the following criteria should essentially be met:\n\nr > 0.1D\nand\nd > 3D\n\nQualitatively, the effects on directivity patterns of measuring at a closer distance than prescribed by these criteria are significant.\nThe measured beam width is broader than the one found at distances in the inverse-square law region. The side lobes of the pattern appear higher, and the minima separating the various lobes begin to fill in. These effects are shown in Figure 16 for an extreme case, where testing distances of 1.5 feet and 9 feet are compared. The critical distance for the projector tested in this example is about 5 feet.\n\nWhen measuring axial response, the first criterion, d > L/\u03bb, is the more important practical one. However, for directivity patterns, the second criterion, d > \u03bbD, is nearly equally important. This is due to the fact that the directivity pattern of a device is determined by its physical dimensions, D, as well as the wavelength, \u03bb.\nThe largely cancellation at certain angles of in-phase and out-of-phase pressures on the active surface is due to the inverse-square-law effect making the amplitude smaller on more distant parts of the transducer. This effect is particularly troublesome for a long-line hydrophone, as the testing distance must be very great to keep the amplitude approximately equal at both ends of the line when it has a radial orientation with respect to the source or receiver.\n\nOther Proximity Effects\nAnother proximity effect which occurs with directional transducers is connected with their beam patterns. If the beam pattern of one is quite sharp, it may allow an appreciable variation of amplitude over the face of the other, independent of the inverse-square-law effect. When a directional source is used,\nThe variation in pressure over the area of the opposing transducers should be less than 1 dB for the proper response. When two transducers face each other during a test, the sound field at the receiver includes the doubly diffracted (or reflected) field produced by the original wave from the source being diffracted by the receiver and then rediffracted by the source back to the receiver. This effect is usually negligible, except when two transducers of large area oppose each other at a short distance, in which case a severe standing wave pattern may be set up between them. The standing waves may even be of sufficient magnitude to change the apparent acoustic impedance of the medium as viewed by the source. While this factor is rarely a cause of trouble, it should be kept in mind when working with transducers of large area.\nFor a test, proximity effects for both instruments should be considered, and allowance made for the nature of each in selecting the testing distance.\n\nCorrection for Proximity Effects: The error due to a spherical wave front can be calculated for many commonly occurring cases, such as the pressure-gradient transducer, the circular piston, and the line. Such corrections can be made for this effect.\n\nFigure 16. Effect of testing distance on directivity pattern. (A) testing distance = 9 ft, (B) testing distance = 1.5 ft.\n\nFor this transducer, L = 5 ft.\n\nHowever, while corrections can be made in such cases, caution is necessary. The calculations are carried out on the basis of the transducer's behaving in a certain well-defined manner. For example, it is assumed that the transducer behaves as a pressure-gradient transducer, a circular piston, or a line source.\nAssumed that all parts of a piston move with the same velocity and in the same phase. Actual instruments only approximate this behavior and in many cases depart significantly. The piston's amplitude is often smaller at the edge than at the center, or the piston may actually break up into areas which oscillate out of phase. Instead of having uniform sensitivity, lines are often made up of an array of discrete elements and are often shaded or tapered, that is, have intentionally reduced sensitivity at the ends to suppress side lobes. The validity of the theoretical formulas is then questionable. One must conclude, as a general rule, that a theoretical correction of more than 5 db is open to considerable question, even if all other criteria as to applicability of the theoretical correction are favorable.\nImportant factors determining the testing geometry for calibration measurements have been discussed. It remains to summarize a procedure for selecting the optimum testing distance and depth. Here's an outline:\n\n1. Select the testing depth:\n   - If the reflection coefficient of the bottom is known, use Figure 12.\n   - If the coefficient is not known, a testing depth of 1/2 to 2/3 the water depth is usually satisfactory.\n   - For very deep water, the greatest depth consistent with safety should be used.\nThe satisfactory rigging of the instruments is desirable. If both instruments are nondirectional, a small testing distance is desirable, not smaller than several times the largest dimension of either instrument. Surface screens and bottom screens may help in reducing reflections. If the instruments have a relatively flat response, that is, low Q or time constant, pulses may be used to advantage with a possible increase in testing distance.\n\nIf one of the instruments is a pressure-gradient device and the other nondirectional, and no spherical wave correction is to be applied to the results, the testing distance should be greater than half a wavelength. If a spherical wave correction is to be applied to the results, it should not be greater than 5 db.\nTesting distance should exceed 0.5 times the wave length. Reflections are not severe until testing distance is greater than depth, and surface screens may increase this distance. Reasonably good calibrations can be obtained down to frequencies where the wave length is about ten times the depth.\n\nIf two pressure-gradient instruments are used, the testing distance should not be less than a wave length, as the pressure gradient is no longer radial closer to a transmitter of this type. If it is necessary to work closer, a correction can be computed and applied to the results.\n\nWhen a directional transducer of the piston type and a nondirectional instrument are used, the testing distance selected should be such that errors due to proximity effects are about equal to errors due to misalignment.\nTo reflective interference. The possible variations in this case are many and depend on the transducer size and frequency. By examining Figures 4 and 14, one can usually reach a reasonable compromise. If possible, the reflected intensity given in Figure 4 should be 10 db or more down. To avoid spherical wave corrections, the testing distance should be larger than D-jX. If it is necessary to use shorter distances, a spherical wave correction from Figure 14 may be applied, but any correction greater than 5 db must be considered unreliable. The pulse technique may be of value in such tests.\n\nThe same considerations given in the preceding paragraph apply to a pressure-gradient instrument facing a directional transducer of the piston type, except that a different spherical wave correction must be used.\nThe pressure-gradient instrument's directionality reduces reflection interference difficulties. The reflected intensity is below the direct intensity in decibels by the sum of values obtained for each instrument from Figure 4. When two piston-type transducers face each other, reflection interference is not usually a source of trouble due to the directivity of the transducers, except at very great separations. On the other hand, proximity effects become more significant, and the separation should be great enough so that:\n\na. Spherical wave effects are small. This requires any testing distance d to satisfy the conditions:\n\nd > (Di + D2) / 2\n\nwhere Di and D2 are the diameters of the two pistons. This also keeps the pressure due to one transducer uniform over the face of the other in spite of the directivity of the instruments.\nNo standing wave pattern is formed between the faces of the two instruments. This is generally taken care of if the criteria in the preceding paragraph are met.\n\nWhen measuring directivity patterns, the last two conditions of equation (50) should be changed to d > lODi and d > IOD2 to avoid the effect of varying pressure due to the inverse-square law.\n\nEssentially the same considerations apply to line instruments as to piston-type transducers, provided one substitutes the length of the line for the diameter of the piston. If the line is suspended vertically, there are ordinarily no great difficulties in obtaining a calibration, except possibly at low frequencies. Spherical wave corrections are useful when a testing distance sufficiently great to eliminate proximity effects cannot be used. If a line is suspended vertically, there are no significant difficulties in obtaining a calibration, except possibly at low frequencies. Spherical wave corrections are necessary when a testing distance large enough to eliminate proximity effects cannot be used.\nThe horizontal surface reflection causes great difficulty and makes it almost impossible to obtain good directivity patterns, except with extensive testing depths. The inverse-square-law effect also makes it difficult to obtain good directivity patterns, except at great distances, which are a result of great depth. The pulsing technique may be helpful, but it should be noted that with the line mounted end-on with respect to the source or receiver, the acoustic constant is at least the length of the line divided by the velocity of sound. Unless deep water is available, this time may be greater than the time required for an interfering reflected pulse to appear. While the outline given above should be useful in fixing the geometry for a test, it must be remembered that each test has its own particular factors involved.\nAnd thus, no general rule can be made. Experience and judgment are of primary value in making a proper choice. It is nearly always helpful to repeat tests with a changed geometry, particularly when it is suspected that reflections or proximity effects are causing trouble. One then has an internal check on the validity of the corrections that may have been applied, as well as a means of recognizing the presence of interfering reflections or other extraneous effects.\n\nFive techniques for establishing sound fields:\n\n1. Absolute and Relative Calibrations\n\nThe calibration of underwater sound devices requires reliable knowledge of the magnitude of sound fields in water. Two techniques for establishing these magnitudes may be distinguished. One involves a direct absolute measurement of the field intensity; the other uses previously calibrated instruments.\nTo establish a known sound field or measure one that exists, several methods are available. These include the Rayleigh disk method, radiation pressure method, reciprocity method, and various motional impedance methods for the first type. The second technique requires calibrated instruments, whose calibrations have been obtained through absolute methods mentioned above or by computation from their design or calibration in air. In the routine calibration and testing of underwater sound devices, relative calibration with a known standard is more convenient than direct absolute calibration, which requires considerable care and is more time-consuming. It has the disadvantage of being based on the stability of the reference standard, but numerous such standards have been constructed whose calibration is well-established.\nThe most satisfactory absolute method in water is the reciprocity method, which is exclusively used by USRL for absolute calibration of standards. In the following sections, various methods of obtaining absolute calibrations are discussed.\n\nAbsolute Calibration from Design of Standard:\n\nIn principle, if the design of a transducer is completely specified, one can theoretically calibrate the device over its entire frequency range by solving the equations of acoustics, mechanics, and electromagnetism involved in its operation. However, the equations are too complicated to allow a practical solution unless some assumptions are made. Despite these approximations, it may often be possible to obtain a reasonably valid theoretical response characteristic.\nThe method is effective for the device over a considerable range of frequencies. This method has been successfully applied to certain standards in use at USRL, particularly to the 3A Rochelle salt crystal hydrophone and the lA pressure-gradient type hydrophone designed by Bell Telephone Laboratories. The principal difficulties in the method are:\n\n1. It is not feasible to take into account all possible modes of vibration of the device and its housing, but only the desired mode and perhaps a few closely-coupled ones. However, some neglected modes are excited in operation, particularly near their resonant frequencies, and may introduce \"break-ups\" in the response which will not be included in the computed calibration.\n2. At all frequencies, but particularly at those having wavelengths of the order of magnitude of the device dimensions, the assumption of a uniform pressure distribution over the diaphragm may not be valid. This can lead to errors in the computed sensitivity.\nThe difficulties in calculating dimensions and higher, diffraction around an instrument are significant. Diffraction's impact is hard to compute, with computations only carried out in idealized cases. Consequently, it's challenging to precisely incorporate diffraction's effect into theoretical calibration.\n\nThree challenges exist:\n1. Mechanical elements' constants in instrument construction are not easily measurable. Mechanical resistance as a function of frequency, as well as effective mass and stiffness of various elements, may be difficult to obtain within the desired frequency range.\n2. This method can only be applied to the few instruments designed with this calibration method in mind, and then only by skilled personnel intimately familiar with every phase of the design.\n\nEstablishment of Sound Fields\nThe reliability of calibration obtained in this way is always questionable, unless a check can be obtained by other methods. The frequency range which can be covered is limited. Consequently, this is not a very satisfactory method of absolute calibration, although its principles are essential to the design of satisfactory reference standards.\n\n5.5.3 Absolute Calibration from Calibration in Air\n\nInitially, the technique of calibration of acoustic devices in air was developed considerably beyond that in water. If one could obtain the calibration of a device in water from its calibration in air, one would have a useful method of calibration for underwater sound devices. The mechanical and electrical elements of a transducer are not functions of the medium in which it is immersed. Therefore, it is possible to calibrate a transducer in air and then use that calibration to determine its performance in water. This method, known as transfer function calibration, is widely used in underwater acoustics. The process involves measuring the response of the transducer in air and then applying the known effects of water on the response to obtain the calibration in water. This method is more practical than calibrating the transducer in water directly, as it eliminates the need for large water tanks and complex underwater measurement systems. However, it requires accurate knowledge of the transfer function of the transducer between air and water, which can be a complex and time-consuming process.\nNecessary to consider only the effect of a change in medium on acoustic elements. The important parameters are the density and sound velocity. If a device is essentially pressure-actuated, the voltage it develops in a sound field is proportional to the pressure properly integrated over its surface, including the pressure due to diffraction. At wave lengths where diffraction is negligible for a stiff device, the pressure acting is simply the pressure in the field, so that the acoustic pressure is the same regardless of the medium. Thus, at low frequencies, a stiff pressure-actuated transducer has the same receiving response in air and in water. The upper frequency limit for this equality is determined by the frequency at which diffraction becomes important. This frequency is 1/4 to 1/2 as high in air as in water.\nFor a device of the order of 1 inch in size, the frequency at which diffraction becomes important is about 12 kc in air and about 60 kc in water. Thus, for a pressure-operated device of this type, such as the 3A hydrophone, a water calibration up to about 10 kc can be obtained from an air calibration. By a judicious frequency translation of diffraction effects, the calibration may often be extended higher. For a pressure-gradient operated instrument, the response is essentially proportional to the pressure gradient in the sound field. For the same frequency and pressure in a plane wave in air and water:\nThe ratio of the pressure gradient in air to that in water is equal to the ratio of the sound velocity in water to that in air. If this were the only effect, a pressure-gradient transducer would be 12.7 dB more sensitive in air than in water at the same frequency. However, in such devices, the change in radiation impedance with medium change is often not negligible. The radiation reactance of the transducer is a function of the medium density, and the functional dependence is different for different instruments. This effect must also be taken into account. For the 1 A hydrophone, the additional correction amounts to 3.3 dB, making the hydrophone 16 dB less sensitive in water than in air at the same frequency. Additionally, diffraction effects become a factor in the response at different frequencies.\nA calibration in air can be used to provide a calibration in water only over a limited frequency range for pressure-type instruments, as noted above. The original calibrations of USRL standards before the reciprocity method was adopted were obtained in this manner. While these methods can provide reasonably good calibrations over the most important part of the frequency spectrum for underwater sound work, they have distinct disadvantages: 1. They are relatively laborious and require intimate knowledge of the instrument, as well as personnel highly skilled in the technique of air calibration and in the principles of acoustic design. 2. They can be applied only to relatively few instruments that are designed with this method of calibration in view.\nThere is no check on their reliability, and no positive assurance that the various modes of vibration of the device may not be excited to different degrees in air and in water. Theoretical corrections, whose validity may be questionable, must be applied to the results. The frequency range which can be covered is limited.\n\nTesting Technique\n5.5.4 Quasi-Static Calibration\nFor an acoustically stiff pressure-operated instrument at frequencies low enough so that the wavelength is long compared to the dimensions of the instrument, the response depends only on the pressure in the neighborhood of the instrument. It is independent of the type of wave giving rise to the pressure, its direction of propagation, and even of whether there is a wave present at all, so long as a hydrostatic pressure variation of corresponding amplitude is applied.\nTo calibrate an instrument for measuring amplitude and frequency in the low-frequency register, it is necessary to introduce a known pressure variation in the medium adjacent to the instrument. Several calibration methods are based on this principle. For frequencies below a few cycles per second, one can create this pressure variation in water simply by raising and lowering the device sinusoidally through a known distance at the desired frequency. If the depth is h, then the rms pressure in dynes per sq cm acting on the transducer is:\n\nP = pgh\n\nWhere p is the density of water (1 gram per cu cm) and g is the acceleration of gravity (980 cm per sec per sec). With careful testing, accurate calibrations in this low-frequency range can be achieved.\n\nAt higher frequencies, it is possible to use a tank filled with the medium to be measured and excite it with a known pressure variation.\nThe pressure is varied sinusoidally in a closed, stiff tank using a low-frequency transmitter built into its wall. If the transmitter is an electromagnetic type with low stiffness compared to the tank in the frequency range of interest, the force exerted by the piston can be calculated from the current into the projector, either by measuring or calculating the force per unit current developed by the piston when it is blocked. Once the force is known, the pressure it produces in an acoustically stiff chamber can be calculated. This method is applicable only for frequencies far below those for the first chamber resonance of the tank, as the tank's stiffness drops significantly as it approaches its lowest resonance.\nAt the first resonance, pressure can no longer be considered uniform throughout the tank, making it impossible to calculate pressure at any point using simple methods from the force exerted by the piston. If the chamber walls have resonances below the cavity resonance of the chamber, these frequencies further reduce the upper limit of the useful frequency range. This method has been used successfully by USRL with a tank of the described type, built by Bell Telephone Laboratories. The lowest resonance frequency for this system is approximately 300 Hz, making it useful up to about 100 Hz. When using such a system, it's essential to avoid any condition that lowers the chamber's stiffness, such as the presence of air bubbles or an insufficiently tight seal.\nacoustically \"soft\" transducer. Over a limited range, corrections may be made for decreased stiffness due to any effect, provided this stiffness can be measured. Other quasi-static absolute calibration methods have been employed. One uses a condenser-type hydrophone\u00ae in which the condenser's capacitance is in one arm of an impedance bridge employing a carrier frequency of 5 kc. Pressure changes on the diaphragm cause a variation in capacitance which unbalances the bridge. The amount of unbalance becomes a measure of the pressure. This particular system is flat from 0 to 75 c, above which the effect of the first resonance of the hydrophone becomes prominent. Hydrostatic pressure equalization is provided to eliminate the variation of calibration with hydrostatic pressure. If, however, equalization cannot be carried out, then, by lowering the pressure on the reference arm of the bridge, the unbalance can be compensated.\nThe hydrophone's absolute calibration can be obtained by determining the unbalance produced when its known distance in water is constant. Since the hydrophone is known to have a flat response up to 75 c, this direct hydrostatic pressure calibration is applicable within this range.\n\nAbsolute methods not involving transducers:\nThere are several ways to establish absolutely the magnitude of a sound field without using an electroacoustic transducer. Among these are the Rayleigh disk method, radiation pressure method, and optical methods. These all require relatively delicate measurements, which, while difficult to perform in air, are even more difficult in water. They are, therefore, of negligible practical significance in underwater sound calibrations.\n\nAs evidence of this, consider the use of a Rayleigh disk method.\nThis is a thin circular disk suspended from a fine torsion filament, making a definite angle of 6 with the direction of propagation of the sound wave. If the wavelength is much greater than the diameter of the disk, there is a torque exerted on the disk of magnitude:\n\np * (v^2 / c) * (a^2)\n\nwhere p is the density of the medium, a the radius of the disk, and v the rms particle velocity. Expressed in terms of pressure, this becomes:\n\n(p * (v^2 / c^2)) * (a^2)\n\nThus, for the same pressure in air and water, the ratio of the torque in water to that in air will be:\n\n(\u03c1w / \u03c1a) * (cw / ca)^2\n\nSince torques obtained with the Rayleigh disk are very difficult to measure in air for any reasonable sound pressures, one sees that it would be almost impossible to measure them in water, even if the experimental difficulties in setting up the apparatus could be overcome.\nThe Rayleigh disk and similar methods must be discarded as impractical for absolute calibration in water. Radiation pressure is the steady pressure exerted on a surface when sound is reflected from it, and, like the torque in the Rayleigh disk, is a second-order effect. If a plane sound wave strikes normally a completely reflecting surface, whose area is numerically much greater than the wavelength, the radiation pressure on the surface is given by:\n\nwhere k is the ratio of specific heats for the medium (practically unity for liquids), p is the rms sound pressure, p the density of the medium, and c the velocity of sound. For a sound pressure of 1 dyne per sq cm in water, the radiation pressure would be about 10 dyne per sq cm. For such low-pressure measurements, very delicate apparatus is required.\nThe method is of little practical value, though it can be used in laboratories with high sound pressures produced by quartz crystals at high frequencies. Various other calibration methods exist that do not utilize an electroacoustic transducer, but they are all subject to the objection that the measurements are extremely delicate. Some are based on the variation of a fluid's index of refraction with pressure or similar effects, and they typically have a limited frequency range. Compared to the easier calibration methods, none of them holds much practical importance at present. For further information, consult references on acoustics.\nThe most accurate, simple, and generally useful method of absolute calibration in general acoustical literature is the reciprocity method. This method, based on the reciprocity principle as applied to electroacoustic transducers, offers several advantages:\n\n1. Applicable over the entire practical range of frequencies.\n2. Easily made measurements, similar to those employed in relative calibrations (comparison method).\n3. Usable by relatively unskilled personnel.\n4. Measurements can be carried out in the field rapidly and easily.\n5. Though the accuracy of the method is currently high.\nThe limitations of comparison methods are imposed by reflection-interference difficulties, thereby limiting their accuracy. If certain easily attainable conditions are maintained, there are no theoretical corrections required for the results. Several independent calibrations can be conducted simultaneously, providing an immediate check on the accuracy of the results.\n\nThe reciprocity method is based on the fact that for a passive linear electroacoustic transducer that obeys the reciprocity principle (which encompasses most transducers currently in use), a definite and simple relationship exists between its response as a transmitter and as a receiver. Consider an electroacoustic transducer with its acoustic center (which may be arbitrarily selected) located at point Fo. The transducer is being operated as a transmitter with a current flowing.\nLet the transmitter produce a pressure p at an arbitrary point P. Let S be the transmitting sensitivity, expressed as the ratio of the pressure at P to the current (S = p/jc). If a source of spherical waves is placed at the center of P, and pc is the pressure produced at Pq when the transducer is not present, the open-circuit voltage E across the transducer's terminals, in the presence of the sound field, is given by the receiving sensitivity M (M = E/pc). According to the reciprocity principle, if d is the distance from P to P', X is the wavelength, and p and c are the density and sound velocity of the medium, respectively:\n\nM = S / (d * X / c)\n\nTo apply the reciprocity principle for the absolute calibration of a transducer, three transducers are required.\nOne is used only as a transmitter or projector, a second only as a receiver, while the third must be a reversible transducer obeying the reciprocity principle. The projector is placed at a point P with a definite orientation. The receiver is placed at a point P' sufficiently distant from P so that the waves reaching it from the projector are essentially plane. For a given current Ip in the projector, the voltage developed by the receiver is measured, either on open-circuit or across an impedance kept constant during the measurements. This voltage is denoted by Epp. The receiver is then replaced by the transducer, and the open-circuit voltage developed by it, Ep, is measured for the same current Ip in the projector. Next, the projector is replaced by the receiver, whose orientation with respect to the transducer must be reversed.\nThe transducer is operated as a transmitter with a current Ip, and the voltage developed by the receiver E.pp is obtained. If Mp denotes the sensitivity of the receiver and Mt the open-circuit receiving sensitivity of the transducer, then, since the pressure developed by the projector is the same in the first two trials, we have:\n\nE.pp = MpMtIp (1)\n\nwhere Sp denotes the transmitting sensitivity of the transducer, that is, the ratio of the pressure produced at the receiver to the current Ip in the transducer. From the reciprocity principle, Sp = Pc/d, where d is the distance from P to P'. Substituting the value of Sp from equation (59) in (58), we eliminate Mp between equations (60) and (57):\n\nr,pT = IpC - Ip - 2dX\n\\_E.ppIpC J\n\nTherefore, we have:\n\nE.pp = (C/d)Ip (2)\n\nBy equating (1) and (2), we get:\n\nMpMt = C/d\n\nThis is the required relationship between the sensitivities and the distance.\nIn this way, the calibration of hydrophone H is expressed in terms of measured quantities. The preceding discussion assumes cgs units for all quantities, including absolute electrical units. If volts and amperes are used in equation (62), Epp must be multiplied by 10**. The absolute calibration may be obtained by a process involving only electrical measurements on the transducers.\n\n5.5.7 Notes on the Reciprocity Method\nTo obviate any misunderstanding concerning the use of the reciprocity method of calibration, the following notes are added:\n\n1. The open-circuit voltage developed by the transducer T operating as a receiver should be measured at the same terminals at which the current into the transducer is measured when operating as a transmitter. The choice of terminals can be arbitrary.\nThe conditions for measuring current and open-circuit voltage of a transducer must be the same, regardless of whether the voltage is directly from the transducer element or through a cable. This can be achieved by connecting two terminals of a four-terminal passive electric network to the transducer, and using the remaining pair of terminals for measurement.\n\nThe distance d between the projector P or transducer T (when transmitting) and the hydrophone H should be large enough for the waves to be effectively plane at this distance for plane wave calibration. However, the distance can be shortened if one desires.\nThe text wishes to obtain a calibration for H in terms of spherical waves of a given radius, or if a spherical wave correction can be applied to reduce a spherical wave calibration to a plane wave calibration. The latter procedure may be necessary if reflection interference is present to a degree which seriously interferes with the accuracy of the measurements. The presence of reflections introduces the same inaccuracies in a reciprocity calibration as in comparison tests, and the methods described in Section 5.3 for eliminating reflection interference may often be profitably applied in reciprocity calibration tests.\n\nWe have indicated that the choice of the acoustic center of the transducers was arbitrary in the preceding discussion, yet the distance d between centers enters explicitly into the formula for the calibration. This can be understood if one remembers that the acoustic centers of the transducers define the reference points for measuring the pressure or particle velocity at each point in the medium. The distance d affects the path length difference between the reference points, which in turn influences the calibration results. Therefore, it is essential to ensure accurate determination of the acoustic center positions and the distance between them for obtaining reliable calibration data.\nThe response reception depends on the choice of the acoustic center, and this dependence on d cancels the explicit dependence on d in the formula (Chapter 4, equation 10). Typically, the acoustic center is chosen close to the geometric center of the instrument, but it may be taken anywhere. If it is chosen far from the actual instrument, the center must be considered as part of the instrument, requiring that the wave be essentially plane. That is, the plane wave response with such a choice for the acoustic center can be obtained only if the wave from the transmitters is essentially plane, not only over the transducer but over the entire region between the center and the transducer. Therefore, there is an advantage, in terms of testing distance selection, in choosing the center within or in the instrument.\nThe reciprocity calculation for a transducer can be performed for any orientation of the involved transducers, but the same relative orientations must be maintained during the tests. The directivity pattern of a transducer obeying reciprocity is the same on transmitting and receiving at the same frequency. One should note that the responses given by the formula represent ratios of magnitudes of quantities without consideration of phase. To obtain the phase of the response, a phase factor must be included, which is not ordinarily known but can be determined in the reciprocity relation shown in equation (56) for the particular reversible transducer. The phase of the response is not usually of interest.\nIn making a reciprocity calibration, one must have a transducer obeying the reciprocity principle and therefore should have a means of establishing this property. Although it is known that it is possible to have a linear passive reversible transducer which does not obey reciprocity, almost all transducers of interest do have this property. No generally applicable conditions have been established to guarantee reciprocity in a transducer, but there are some general principles which serve as useful guides. Theory indicates that if the electromechanical coupling is of the electromagnetic or magnetostrictive type, or a combination of these, reciprocity is obeyed. Similarly, there are indications that electrostatic or piezoelectric coupling or a combination of these also ensures reciprocity. A parallel combination of one of the first types is also suggested.\nA grouping of transducers, consisting of one electromagnetic or magnetostrictive type and one of the second type, whether electrostatic or piezoelectric, results in a transducer that does not adhere to reciprocity. Due to the rarity of such combinations, most actual transducers will apparently obey reciprocity. The condition for reciprocity is met if the transducer's efficiency is 100 percent. Since no actual transducers achieve this efficiency, this criterion is of questionable value for practical applications. One must therefore rely on the criterion of internal consistency between the calibrations obtained with several reversible transducers as a means of verifying they adhere to the reciprocity principle. It is highly unlikely that, if these reversible transducers did not obey the reciprocity principle, one would obtain the same calibration using each.\nIf a calibrated resistor is available so that current can be measured by measuring the voltage drop across the resistor in series with the transducer, one doesn't need an absolutely calibrated voltmeter to perform a reciprocity calibration. For, if one substitutes EjjR for It in equation (62), it can be seen that only the ratio of voltages, and not their absolute magnitudes, enters into the formula.\n\n5.5.8 Motional Impedance Methods\n\nThere have been proposed and applied several methods of absolute calibration, based on the measurement of the impedance of the transducer, which can be applied to transducers obeying the reciprocity principle. It is sufficient here to indicate how one of these methods leads to an absolute calibration. If one considers a transducer which has a sharp mechanical resonance at some frequency, the impedance at this resonant frequency is given by the product of the mechanical compliance and the mass-spring constant of the transducer. By measuring the impedance at this resonant frequency and comparing it to the impedance of a standard reference impedance, the transducer's calibration can be determined.\nThe resistance and reactance show a rapid variation with frequency in the neighborhood of the resonant value. If one plots resistance and reactance as a function of frequency, smooth curves can be drawn connecting the portions of the resistance curve and the reactance curve far above and far below resonance. These curves are referred to as the blocked resistance and reactance, since they correspond to the impedance that would be measured if the diaphragm of the transducer were prevented from moving. The difference between the actual impedance and the blocked impedance is referred to as the motional impedance. If the motional resistance is plotted against the motional reactance in rectangular coordinates, with frequency as the parameter, a figure is obtained known as the motional impedance circle. The diameter of the motional impedance circle is measured in ohms for the instrument immersed.\nThe efficiency E of a transducer in water, which is the ratio of acoustic power output to electric power input, at resonance, is given by:\n\nE = 1 / [(1 + (\u03c9n\u00b2R/Xm)\u00b2) ^ 0.5]\n\nwhere R is the actual resistance of the device in water. The directivity pattern and directivity index can be measured with an uncalibrated transducer. From equation (8), Chapter 4, the efficiency and directivity index of a transducer can be used to determine its response. In this way, the device can be absolutely calibrated at its resonant frequency from the motional impedance circle (which gives the efficiency) and a directivity pattern (which gives the directivity index).\n\nSince this method provides an absolute calibration at only one frequency, it is not of great value as a calibration method.\nThe reciprocity method, while a general calibration method, is useful for obtaining a device's efficiency at resonance through purely electrical impedance methods. Other methods of motional impedance analysis are more refined and allow calibration over an extended frequency range, but they are not as convenient to use as the reciprocity method.\n\n5.5.9 Relative Calibration of Transducer\n\nEven the reciprocity method requires more effort than desired for the calibration of most devices. The comparison method, which involves calibrating one transducer against another that has already been calibrated, provides a practical means for the rapid calibration of most devices. In the comparison method, the sound field magnitude is first established using a previously calibrated standard. This is followed by the calibration of the device.\nIt is presumed that in a calibration, the reference standard is sufficiently stable in construction and operation, allowing its calibration to be retained between its own calibration and application in a relative calibration. Either a transmitter or a receiver can be used as a reference standard. The former can establish a known sound held, while the latter can measure the magnitude of the sound held produced by an uncalibrated transmitter. USRL has found that properly constructed receivers are more reliable than transmitters as reference standards, but the difference is not great. By using both a calibrated receiver and a calibrated transmitter in a comparison test, a cross-check on the stability of the standards may be obtained in conjunction with the test.\nThe procedure for calibrating a receiver involves placing a transmitter at one point in the water and establishing a constant voltage or current at some frequency. A standard receiver is then positioned in the sound field, and the magnitude of the sound field is obtained from its generated voltage. The reference standard is then replaced with the receiver under test, and its generated voltage is obtained, providing its response at that frequency. The frequency may be swept during each test, and by comparing measured voltages of the standard and transducer under test at equal frequencies, the frequency response characteristic of the transducer can be obtained.\n\nNote: If a plane wave calibration is used.\nIf the plane waves from the transmitter are desired at the receiver positions, then the waves must be essentially plane with respect to the instruments. This depends on the nature of the instruments themselves, particularly their size. If the waves are not essentially plane for one receiver but are for the other, it may be more convenient to test the two instruments at different distances from the source. This can be done as long as both distances lie in the inverse-square-law region for the source, requiring only an inverse-square-law correction. In some cases, it may be desirable or expedient, due to reflection interference, to operate the instruments at closer distances.\nIn calibrating a transmitter, use a calibrated receiver located in the inverse-square-law region of the field. Determine the pressure produced at this point from the voltage generated by the receiver. It may be desirable or expedient to locate the receiver closer to the transmitter and apply a spherical wave correction. Since a relative calibration is based on the stability of calibration of the standard, frequent checks on the calibration of the standards are necessary for any testing program extending over a long period. Conveniently make these checks at regular intervals using the reciprocity method. The reciprocity method is particularly valuable for calibration.\nThis purpose at a test station since the procedures used are the same as for relative calibrations. Thus, the equipment necessary for a reciprocity calibration is available at all times, and no extra equipment is necessary. A running check on all tests may be made by using several standards and checking the calibrations obtained against each other. A calibrated transmitter may serve as one of the standards.\n\n5.5.10 Choice of Standards\n\nFor maximum accuracy, reliability, and general versatility, a standard should possess certain characteristics which are outlined below.\n\nStability with Time\nStability is essential, since the accuracy of a relative calibration is limited by any change in the response of the standard from the time that it was calibrated to the time of its use. For this reason, it should be sufficiently rugged so that slight jars do not change its response.\nThe calibration should be constructed of materials whose properties do not change with time. Permanent magnets, if used, should have a permanent flux density. The stiffness of springs should not vary due to aging or cold working from extension and retraction. The instrument should be built so that dampness or moderate heat or cold do not affect its calibration, and all exposed parts should be resistant to corrosion.\n\nTemperature Independence\n\nIt is desirable that the response of a standard be independent of temperature over the useful frequency range of the instrument, as temperature control is rarely achievable in calibration tests. Otherwise, it is necessary to know how the calibration varies with temperature, which would require considerable additional labor. Temperature dependence.\nThe response of Rochelle salt crystal devices is an important factor due to the rapid variation of the dielectric constant of x-cut crystals and consequent change of impedance in the neighborhood of the upper Curie point (24 C or 75 F). This temperature variation does not have a serious effect on the response of a Rochelle salt crystal receiver if the impedance into which the crystal operates is high compared to its own impedance. For a Rochelle salt crystal transmitter, the response, expressed in terms of pressure per unit current input, does not vary appreciably with temperature. However, the response expressed on a per volt or per available watt basis may vary greatly. It is therefore desirable to operate Rochelle salt crystal projectors on a constant current basis, which may be accomplished by making the current input constant.\nSource of electrical power have a high output impedance compared to the impedance of the crystal. Wide-Band Uniform Response It is desirable that a standard have a smooth frequency response over a wide frequency band. Rapid variations in response with frequency make it difficult to compare the responses of two instruments in such a range due to the difficulty of reading accurately a steep curve on a recorder chart. A wide frequency band is desirable so that the number of standards required to cover the entire frequency range of interest be as small as possible to reduce rigging time. For high-frequency transmitters, it is difficult to obtain a flat frequency response. However, a smoothly varying response is in general satisfactory and can be obtained readily with crystal projectors. Linearity, Large Dynamic Range Over the range of pressures which a standard is subjected, it is essential that it shall remain linear and have a large dynamic range.\nThe device should be linear for measuring or producing sound, with voltage proportional to pressure in the sound field and pressure proportional to input current or voltage. Nonlinearity occurs when a sinusoidal input signal no longer produces a sinusoidal output of the same frequency in general. Most instruments are linear over a limited range of input signal amplitudes. For maximum usefulness of a standard, the dynamic range should be as great as possible, allowing a large range of sound field pressures to be produced or measured by a single instrument. A transmitter may have variations.\nIn order to make a comparison calibration with a single standard receiver, the standard must have a corresponding dynamic range, limited by nonlinearity on the high end and inherent noise on the low end. The lowest pressure that can be measured by a receiver is determined by its inherent noise voltage. This may be due to thermal noise, vacuum-tube noise (of an associated preamplifier), contact noise, or other similar factors. At each frequency, the pressure at which the signal voltage of the instrument is equal to the noise voltage, in a 1-Hz band centered at the frequency, is known as the threshold of the transducer. It is desirable to have the threshold of a standard as low as possible in order to extend the dynamic range as far as possible in the direction of low pressure.\nThe response magnitude of a standard is important, regardless of its noise characteristic. For instance, a low response may result in electric crosstalk between a receiver and a transmitter exceeding the electrical signal level. A similar issue arises when using a transmitter as a sound source due to ambient noise in the water. To ensure the response of a transmitter standard exceeds the ambient noise sound field, various standard transducers have been developed. Their characteristics are detailed in another part of this volume.\n\nCalibration of Devices Covering Wide Frequency Ranges\n\nWhen a transducer is used for wide-band applications, calibration is essential to maintain accuracy and reliability. Proper calibration involves comparing the transducer's output to a known reference standard under controlled conditions. This process ensures that the transducer's response remains consistent and accurate over the entire frequency range.\n\nTo calibrate a transducer, follow these steps:\n\n1. Prepare the test setup: Set up the test environment, ensuring it is free from external noise and vibrations. Connect the transducer to the measurement system and the reference standard.\n\n2. Verify the reference standard: Before calibrating the transducer, ensure the reference standard is accurate and reliable. Compare its output to a known calibration standard or trace it back to a national standard.\n\n3. Apply the input signal: Generate a known input signal, such as a sine wave, and apply it to the transducer under test.\n\n4. Measure the output signal: Record the transducer's output signal using the measurement system.\n\n5. Analyze the data: Compare the transducer's output signal to the known input signal. Calculate the transducer's response, sensitivity, and any other relevant parameters.\n\n6. Document the results: Record the calibration results, including the transducer's response, sensitivity, and any other relevant data.\n\n7. Verify the calibration: Repeat the calibration process multiple times to ensure consistency and accuracy.\n\n8. Store the calibration data: Keep the calibration data in a secure location, such as a calibration log or database, for future reference.\n\n9. Regularly re-calibrate: Periodically re-calibrate the transducer to account for any changes in its performance due to aging, environmental conditions, or other factors.\n\nBy following these steps, you can ensure that your transducer remains accurate and reliable, providing consistent and reliable measurements over its entire frequency range.\nReception: A single frequency calibration is still significant because, if the hydrophone is linear, its wide-band response can be determined from the single frequency response using superposition, according to Fourier's theory. The calibration then consists of determining over what range the hydrophone is linear and taking a single frequency characteristic within that range. The procedure for taking a single frequency characteristic has been described. The linearity at any given frequency is best observed by varying the input level at that frequency and seeing if the output level follows proportionately. Instead of taking a single frequency characteristic, it is also possible to measure the response for a signal with any type of frequency spectrum. In particular, the response may be measured for a signal with a specific frequency spectrum.\nSignals consisting of very complex aperiodic wave forms are referred to as noises. Thermal agitation, or thermal noise, is an illustrative example. Measuring such signals imposes severe requirements on the measuring system. Calibration for wide frequency ranges is usual. The overall signal level and frequency analysis of the noise are obtained. Often, the time variation of the noise is of interest, which can be obtained in the form of a time-level distribution or as the crest factor of the noise. The crest factor is defined as the ratio of the crest value to the effective value of the quantity. The overall signal level is determined with a wide-band measuring circuit. This circuit must carry the highest noise peak without overloading and include appropriate filtering.\nA square-law measuring device is the only type that adds up the contributions of various frequencies in a signal to give the root mean square (rms) signal level. For frequency analysis, sweep over the noise frequency range with a narrow heterodyne band-pass filter. Carefully consider the design of this filter from the transient response standpoint. The requirements for the rest of the system are the same as those discussed above for measuring overall signal levels.\n\nThe crest factor can be measured by obtaining a wide-band response with a square-law rectifier (thermocouple) and the peak response on an oscilloscope.\n\nOne challenge in all these measurements is the requirement of using a square-law measuring device. The only true square-law device is the thermocouple.\nA couple of methods exist for measuring noise in oscilloscopes. However, the mocouple method is slow-acting and can only provide a long-term average with a limited dynamic range. Consequently, vacuum tube detectors are typically used instead due to their speed. Vacuum tube detectors follow the square law over a limited range of input levels, leading to the question of whether the noise can be accurately measured with the available rectifier. One approach to answering this question involves measuring the crest factor and determining if the rectifier remains square law for the highest peaks in the noise. While this method is helpful, there are theoretical concerns about its sufficiency. Therefore, it's desirable to explore other perspectives on the problem as well. Previous measurements on similar noises that have been satisfactory are sometimes used as a reference.\nThe requirements for the measuring system include: (1) not overloading on highest noise peaks, (2) adequate coverage of noise frequency range, and (3) a square-law rectifier, to ensure level measurement and frequency analysis of the noise. In some cases, a graph of the noise or oscilloscope view is desired, adding the requirement of a system with linear phase shift with frequency to maintain phase relations between different frequencies. The pick-up device used in tests has similar requirements. If the hydrophone has a uniform response.\nThe mountain lakes test station, located on Crystal Lake in Mountain Lakes, New Jersey, is satisfactory for use in tests over the frequency range of interest, which implies a phase shift linear with frequency for obtaining level measurements and maintaining phase relations.\n\nChapter 6\nDESCRIPTION AND OPERATIONAL PROCEDURES OF THE USRL TEST STATIONS\n\nBy Erhard Hartmann and Earle C. Gregg, Jr.\n\n6.1 DESCRIPTION OF MOUNTAIN LAKES TEST STATION\n\nThe mountain lakes test station is situated on Crystal Lake, in the township of Mountain Lakes, New Jersey. The lake is approximately 650 yards long and 230 yards wide, with a small island near the center. The depth of the lake averages about 15 feet, and its bottom is a thick stratum of mud with good sound-absorbing properties, especially at supersonic frequencies.\nThe decomposing organic material in the mud, which produces gas bubbles and reflects sound, has been removed from the test areas by dredging. The water depth in these areas has been increased to approximately 18 feet. The lake has been treated frequently with copper sulfate to inhibit decomposition and algae growth.\n\nTest Area\nTerm Boxes\nREC BOOTH\n4, F SYSTEM\nj istorageI\nit rf'\n-POWER ROOM\n-PAINT STORAGE\n\nFigure 1. Plan view of Mountain Lakes laboratories and surroundings.\n\nDescription of Mountain Lakes Test Station\n\nFigure 2. New of Mountain Lakes laboratory from Pier 2.\n\nThe Mountain Lakes test station offers facilities for calibrating underwater acoustic devices from a frequency of 2 cycles per second to 3.5 megacycles.\nThe text covers a frequency range from 2 Hz to about 150 kHz using four testing systems. A low-frequency tank operates up to 2.2 MHz. The first system covers the frequency range from 15 Hz to 150 kHz and can test apparatus with power inputs up to 1,500 watts. Two intermediate-frequency units, systems 1 and 2, are used for free field calibration in the lake, operating from 15 Hz to 150 kHz and capable of testing apparatus with power inputs up to 1,500 watts. The apparatus is arranged in bays to provide maximum separation between high- and low-level signal paths to minimize cross talk, a practice maintained throughout both systems, including the transmission.\nLines and transducer coupling booths on the piers. A high-frequency unit, which includes an elliptically shaped tank, covers the range from 100 kc to 2.2 me. This unit may also be used in conjunction with one of the piers. Other acoustic testing facilities include an open tank with sound-absorbing walls (a type used for production testing by the Western Electric Company) and a closed cylindrical tank about 15 feet long and 8 feet in diameter. The latter can be used at hydrostatic pressures up to 300 lb per sq in and at frequencies up to about 150 kc. Tests at high pressures are conducted at the Mountain Lakes station. The booths housing terminal equipment and the overhead monorail systems are visible in Figure 3.\n\nUSRL Test Stations\nFigure 4. General view of test area of Pier 1. Several suspension carriages and the rotator are visible.\nThe foreground is used for impedance measurements related to underwater sound gear on submarines. One of the two outdoor piers is equipped for handling devices up to 2,000 pounds using chain hoists traveling on an overhead rail between the loading platform and the pier's end. The second pier is for devices under 250 pounds. For testing distances beyond the piers' capabilities, a raft with a 3,000-pound working load is available. Signal transmission and power cables from the laboratory extend to a position 250 yards out in the lake, enabling equipment operation on this raft. The laboratory has its own machine shop, water supply, and heating system. Compressed air and electric power are available throughout the building.\nAuxiliary equipment includes meters for measuring current, voltage, or power; impedance bridges; vacuum-tube test sets; cathode-ray oscilloscopes for observing wave shapes; and filters for limiting frequency bands. The electric energy is supplied at 230 volts, 60 cycles, with the midpoint grounded. This voltage is used on the larger motors. The 115-volt supply is regulated to keep a uniform voltage on the signal generators, amplifiers, detectors, and recorders. All high-voltage requirements are supplied by regulated rectifiers associated with the various system components. Thus, drifts in the calibrating apparatus resulting from variation in the supply voltage are held at a minimum. A 24-volt DC supply for the operation of relays and indicator lamps is obtained from rectifiers energized by the 115-volt line. Most of the electrical equipment was designed and manufactured in-house.\nThe Bell Laboratories constructed this under contract with the National Defense Research Committee at Mountain Lakes (NDRC). USRL designed and built most of the mechanical equipment and developed the high-power equipment, pulsing system, polar recording system, and additional features for special testing.\n\nCalibration and Testing Equipment at Mountain Lakes\n\nThe calibration and testing systems of USRL are described based on their current status. However, it's important to note that advancements in sonar gear and testing techniques are making new demands, often exceeding the capabilities of existing equipment. Therefore, it must be constantly changed and improved to maintain the standards of a reference laboratory.\nFor example, system 1, installed in June 1942, incorporated a narrow band-pass filter which discriminated against noise and other interference. This was at the time a distinct improvement but after the development of the pulse method, which requires a wider transmission band, system 1 was inadequate. For this reason, and also because of the increasing importance of noise analysis, system 1 is now limited in its applications, and a continuously increasing proportion of the work is handled by system 2.\n\nElectrical Components of Systems\nThe essential parts of systems 1 and 2 are described in a sequence which traces a typical signal from the generator to the projector and from the hydrophone to the recorder.\n\nTest Signal Generators\nThe primary signal generators are beat-frequency oscillators covering the 15-1500 Hz range.\nResponse: A uniform response within 0.3 dB is achieved for the frequency setting. A visual indication of the frequency is provided by a calibrated scale on a 35-mm motion picture film, 30 feet long, coupled through a sprocket chain to the air condenser controlling the frequency. The length of this scale indicates the degree of frequency resolution. The shape of the condenser plates is such that the scale provides adequate frequency resolution throughout the entire range.\n\nA synchronous motor drive provides the lock between oscillator and recorder during frequency recording. Spouse traces are taken, although the dial may be operated manually.\n\nThe heterodyne oscillator assembly contains three separate circuits. Two of them operate as a beat frequency oscillator, one fixed at 650 kc and the other variable from 500 to 650 kc. The difference frequency is produced by these circuits.\nThe heterodyned outputs provide a signal range from 0 to 150 kc. This arrangement is identical in both systems, but the third circuit is fixed at 678 kc in system 1 and 747 kc in system 2 for use in tuning the detector circuit described later in this section.\n\nFrequency stability has been obtained by design features such as: 1) mounting the three oscillator circuits in the same chassis to have the same ambient temperature, 2) separating the component parts with networks and buffer amplifiers, and 3) using suitable shielding and filters. To correct for the slight drift in frequency that may still occur, means for adjusting the carrier frequencies are provided, and the frequency scale can be checked by aligning with the 60-c power supply and a 100-kc crystal shunted across the oscillator output. Since the adjustment is based on these measures.\nThe difference in frequency, no attempt is made to observe the actual frequencies of the carrier oscillators. The oscillator provides a maximum output level of 150 dB vs 10-16 watts, adjustable over a 40-db range. Harmonics in the output voltage are at least 40 dB below the fundamental, and a minimum signal-to-noise ratio of 50 dB is realized.\n\nIn system 2, a thermal noise signal may be generated by using the noise generator in conjunction with the heterodyne oscillator. The noise generator includes a voltage regulator tube functioning as a wide-band thermal noise source. Two band-pass filters limit the frequency spectrum to 650 \u00b1 0.15 kc or 650 \u00b1 3 kc, as desired. These signals are used to replace the fixed 650-kc signal in the heterodyne oscillator.\nThe output signal is a band of thermal noise, 300 degrees Celsius or 6,000 degrees Celsius wide, centered at the frequency given by the oscillator setting. The noise output should be at least 10 db below the single frequency output to prevent peak clipping in the modulator circuit. This adjustment is made by controlling the output of the noise generator circuit. The midpoint of the noise band in this generator is 650 kc for correct frequency alignment of the output band. The frequency range of the variable oscillator must be exactly 650 kc to 500 kc. To obtain this condition, adjustments are made on the generators as follows: The noise generator circuit, functioning only as an amplifier, is sharply tuned by a filter 20 c wide, centered at 650 kc. This is connected between the fixed-frequency oscillator and the following modulator. The fixed oscillator is then tuned for maximum output.\nWith the frequency of the fixed oscillator established at 650 kc, the frequency scale is aligned at 60 c and 100 kc through adjustments on the variable oscillator. Power amplifiers with a maximum gain of 40 db are associated with each system. The maximum undistorted power level of system 1 is 177 db and that of system 2 is 173 db. An auxiliary amplifier, described later, may be used with either system to reach an undistorted level of 192 db vs 10 watts, or about 1500 watts. System 1, covering the range from 1.5 c to 150 kc, requires two output transformers for its power amplifier. Automatic transfer between them is effected near 2 kc by a switching circuit operated by a cam on the oscillator frequency dial. System 2 employs two power amplifiers, covering ranges from 15 c to 30 kc and...\nFrom 300 c to 150 kc, the amplifiers of both systems have been designed to operate into a load impedance of 135 ohms. This impedance corresponds to that of the coaxial transmission lines to the piers. Adjustable 135-ohm attenuators, capable of carrying the full power to the amplifiers, are connected in the output circuits to supplement the amplifier gain controls, stabilize the output impedance, and improve the amplifier signal-to-noise ratios. The amplifier design and use of output attenuator pads permit a 55-decibel margin between signal and amplifier noise. A bridging network of 30-decibel loss at the amplifier output terminals allows a 30A transmission measuring set, described later in this section, to be used for monitoring purposes.\n\nTransmission Lines.\nThe 135-ohm insertion loss of the combined transmitting, receiving, and pier booth cross-connecting lines does not exceed 0.25 db at 150 kc, which is too small to require any correction for line attenuation. Balanced coaxial lines (Figure 11 A) are used for signals from power amplifiers to coupling booths on the piers, return signals from pier receiving booths, for linking transmitting and receiving booths, and for interconnecting various systems. The four-wire groups marked \u201cquads\u201d are used for controls such as relay operation, intercommunication, and indexing. The requirements to prevent cross talk are severe, as indicated by the difference in outgoing and incoming levels that may exist. For instance, the hydrophone level in the receiving line may be as low as 10-16 watts, while the power supplied to a projector is much higher.\nThe cross talk must be lower than the received level by at least 15 or 20 dB to avoid affecting measurements. This requires a margin of nearly 170 dB between transmitting and receiving apparatus. In addition to using coaxial cable, other precautions to minimize cross talk include a minimum 6-foot spacing between all transmitting and receiving lines and careful attention to the laboratory grounding system, as described later in this section.\n\nUSRL TEST STATIONS\n\nFor relatively short runs, equally good performance can be achieved using a twisted pair of flexible, single coaxial cables (Figures IIB and IIC). The rubber-covered cable is used for lines.\nThe projector coupling equipment is housed near the test area in the transmitting booth. Its primary function is to provide suitable impedances for matching various test projectors as they are connected to the 135-ohm transmitting line. Repeating coils provide various sending impedances. H-type resistance pads, designed to be used between each sending impedance and 135 ohms, permit the measurement of available power at any sending impedance. Two repeating coils are available for handling power outputs up to 100 watts. One of these has seven secondary windings terminating in a multi-contact receptacle. The sending impedance is varied by inserting in this receptacle one of seven plugs, with contacts strapped together in various patterns.\nThe second coil offers impedances of 135, 600, or 2400 ohms. A third coil manages power outputs up to 1000 watts at 50, 100, or 500 ohms, and resistance pads are available for measuring the available power at these high outputs. A watt-meter circuit for measuring actual power delivered to the projector is also available.\n\nHydrophone Coupling Equipment:\n\nThe hydrophone coupling apparatus is housed on the piers in the receiving booths. Its primary function is to provide suitable coupling between hydrophones and the 135-ohm receiving lines to the laboratory. A battery-operated preamplifier of novel design offers either balanced or unbalanced operation. In the former case, impedance may be represented by a shunt resistance of 100 megohms.\nThe shunt capacitance is approximately bfxixi, with a ground at the electric center. In the other position, the input impedance is set for unbalanced operation and can be represented as a shunt resistance of 50 megohms and a shunt capacitance of about 10/x/xf, with one terminal at ground. The amplifier output has been designed to feed into the 135-ohm receiving line. The Figure 8.15 c to 150 kc recording system. Bay on the left shows the receiving amplifier and detector. To the right, shown in order, are the signal and noise generators, recorder, and thyratron control panel, and power amplifiers.\n\nEquipment at Mountain Lakes\nFigure 9. The frequency characteristic is essentially flat through the range from 15 c to 150 kc, and the voltage gains for the unbalanced and balanced input conditions are approximately +0.5 db and \u20136.0 db, respectively.\nA battery supply and coupling circuit are provided for frequently used standard hydrophones such as the 3A, 5C, and 51 types. A metering panel permits monitoring of all A and B voltages and currents. Switches and jack-terminals provide for measurements of various quantities, such as response, coupling, and available power. To calibrate a hydrophone on open circuit, knowledge of the loss in the coupling circuit is required. The procedure for determining this is to place in series with the hydrophone a resistance that is very small in comparison to the resistance of the instrument. A low-voltage oscillator is applied to this resistor, and the signal is carried through to the recorder as if from the hydrophone itself. After the range of frequencies has been covered, the same voltage is connected directly to the hydrophone.\nThe difference between the records in decibels is due to the loss in the coupling circuit. Various types of supplementary apparatus are frequently required. One such device is a portable battery-operated preamplifier that may be placed at the edge of the testing area to reduce the length of the hydrophone cable. Another is an underwater preamplifier, operated from the battery for use with high-impedance instruments, such as tourmaline gauges (tourmaline crystal hydrophones). This amplifier, mounted in a watertight housing, is equipped with cable glands for hydrophone leads, battery supply connections, and lines for calibration and output signals. Several special battery supply, coupling, and metering circuits for miscellaneous standard hydrophones.\nphones are available. Portable low-power DC supply circuits, suitable for various preamplifiers, have been designed and discussed later.\n\nRf receiving Amplifiers\n\nIn both system 1 and system 2, high-gain, wide-band, low-noise-level amplifiers are used to increase the incoming signal to levels suitable for recording. The frequency characteristics of these amplifiers are flat within 0.2 db from 15 Hz to 150 kHz.\n\nThe coaxial lines are coupled to these amplifiers by magnetically and electrically shielded input transformers, with the input winding balanced to ground.\n\nReceiving amplifiers use four low-noise-level amplifiers.\n\nUSRL TEST STATIONS\n2 COPPER COTTON RUBBER COVERED TWISTED COPPER COTTON W.E. CO DUAL Coaxial Cable WITH TWO QUADS RUBBER COVERED COAXIAL CABLE COTTON COVERED COAXIAL CABLE W.E.CO. 720 Cable FOUR COAX RUBBER COVERED Cable\n\nFigure 11. Types of coaxial cable used by USRL.\nTubes with a maximum gain of approximately +60 dB (variable in 10-db steps) are used, heated by regulated direct current. The gain is controllable from -20 dB to +60 dB using a split attenuator, consisting of two 40-db sections, connected at the grids of the first and third stages. The attenuation preceding the first stage is completely inserted before attenuation of the second section is introduced, though both are operated from a single shaft. Improved signal-to-amplifier noise margin and higher undistorted output levels are obtained by this method of gain control.\n\nIn the receiving amplifier of system 2, there is a second attenuator covering 10 dB in 1-db steps. Additionally, a supplementary amplifier is included, continuously adjustable from approximately +20 dB to +25 dB.\nThe primary receiving amplifier uses this component when extra gain is necessary. Detector circuits are employed with each system for frequency discrimination against background and inherent noise, harmonics, and water-borne interference, particularly from other systems. The general principle of operation is depicted in the system block diagrams (Figures 6 and 7). The input signal / is applied to the grid of a balanced carrier suppression-type modulator via an attenuator and a 150-kc low-pass filter circuit. The carrier frequency, 650 kc \u2013 dc, is delivered to this modulator from the signal generator through a tuned buffer amplifier, controlled by an automatic volume control circuit. The buffer amplifier is primarily used to secure a sufficient margin between the carrier level and the maximum signal level to minimize interference.\nThe unwanted modulation products other than the sum frequency are removed. The output of the first modulator is then passed through a buffer stage incorporating tuned circuits. The tuned circuits pass only the sum frequency (650 kc) which is impressed on the grid of the second modulator. The second carrier frequency, from the detector tuning oscillator circuit of the signal generator, is brought to this modulator through a tuned buffer amplifier. This amplifier has primarily the function of providing an adequate carrier-to-signal level margin. In system 1, the detector tuning frequency is 678 kc. The 28-kc difference frequency from the second modulator is then impressed on a crystal filter having an essentially square-top pass band of about 12 c centered at 28 kc. The filter is followed by one stage of tuned amplification terminating in 135 ohms.\nThe detector circuit of system 2 has three acceptance band widths provided by three crystal filters.\n\nEquipment at Mountain Lakes\n\nFigure 12. Circuit schematic of coupling amplifier. This amplifier provides extremely high input impedances for operation in balanced or unbalanced circuits.\n\nDesign considerations in the construction of these required the selection of a mid-frequency of 97 kc. The detector tuning oscillator of the signal generator of system 2, therefore, supplies a frequency of 747 kc. A rotary switch permits the rapid selection of any of the three band-pass filters, which have widths of 10, 300, and 6000 Hz, centered at 97 kc. Following the filter circuits are three stages of amplification terminating in a 135-ohm output circuit.\n\nMonitor Converter\n\nSystem 2 is provided with a converter circuit comprising a modulator and a local oscillator which may be used to monitor the signal.\nThe primary function of this circuit is to permit aural monitoring of supersonic frequencies by converting the normal 97-kc signal output of the detector circuit to an audio frequency range of 0 to 3,000 c.\n\nThe use of narrow-band crystal filters in the detector circuit makes it necessary to center the output of the second modulator precisely on the mid-frequency. The adjustment of the detector-tuning oscillator to accomplish this is referred to as \"tuning the detector\" and it is correct when maximum detector output is obtained. It has been found expedient to provide for a continuous visual indication of this adjustment.\n\nThis indication is produced by taking a portion of the detector output signal from a constant voltage source in the recorder circuit and modulating it.\nA signal from a crystal-controlled oscillator tuned to the mid-frequency of the crystal filter in the detector circuit produces a difference signal. This difference signal is rectified and applied to an electron-ray tube. The shadow angle of this tube opens and closes at the difference frequency, providing a direct indication of deviations in cycles per second from the center frequency of the crystal filter. Tuning adjustments can be maintained within a fraction of a cycle at all times due to minimized frequency drifts of the oscillator with respect to the filters, achieved through the use of oscillator-stabilizing crystals with the same temperature characteristics as those in the detector circuit.\n\nContinuous indication of tuning is essential, particularly for frequency response measurements beyond approximately 3 meters.\nThe length of a path through water causes a significant delay in transmission. To tune the detector correctly for the incoming signal, it must lag behind the oscillator by an amount which is a function of the frequency sweep rate and the travel time of sound through the water. The tuning indicator, which gives a continuous reading, permits compensating adjustments to be made during the test period.\n\nLinear Level Recorder\n\nElectromechanical recorders are used with each system to provide continuous and permanent records of the response of the devices under examination. Each recorder consists of an amplifier which maintains an arbitrary equilibrium voltage at its output terminals by controlling, through a motor drive, the position of a sliding contactor on a strip attenuator at the input. A pen attached to this contactor records the data.\nThe electronic level recorder in system 1 consists of a special strip attenuator, a presetting attenuator, an amplifier tuned to 28 kc, and a half-wave rectifier circuit. The normal DC output of this circuit is approximately 100 volts at equilibrium and is applied to the grids of a pair of DC amplifiers. These amplifiers isolate the a-c thyratrons that follow. The anode current of each thyratron passes through one winding of a small dual armature motor, the field of which is a permanent magnet. The thyratron and DC amplifier circuits are arranged such that an increase in DC voltage decreases the normally negative grid potential.\nThe voltage of one thyratron in relation to its cathode determines its firing, enabling current passage and motor direction. Conversely, a decrease in DC voltage affects the second thyratron, driving the motor in the opposite direction. A continuous silk cord, after a few turns around the motor shaft, runs over three pulleys and returns to the shaft. The pulleys are arranged so a cord section extends the length of the attenuator strip and is parallel to it. A carriage with an arm, making contact on the strip, is mounted on guides parallel to the strip. This carriage is clamped to the cord, allowing contact movement to any attenuator point via motor rotation. The recorder maintains the equilibrium DC voltage for thyratron operation.\nThe recorder extinguishes changes in impressed level by altering the contact setting on the input attenuator strip. The recorder can respond to changes in impressed level at a maximum rate of approximately 100 db per second. The system's resolution is determined by the marginal DC bias on the thyratrons and can be adjusted to less than 0.1 db. The effective overall stiffness of the electronic and mechanical system in the balance region is determined primarily by an injected AC bias, used mainly to control overshooting.\n\nThe strip attenuators are wound for a total attenuation of 50 db at 5 db per inch. They are mounted horizontally, directly over the recording paper which is a continuous strip with perforations along each edge. The paper moves over a roller with matching sprocket teeth that is driven by a small synchronous motor through an adjustable gear train.\nThe rates allow for 2, 6, or 18 inches per minute or hour. A friction clutch with a double ratchet attachment permits the paper to be advanced or rewound on the supply spool using a hand crank. The paper drive motor is connected to the oscillator drive motor, allowing both to be operated by a single switch.\n\nThe frequency resolution of the recorder is determined by the frequency sweep rate of the oscillator and the speed of the recording paper. Normally, the oscillator and recorder are driven at the same relative speed (usually the intermediate one) to maintain the proper relationship between oscillator frequency and the frequency calibration of the paper. Under these conditions, individual charts for 0 to 150 kc are approximately 32 inches long. However, the frequency resolution can be improved.\nThe system is operated most frequently with the oscillator sweep rate at minimum and the paper drive at maximum for frequency coverage from 0 to 460 c, requiring a chart that is 32.5 inches long. The level recorder of System 2 differs from that of System 1 primarily in its amplifier's design for a flat frequency response from 100 c to 150 kc, and the use of a full-wave rectifier operating on a square law characteristic over a level range of some 9 db. These differences allow the recorder to be used for energy measurements of wide-band complex signals.\n\nFigure 13. Polar recorder in use with System 2.\nFigure 14. Polar recorder turntable assembly with record arm raised.\nFigure 15. Magnetic clutch and drive assembly of polar recorder turntable.\nIt is often desirable to know an instrument's response for various directions of projection or reception. For this purpose, auxiliary apparatus is provided for both systems. This involves a rotator on which the instrument is mounted and a recorder in polar coordinates. It is evident that these must rotate in exact synchronism for the record to be correctly interpreted. Figures 13 and 14 show the turntable assembly of the polar recorder for system 2, and Figure 15, the driving mechanism and motor. The turntable has suitable positioning and holding devices for Sly' X 11-inch sheets of polar coordinate paper. The gear train and several electromagnetic clutches allow rotation of the turntable in either direction at an angular rate of 1 or 0.5 rpm, both direction and rate being selected by switches. A 5F synchro is used.\nMounted on the end of the drive shaft, which thus couples it to the turntable through a 60:1 worm gear, is a syncro. This syncro acts as the director of a 5CT syncro attached to the rotator carrying the acoustic unit being tested. Whenever the angular position of this syncro does not correspond with that of the director, it generates error signals which are impressed on a thyristor servo amplifier. The altered output of the amplifier at once modifies the speed of the HP DC motor driving the rotator and thus keeps the turntable and rotator in nearly the same angular position. The error signal is about 1 volt for each degree of angular difference and is thus a measure of the lack of synchronization, which, with proper adjustment, should be less than 0.1 of a degree. A hand crank permits angular positioning of the turntable independently.\nThe motor drive. As shown in Figure 15, the turntable can be set readily with the hand wheel if disconnected from the driving motor by the release of clutches. This allows it to be set to any desired relation to the rotator if the circuit between the synchros is open. The strip attenuator, sliding contactor, penholder assembly, and a dual armature motor are mounted on a tilt arm pivoted in such a manner that it may be lowered into position over the turntable (see Figure 14). The strip attenuator is wound at 10 db per inch to a total of 50 db.\n\nFigure 16. Schematic of polar recorder servo system. The 5FT synchro coil connected to the turntable is the director.\nThe thytatron servo amplifier, controlled by the 5CT synchro, provides power for the 1/4-hp rotator drive motor. Plug-terminated patch cords are used to establish connections to the electronic circuit and the required power supplies.\n\nThe pulse system consists of a pulse generator, transmitter modulator, receiver modulator, and pulse rectifier, all designed and built by USRL. With the 15-c to 150-kc system, acoustic pulses of durations between 0.1 and 30 milliseconds can be produced and recorded. The operation of the pulse system is illustrated in Figure 17. A continuous signal is applied to the input of the transmitter modulator, which functions as a \"gating circuit.\" The output of the transmitter modulator is a pulse, that is, a limited train of constant amplitude waves.\nThe signal frequency is determined by the length and recurrence rate of these pids. They can be observed and checked on a cathode-ray oscilloscope connected across the output of the modulator. After checking, they are amplified and applied to the underwater transducer acting as a sound source or projector. The nature of the resulting acoustic signal depends on the electro-acoustic properties of the transducer.\n\nThe acoustic signal generates an electric signal in the hydrophone, which is amplified and applied to the linear or polar recorder attenuator as desired. After further amplification, the signal is passed through the receiver modulator, which is another gating circuit.\nThe receiving time can be controlled by the pulse generator, enabling acceptance of any portion of the received signal for measurement while rejecting the rest. A cathode-ray oscilloscope is used to observe the incoming signal after it passes through the receiver modulator, allowing for direct comparison of the total signal with the accepted portion. This setup eliminates reflections, which would be present in continuous-wave measurements and result in erroneous signal levels.\n\nIf pulses occur at a rate of 15 per second or more, the pulse rectifier generates a DC voltage suitable for controlling the recorder circuit.\n\nComponents of the Pulsing System:\n- Pulse generator\n- Rectifier. The generator produces the\nThe text describes a three-multivibrator circuit, consisting of unbalanced multivibrators A, B, and C. When triggered, they produce negative rectangular pulses. There is also a relaxation oscillator that can be synchronized with subharmonics of the 60-cycle filament supply. Short, sharp positive impulses from this oscillator trigger stages A and B simultaneously. The rectangular pulse from A controls the transmitter modulator, with length determining the modulator signal. The negative rectangular pulse from B is differentiated, yielding a sharp negative impulse at the beginning and a sharp positive impulse at the end. Multivibrator C is triggered by the positive impulse from the end of B, responding only to positive impulses after A and B are triggered.\nThe rectangular pulse from stage B determines the time in stage C, which is used to control the receiver modulator's active receiving time. The idle recurrence rate of this science can be set at 60, 30, 15, or 3 times per second using a selector switch. The multivibrator's pulse length is controlled by the time constants of the associated RC circuits. Each stage has two such controls. A calibrated smooth change of resistance covers a time ratio of 20, and three fixed condensers provide three decades of pulse length. With this arrangement, it's possible to cover pulse durations from 0.1 to 30 milliseconds with overlapping scales for the entire range.\n\nThe transmitter modulator is essentially a stage of push-pull amplification.\nWith a cathode resistor which serves also as the cathode resistor of a 6L6 tube. The voltage drop across this resistor, due to the current drain of the 6L6, is made sufficient to bias the amplifying tubes of the push-pull stage beyond cutoff and thus keep them from passing any signal. The surge from the generator is amplified, and the resulting large negative pulse is applied to the grid of the 6L6, which stops conducting and allows the push-pull amplification to act normally for the pulse period. An output transformer is used with this push-pull stage in order to eliminate the DC components owing to the amplifying tubes' joule heating and back EMF during the pulsing sequence. These components may be observed on a cathode-ray oscilloscope when there is no signal frequency being amplified.\nThe problems in the text are minimal. Here's the cleaned text:\n\nThe problems are balanced by adjusting the screen-grid potentials of the amplifying tubes. An output transformer is used, which has an essentially flat frequency characteristic from 1 to 150 kc. The transmitter modulator has input and output impedances of 1.35 ohms. It operates from a DC supply of 275 volts and an AC filament supply of 6.3 volts. The gain of the unit is 10 db and the maximum undistorted power output is 145 db vs 10-15 watt. The power output between pulses is more than 70 db below the maximum undistorted pulse output. The transients due to imperfect DC balance are 50 db below the same maximum.\n\nReceiver Modulator and Pulse Rectifier. The operation of the modulator section of the receiver modulator and pulse rectifier unit is very similar to that of the transmitter modulator, but the operational characteristics are:\n\nInput Impedance: 1.35 ohms\nOperating Voltage: 275 volts DC, 6.3 volts AC\nGain: 10 db\nMaximum Undistorted Power Output: 145 db vs 10-15 watt\nPower Output Between Pulses: More than 70 db below Maximum Undistorted Pulse Output\nTransients due to Imperfect DC Balance: 50 db below Maximum Undistorted Pulse Output.\nThe characteristics differ. It has a high input impedance designed to work with the amplifier of the recorder circuit. It is capable of discriminating against the highest signal output of the cathode-foldexpvalve stage in the preceding amplifier. Consequently, any portion of the incoming signal may be selected without interference from the rest. This selection is controlled by adjustments on the pulse generator.\n\nThe conversion of the recurrent pulses from the modulator into a d-c voltage suitable for operating the power level recorder is not simple. This voltage produced must satisfy two requirements:\n\n1. Its a-c component must be smaller than the change in the d-c voltage inherent in the recorder's resolution. In other words, its magnitude determines the obtainable resolution without appreciable instability, though the final limit is set by the recorder.\nThe recorder circuit must be capable of changing its equilibrium value at least as fast as the pen-drive motor changes the level of the signal into the pulse rectifier. If this condition is not met, the recorder system will hunt, though this can always be avoided by decreasing the motor speed. The circuit producing the voltage that meets these requirements is shown schematically in Figure 18. The operation is as follows: The receiver modulator is adjusted to pass a short pulse (0.3 to 0.6 milliseconds) of the acoustic signal to be measured. This input to the pulse rectifier at point a and the resulting rectified voltage at point b are indicated on the drawing. The condenser C is made small (0.005 \u00b5F) to allow it to charge to full value within the duration of the pulse. The resistor R is chosen accordingly.\nThe schematic of the pulse rectifier circuit is shown in Figure 18. The voltage waveform of the pulse is indicated at various points in the circuit.\n\nTo ensure that 1/RC is approximately equal to the pulse repetition frequency, a gain control is located at the input of the receiver modulator. This allows the sensitivity of the pulse recording system to be made equal to that of a typical continuous-wave system. However, the sensitivity of the pulse system is somewhat dependent on the length of the received pulse and the repetition rate. In most tests, these variables will be chosen and held constant.\n\nThe frequency response of the receiver modulator and pulse rectifier is flat within \u00b10.5 dB from 1 to 120 kc. The response at the low-frequency end is con-\nThe signal is primarily influenced by the number of cycles within the pulse being measured. Miscellaneous Features. Auxiliary Apparatus become almost completely discharged between pulses. Consequently, the grid signal is a saw-tooth wave, the amplitude of which can change rapidly with changes in the incoming pulse.\n\nThe first section of the 6SN7 functions as an impedance changer and phase inverter. The voltage at point c still contains the DC and AC components of the rectified signal at b. The AC component of this voltage is applied to the grid of the second section of the 6SN7 through the RC network. The time constant of this RC combination should be approximately equal to that of the filter section. By proper adjustment, the signal at d can be made equal to the AC component of the signal at c, but inverted in phase so that the mixed voltage at e will be approximately equal.\nTo one-half the d-c component of the voltage at c with the a-c components balanced out. A terminal is supplied for observation with a cathode-ray oscilloscope. An increase in the intensity of the received acoustic signal causes the d-c voltage at e to rise. The thyratron control circuit used with the pulse system requires, however, a decrease in the d-c voltage with increase in signal intensity. For this reason, the final tube is used.\n\nTo be used with the pulse system, one of the thyratron control circuits is modified and a single coaxial jack installed to take the d-c output of the pulse rectifier. A switch on the front of the panel allows the operator to choose the output of either the recorder circuit or the pulse rectifier. When the latter is chosen, 50-ohm resistors are automatically connected.\nMethods of connecting. Great flexibility is obtained by using jack fields as terminals for individual pieces of electric apparatus mounted in the bays. The arrangement of jacks within the field is based on accessibility, convenience in wiring, and consideration of cross talk. Many jacks are interconnected to establish commonly used combinations of apparatus without the use of external connectors. Jack fields provide terminals for inter-bay, inter-system, and system-to-pier lines, and for frequently used coils, attenuator pads, and load resistors. Connections between jacks are made with plug-terminated, flexible, shielded cords referred to as patch cords.\npatch cords. Where the jack grouping permits, connection between adjacent jacks is made with short-circuited cordless plugs. The types of patch cords and plugs may be seen in Figures 9 and 10.\n\nGrounding. Each system is provided with a fundamental circuit ground comprising a copper pipe driven into the lake bottom adjacent to the pier testing area. Four No. 0000 stranded copper cables connect each fundamental ground to heavy copper bus bars in the pier booths and apparatus bays, and to copper strips mounted along the test areas which are used for grounding test apparatus. Individual circuit ground connections are made directly from the bus bars to all panel-mounted equipment. The lead sheath and outer conductors of the coaxial transmission lines between the pier booths and the laboratory are grounded at the jacks in the pier booths.\nTypes of ground are indicated on the jack fields by means of colored celluloid windows over the designation strips.\n\nUSRL TEST STATIONS\nFigure 19: 30A transmission measuring set in system jack field.\n\nTransmission Measuring Set. The standard instrument adopted for power level measurements is a Western Electric 30A transmission measuring set. The essential elements are a thermocouple, indicating meter, attenuators, and switching circuits. The input impedance is 135 ohms and the set operates at frequencies up to 150 kc. The readings can be varied in increments of 1 db through a range of 90 db by means of attenuator sections connected by dials and switches. A high degree of convenience has been obtained by the use of jack terminations for the individual circuit elements. The circuit of the instrument provides for both gain and loss comparison paths.\nThe meter scale covers a range from -10 to +3 db around a center zero. The design maintains a power level of 130 db vs 10-1 watt (1 milliwatt) at the zero reading. An internal DC circuit ensures thermocouple and metering circuit calibration. Recalibration may be required due to thermocouple aging, temperature changes, and thermocouple replacements. The overall accuracy of the transmission measuring set is \u00b10.1 db.\n\nMonitor Amplifiers and Speakers. Each system includes means for listening to the received signal. System 1 features an audio-amplifier with a maximum gain of approximately 60 db and an output power of some 12 watts, used with a dynamic speaker. System 2 is equipped with a monitor converter circuit enabling the use of various speakers.\nReproducer Set: A transcriber is provided for reproducing, electrically and acoustically, various types of water noises including a number of ship noises. The transcriber has two separate turntables, each with a reproducer for vertical or lateral cut records at 33^ or 78 rpm. A preamplifier associated with each head permits individual control of level and of frequency weighting characteristics. A 50-watt power amplifier is used for the operation of a high-quality speaker. The frequency response of the amplifier without equalization is substantially flat from 30 to 10,000 Hz.\n\nHigh-Pass and Low-Pass Filters: A number of high-pass and low-pass filters are available for filtering the output signal. The high-pass filter cuts off frequencies below a certain threshold, while the low-pass filter attenuates frequencies above a certain threshold. These filters can be used to remove unwanted noise or to focus on specific frequency ranges.\nAnd 600-ohm low-pass filters have been assembled and connected through suitable switches for single units or combinations. The high-pass filters have cutoff frequencies of 0.2, 0.7, 2, 15, and 150 kc. All filters have attenuation beyond the cutoff frequencies of more than 50 db.\n\nLaboratory Intercommunication Systems. Each test system has microphone-speaker communication between the laboratory and the piers. It has been arranged so that it is possible to contact each pier from any one of the systems and vice versa. This intercommunication is required to permit proper coordination between operators at separate locations while making calibration measurements.\n\nMechanical Features of Outdoor Facilities\n\nHandling Facilities. Overhead monorails are provided for trolleys to which chain hoists are attached. Rail switches permit the placing of hoists carrying equipment.\nEquipment at mountain lakes can be rigged on storage spurs or in any desired arrangement for testing. The hoists have capacities up to 1 ton, and the rail height permits a lift above the piers of 16 feet.\n\nSuspension Members. Standard laboratory hydrophones and small test devices are usually rigged on three-piece extension rods. The upper section may be adjusted over some 2 feet by means of a crank-operated screw. The lower section is also adjustable, but only in steps. Center sections of various lengths may be inserted between these two ends. The upper section has a screw mounting plate set in gimbals which permits the rod to hang vertically, if symmetrically loaded. This plate rests on a shock-absorbing receptacle and allows an assembly to face in any one direction.\n\nFig. 20. Typical hydrophone mountings: (A) LA hydrophone, (B) 3. hydrophone, (C) XMX hydrophone.\nDevices up to 1,500 pounds are suspended from 1-inch extra-heavy pipe, available in convenient lengths. One end has a heavy-duty eye for hoist hooks, and the other has standard pipe thread for attachments such as flanges, yokes, F bars, and brackets. Figure 21 shows the more common fittings. Pipe is the usual support for standard projectors rigged for semi-permanent service and for those not rotated for pattern studies. Keep lengths that are not in use hung vertically to avoid bending. Clamping block assemblies, designed for securing pipes at the required positions, are shown in Figure 22. Convenient features include: rapid locking.\nAnd release without separate wrenches, the angular motion of 40 degrees between the block and its base is free for Fig. 21. Fransclucer suspension pipes. To orient the transducers, interchangeable antishock mountings are provided to suit the transducer loading, leveling screws and built-in levels for trimming the entire assembly to the vertical.\n\nRotator. All test devices which require continuous rotation for observation of beam patterns are suspended from a rotator mechanism. The assembly may be seen in Figures 23 and 24. The rotator has two concentric drive shafts that rotate either individually or in synchronism with the polar recorder turn-table previously described in this section. Independent rotation of the concentric shafts is required for studies of transducer-dome assemblies. For other tests, a single shaft is sufficient.\n\nThe housing of the rotator contains the driving mechanism.\nEach shaft has a clutch and is attached to radial and end-thrust bearings, as well as the mechanical clutch assembly. The rotator and suspension framework are depicted in Figure 23, with Figure 24 showing the process of placing the rotator in the carriage. The driving motor engages and has controls that project through the housing. Each shaft is synced with a 5CT synchro via a 60:1 gear train. The synchros are housed on the opposite side of the clutch controls in an auxiliary housing. The driving motor rests atop the gear box and is connected to the internal gear train through an assembly allowing for manual operation by a crank. The concentric shafts, approximately 3 feet long, consist of a 3-inch outer tube terminating in a metal framework, adjustable in length.\nOne is extended by a 1-inch pipe of adjustable length, terminated in a 4-inch flange, and centered with the bottom plate of the outer shaft assembly. The approximate load capacity of the rotator is 1,000 pounds per shaft.\n\nMounting Fixtures. Universal mounting fixtures and others of special application are used for attaching test transducers to the various suspension members. Figures 20A and 20B illustrate the devices for LA and 3 A hydrophones. Figure 20C shows a fixture used for rigging a variety of small and medium-size transducers.\n\nCarriages. The carriages that are used to support the suspension members roll across the test areas on flanged wheels fitted with brakes and matched to the side rails. An H-type carriage, shown in the foreground of Figure 25, is used for supporting transducers.\nProducers that don't require rotation. A turret type is shown in Figures 22 and 26. The upper assembly can be rotated at % rpm by a small synchronous motor acting through reducing gears and a rubber friction wheel. Studs attached to the underside at 30-degree intervals operate a microswitch to indicate at a remote point the angular position of the turret. However, due to the superior facilities provided by the rotator, the turret type is now used only for medium and heavyweight instruments not requiring steady rotation.\n\nA special carriage is used for the rotator assembly with the housing resting on a flat bedplate. A split radial thrust bearing on the underside engages the 3-inch outer shaft and adds to the rigidity of the system. Two lever-operated brakes secure the carriage at any position.\n\nScreens are used frequently to minimize interference.\nFigure 25: Determining the testing distance between transducers. A rotator is shown at the far end of the test area, mounted on an \"H\" type carriage.\n\nReflections: The most common screens are thin-walled watertight metal envelopes, approximately 2 by 4 feet by 1 inch, containing a sheet of hard felt. Flanges along the 2-foot edges allow for the assembly of several screens in multiple-unit configurations. Figure 27 depicts a V assembly being placed in position to function as a surface screen, i.e., to reduce surface reflections from the region between a projector and a hydrophone. Similar assemblies are sometimes placed below the acoustic axis of transmission with the V inverted to minimize bottom reflections.\n\nSpecial Facilities: Compressed air is generally available from an outlet and a special filter in the facility.\nThis installation in pier 1's transmission booth is primarily used for charging the reservoirs of 4A- and 4B-type low-frequency projectors. Other general uses include cleaning and drying less accessible parts of miscellaneous gear with air blasts. A portable gear pump delivering approximately 10 gallons per minute and driven by a reversible motor is provided for use on the piers. A long connecting shaft allows the pump to be immersed in the lake, providing a water supply free from air. The pump is used for washing and debubbling test transducers and for filling and emptying domes not provided with drain plugs. An underwater lamp and a viewing device are available for examining transducers and their rigging in test positions.\n\nChapter 4 provides a general discussion of screens from a theoretical standpoint.\n\nFigure 26 depicts a typical test arrangement using a turret-type setup.\nA portable coupling amplifier is in the foreground. A box of wrenches, screwdrivers, pliers, and other rigging tools is maintained at each pier. A complete supply of rules, graduated steel tapes, levels, and general marine hardware is available for measurements and rigging.\n\nMaintenance and Safety Precautions: Units with dangerously high voltages are equipped with safety switches that must be opened before access is made. This is accomplished by an interlocking mechanism, which must be checked frequently for correct operation.\n\nFigure 27: Lowering the \u201cV\u201d screen into position for reducing surface reflections.\n\nUSRL Test Stations: No one is allowed to work on a pier alone when weather conditions are hazardous.\n\nElectrical: The power is turned on three hours before any measurements are made to allow thermal equilibrium.\nEquilibrium is reached to minimize any drift in frequency or level. Check observations are always made at the beginning of each day and, if necessary, repeated at intervals. The performance of each regulator rectifier is checked by means of a built-in metering circuit, which permits the observation of output voltage and load current distribution among various tubes. This is required frequently as faulty tubes result in a nonuniform load distribution.\n\nThe calibration of the 30A transmission measuring set is described earlier in this section.\n\nThe signal generator is adjusted for continuous-wave, noise, pulse, or other types of tests.\n\nThe wide-band receiving amplifier, detector, and recorder are checked as a unit. Individual circuits are tested only when the unit fails. To observe the overall performance and adjust the sensitivity, the oscilloscope is used.\nThe lathe is set at 10 kc and adjusted to 130 dB vs 10 watts with the 30A set. The signal is fed through the wide-band amplifier and the detector with zero gain, and the recorder is adjusted to the same level entering the amplifier.\n\nThe resolution, stiffness, and overshoot of the recorder are adjusted, and the rate of response to changing levels is observed. Any substance that increases friction between the sliding surfaces reduces the response rate and may soon cause serious wear.\n\nThe carrier frequency can be balanced out at the first modulator of the detector circuit with the signal generator set at 0 c. The controls for balancing the rejection circuit are adjusted until the recorder signal is at a minimum.\n\nIn addition to these individual adjustments, it is desirable to determine the overall gain of the test system. The circuit and the levels used are shown in [omitted due to text length constraints]\nFigure 28. A level of 160 dB is established at the projector side of the impedance matching coil with the 30A set connected to this coil through a 20-db matching pad. The oscillator and power amplifier gain controls are adjusted until the correct power level is indicated on the set. Then, the oscillator frequency dial and recorder paper scale are synchronized at 0 c and a response is taken up to 150 kc. Since irregularities in the performance of any of the component parts will show up in the record, the system is considered to be in operating condition if 0.08 CAIN adjustment \u2022 (.LEVEL IS GREATER THAN INDICATED in the impedance matching coil.\n\nFigure 28. Arrangement for overall system check. Signal levels are given in decibels versus 10^-3 watt. The recorder curve is satisfactory in magnitude and flatness.\nThe test systems undergo complete overhaul annually. All tubes are tested, patch cords checked for continuity and leakage, coil and attenuator characteristics measured, and transmission and leakage characteristics of all lines checked. Poor leakage-to-ground in coaxial lines may result from foreign particles, which is usually corrected by discharging a 500-pF condenser at 200 volts over the path. After reassembly, individual circuits are checked and adjusted if necessary.\n\nMechanical maintenance involves establishing certain routines. Important groups of these include:\n\n1. All electric contacts, including plugs and jacks, are cleaned at regular intervals to prevent troubles caused by dirt and corrosion. Rough or damaged surfaces are refinished or replaced.\nThe piers are examined periodically for settling by placing levels on and across the rails, which were designed with bolts for adjustment. The test equipment, especially that used outdoors, is protected from the weather as much as possible. This includes covering when not in use, keeping pier booths and windows closed, and draining or providing underwater storage for free-flooding devices. All mechanical equipment, such as chain hoists, rigging fixtures, etc., is regularly inspected, lubricated, and stored under shelter during the winter.\n\n2.2 Practical Calibration Procedure\nComparison Tests\n\nA large part of the calibration work done by USRL, particularly in the range from 15 c to 150 kc, was comparison of instruments in a free field. Reference has been made in Chapter 5 to the advantages of this method.\nThis method is probable and important for testing transducers in general. The following discussion pertains to transducers, with the distinction between hydrophones and projectors made only when necessary. In planning an efficient program, it has been found expedient to know in advance the size, shape, and other characteristics of each device. The most essential information is its actual performance. However, knowledge of the end application and operating principle permits emphasis on the characteristics of primary importance. The following illustrates the type of information to be included:\n\n1. Physical Characteristics\nSize of diaphragm\nLocation of diaphragm center\nLocation of center of rotation\nConfiguration and type of active elements.\nPosition in use with and without auxiliary gear\nDrawings showing dimensions and mounting details\nTemperature and pressure limitations\n\nElectrical Characteristics:\nTerminal impedances\nDirect-current power requirements\nWorking and maximum power input for continuous-wave and for pulse operation\nTuning and associated network requirements\nCircuit schematics\nFrequency range\n\nOrdinarily, there are points of particular interest in each program. For example, it may be desired to give special attention to a restricted portion of the frequency range, take directivity patterns about certain axes or at specific frequencies, make a detailed investigation of the secondary or tertiary resonance of a sharply resonant device, or study the performance of a projector at specific power inputs.\n\nPreparation for the tests may be expedited if all preparations are made.\nA person familiar with the instrument is helpful during testing. Every precaution is taken to protect the instrument from mechanical shock or injury, and crystal devices are shielded from the sun as much as possible. A significant portion of time is devoted to rigging test devices and associated gear. Each device presents different rigging problems due to disparities in weight, size, frequency range, and test types. However, there are common rigging considerations for most testing programs, which will be discussed in order as they arise.\nThe types of suspension for positioning transducers are described in Section 6.2.1. The selection of a particular one depends on the physical characteristics of the instrument as well as the nature of the observations to be made. In rigging for tests where the response is wanted only at a few angular positions, a heavy instrument is mounted on a 1-inch pipe, while a light one is usually mounted on a hydrophone rod. Since the rod is supported by gimbals and an anti-shock mounting, it requires symmetrical loading. In cases where the instrument construction does not allow this loading, the 1-inch pipe may be used or the device may be mounted on the rotator. When the pipe is used, it is clamped in position by blocks on rubber mountings. This protects against shock but does not provide a completely free suspension. In any case.\nCase and care must be taken to ensure the entire assembly hangs in a truly vertical line, particularly if the distance between instruments is measured after they are submerged. The test distance is taken to be that between the upper parts of the suspension rods, with corrections for the position of the transducers relative to these rods. Where the testing distance is short, small deviations from the vertical may result in appreciable errors. Such irregularities in hanging may also displace the instrument with respect to the acoustic axis of the standard instrument, introducing serious errors at frequencies where sharp beam patterns occur.\n\nIn rigging a test device to a pipe suspension, an attempt is made to have the center of gravity of the instrument lie on the major axis of the support and the plane of its active face parallel to the axis. Adjustments are made accordingly.\nment and small levels in the mounting blocks facilitate the process, and counterweights may also be employed if the required adjustment is not too large. USRL TEST STATIONS The assembly may be leveled after immersion. The mounting of even the heaviest instruments on the rotator does not require leveling due to its rigidity.\n\nDetermination of Test Conditions. Before an instrument is finally positioned, the depth, testing distance, and electric coupling are determined in as close accord as possible with the principles set forth in Chapter 5. It is evident that the final setup will often be a compromise with ideal conditions.\n\nThe depth of the testing areas is about 6 meters, though most instruments are tested at 2 to 3 meters. The exact depth may be selected with the hydrophone rod and the pipe suspensions. The length of the testing pipe is also specified.\nThe hydrophone rod may be set approximately before immersion and adjusted afterward using the lead screw. With the rotator, depth adjustment can only be made in rather large steps and with no change possible after immersion. This necessitates that associated testing instruments be adjusted to operate with it, regardless of its position.\n\nEstimates of testing distance based on instrument size and frequency range are typically made before tests to tentatively determine pier location. Several testing distances are commonly used to observe bottom and surface reflections and standing waves between instruments. Projectors are usually faced away from the shore to avoid first-order shore reflections.\n\nWhen several projectors are mounted to calibrate a sound field over a wide frequency range, the higher frequencies require more careful attention to ensure accurate results.\nFrequencies have ones mounted near the shore and directed toward open water, while lower frequency devices are suspended at the far end of the pier and directed toward shore. The test hydrophone is mounted on the turret between the two projector assemblies. This arrangement permits the hydrophone to be positioned with respect to either projector. An alternative method involves mounting the two projectors back to back in the turret so that either may be quickly set into proper relation to the fixed hydrophone. Such an arrangement can be seen in Figure 22.\n\nUsually, the recommended electrical conditions are approximated as closely as possible. If the device is a projector, the recommended source impedance can usually be matched with an available coil. If it is a hydrophone, it may be connected directly to a high-impedance coupling amplifier or terminated in ac-termination.\nAll leads must be of sufficient length for testing according to recommended operating conditions. Final preparation for testing involves using single coaxial cables to extend leads as necessary. Splices are made watertight with several layers of rubber tape or underwater junction boxes. The cable is then taped to the supporting rod and wound around it for heavy cables to prevent asymmetrical loading.\n\nBefore testing any instrument, it must be thoroughly washed and debubbled. Significant errors can be introduced by air bubbles or films. Active surfaces are washed with a soft cloth soaked in a strong soap solution with added wetting agent to remove oil, grease, or dirt particles that occlude air.\nThe meniscus traversing an instrument's face, where it is lowered and raised in water, is a good criterion of cleanliness. The meniscus progresses smoothly and without breaks if the face is thoroughly wetted. A device with structural irregularities that may trap air on or near the face is carefully debubbled after submergence by an air-free stream of water from an underwater pump or hand syringe.\n\nAfter an instrument has been rigged and thoroughly cleaned, it may still require soaking. This is necessary to reach thermal equilibrium for x-cut Rochelle salt crystals or others of high thermal inertia. Such instruments are suspended in the water for several hours before tests or even overnight, depending on the size of the device and the difference between air and water temperatures.\n\nThe resistance of the device and the insulation.\nResistance between terminals and case are checked before submersion and during tests if leakage is suspected. After the instruments are positioned and electric connections made, preliminary trials are made to detect extraneous noise, cross talk, or signs of overloading the hydrophone or receiving equipment. Excessive noise is easily heard. Many test devices used in salt water are not provided with electric shielding, so they pick up power-line frequency from ground currents. When grounding adjustments do not improve the signal-to-noise ratio sufficiently, it may be necessary to insert suitable rejection filters ahead of the wide-band receiving amplifier to prevent overloading.\n\nEquipment at Mountain Lakes\nLOG\nMr., _ TEST STATION _ SYSTEM; _/_PIER\nProject No. OOP NATF rnPTFS to STATION FILE AND N. Y. OFHCE SHEET No. H L\n\u2022Water\nTemp\nTransmitting\nFrequency-KC\nRates\nReceiving\nRua.\n[NO, TRP, REF, CCI, TIME, PRO, TYPE-NO, PIER, POS, CM, Dptl, CM-, AVAIL., POWER, SINGLE., RANGE, MID-BAND, Btod with PU, HYDRO, TYPE-NO, V, Depth, CM, Horix, Disc, CM, Sys, Gtia, db, C, DcDh, CM, Tr., Rec., L*, li-MS, Dl-y, MS, Race, PPS, Sw\u2019i, Ptp'r, IPM, RPM, Zo, Level, Tr., X, ISO, /oo, ZZi, C3S, /iTo, ZlS-zoo, zxc, fC>o, n, H, US'* To R, If, cr, Ft, EL, jr, LB-n, X2JI^, 3FU, IZ(, (fi, V, Cr, C, or, t, Ocul, i-9o, Zo, i, V, c, -jpic, i, f, ^/fo, SLo, c, su>, lo, D, p, If, y, E, Ez: QCU-JL /j<r, /aO, /sr-Ss, fl, A, e, SZo, a, e, E, Tzr, Z, E, A, E, X, E, t, n, CO, C, VET, jOUfxP{h7f ;lo, ft, cr\\, c, EL, Zo, ff, y, F, IS. ZS~o (oQ-zf, Zzx, fSo, Oca z, 3ko, Zo, lo, P, ZM.JLo, n, P, H, XL, t, ZMio, ii, P, X, wA, y, X, JilL /O-sio yy), G, OCaS lilld, ITERN !NHN T NO SE; NA-NO SE AG TAT N; 1-PROj.CUR; E-PRC Figure 29. Sample log sheet.\n\nOverloading of the preamplifier, associated with the test hydrophone, should be investigated.]\nGated particularly in the case of devices having a high sensitivity, overloading can be detected with a cathode-ray oscilloscope, which shows a nonlinear relationship between the input pressure and the output signal. The sound pressure on the hydrophone can be reduced by decreasing the driving power of the projector or by increasing the test distance. Cross-talk levels can be investigated by spacing the projector and hydrophone about 3 meters apart and adjusting the system gain controls to a high recorder level at some convenient frequency. A rapid change in frequency, effected by manual operation of the dial, should show an abrupt drop in the output signal due to the effective detuning action of the detector. The magnitude of this change is a direct measure of the margin between the acoustic signal and the electric interference.\nThe recorder charts for acoustical and electrical data are supplemented with detailed logs and circuit sheets. These documents provide an index to the series of tests, identifying various runs, instruments used, and circuit arrangements. Each run is numbered according to the test sequence, and each chart is given an identifying letter. Water temperature, testing depth, pier positions of instruments, and the time of each run are also noted on the log sheets. Sample log and circuit sheets are shown in Figures 29, 30, and 31. In addition to the data, descriptions of the test devices are included in the form of blueprints and schematics provided by the apparatus maker, rough sketches made at the laboratory, or photographs.\nTest observations are made to calibrate a sound field with a standard hydrophone, to calibrate USRL TEST STATIONS circuits.\n\nTest Station\nProject No. Date Copies _ Sheet No. T -\nPeFtrirVO^ QCjj ^5/7/Oa^ - * -d\"\nFigure 31. Sample circuit sheet No. 1-2.\n\nUSRL TEST STATIONS transducers function primarily as hydrophones, and to calibrate transducers designed to function primarily as projectors. Reversible transducers are calibrated functioning in each capacity.\n\nReference data from the first procedure are recorded.\nWhen calibrating a test transducer as a hydrophone, specific runs are required. These runs typically precede observations on the test instruments and are repeated at least once each day during the test period.\n\nReference Data. To calibrate a device as a hydrophone, one or more standard projectors are selected to cover the frequency range of the test instrument. The sound field established by each projector is calibrated using at least two standard hydrophones. One hydrophone should have directional characteristics that discriminate against surface and bottom reflections, although reflective effects may be decreased by operating at short distances within the discussed limits in Chapter 5. Whenever certain frequencies are of particular interest, such as in the case of sharply resonant devices, it is advisable to calibrate these frequencies specifically.\nChoose standard hydrophones with minimum irregularities of response at these frequencies. Before reference runs are made, the angular position of each projector is set where the maximum acoustic output appears on the recorder. This training is done at a frequency where the beam pattern of the projector is sharp, and at a distance sufficient to minimize the effect of standing wave patterns between transducers. With low-frequency projectors, the beams are usually broad enough so that careful mechanical alignment in rigging is adequate. Once adjusted, each projector remains undisturbed throughout the tests.\n\nRuns are taken at several distances, and agreement between the computed and observed distance losses indicates the absence of significant standing waves or reflections. The sound field of each projector is then computed at several frequencies, from the data obtained.\nWith each standard hydrophone, agreement within 1 db ensures reasonable assurance of projector and hydrophone stability. When differences between computed sound pressures exceed 1 db, include data from a third standard to identify discrepancy causes.\n\nInstruments designed for hydrophone operation are calibrated in a sound field established by the above-described procedure. The instrument is acoustically oriented before recording test data, but the device may or may not be tuned according to the program specifications.\n\nBased on exploratory observation, the receiving amplifier gain is adjusted to keep the curve on the chart as the frequency range is covered. If the instrument's level range exceeds:\nThe recorder's record may require adjustments, such as changing the gain during a run or repeating a portion at a different gain setting. Runs at various test distances are typically recorded on the same chart, ideally with the same gain. For resonant devices, supplementary records are made of the level at peak frequency through slow manual oscillator variation. Measurements are taken at frequencies on each side until levels are 3 and 10 db below the peak response. These observations determine the Q of the instrument. Generally, the response of essentially nondirectional apparatus is taken at several angular positions, such as 0, 90, 180, and 270 degrees. Comparison of these runs may reveal rigging inaccuracies, particularly at low frequencies where diffraction effects are significant.\nThe recorded data are a measure of the signal level at the 135-ohm input to the receiving system in db relative to 10^-12 watts. Since instrument calibration is usually wanted in terms of open-circuit voltage or voltage across a specified impedance, it is necessary to determine the relationship between these quantities and the recorder level. This is obtained by injecting a signal from a low impedance in series with the hydrophone circuit, thus simulating the voltage generated under acoustic excitation. The difference in level between the injected signal and the input to the receiving amplifier determines the hydrophone coupling. Typical circuit arrangements for observing coupling characteristics are shown in circuits A and B on Figure 32. The hydrophone calibration may be required.\nTerms of the voltage delivered to a specific resistor, in this case the hydrophone bridged by the required resistance, is connected to the coupling amplifier. The conversion of the recorded level to the voltage at the input of the coupling amplifier requires a knowledge of the gain's relation to frequency for this amplifier. This relation can be obtained using the circuit arrangements shown in Figure 33.\n\nLow-sensitivity, high-impedance hydrophones are typically tested in conjunction with the underwater preamplifier described in Section 6.2.1. This arrangement permits the hydrophone calibration to be referred to the ends of extremely short leads, resulting in more accurate measurements.\n\nFigure 32: Typical circuit arrangements for hydrophone coupling characteristic measurements: (A) observation of input signal, (B) observation of output signal.\n\nFigure 33: Circuit arrangements for obtaining the gain's relation to frequency for the amplifier.\nAn essentially open-circuit calibration involves measuring hydrophone output in terms of charge generated rather than open-circuit voltage, particularly suitable for high-impedance tourmaline gauges. This method, described in Chapter 4, requires minor modifications in the underwater preamplifier.\n\nMeasurements of inherent noise are taken with the instrument in quiet water. When open water conditions are not sufficiently quiet, a bucket with suitable anti-shock mounting or an acoustically treated tank is used. A highly efficient unit, the noise level of which is greatly affected by changes in radiation impedance.\n\nCircuit arrangements for determination of gain frequency characteristic of coupling amplifier:\n(A) observation of input signal,\n(B) observation of output signal.\nDance should not be tested in the bucket due to probable standing waves. An acoustically treated tank may allow the formation of standing waves sufficient to prevent exact noise level measurements. Standing waves cause variations in the impedance that the medium offers to the diaphragm. In well-designed radiators, the mechanical impedance of the diaphragm more or less matches the impedance of the medium to which the energy is transferred. The more efficient the device, the less will be the loss between the electric power supplied and the acoustic power radiated, and therefore, the closer the coupling between the impedance of the device and the impedance of radiation. Since thermal noise is proportional to the resistance, small confined areas which produce standing waves are not conducive to accurate measurements on the more efficient devices.\nTo minimize mechanical vibration, test units are suspended in low-period antishock mounts, and every effort is made to reduce background noise to a minimum during observations. Measurements of the hydrophone noise level and its distribution through the operating frequency range are made on system 2 with each of the acceptance band widths, 10, 300, and 6,000 Hz, ensuring adequate overlap. To determine if the noise level of the system is sufficiently high to affect the measurement of the hydrophone noise level, observations are made with a resistor in place of the test instrument. The resistance is selected by trial to be small enough that the thermal noise generated in it is negligible. Progressively smaller values are tried until there is no effect on the measurement.\nNo observable change in output noise level. Receiving directivity patterns. Directivity patterns of transducers can be obtained rapidly and with good angular accuracy using the rotator and recording turntable assemblies described in Section 6.2.1. Exploratory observations are first made to check angular orientation and adjust system gain so that the pattern traced will lie within the boundaries of the recorder paper. Whenever possible, the signal level at zero angle is adjusted to the upper limit of the chart to utilize its full 50-db range and to facilitate subsequent chart comparisons.\n\nUSRL TEST STATIONS\nSYSTEM I\nPIER 1\nTRANSMITTING BOOTH\nPROJECTOR\n\nFigure 34: Typical circuit arrangement for observations of projector acoustic output versus electric power input.\n\nBy superposition. The rate of rotation is selected.\nThe basis for instrument size, driving torque required, and pattern complexity determine the maximum rotation rate. Small devices can be rotated at the maximum rate as long as the rate of signal variations does not exceed the recorder's response rate. After preliminary observations and adjustments, the pattern is recorded with the turntable completing a full revolution. System and transducer stability can be checked by noting the recorded trace at the point of overlap. For all critical test conditions, the pattern should be repeated at a second distance. If the pattern changes radically with distance, this usually indicates either too small a test distance or the presence of reflections. In the former, the distance should be increased, while in the latter, it should be decreased, the frequency slightly displaced, or other means employed to reduce reflections.\nSharpely resonant transducers are investigated for pattern characteristics at the frequency of resonance, at frequencies slightly above and below this point, and occasionally at the frequencies of secondary and tertiary resonance. Design symmetries or asymmetries which control the beam pattern are investigated by making records about several axes of rotation. The positioning of a transducer for an investigation of design symmetry is illustrated in the sample circuit sheet shown in Fig-.\n\nSplit transducers, designed for bearing deviation indicator (BDI) operation, may be studied for phase shift and symmetry using a special circuit designed by the Harvard Underwater Sound Laboratory. This circuit provides for the halves of the transducer to be in parallel, but the connections to one may be reversed so that its output may be inverted.\nEquipment at mountain lakes uses a three-position switch to determine if the outputs of lag lines, which provide various phase shifts, should match or if one should lag. The patterns taken for BDI characterization of a transducer include halves in phase with no shift, halves in opposite phase with no shift, halves in phase with one lagging, and halves in phase with the other lagging. The gain for the first condition should be maintained for the others. The first two patterns are typically recorded on one chart, and the second two on another. Pattern investigations of hydrophones are usually conducted with a continuous sinusoidal frequency, but may be made by pulsing within the discussed limits.\nChapter 5. It is of interest occasionally to take pattern representations of listening conditions with a broad noise band covering approximately the audio range. A 6-kc band centered at 4 kc is most satisfactory.\n\nTransmitting Response Measuring?. In obtaining data on transmitters, it is not necessary to establish a definite sound field. The calibration is made with standard hydrophones, selected on the basis of frequency coverage and uniformity of response at specified frequencies. Most measurements are made with only one standard, but this is checked by at least one other. This is not only to check the standard hydrophone but also to test the projector stability. Most preliminary observations are made at low power levels and then extended to maximum values.\n\nProjectors are usually calibrated with continuous calibration.\nProjectors use sinusoidal or pulsed signals for tests. The impedance of the driving source is chosen to match the recommended value. A convenient power level is 160 dB vs. 10 watts, but it must not exceed the maximum. Projectors with power factor improvement circuits require calibration with and without these circuits. Some projectors need a polarizing current, typically supplied through a universal-junction box. This box offers current adjustment and metering, as well as adjustable capacitance networks with a flexible plug-in design for these networks.\n\nPreliminary observations include checks for leakage, crosstalk, noise, overloading, angular orientation, and required circuit gain. Following these checks, re-calibration may be necessary.\nsponse data  are  taken,  usually  at  two  distances,  and \ncoupling  measurements  are  made  for  the  standard \nhydrophone  used. \nL TEST  STATION \nPROJ.  NO \u2014 QO \u2014 DATE  ?-  ^ \u2018\u25a0^<COPlES  TO  STATION  FILE  AND  N.  Y.  OFFICE \nSHEET  NO.  B V* \nNOTES \nf1c.OU!tT-  IC.  OuTPDT-  e^OLAJ^!^  T~a/OoT- \n(pG-iS  Pf!ortLC-r-oir  - / Oreis  \u00a3> \n(See  F~o/r \nFire\u2019S. \nftrren \n/feciofioei^  b\u2019/vo-S  of \nDisr \n7iwe/r \nAcowS. \nOuTPu \n\u25a0 jr \nE \nA \ni \nKcl \nJb \ndb \noLl \n3 irxf \nto\u2019' \nfs \nCFf \n/Go \nZo \nHo \n/DD.I \nf \nz4s7 \nZ4st: \nIGG \nloS.I \nIG9 \nm \nIXI.I \nlo4s: \nlos.'i \nnz \nloin \n/ox.c \nns- \n/z.t \nn/.o \n/os.o \nlOS.o \nzV.si \ntis \nZ4.Fg \n7 so \nUSS \n/Zo.i \nHf7 \n//af \nIfZ \nto \nloSI \nlol.l \n/OZrS \nii \ntri \nIZG.2 \n/oi.i \ni \n/-rc \nles \nIZ^.i \n/ot.o \nHS.S \n/i-r \nItG \nt.Z \nixt.7 \ni \nZ4sz \nns- \n/ztt \nm.z \nlo4s \nl/S4 \nS.i \nIZG.2 \nioL7 \nm \n/ofi.o \nlos.  i \nlo4s- \n\\H\u00a3Z \nLG \nZo \n/Z/Z \nffo \nT-F \nl/Z.S \nMz \n/Tr \nlo77 \n/n.z \nU-F \nl/a7 \n/oSo \njl \nnz \n/oT? \n/of.G \nHZ.o \nZ4st \n/bi \n/oZ-o \nui.L \nloi.r \n9s.G \nlol.l \nJ4s7 \nns.s \n9G.I \ni \nJi.3 \nFigure 35. Typical data sheet: projector output versus electric power input.\n\nTransmitting Directivity Patterns. Directivity patterns around one or more axes of rotation are required in a projector calibration to determine the radiation field. The procedure for taking these with the polar recorder has already been given under Receiving Directivity Patterns.\n\nLoad Characteristics. Load-run observations to determine the relationships between the various projector characteristics and the impressed power may be made by means of the circuit arrangement shown in Figure 34. These data should include observations of linearity, frequency shift, distortion, and impedance. Additional patterns may be taken to observe the variation of any quantity as a function of power.\n\nFigure 35 is a copy of an original data sheet showing typical load-run observations. The time entries:\n\n(End of Text)\nIndicative of the soaking periods required for adequate thermal stability after each change in impressed power are presented in this chapter, in Section 6.2.8. A description of the watt-meters and their circuits, along with theory, is given later in this chapter.\n\nImpedance data are taken on all USRL test stations for transducers not connected to preamplifiers. The devices are typically suspended from the pier, well below the lake surface, during measurements. Occasionally, impedance measurements are made with the transducer suspended in the acoustically treated tank. Such data are checked for standing wave effects by repeating a few observations from a different position. The temperature of the water adjacent to the transducers is always recorded, and an adequate soaking period is provided to allow for complete thermal equilibrium.\nObservations on wide-band transducers that have no sharp resonances are taken to cover the frequency range in increments permitting the construction of accurate resistance and reactance curves. Additional observations are taken on resonant transducers in the resonance regions for motional impedance computations. These observations include not only measurements at the frequency of maximum response but also at frequencies above and below this value until the response returns to the baseline.\n\nConsidering the bridges available for direct impedance measurements, the usual procedure is to take the series impedance if its value is not over 10,000 ohms and one terminal can be grounded. For larger values and devices that cannot be grounded, the shunt admittance is used. Attention must be given to the choice of the frequency that should be measured.\nA description of the bridges is given in Section [...]. Whenever possible, measurements are made at the apparatus terminals. However, when additional cable must be used, measurements are made of the device with cable and of the cable alone, so that a correction for the latter may be applied. To facilitate making these corrections, all bridge readings are expressed in the same unit, that is, impedance or admittance. When auxiliary apparatus is used, impedance measurements are also made on it to allow the computation of the values for the instrument itself regardless of the circuit used.\n\nThe impedance of a transducer may also be obtained from the readings of the wattmeter. Though the accuracy is not as good as with the bridge, it affords a continuous indication and permits the detection of all resonances. It has the further advantage\nthat impedance data is obtained at all power levels, instead of at the low levels bridges require, and impedance as a function of power may be observed. Reciprocity Test Procedure Several times during the year, a series of free field reciprocity calibrations are made on all laboratory standard hydrophones. Comprehensive periodic checks are essential, since most of the calibration work is based on an accurate knowledge of the performance of these instruments. A large part of the preparation procedure is identical to comparison testing. The instruments are rigged, washed, and oriented in the same manner. The required measurements include response, hydrophone coupling, and projector current, but the number and sequence differ materially. A discussion of the theoretical considerations involved in reciprocity calibrations and of the general procedure used is included.\nRequisites for a reciprocity calibration involve the use of a reversible transducer that adheres to reciprocity. Since two semi-independent calibrations can be obtained with minimal additional effort using a pair of such transducers, this procedure is favored. It may be necessary to utilize multiple pairs of transducers to span the frequency range from 15 c to 150 kc. In each test run, one of the given pair operates as a hydrophone, while the other supplies the sound field. In a reciprocity calibration, it is essential to know the open-circuit voltage of the instrument, although it may be more convenient to measure the voltage across a known impedance and calculate the open-circuit value. The driving and receiving impedances are chosen to provide the most uniform frequency response.\nThe equations in Chapter 5 require knowledge of the distances between acoustical centers. The selection of a center is arbitrary but once chosen, must remain constant throughout the test. It is typically chosen to approximate the center of the spherical waves produced by the transducer at large distances, for which runs are taken at several hydrophone-projector separations. From the distance-loss relationships, the effective acoustic center of the transducer can be determined. The runs also assist in evaluating the effect of reflections and standing waves.\n\nTesting Procedure. According to Chapter 5, there is no simple a priori test to determine if a specific transducer obeys the reciprocity principle. The most satisfactory substitute is a cross-check between two reversible instruments separated.\nThe ratio of the open-circuit voltage developed by one transducer to the current supplied to the other is obtained when they function as a hydrophone and projector, respectively. The electric connections are then interchanged, and the process is repeated to obtain the same ratio with the functions of each reversed. If the two transducers obey reciprocity, these ratios will be equal at each frequency. It's possible for these ratios to be equal even if the transducers do not obey reciprocity, but there's little chance of this unless they are identical, in which case they may violate the reciprocity principle to the same degree.\n\nWhen reciprocity has been established, the transducers are placed at opposite ends of the testing area with no change in their orientation or depth. The hydrophone to be calibrated is then mounted on a support.\nmovable carriage between the two and tested against each in turn. The procedure outlined in Chapter 5 is then carried through, using each transducer as a projector and as a reversible transducer as described. This procedure yields two semi-independent reciprocity calibrations of the hydrophone. It is usual to test successively all hydrophones of the same type, since this procedure entails a minimum number of changes in rigging and electric connections.\n\nOther Free Field Acoustical Observations. In addition to the usual calibrations, acoustic studies are made which involve somewhat different testing techniques, such as observations on domes, baffles, generators of complex acoustic waves, and complete echo-ranging systems.\n\nDome Studies. When a dome is submitted for investigation, the projector to be used with it may not be included and a suitable one must be selected.\nA device may be wide-band or sharply resonant, but it must have low side lobes at the frequencies of interest and have as nearly as possible the same size and directivity as the projector for which the dome was designed. This is very important, as a projector with unsuitable directional characteristics can completely obscure important dome characteristics.\n\nThe transducer is typically tested first without the dome by rigging it to the inner shaft of the rotator. Measurements usually include frequency response as a hydrophone or as a projector and directivity patterns as a hydrophone. The character of the transducer will largely determine the frequencies at which the dome is tested. If the transducer is sharply resonant, patterns may be taken only at the resonant frequencies.\n\nFollowing these tests, the dome is thoroughly cleaned.\nThe cleaned dome is carefully attached to the rotator's outer shaft. Positioning of the dome to the transducer is ensured with care. The assembly is then de-bubbled and allowed to reach temperature equilibrium.\n\nThe type and character of test data required for a comprehensive investigation are illustrated in Table 1. Figure 36 demonstrates the various configurations of the acoustic gear. Reciprocity, as shown in Chapter 5, means the dome, baffle, and their surroundings have the same effect on the transducer's response and directivity during sending and receiving. For practical reasons, receiving is preferred.\n\nConsiderations for making dome directivity tests require different arrangements. To investigate the effects of a specific target or noise source at a defined bearing, the dome's nose is set at the bearing.\nThe transducer is rotated as indicated in Figure 36D. The same procedure with the dome reversed, as shown in C, is used to simulate propeller noise from one\u2019s own ship. The effect of the dome on the pickup of water noise and reverberation for any particular position of the transducer can best be shown by rotating the dome and projector together with the angle between them fixed during each trial (Figure 36E). This plan calibrates the response of this combination of dome and transducer to noise from any direction.\n\nAccurate positioning of the dome and hydrophone is easily accomplished by means of the rotator and turntable. Either rotator shaft may be locked in position while the other is rotated. It is thus possible to secure the required angular separation between the hydrophone face and the dome nose. By engaging the appropriate locks, the dome and transducer combination can be calibrated for optimal performance.\nBoth shafts allow the entire assembly to be rotated while the relative angular position of the dome and hydrophone remains fixed.\n\nBaffle Studies. The reflective and absorptive properties of baffles can be studied independently of domes. Although no direct measurement of absorption is made, this characteristic can be estimated from reflection and transmission measurements.\n\nUSRL TEST STATIONS\n\nAngle Notation:\nO = Angle of acoustic axis of transducer with respect to direction of sound propagation\n6 = Angle of dome with respect to direction of sound propagation\n<l) = Angle of dome with respect to acoustic axis of transducer\n/ = Continuous rotation through indicated angular range\n\nFigure 36. Typical testing geometries for dome and baffle measurements: (A) reference innards, (B) transmission through baffle.\nThe nose of the dome, transmission through baffle, dome loss versus angle, and specular reflection studies are depicted in Figure 37's sketches. Comparison of the reference pressure between the hydrophone and projector with and without the baffle provides the baffle's insertion loss characteristic. A sound pressure exists on the far side of the baffle due to transmission through it and diffraction around it. This is further discussed in Chapter 9.\n\nThe reflecting and absorbing properties of the baffle can be further studied by modifying the testing setup as shown in Figure 37D. The baffle and transducers are positioned so that the overall path length of the reflected sound is equal to d. With the baffle removed, a screen is placed between the projector and hydrophone, as in Figure 37C, to minimize the direct sound.\nThe magnitude of the sound received determines the threshold in reflection measurements. If the sound pressure measured by the hydrophone with the baffle in place, as in Figure 37D, is equal to that measured in the reference run of 37A, the baffle is a perfect reflector. The difference between the two is a measure of the sound transmitted, absorbed, and diffracted by the baffle.\n\nStudies of Acoustic Properties of Various Materials. Occasionally, the acoustic properties of a particular material are investigated to determine its suitability for a proposed application. Reflection and transmission tests, similar to those made on baffles, are made on samples of the material. These should be large enough to avoid diffraction in the frequency range under consideration. Before testing, the samples are thoroughly washed, debubbled, and submerged until settled.\nThey are in temperature equilibrium with the water. Additional tests are made to discover the critical angles at which incident sound will be completely reflected by the material. The sample is rotated in the setup of Figure 37B, and the angles observed at which minimum transmission occurs. This information is particularly valuable in the design of dome windows and in the selection of materials for them.\n\nTable 1. Test data required for dome investigation.\n\nPurpose of observation Angle position Arrangement Transducer response without dome Transducer pattern without dome Transmission response through nose of dome Transmission response through rear of dome Transducer pattern with baffle and rear of dome interposed Transmission pattern through dome vs angle position Transducer patterns through dome etc., inch.\nKnown critical angles:\n\n1. Transducer used as a receiver only. If the dome is equipped with a removable baffle, tests should be made with (a) dome and baffle, (b) dome alone, and (c) baffle alone, to see how baffle and dome affect noise pickup over a range of angles about the rear of the transducer.\n\nStudies of Acoustic Wave Signal Generators of Complex Waves:\n\nDevices designed to generate acoustic signals of complex wave forms are divided into two major categories, each requiring a special testing technique. In general, the choice of technique is based on factors such as a continuous signal, recurrent signal and its rate, and the crest factor (ratio of peak to rms values).\n\nThe use of electromechanical equipment for the recording of random events is limited by factors such as speed and dynamic range of the recorder.\nSignals with intermittent patterns, low recurrence rates, and crest factors greater than 2.5 are typically investigated using a cathode-ray oscilloscope and high-speed oscillograms. Signals that are continuous or have high recurrence rates, with crest factors not exceeding 2.5, can be studied with the apparatus of system 2. The procedure for investigating such signals with system 2 is outlined below and can be used for those of periodic or aperiodic nature.\n\nThe devices are set up and positioned using the standard procedure for testing projectors.\n\nBAFFLE\nPROJECTOR -- HYDROPHONE\nPROJECTOR\n\nPlan view of a typical test setup for studying baffle characteristics:\n(A) reference runs\n(B) sound transmission through baffle\n(C) threshold signal without baffles\n(D) sound reflection by baffle.\nThe selected hydrophone, used for observation and control of driving power, should have a uniform frequency response. When making the observation, the maximum instantaneous pressure must be considered to prevent preamplifier overloading. First, observe the crest factor using the arrangement in Figure 38. The rms signal is obtained on the 30A set, while the peak amplitude is measured on the cathode-ray oscilloscope. Replace the complex wave signal with a sinusoidal one from an oscillator set at a level that provides the same deflection on the oscilloscope as the test signal. The difference between the 30A set readings for the test and oscillator signals gives the difference in decibels.\n\nFigure 38. Simplified circuit arrangement for determination of peak factors.\nThe crest factor of the complex wave must be determined in volts, as the crest factor of a sine wave is 1.41 (3 dB. To obtain the crest factor of the complex wave, this amount must be added to the observed difference in decibels before converting to the ratio expressing the complex wave's crest factor.\n\nThis investigation involves observations of the total (broad-band) energy and energy distribution with respect to frequency, from 100 c to 150 kc, with the receiving amplifier output connected directly to the broad-band recorder. Energy distribution with respect to frequency over the test signal spectrum can be examined using the normal facilities of System 2, which has three acceptance bands in the detector circuit: 10, 300, and 6,000 c. As these bands represent a continuously smaller percentage of the total.\nthe  frequency  as  it  increases,  the  10-cycle  band  usually \nis  carried  only  to  20  c and  the  6-kc  band  is  not  used \nbelow  4 kc.  When  the  recurrence  rate  of  the  signal  is \ntoo  low,  the  recorder  will  follow  the  individual  cycles \nwhich  involve  the  difficulty  of  evaluating  wide  and \nirregular  traces.  Suitable  resistors  are  inserted  in  the \npen-drive  motor  circuit  to  reduce  the  response  rate \nand  thereby  minimize  the  recorder  excursions. \nThe  energy  in  band  widths  other  than  those  pro- \nvided by  the  detector  circuit  may  be  obtained  by  the \nuse  of  the  circuit  arrangement  shown  in  Figure  39. \nThe  plan  of  this  circuit  is  to  transpose  the  signal  fre- \nquencies by  heterodyning  them  so  that  the  desired \nsignal  band  may  be  obtained  with  available  filters. \nThe  method  is  illustrated  in  Table  2,  which  gives  the \nvalue  of  the  signal  frequency  at  various  stages,  with \nThe circuit is adjusted to pass a band of frequencies, 1 kc wide, centered at 10 kc. Band widths commonly used in such investigations are 40 \u00b1 2 kc. It is obvious that the system may be adjusted for any band width and mid-band frequency requirement within the limits indicated on Figure 39. A determination of the rate of signal recurrence are usually made by inspection of the broad-band recorder traces. For high values, the speed of paper drive on the recorder should be at a maximum. The investigation of the operational stability or life characteristics of expendable devices is made by Table 2. Value of signal frequency in kilocycles per second at various stages when circuit is adjusted to pass all frequencies in the band 10 \u00b1 0.5 kc.\nThe dial setting of the heterodyne oscillator is 12.5 kc to obtain 637.5 kc - this is the sum of the lowest signal frequency to be passed and the half-band width of the filter in the detector circuit added to a fixed frequency.\n\nFrequency of oscillator No. 3 is set at the sum of the upper cutoff frequency of the detector filter and the cutoff frequency of the low-pass filter minus the desired band width.\n\nXXX indicates the filter that cuts off frequencies outside the desired band.\n\nDetector circuit:\nFreq. of signal\nVar. freq.\noutput\noutput\nB.P. filter\noutput\noutput\nL.P. filter\noutput\nXXX\nXXX\n\nEquipment at Mountain Lakes:\n\nFigure 39. Simplified circuit arrangement using System 2 with auxiliary apparatus for obtaining a band-pass filter adjustable in width up to 6 kc and with a mid-band frequency variable between 3 and 150 kc.\n\nPermitting the recorder to run for an adequate period.\nThe circuit is arranged for broad-band observations. The synchronous motor of the paper drive measures the time of these observations, and the paper speed should be at a minimum.\n\nThe circuit arrangement in Figure 40 permits observations on the effectiveness of complex acoustic signals in aural masking. A variety of characteristic sounds on phonograph records is available with which to study masking effects at sonic or supersonic frequencies.\n\nWith the apparatus connected into a complete system for echo ranging, actual trials are made to test the ability to locate small objects in shallow water at distances under 350 meters. A common method is to suspend a small target from a rowboat which travels slowly over the range while the attempt is made to locate the target and maintain contact with it.\nCommon targets are 2- and 3-foot hollow spheres and a 4-foot length of 7-inch heavy walled pipe. One is suspended from the stern of the boat at the same depth as that of the transducer. Directions for the boat's course and other communications are carried on by radio telephone.\n\nThe raft has a working space running its full length through the center. The apparatus rests on carriages moving on steel rails, the same as on the piers. An overhead rail and hoist facilitate positioning on the carriages. The monorail on pier 1 offers the easiest transfer of equipment to the raft, which must be kept level by proper weight distribution. With the gear in place, the raft is located at one end of the range and secured to the shore by 1-inch cables with wide angular spacing. Connections are made.\nThe simplified circuit arrangement for acoustic masking observations at the USRL test stations includes a phonograph system. Telephones connect the laboratory. The raft permanently carries a 6-kva, 60-cycle regulator maintaining any voltage from 105 to 125 volts. Canvas drops protect operators in bad weather. Temperature gradients in the lake are checked by bathythermograph records taken several times throughout the test period. Since gas bubble accumulations on the bottom may affect acoustic conditions, it is advisable to make simultaneous observations on a reference system maintained at the laboratory for this purpose.\n\nSection 6.2.3: High-Frequency System\nGeneral Description\nThe high-frequency system at the Mountain Lakes laboratory covers the range from 100 kc to 2.2 megahertz.\nThe electronic system can calibrate up to 3.5 MHz, but no standard transducers are available for those frequencies. The system consists of the following components:\n\n1. An electric system producing, measuring, detecting, and recording signals in the frequency range 50 kc to 3.5 MHz.\n2. An indoor calibration tank with necessary mechanical equipment for positioning and aligning the units under test. It includes various acoustical devices for reduction of reverberation.\n3. Two sets of mechanically interchangeable transducers with overlapping frequency responses. One set covers the range 100 kc to 800 kc, and the other is not specified in the text.\n4. Mechanical and electrical components for measurements in outdoor test areas.\n\nElectric System\nThe electric system consists of a heterodyne oscillator, power amplifier, and coupling network for driving a projector, and of a detector and recording circuit coupled through a preamplifier for measuring the output of a hydrophone. This system will make continuous ink recordings of the combined response of a pair of instruments throughout the frequency range 50 to 3500 kc. A block diagram of this system is shown in Figure 41. Frequencies and signal transmission direction are also shown on the diagram.\n\nThe heterodyne oscillator consists of one oscillator fixed at 15 MHz and the other variable from 1.15 to 15 MHz. Each feeds through its own buffer to the same modulator, which is followed by a filter designed to pass only the difference frequencies of the oscillators. An amplifier stage follows the filter and terminates in a transformer designed to supply a current.\nThe oscillator has a standard 72-ohm impedance. A 72-ohm attenuator is inserted between the transformer and the output jack. The block diagram shows that a small portion of the output is rectified, converted, amplified, and fed into the buffer stage for the fixed oscillator. This forms an automatic volume control (AVC), which keeps the output within 0.15 db of the ideal level across the entire frequency range. Without the AVC, variations could be up to 1.5 db. The oscillator's maximum output is 222 milliwatts, which corresponds to 4 volts across 72 ohms, and its harmonic level is 45 db below that of the fundamental frequency. The mechanical construction is similar to that of other systems. The variable-frequency oscillator can be driven manually or by a synchronous motor, allowing the entire frequency range to be covered.\nThe calibrated scale is a 30-foot strip of 35-millimeter film with values determined between its lines through interpolation using a vernier dial. The oscillator frequency is adjusted to the scale calibration at 76 kc via a high-Q tuned circuit and at 2 MHz using a quartz crystal. These adjustments are made using a trimmer condenser and a small adjustable inductor in the variable oscillator's circuit. A frequency check is conducted several times daily to correct for any drift, which, however, becomes negligible after 72 hours of continuous operation, resulting in the power not being turned off unless for a prolonged period.\n\nPower Amplifier and Power Level Measurements.\nThe power amplifier is a wide-band type, covering 50 to 3500 kc with a flat gain of 35 dB to 0.5 dB.\nInput and output impedances are both 72 ohms, and the maximum power available is 25 watts (174 dB vs 10-16 watts). It should be noted that the output of this amplifier can be either balanced or unbalanced with respect to ground.\n\nAs indicated on the block diagram, a power level measuring set is used to measure the available power at the output of the oscillator or power amplifier. This instrument is a high-frequency equivalent of the Western Electric 30A transmission measuring set.\n\nEquipment at Mountain Lakes\n\nFigure 41. Lock diagram of high-frequency system. It consists essentially of a high-frequency thermocouple calibrated on direct current and matched to 72 ohms. When properly used, this instrument will measure the power dissipated in a 72-ohm load.\n\nProjector Coupling Network. The purpose of the projector coupling network is to match the impedance.\nThe projector's impedance is aligned with that of the driver and the transmission line. Arrangements are also provided for measuring the projector's current. The most common network is a transformer designed for standard instruments over this frequency range. Most encountered projectors have the same general characteristics as standards and thus operate satisfactorily with this transformer. If a closer match is required, various resistances may be added to bring the impedance to the desired value.\n\nThe transformer for high-frequency standards has a nominal impedance ratio of 72:1,000 ohms and is designed specifically for a capacitive (crystal) load.\n\nFor high-impedance hydrophones, the usual coupling circuit is a high-impedance input amplifier. Since it is necessary to match the coupling circuit to a low (72-ohm) impedance, a transformer is used for this purpose.\npedance transmission line are conveniently considered as impedance transformers. One of the best electronic circuits for this purpose (an electron tube is necessary due to the high input impedance requirements) is a cathode-follower type circuit. These circuits, used in connection with underwater acoustic devices, are known as preamplifiers. The single-stage preamplifiers used in the high-frequency system have an input impedance of about 25 megohms in parallel with about 5.6xf. The output impedance is 72 ohms balanced or unbalanced, and the gain is \u201320 db flat to within 0.25 db over the entire range. One preamplifier is designed specifically for high-frequency standards, while the others are portable for use in current measurements and with other hydrophones.\n\nIt should be noted that the abnormally high values of impedance are required for these circuits.\nOf grid resistors are not necessary at the lower frequencies because the input capacity is the controlling impedance. USRL TEST STATIONS\n\nA calibrating resistor has been included in these preamplifiers to obtain the coupling loss of the circuit, which is required in order to evaluate the open-circuit voltage of the hydrophone.\n\nWide-Band Amplifier. The wide-band amplifier shown on the diagram has a gain of 40 dB and its flat response is down 3 dB. Both the input and output impedances are 72 ohms.\n\nThe purpose of this amplifier is to increase the signals that are too small to record, even with the full gain of the detector.\n\nSince the amplifier is unbalanced, it is associated with a combination of 72:72-ohm coils which allows changing the condition to ground from unbalanced to balanced and vice versa. By means of terminations.\nThe coaxial jack-strips can connect the coils and amplifier to any part of the circuit, although they are typically used as shown in the diagram for the detector. The detector's function is best explained by tracing a signal from the input. The signal frequency is first amplified and then applied to a modulator, which receives another signal from the variable-frequency oscillator with a value of 15 MHz. One of the modulation products (15 MHz + 15 MHz = 30 MHz) is selected, filtered, amplified, and sent to a second modulator. The second signal to this modulator is from a local oscillator with a frequency of 15.097 MHz, resulting in 97 kc as one of the modulation products of this stage. This signal is carried through a band-pass filter centered at 97 kc and 6 kc wide to subsequent stages of amplification.\nThe reason for bringing the 15 MHz signal to the detector is that it ties the detector so completely to the oscillator, allowing it to detect no signal more than 3 kc on either side of the one to which the oscillator is set. The primary advantage of this plan is that most amplification takes place in a 6 kc wide channel, resulting in a much better signal-to-noise ratio. Another advantage is the relative ease of recording at a single frequency (97 kc) compared to wide-band recording. The final stages consist of amplifiers and buffers for the 97 kc signal. A meter with a logarithmic scale may be connected beyond these stages to indicate the signal level, particularly useful when aligning and positioning the instruments in the tank.\n\nThe purpose of the buffer stages is to isolate various circuits from each other. One buffer output goes to the mixer.\nTo the RMS detector and recorder. The others are used for monitoring and making frequency adjustments.\n\nFor correcting drift in the 15.097-mc oscillator, provisions have been made for checking and maintaining the 97-kc carrier in the center of the 6-kc pass band.\n\nA visual indicator of frequency drift, such as that used in the other systems, is not practical because of the relatively larger drifts in this system and because the eye is unable to perceive flickers above 30 per second. As mechanical shock alone may change the frequency as much as 100 c, tone discrimination by the ear is the method used. The 97-kc signal is led to a heterodyne listener consisting of a 94- to 100-kc oscillator, a modulator stage, and a loudspeaker. If the listener is set at 97 kc, no tone will be heard from the speaker when the carrier is 97 kc, but any drift from this frequency will produce a tone that can be detected by the ear.\nThis will be observed as a beat-frequency tone. A separate quartz-crystal oscillator of 100 kc is available for calibration of the heterodyne listener. As with all balanced modulator circuits, spurious signals will arise if there is a lack of proper balance. Since the first modulator stage in the detector is of this design, provision must be made for indicating the point of balance. In this particular circuit, the modulator unbalance results in an amplitude modulation of the 97-kc carrier, which is greatest when the signal in the detector input is 97 kc. Using a cathode-ray oscilloscope to observe the 97-kc carrier envelope, the balance controls are adjusted for minimum amplitude modulation of the carrier. Audible monitoring of the carrier can be used in conjunction with the oscilloscope and provides an extremely sensitive indication of the balance point.\nThe tone at this point will become less mushy. The external meter circuit in the block diagram is similar to the meter circuit in the detector but has the advantage of being portable, enabling its use for aligning acoustic instruments in pier test areas away from the electric system. The detector input is 72 ohms unbalanced, and the gain of the detector and recorder is such that 75 dB is required to produce a full-scale deflection on the recorder from a 10-12 watt input into 72 ohms. The recorder circuit used in this system is practically identical to those in the lower frequency systems and operates only at 97 kc.\nFrequency-calibrated paper is available but only for one relative speed of oscillator to recorder. However, if it is necessary to make records at other speeds, calibrated transparent scales may be used at predetermined points on the oscillator scale or when directivity patterns are being taken.\n\nFrequency-calibrated paper is used only for one specific relative speed between the oscillator and the recorder. However, if records need to be made at other speeds, calibrated transparent scales can be used at specific points on the oscillator scale or when taking directivity patterns.\n\nNoise Generator. In the block diagram, the noise generator can be substituted for the fixed oscillator at the entrance to the first buffer stage in the high-frequency system. The noise signal is a 6.6-kc band centered at 15 MHz, and when heterodyned with the variable-frequency oscillator, the resulting output is the same width, centered at the frequency /.\n\nThe random noise signal is first generated by a gas discharge tube (RCA 150-30), amplified, and then passed through a 1.1-kc band-pass filter centered at 455 kHz.\nIt is used to modulate a 2.095-mc signal from a crystal oscillator. The products in the band centered at 2.5 me are selected, doubled, and then tripled in frequency. This gives an output of a noise band 6.6 kc wide, centered at 15 me. The maximum signal level is approximately 0.5 rms volts across 72 ohms.\n\nThe addition of a narrow band-pass filter and a local 455-kc oscillator in the noise generator makes it a very useful tool for accurately aligning the fixed-frequency oscillator at 15 me. This is done by first adjusting the variable oscillator to one of the film scale calibration points with the noise generator and filter circuit substituted for the fixed oscillator. The fixed oscillator is then replaced in the circuit and its trimmer capacitors adjusted until the same calibration point is attained.\n\nPower Requirements and Power Supplies. The equipment requires a power supply capable of delivering the following voltages and currents:\n\n+12V DC, 1 A\n+200V DC, 50 mA\n-12V DC, 1 A\n\nThe power supplies should be filtered to prevent ripple and noise from affecting the accuracy of the measurements. The power supply connections are indicated on the rear panel of the equipment.\nThe tire electric system is powered from the regulated 115-volt, 60-cycle source available in the laboratory. The filament supplies to all the tubes are constant voltage transformers which provide additional regulation to the electronic circuits. This type of transformer may be used, since the harmonics arising from this regulation do not interfere with the measurements. This is evident from the fact that the lowest frequency detectable with this system is 50 kc; this simplifies considerably the various power and distribution requirements.\n\nThe plate supplies are three units of regulated d-c power which can supply up to 450 milliamperes at 300 volts and are identical with the units used on the intermediate-frequency systems.\n\nFor the low-level signal circuits (hydrophone pre-amplifiers), the plate supplies are taken from a common bus and are regulated by a voltage regulator which maintains a constant voltage of 150 volts. The filament supplies are taken from a separate bus and are unregulated. The plate supplies are connected to the input of the pre-amplifiers through a potential divider network consisting of resistors and capacitors. The filament supplies are connected to the pre-amplifiers through a separate filament transformer.\n\nThe pre-amplifiers are of the cathode follower type and are designed to have a high input impedance and a low output impedance. They are also designed to have a high gain, typically in the range of 50 to 100. The output of the pre-amplifiers is connected to the input of the main amplifiers through a transformer.\n\nThe main amplifiers are of the Class A type and are designed to have a high gain, typically in the range of 1000 to 5000. They are also designed to have a high power output, typically in the range of 1 to 10 watts. The output of the main amplifiers is connected to the recording and playback equipment through a line amplifier.\n\nThe recording and playback equipment consists of a magnetic tape recorder and a loudspeaker. The magnetic tape recorder is capable of recording and playing back sounds in the frequency range of 20 Hz to 20 kHz. The loudspeaker is capable of reproducing sounds in the same frequency range with a high degree of fidelity.\n\nThe entire system is housed in a shielded enclosure to minimize the effects of external electromagnetic interference. The enclosure is also designed to provide good acoustic insulation to minimize the effects of external noise.\n\nThe system is operated by means of a control panel which contains switches for selecting the various functions of the system, such as recording, playback, and calibration. The control panel also contains meters for monitoring the various parameters of the system, such as voltage, current, and power.\n\nThe system is calibrated using a calibration signal generator which is capable of generating signals of known amplitude and frequency. The calibration signal generator is connected to the input of the system through a calibration transformer. The calibration signal generator is also connected to a calibration meter which displays the calibration results.\n\nThe system is designed to be operated in a temperature range of 20\u00b0C to 40\u00b0C and in a relative humidity range of 30% to 70%. It is also designed to be operated in an environment free from electromagnetic interference and external noise.\n\nThe system is maintained by periodic inspection and replacement of worn-out components. The filament transformers and the potential divider network are replaced every six months, while the other components are replaced as needed. The system is also periodically calibrated to ensure accurate measurements.\nThe special power supply for amplifiers and wide-band amplifiers was constructed with higher regulation than the above, providing 150 milliamperes at 140 volts with a stabilization ratio of approximately 1:10,000 and an internal resistance of about 1 ohm. A similar power supply is available for outdoor test equipment and is built into the same portable case with the external meter circuit.\n\nThe transmission line and jack fields are depicted in the electric system's photograph (Figure 42). The transmitting jack field is located below the oscillator, and the receiving jack field is below the detector. Transmission lines connect each field with the corresponding junction box at each end of the tank. There are also crossties between the boxes and between the jack fields, with the exception of the control lines for indexing.\nAll lines and crossties are standard rubber-covered coaxial cable. Terminations are all coaxial jacks (Western Electric Type 464A). This type of line and terminal is also used on the d-c power leads to the hydrophone preamplifiers, as pickup in the power leads may be impressed on the signal leads by stray coupling capacities in the preamplifiers. Connections to the jack fields and to the instruments are made with patch cords terminating in standard coaxial plugs (Western Electric Types 337A and D 122403). The control lines are all standard twinex cable terminating in standard telephone jacks (Western Electric Type 218A). The use of such standard jack fields and patch cords greatly enhances the flexibility of the system. Lines from other systems also terminate in the jack fields.\nThe arrangement allows for the interchange of equipment between systems for special testing. A notable feature is the ability to extend lines to other systems' pier installations using their jack fields, facilitating outdoor measurements. The characteristic impedance of the lines is approximately 72 ohms, and line loss is negligible in most cases. For instance, the loss on a complete loop from the high-frequency room to the end of the pier and back again (approximately 425 feet) was about 1 dB at 2.2 MHz and only 2 dB at 3.5 MHz. However, it's crucial to emphasize that unless the lines are properly terminated, standing waves will occur and lead to erroneous results.\n\nGround loop and cross talk problems arise from the components of specific apparatus and their arrangements.\nThe use of adequate shielding is essential in circuit arrangements, particularly at high frequencies and low signal levels encountered in this system. It is almost impossible to specify conditions applicable to all circuits. Extensive use of heavy copper shield cans is necessary to isolate individual stages in each amplifier, oscillator, etc. Copper shield cans have even been found necessary around metal tubes to decrease radiation. The same precautions apply to all external wiring. In most cases, coaxial cables used for transmission lines have two shields, one wound on top of the other, for more adequate results. All connections are made by coaxial jacks and plugs.\nIt is important to remember that shielding high-level lines is as necessary as shielding low-level ones. Power leads, particularly to low-level circuits, also require shielding. Adequate filtering (decoupling) must be used in each individual stage for all electronic equipment, and extended filtering is often necessary for filament supplies. This is especially true in the case of cathode-follower circuits. Extreme care must be exercised in the choice of ground conditions in each individual stage. All of these precautions are necessary due to lead inductance and stray capacitances. In fact, at these frequencies, some commercial capacitors will appear inductive and some commercial inductors, capacitative. Resistors must be especially designed to operate at these frequencies.\nWith all the above precautions, ground loops can still occur. This issue is resolved by various methods. The first and most important is to establish a good ground and connect all other grounds to it. In this case, the tank is chosen and the heavy copper straps in the bays of electronic equipment are connected to it using No. 2 copper wire. The tank is connected to the fundamental ground at Pier 2 using No. 0 copper wire. Once grounds are established, it is necessary to connect all shielding to them in a manner that minimizes ground loops.\n\nSince ground loop conditions change as experimental setups do, the system must be constructed with the greatest flexibility in grounding. This is achieved by isolating from ground the shields of transmission lines and similar equipment.\nThe ment and carrying the connections from the shields through patch cords to the particular piece of equipment terminating the line. The shields could be connected to ground at this point or isolated by means of a doubly shielded transformer. In general, it was found best to ground the line at one end only, and leave the other end floating. However, all these matters are subject to experimental conditions.\n\nThe subject of ground loops and cross talk would not be complete without emphasis on internally doubly shielded transformers. These make it possible to transmit or receive, at will, on balanced or unbalanced lines. Under most circumstances, balanced lines are much more effective in reducing cross talk.\nThe use of internal shields in transformers leads to the accumulation of all stray capacities between them, decreasing cross-talk even further. These transformers also facilitate a better treatment of the ground loop problem and are utilized for coupling between all circuits and lines.\n\nThe acoustical system encompasses an indoor calibration tank, mechanical equipment for holding and positioning instruments, absorbers for reverberation control, transducers, and outdoor test equipment. Calibrations can be conducted in the tank between 80 kc and 2200 kc. The lower limit is determined by reverberation, while the upper limit is imposed by the response of standard transducers.\n\nThe calibration tank is made of \u00bd-inch steel and has an elliptical cross-section with approximate dimensions:\nThe major axis of the tank is 7 feet, and the minor axis is 4 feet. The tank is 4 feet deep. It has a capacity of 650 gallons and is equipped with a drain and a water inlet at the bottom, and an overflow pipe at the top. Water is pumped directly from the lake, resulting in major problems with fungus and slime. Water from a community system typically contains the same organisms in much smaller numbers. Care must be taken in the choice of a fungicide due to the various materials used in the tank. It must be noncorrosive, nonpoisonous, odorless, and only slightly electrolytic. Furthermore, it must have no effect on rubber. Experience showed that a 2 to 5 percent solution of sodium dichromate was excellent, except for its staining and slightly poisonous nature.\nA commercial product, \"Nalco 21M,\" manufactured by The National Aluminate Corporation, was finally obtained and used successfully. This substance comes in small briquettes placed in a holder in the inlet water line and requires no attention except replenishing. Its only disadvantage is that it makes the water slightly milky, as do most products of this nature. Its poisonous qualities are negligible as long as the concentration is kept at 3 to 5 parts per million.\n\nThe positioning equipment of the transducer consists of two heavy carriages that can be moved the length of the tank on two steel rails, mounted lengthwise on top. Each carriage provides for positioning the transducer by one screw parallel to the long dimension of the tank and a second at right angles. The vertical adjustment is made by four screws.\nscrews driven at the same rate by a sprocket chain. Rotation may be made about a vertical axis for a full circle. In addition to these degrees of freedom, one carriage is provided with two more adjustments of the transducer suspension. One permits the vertical angle of the transducer to be changed and the other allows it to be displaced with respect to the axis of rotation. These arrangements are necessary to permit adjustment of the direction of the acoustic axis of the transducer in the vertical plane lengthwise of the tank and to permit rotation of the transducer about an axis through its acoustic center. This same carriage has motor-driven rotation about the vertical axis to facilitate the taking of directivity patterns. The transducer holders are designed to include the cylindrical case of the preamplifier. Adapters are included.\nFor suspending non-standard transducers. The positioning equipment is very rugged in construction to reduce vibration and other extraneous motion to a minimum. This is necessary due to the small wave lengths and extremely sharp directivity patterns involved. In addition to the two carriages on the guide rails, platforms are available for suspending other equipment for more complex measurements.\n\nFor tests in outdoor areas, two extra T rails are available that can be suspended from the guide rails. When these rails are fastened in position, the instrument platforms can be mounted on them in the same manner as on the top of the tank. Simpler rigging, consisting of a plate with several cylinders attached, is available for special tests. The cylinders fit the transducers in the high-frequency tank. (Figure 44. Schematic arrangement of absorbers and transducers in high-frequency tank.)\nStandard transducers and the plate is of a size to fit across the guides in the test area.\n\nReverberation Control. Several factors influence the reverberation in a tank. Among these are the size and nature of the walls and the directivity pattern (or beam width) of the projector. It is fairly obvious that a narrow beam is much easier to control than is a broad beam that spreads out and strikes the tank walls close to the projector.\n\nSince at these high frequencies the beam widths are relatively narrow, it was decided to place absorbing units around and behind the hydrophone only, in such a manner that the portion of the sound beam that passes the instrument will strike the absorbers and be reduced to a negligible intensity. The particular arrangement used is a cluster of 21 cylindrical absorbers.\nabsorbers are grouped as shown in Figure 44. The projector is beamed at the hydrophone from the opposite end of the tank. The tank was made elliptical with the thought that having the projector at one focal point, any stray radiation would strike the walls and pass through the other focal point. If the hydrophone were then placed about 4 inches in front of the focus, the stray radiation would have to pass through the absorbers before striking it. However, in practice, this action contributed little to the reduction of reverberation, and the projector equipment could be placed anywhere in the tank as long as it was beamed at the hydrophone and absorbers. Each absorber unit is a hollow cylinder of acoustic rubber, 4 inches in diameter and 46.4 inches long, packed with 29 ounces of No. 00 mesh steel wool and\nThe absorber units are filled with deaerated castor oil and rigid enough to stand unsupported in water. With the specific stacking arrangements used, sound must travel through the equivalent of four such units before reradiating into the tank. The characteristics of one absorber are shown in Figure 45. The insertion loss for frequencies above 1 MHz was beyond the sensitivity of the measuring system and transducers.\n\nTwo types of standard transducers are used with this system. One set, with an active face 3 cm in diameter, has an exceptionally narrow beam and goes down to 80 kHz before reverberation affects the results. This type of unit is used up to 800 kHz. The diameter of the second type is 1 cm, and it is satisfactorily used as far as 2,200 kHz. Its directivity is such that reverberation interferes below 300 kHz.\nOne method of minimizing the effects of reverberation is pulsing, which has been used successfully with intermediate-frequency systems but not with this system due to lack of time. The required modification is not difficult, and the benefits should be as great as in the other systems. Another method tried utilized acoustic lenses. The idea behind the use of such lenses was that, if the beam from a small projector could be focused by the lens on the hydrophone, the ratio of signal-to-reverberation intensity should be raised considerably\u2014high enough in most cases to give an accurate evaluation of the sound field.\n\nA lens 10 centimeters in diameter was constructed of polystyrene for operation at 150 kc. A projector was set 25 cm from the lens center and a hydrophone was used.\nThe phone is placed at the conjugate focus, which is 125 cm on the opposite side. Corrections were applied for spherical aberration and thick-lens effects, and the coincidence of center of curvature and focus was avoided to prevent standing waves. The theory of geometrical optics can be used in designing sonic lenses, and if due care is taken, the actual lenses will perform according to the theory. For the lens described, the increase in signal strength at the focus is calculated to be 1.1 db for the 1-cm projector and 8 db for the 3-cm projector. These values were obtained experimentally. It should be mentioned that lenses can be used in making reciprocity calibrations, if a properly modified parameter is used. One objection to the use of lenses is that the sound velocity in them changes considerably with frequency.\n\nFigure 45. Insertion loss of one sound-absorbing unit.\n\nLenses can be used in making reciprocity calibrations if a properly modified parameter is used. It was mentioned that the sound velocity in lenses changes significantly with frequency.\nThis is to be expected from the analogous optical dispersion, but it adds to testing difficulty as instruments in focus at one frequency are not at another. To eliminate dispersion, various shapes of reflectors may be used. These behave as expected, but the problem of preparing and maintaining surfaces sufficiently smooth for the high frequencies is too difficult. Another objection to lenses is that reflections are excessive in some cases. In addition, lenses are inconvenient to mount and modified parameters must be used in calculations. All in all, the use of more directive beams and sound absorbers is found to be the most effective.\n\nAnother problem in all acoustical measurements is the presence of standing waves. Even with no reflections from the boundaries, they still occur.\nDium, standing waves may still occur between projector and hydrophone, or simultaneously between each instrument and a third object in the sound field. In USRL test stations, 100 to 800 KC head (with storage cover removed) coaxial conduit pipes coupling network housing-hydrophone pre-amplifier withdrawn from housing. Figure 46. High-frequency transducers.\n\nOne measurement on lenses, standing waves were generated between the projector and the first face of the lens and between the lens\u2019 faces. It can be shown that if a condition for interfacial standing waves exists and a frequency sweep is made with a sinusoidal source of sound, the response of the hydrophone as a function of frequency will be composed of a series of alternate maxima and minima. The frequency difference, A/, between maxima and minima may be shown to be A/ = c/2d, where c is the speed of sound.\nThe velocity of sound and d is the distance between the reflecting surfaces. If a sound source comprises a band of frequencies greater than A/2, standing waves will be disrupted. This is the purpose of the noise generator mentioned earlier. Based on a 6-kc band for this noise generator, the minimum tolerated distance is 12.5 cm. In actuality, this figure must be adjusted by the fluctuation in the recorded data. Another method of eliminating standing waves is to separate instruments until normal acoustical losses reduce reflections to a negligible intensity.\n\nThe above expression for A/ provides an excellent analytical tool for certain observations and offers a basis for analyses of the geometry involved in a particular experimental setup.\nThe transducers consist of three sections: (1) sound piston and coaxial leads, (2) network housing, and (3) networks. Any part is interchangeable with parts from other instruments. Connections between parts are kept watertight by rubber gaskets. The tops of pipes containing coaxial leads have coaxial jacks for coaxial plugs on network assemblies, and assemblies have coaxial jack outputs for junction box connections. Connections are made using coaxial patch cords. Networks match transducers to transmission lines. There are two types of networks.\nOne network is a hydrophone pre-amplifier, and the other is a transformer for use with the projector. The two coupling networks have been described.\n\nElectroacoustical Measurements\n\nThe technique of measurement with the high-frequency system parallels to a great extent those used in the lower frequency systems. However, the frequencies and wave lengths involved necessitate more exact control of some of the electric and acoustic parameters. These are treated in detail in the following discussion.\n\nAdjustment and Maintenance of Electric System.\n\nAfter the electric system is in thermal equilibrium, the frequency scale on the oscillator must be set. As mentioned previously, this is done at only two points, 76 kc and 2 me, and the scale is then assumed to be correct over the rest of the range.\nThe output level is determined by connecting the oscillator (or power amplifier, if used) to the transmission measuring set and finding the power dispersed in 72 ohms. The set is calibrated to read a specific power level of 133 dB vs. 10 watts, but the introduction of standardized attenuators between the source and the set allows the measurement of higher powers. The power level adjustment for the oscillator can be made at any frequency, as its output is flat within 0.15 dB over the entire range. In the case of the power amplifier, which does not have a flat response, the adjustment is usually made at 50 kc.\n\nThe carrier frequency and modulation balance of the detector are then adjusted. The sensitivity of the receiving system (detector plus recorder) is adjusted at a specific frequency, usually 50 kc, since the detector's sensitivity is optimized at this frequency.\nThe tor does not have a flat response. This adjustment is made with the fine gain control so that, with the gain dials of the detector set at zero, the recorder reads directly the input level to the detector. The adjustment results in a full-scale deflection of the recorder for an input level to the detector of 135 dB vs 10^-12 watt. The level of any recorded signal is then, the recorded level minus the gain of the detector as indicated by the dial settings.\n\nWith these adjustments, the equipment is ready for use but checks of this nature must be made several times each day to correct for minor changes which may have occurred.\n\nThe fact that the power amplifier and the detector do not have flat frequency characteristics entails no serious difficulty as long as the variations are recognized and corrections made. In most acoustical applications, this is not a significant issue.\nMeasurations and comparisons are made between an unknown and a standard. If the same equipment is used with each instrument, the ratio between their response records is correct, although the actual readings are not. Only the measurement and interpretation of specific quantities, such as current to a projector, require consideration of the frequency.\n\nCalibration of Standards: The principle of reciprocity (see Chapter 5) was used in calibrating the high-frequency standards. The actual testing procedure has already been described, so only the precautions peculiar to this range will be treated here.\n\nWith the short waves and narrow beams involved, the hydrophone must be accurately oriented with respect to the projector, and both must be rigidly clamped. A very small movement may introduce serious errors. Care must also be taken to have the hydrophone at the correct temperature, as temperature changes can affect the calibration.\nThe projector beam should completely cover the active acoustic face of the hydrophone. Unfortunately, in many high-frequency units, the beam tends to wander from the established acoustic axis as the frequency is varied. This will introduce serious errors unless the hydrophone is located far enough from the projector to have only negligible variations in the portion of the field being measured. This variation in beam pattern can be detected by reorienting the projector at various frequencies and noting the change in direction of the axis. Effects such as these necessitate complex positioning equipment.\n\nThe orientation of the projector and hydrophone is made at the highest possible frequency because of the increased accuracy afforded by the sharper beam pattern. However, the possibility of beam wandering must always be taken into consideration.\nThe units should be far enough apart so that corrections for spherical waves are unnecessary (See Chapter 5). The method of testing for this effect, as well as for incomplete coverage of the hydrophone face by the sound field, is to take response runs at several distances. The shortest distance at which the inverse distance law holds determines the minimum testing distance that should be used.\n\nTo date, no instrument tested in the tank has necessitated spherical wave corrections. Such an instrument could be calibrated in the pier test areas, which allow a much larger testing distance.\n\nIf standing waves are present between transducer faces, they can be eliminated in some instances by rotating the face of the hydrophone through a small angle.\n\nIn measuring the current to the projector at these frequencies, special precautions have to be taken.\nFigure 47 shows the circuit schematic for current measurements in an unbalanced circuit. The circuit should be noted as having both leads isolated from ground. Even with the ground between the resistor and USRL TEST STATIONS removed, the circuit cannot be used for a projector with one side grounded because the current flowing through the coil and leads' stray capacities will be included in the reading. For the same reason, the circuit for the intermediate-frequency system shown in Figure 48 cannot be used.\n\nCalibrating Unknown Instruments: When a set of calibrated standards is available, calibrating unknown units is fairly straightforward. A known sound field is established between a standard projector and a hydrophone. The hydrophone is then replaced by the unknown unit to be calibrated.\nThe response of an unknown device is found in the same field. It is assumed that the unknown will satisfy the acoustic restrictions for proper beaming, absence of standing waves and reverberation, and the use of a testing distance that does not require correction for spherical waves. The sensitivity of the unknown is determined by comparison with the response of a standard, but all coupling losses are to be accounted for. If the unknown is a projector, a standard hydrophone is used to measure the sound field it generates for a given current or power. Occasionally, a hydrophone is found with only one high lead and the case grounded. A coupling loss measurement can be made on this instrument by immersing it in a glass container of water which insulates it from ground. However, care must be taken to avoid standing waves between the transducer head and the hydrophone.\nThe measurement of current to a high-impedance projector with unbalanced electrical connections requires special treatment. If the water resistance is high enough, the method outlined previously will provide fairly accurate results if the case-to-system ground is removed. If the water resistance is not sufficiently high, measuring the projector's impedance and driving it from a known voltage to calculate the current is necessary. If the projector's impedance is high enough, the transmission line can be terminated with a 72-ohm resistor, and the projector connected across it. The voltage across the projector can then be calculated from the current through the resistor. (Figure 48. Circuit schematic for current measurements in a balanced circuit.)\nThe main reason for focusing more on measuring current than calibrating for available power is that transformers used in coupling projectors to the line do not behave like ideal transformers within this frequency range. As a result, they cannot be represented by a voltage source in series with a resistance, which destroys the concept of available power. Similarly, the power amplifier output does not conform to such a representation and will not meet the conditions required for defining available power. Using a resistance pad to eliminate impedance variations would significantly increase the size of the power amplifier while maintaining the same power output. Additionally, providing pads for various projector impedances for this frequency range poses an additional challenge.\nThe range is tremendous, resulting in all calibrations of projectors being made on a current basis. The recording of data for all acoustic tests follows the same procedure and printed forms used on lower frequency systems.\n\nFrequency Scaling\nThe high-frequency system is well-suited for performing tests on scale models, with the sound wave length shortened proportionally. Measurements of the reflection coefficient of such models will yield a value for the reflection coefficient of the actual target. Since both the dimensions of the target and the wave length of the sound in actual operations are reduced in the same ratio, all reflection and diffraction of sound from the scale model and the actual target are comparable.\n\nEquipment at Mountain Lakes\n[Figure 49: Application of high-frequency system in testing a scale model submarine in an outdoor test area.]\nFigure 49 displays a scale model of a submarine with all linear dimensions reduced by a factor of 60. Measurements of the reflection coefficient conducted at 1565 kc yield the results that would be obtained for similar measurements on the actual object at 26 kc and distances 60 times greater. Sound reflected from the model is measured by an adjacent hydrophone shielded from the direct radiation of the projector. As the model is placed at various distances from the projector and rotated around different axes of symmetry, reflection coefficient measurements are obtained as functions of range and aspect relative to the projector.\n\nLow-frequency pressure system:\nThe low-frequency pressure system at the Mountain Lakes laboratory covers the frequency range of 2 to 100 c.\nThe system evolved as a result of the increasing need for an accurate method of hydrophone calibration at these frequencies under controlled conditions of temperature and pressure. The Bell Telephone Laboratories, Inc., designed and constructed the system under NDRC contract.\n\nUses and Limitations\n\nThis testing technique with this apparatus is independent of auxiliary hydrophone standards. The USRL test station tank consists of a rigid closed cylinder, 10 inches in diameter and 20 inches high, in which the test hydrophone is hung. A coil-driven diaphragm from an XDRC IK projector is mounted in the chamber wall and produces high sound pressures of known magnitude in the water-filled chamber. The sound pressure is dependent mainly on the force factor of the sound source and on the mass and stiffness reactances of the diaphragm and the enclosed neaper.\nThe circular sound source and mounting are shown in Figure 51. The chamber and source meet the requirements of a stiffness-controlled system operating over a fairly wide range of low frequency. The chamber and associated electrical circuit have limitations, limiting the effective range for accurate calibrations of \"hard\" (essentially incompressible) hydrophones to between 2 and 100 c. Calibrations can only be made on hydrophones that are sufficiently hard not to lower the system stiffness appreciably. Reduction of the system stiffness lowers the resonant frequency and, consequently, the upper limit of the frequency range through which calibrations may be made.\n\nFacilities are incorporated to obtain measurements at temperatures between 35 and 100 F and at pressures up to 100 pounds per sq in. The use of a closed system.\nThe testing chamber permits more convenient measurements of a hydrophone's dependence on temperature and pressure than under free field conditions. Approximately six hours are required to obtain a characteristic frequency response over a complete temperature cycle at each hydrostatic pressure.\n\nHydraulic System\nA schematic diagram of the hydraulic system appears in Figure 52.\n\nCalibration Chamber: The chamber consists of two bronze castings, one inch thick, weighing approximately 500 pounds. Its dimensions and construction are shown in Figure 53. The strength and size ensure no chamber or wall resonances occur below 200 Hz. The resonant frequency of the sound source is well above 250 Hz.\n\nSince even small quantities of air significantly reduce the chamber's stiffness, provisions have been made for deaerating the water by reduced pressure.\nThe chamber's shape facilitates air venting, with air directed to the venting cock at the top. When freshly filled, water may be heated and circulated under vacuum to decrease air in solution. The chamber and instrument are carefully debubbled by hand before each test. Hydrostatic pressures up to 100 pounds per square inch are obtained using air from a small compressor unit. (Figure 50: Electrical equipment of low-frequency system. Figure 51: Calibration chamber section of low-frequency system tank, showing sound source and other details. Figure 52: Operating schematic of hydraulic arrangement for low-frequency system.) Equipment at mountain lakes. Hydrostatic pressures are achieved through the use of air from a small compressor unit.\nPressure is transmitted through a moulded rubber bag of negligible stiffness, mounted in a bronze chamber. The water side of the bag connects to the calibration chamber through a line with high acoustic impedance. The air line connects to both the pressure chamber and the rear chamber of the sound source through suitable control valves, thus equalizing the pressures on the sound source diaphragm. A manometer is connected to the system in such a way that the pressure differential can be checked at all times. Since there is a need during a hydrophone calibration to read the mercury column to within 0.1 mm, an optical system was used which allows displacements of less than 1 cm to be read within \u00b10.05 mm without parallax.\n\nFigure 53. Calibration section of low-frequency system tank, showing top lifting mechanism and major dimensions.\nEquipment for Cooling, Heating, and Circulating the Water. The water line from the test chamber leads to a 13x25-inch pressure tank, where the impeller of a circulating pump and the evaporating coils of a cooling system are sealed. A 2,000-watt, 110-volt immersion heater is located in the line returning from the tank to the test chamber. Control facilities enable the system to be held within 1 degree of any desired temperature.\n\nTemperature reduction is accomplished by an air-cooled Freon compressor with motor. A close control of temperature in cooling is obtained by using the heater in conjunction with the refrigerating unit. Safety controls are incorporated which prevent the system from either freezing or rising above 105 F. Circulation is maintained by a rotary pump of hp while the temperature is being changed, but when it is stable, the pump shuts off.\nThe circulation is stopped and the test chamber is closed off by valves once the desired value is reached. The water is deaerated by a vacuum pump with a %-hp motor.\n\nThe apparatus consists of an oscillator, power amplifier, variable attenuator, and receiving amplifier and level indicator. Figure 54 shows the connections in a typical testing setup. Units permanently installed are mounted in bays adjacent to the hydraulic system. For flexibility and ease of operation, the equipment is terminated in several jack strips.\n\nThe signal generator is a Hewlett Packard audio oscillator. Model 202DR. It imposes the lower limit of 2 c on the system. Sound pressures up to 10 dynes per sq cm may be used at any point in the frequency range.\n\nThe power amplifier was designed specifically for low frequency. It operates on alternating current.\nThe amplifier has a maximum output of 6 watts. The gain can be controlled over 45 dB in 5-db steps with continuous adjustment through each step. The circuit has been equalized to provide a frequency response that is flat to 0.1 dB over the working range. The input and output impedances are 600 ohms and 50 ohms, respectively.\n\nThe attenuator provides 45 dB in 1-db steps, giving a dial that reads hydrophone responses directly from \u201380 to \u2013125 dB vs 1 volt per dyne per sq cm when the chamber stiffness is 10^ dynes per cm.\n\nThe component parts of the receiving amplifier include the amplifier, a copper oxide rectifier, and a meter reading from \u201310 to +10 dB. Input impedances of 80,000 ohms unbalanced and 600 ohms balanced or unbalanced are available.\nThe gain is essentially flat over the range of 2 to 100 c. The dial of the amplifier-gain control covers 50 dB in 5-db steps. Its setting plus the meter reading gives the input signal level into the 600 ohms in dB vs 10-1\u00ae watt. With a fixed 20-db gain which may be added, a range from 50 to 120 dB can be read directly. Two combinations of capacitors and resistors are available for insertion in the meter circuit. For frequencies up to 10 c, the one with the larger time constant is selected to give a fairly steady meter deflection. At higher frequencies, the lower time constant is chosen to increase the rate of meter response.\n\nProcedure:\nThe stiffness of the chamber must be measured over the whole range of both pressure and temperature since it enters as a correction in all determinations of hydrophone sensitivity. The procedure is:\n\n1. Calibrate the pressure transducer and temperature sensor.\n2. Place the hydrophone in the chamber and apply a known pressure and temperature.\n3. Measure the resulting output from the pressure transducer and temperature sensor.\n4. Calculate the hydrophone sensitivity using the known pressure, temperature, and output.\n5. Repeat steps 2-4 for various pressure and temperature combinations.\n6. Use the measured sensitivity data to determine the chamber stiffness as a function of pressure and temperature.\nThe small direct current passed through the projector coil (Figure 54) produces a pressure indicated on the manometer. From this measurement and known diaphragm constants, the stiffness may be computed. Extensive computations are avoided by using a chart relating these factors.\n\nThe system is calibrated such that the sound pressure in the chamber is known for any projector current within the range of stiffness. Therefore, the sound pressure that produces the measured output voltage of the hydrophone could be calculated from the projector current. However, the circuit is arranged to save the calculation and calibrate the hydrophone in absolute units. With key 1 in one position, the meter is connected to the hydrophone and deflected by its output voltage. With key 2 in the reversed position, the meter is disconnected from the hydrophone.\nThe resistor across the projector carrying the projector current produces the sound field. The attenuator is then adjusted until the meter reads the same as when connected to the hydrophone. As the position of the attenuator is related to the sound field and its output voltage matched to that of the hydrophone, it may be calibrated to read the sensitivity of the hydrophone directly in units referred to as 1 volt per dyne per sq cm for the normal tank stiffness of 10^ dynes per cm. Corrections for other values of the stiffness are taken from a chart.\n\nHigh-Power System\n\nThe high-power amplifiers at the Orlando and Mountain Lakes stations have approximately the same electric characteristics. The overall gain of each amplifier is about 24 db and the response is flat within 1.5 db from 1 to 100 kc. At the extreme ends.\nThe response falls off, 4 dB at 150 kc, 10 dB at 200 c. Amplifiers should not be driven at high powers below 200 c due to increased coil losses. The output impedance is 100 ohms; the input may be either 135 or 600 ohms. The power available with a minimum of distortion is 1,200 watts, but 1,500 watts may be obtained with a slight increase in harmonic content. Each system is provided with a repeating coil that will match the line impedance of 100 ohms to a 50-, 100-, or 500-ohm load. In addition, there is a 30-db pad capable of dissipating 1,500 watts and having a 100-ohm input and a 135-ohm output to match the repeating coil to the transmission measuring set. At both stations, the pads and repeating coils are mounted in the transmitting booth and the connections appear on a coaxial jack strip in the booth. Care must be exercised.\nThe choice of lines and switching elements for currents that may reach 6 amperes and potentials as high as 500 volts has been found to be satisfactorily handled by lead-covered coaxial pier lines and coaxial jacks. However, special patch cords had to be constructed to provide connections of adequate capacity. The plan of using patch cords and jack strips at these powers involves the danger of disconnecting the high-level side when in use. Large arcs may result, and the damage to the jacks and terminals will be minor compared to that which may occur from the overload voltage developed in the final stage of the amplifier. With this in mind, particular attention is given to the location of the jacks, and special lines are run whenever possible. Warning signs are kept at the critical junction points.\n\nThe connections from the intermediate-frequency equipment are made with great care to avoid any disruptions or arcing.\nSystems connect to the low-level input of the power amplifier in a jack field associated with it. No caution is required for these connections, as breaking them under load causes no damage.\n\nIn using the amplifiers, power-level measurements are made in two ways. The first involves a 30-db pad and the transmission measuring set to determine the available power for the 100-ohm output. The second requires either a thermocouple wattmeter or a recording wattmeter to measure the power delivered to the load. Apart from the precautions needed for the high powers involved, these amplifiers are treated merely as extensions to the existing equipment.\n\nIn their electrical details, the amplifiers at Orlando and Mountain Lakes differ considerably. While both are essentially two-stage, push-pull, transformer-coupled units, the power requirements are quite different.\nThe Orlando amplifier is a Navy echo-ranging type with special transformers replacing input, output, and interstage transformers for specific frequency and power ranges. The power supply and control circuits are retained, requiring a 3-phase, 440-volt, 60-cycle supply. Since this is not available from power lines, a motor-generator set was used with a maximum output of 6 kva.\n\nTo compensate for line voltage fluctuations, generator internal impedance, and other instability sources, an electronic regulator is used to maintain peak voltage within 1 percent. Control of peak voltage is chosen because critical voltages in the amplifier depend on the peak rather than the rms value. Due to the waveform change, the rms value shows a variation.\nThe amplifier at Mountain Lakes operates at 220 volts directly off the single-phase, 60-cycle supply. It regulates all grid-supply voltages closely as grid currents may rise to 20 or 30 milliamperes in the final power stage. Adjustments are necessary to control peak voltage for a variation of only 1% and to prevent hunting with rotating machinery of this size to realize the point of greatest stability. The Mountain Lakes amplifier, shown in Figure 55, differs from the Orlando unit as all grid-supply voltages are closely regulated.\nMining crossties to other systems and connections to the amplifier. In this bay are a master intercommunication station, attenuators, and a separate signal source (AVTstern Electric Company 17B oscillator). Plans are being considered to incorporate in this bay a generator and transmitter modulator with longer pulses than are now available. This pulsing equipment would be used with the power amplifier to simulate actual operating conditions in echo-ranging systems. The arrangement would allow projector characteristics to be measured under typical working conditions. This is of particular importance in the study of cavitation and heating due to power losses on the transmitting efficiency.\n\nHigh-Pressure System:\nMeasurements on transducers operating in the intermediate-frequency range and under hydrostatic pressure up to 300 lb per sq in may be made in this system.\nThe high-pressure tank, made of firebox steel, is a horizontal cylinder that is 8 feet in diameter and 14 feet long. It has eight glass-covered viewing ports along its sides and two ports on top, providing access to the interior. One port is oval-shaped, with a width of 1 foot and a length of 3 feet, and is covered with a 2.5-inch thick steel cover. The other port is circular, with a diameter of 2 feet. A single shaft rotator, similar to the rotator described in relation to the intermediate system, is built as an integral part of the cover of this port. This rotator can be used in conjunction with the polar recorder turntables of either.\n\nDescription of High-Pressure Tank:\n\nThe tank, made of firebox steel, is a horizontal cylinder 8 feet in diameter and 14 feet long. It has eight glass-covered viewing ports along its sides and two ports on top. Two ports provide access to the interior. One port is oval-shaped, with a width of 1 foot and a length of 3 feet, and is covered with a 2.5-inch thick steel cover. The other port is circular, with a diameter of 2 feet. A single shaft rotator, similar to the rotator described in relation to the intermediate system, is built as an integral part of the cover of this port. This rotator can be used in conjunction with the polar recorder turntables of either.\nThe intermediate-frequency system utilizes a rotator shaft that passes through a pressure gland in the cover's center. The circular port is situated 4.5 feet from one end of the tank, and the oval part is located 3.5 feet from the other end. One-inch steel baffles have been installed at the tank's center, as depicted in Figure 61, leaving a 3-foot square aperture. An overhead monorail and hoist system are employed to manage the heavy port covers and test instruments.\n\nRails for a carriage, on which transmitters are mounted, are installed in the tank beneath the oval port. The carriage is regulated by two threaded rods that pass through stuffing boxes at the tank's end and conclude in hand cranks. One rod maneuvers the carriage.\nFigure 57. View of oval port of high-pressure tank\nFigure 58. View of circular port of high-pressure tank\n\nUSRL TEST STATIONS\n\nFigure 59. View of high-pressure tank, showing top working area.\nThe carriage moves lengthwise along the tank, while the other rotates it about a vertical axis through a maximum of 30 degrees. The travel of the carriage allows the distance between two transducers to be varied from 4 to 8 feet.\n\nEach port cover is held securely in place by four hydraulically operated wedges, constrained in the vertical direction by bridges. Each wedge, cut at an angle of 10 degrees, exerts a downward force of 60,000 pounds on the cover when actuated by a hydraulic cylinder operated at a fluid pressure of 1.000 pounds per square inch. The hydraulic system for operating the wedges is shown in Figure 60. The hydraulic system pump is equipped with a 1,000-pound capacity.\nThe automatic system delivers 3 gallons per minute at a pressure of up to 300 pounds per square inch. The tank is filled directly from the lake and drained frequently, with chemical briquettes used to inhibit organism growth. A pump with a capacity of 1,500 gallons per hour is used for filling and circulating water through a heat exchanger. With all valves closed, pressure is applied by a high-pressure pump governed by an adjustable pressure switch. The control is automatic.\nTwo safety valves protect the system from excessive hydrostatic pressures. The interior of the tank has been coated with the bubble layer developed by the Massachusetts Institute of Technology to obtain some sound absorption at the walls.\n\nAcoustic Measurements in High-Pressure Tank\n\nAcoustic measurements in the tank differ from those in a free field due to the relatively small size of the tank and the absence of perfectly absorbing walls. The limitations imposed by the relatively short testing distances and the use of padding to make the measurements independent of reflection have been discussed in Chapter 5.\n\nIn actual testing, the optimum values of testing distances are when sides \"A\" are connected to the high-pressure line and sides \"B\" are connected to the return line.\nPORT LOCKS OPEN WHEN SIDES \"B\" ARE CONNECTED TO THE HIGH PRESSURE LINE AND SIDES \"A\" ARE CONNECTED TO THE RETURN LINE\n\nFigure 60. Hydraulic system for holding port covers on high-pressure tank.\n\nFigure 61. Hydraulic system of high-pressure tank. Pump No. 1 is used for filling tank and circulating water through heat exchanger. Pump No. 2 applies pressure to tank when all valves are closed.\n\nThe transience and pulse length being somewhat interdependent within certain limits, the distance may be increased by using shorter pulse lengths and vice versa. Larger test distances may be used with transducers of good transient response than with sharply resonant ones. A pulse of 1.8 milliseconds is permissible when the test distance is 5 feet because of the baffles which prevent reflections from the sides of the tank.\nThe reflections would be delayed by 0.8 milliseconds. At the maximum distance of 8 feet, the permissible pulse length is 0.4 milliseconds. For many transducers, these distances and pulse lengths provide results equivalent to those in a free field. Even when the tank does not permit such equivalent calibrations, it should be possible to observe the relative performance of transducers as functions of temperature and hydrostatic pressure. Observation of these functions is not possible with tests made in the lake.\n\nThe cleaning, rigging, and debubbling preparation of the transducers is identical to that for free field testing, with the added precaution that the instruments must be capable of operating at the desired test pressures. The available power is measured with the 30A set, with the transmitter modulator of the transducer.\nThe pulse system is arranged for continuous-wave output. By the nature of the modulator circuit, the same instantaneous value of power is maintained when it is switched to the pulsing operation. Observations on the cathode-ray oscilloscope (CRO) allow for rapid adjustment of the proper pulse length, delay time, and received pulse. The recurrence rate is set so that the reverberation from one pulse does not interfere with the measurement of the succeeding pulse.\n\nSection 6.2.7: Noise and Transient Measurments\n\nAs pointed out in Chapter 5, acoustic noise can be classified, for the purpose of analysis, as continuous such as thermal or cavitation noise, or as intermittent, such as waves of explosive origin. The method used in measuring continuous noise has been treated under the description of the intermediate-frequency system (15 c \u2013 150 kc) in Section 6.2. None of the methods described therein are mentioned.\nThe analysis and measurement of transients are suitable for intermittent sound. Transients can be considered composed of sinusoidal signals with a continuous distribution. At USRL test stations, they may be represented by the Fourier integral:\n\nI\u2099 = \u222b[Amj sin(\u03c9jt + \u03c6j) + A\u03bcj cos(\u03c9jt + \u03c6j)] dt\n\nwhere Amj and \u03c6j are the amplitude and phase of each component frequency, and Et(t) gives the time variation of the resultant pulse amplitude and phase. For most practical work, only the dependence of A(f) on frequency needs to be determined.\n\nOne method of obtaining this information about a transient is to record its waveform and analyze it. This technique can be used for high crest-factor noises which cannot be analyzed with the usual electric and recording systems.\n\nA schematic of the electric circuits for detecting and recording transient waveforms of high peak pressures:\nA transducer is used to convert acoustic pressure to an equivalent voltage, which is amplified and impressed on a cathode-ray oscilloscope, producing a beam deflection proportional at each instant to the acoustic pressure. By photographing the oscilloscope screen on motion-picture film traveling at constant velocity, a record of the transient wave form in amplitude and duration is obtained. For accurate reproduction of the acoustic transient, phase distortion and frequency discrimination must be kept to a minimum.\n\nA transducer with the XMX crystal head is selected primarily because of its small size and uniform frequency response. However, since this head has an x-Clit crystal of Rochelle salt, it is necessary that it be terminated in an impedance much higher than its own to minimize the effect of temperature.\nTo reduce microphonic effects, electronic equipment must be placed a considerable distance away, preferably out of the water entirely. This requires long leads to the preamplifier. To prevent the hydrophone from becoming temperature-dependent due to the capacity of the connecting cable, a very small non-microphonic capacity (C in Figure 62) is connected in series with the crystal head at the junction of the head and connecting cable. This functions as a capacitive voltage divider with an input impedance high compared to the XMX head. As a divider, it has good phase and frequency characteristics as long as any resistive components involved are high compared to the shunt capacitative reactance. It is also important to note that any external capacity shunting Figure 62 affects the schematic of the circuit used in measuring transients.\nThe cable capacity will further increase the voltage division. The voltage-dividing effect of the network serves a second essential purpose in reducing peak voltages resulting from high peak pressures to the point where they are on the linear portion of the preamplifier curve. The combination of crystal head, voltage-dividing network, and cable is treated as a unit, and all acoustic calibrations are referred to the end of the cable.\n\nThe preamplifier also functions as an impedance transformer to provide a 100-megohm impedance to the hydrophone and 72 ohms to the transmission line. Two such preamplifiers are available: one with a gain of -11 db for high sensitivity heads, such as XMX type, and one with a gain of 35 db for low sensitivity heads, such as tourmaline types. Both have a flat response and a linear phase-frequency characteristic.\nFrom 2 c to over 600 kc. For almost all measurements of transient phenomena, as well as those with high peak pressures, this laboratory has used the XMX head in conjunction with the first preamplifier. The oscilloscope used for these measurements is a Dumont type 247 provided with an external supplementary intensifier voltage for more brilliant traces. The records of the wave form were made on a moving film camera (Western Electric Fastax) with film speeds up to 100 feet per second. Theoretically, frequencies as high as 600 kc may be resolved at this speed. The camera was used without the shutter mechanism. With the moving film, no horizontal sweep signal or transient sweep circuits are used in the oscilloscope, but the vertical amplifier which multiplies the voltage from the transient is essential. It is best to point out here that, while all measurements were taken using this method, some later measurements may have utilized different techniques.\nThe electronic equipment was constructed with linear phase-frequency characteristics over the entire range of 2 to 700 kc. The phase characteristics of the hydrophones are not entirely known. In general, if a hydrophone does not have any rising sensitivity with frequency and if there are no \"breakups\" in the response, it may be assumed that the phase relation is fairly linear. This assumption should be further investigated. However, the phase-frequency characteristic does not affect the amplitude-frequency analysis of the transient but only its wave form. The frequency analysis of the transient is made from the photographic record by the use of a harmonic analyzer.\nThe USRL used a Henrici Analyzer, provided by the Department of Physics at Case School of Applied Science. This analyzer determines the relative amplitudes of thirty harmonics. A complete frequency analysis of a transient can take several hours to several days, depending on its complexity. The resulting data are relative and require supplementary computations for conversion to actual units such as pressure and frequency. Figure 63 shows an analysis of an explosive wave using this method, presenting the rms pressure in db versus 1 dyne per sq cm in a 1-c band as a function of frequency.\n\nConsiderable auxiliary equipment is required for the calibration and maintenance of the measuring system.\nThe apparatus is divided into six groups: resistance and impedance bridges, test meters, portable signal generators, cathode-ray oscilloscopes, wattmeters, and miscellaneous equipment.\n\nResistance and Impedance Measuring Bridges\nThe laboratories are provided with a number of admittance and impedance bridges suitable for measurements over a wide range of values with various frequency ranges.\n\nThe Western Electric Company 3A Impedance Bridge is used in the frequency range 1 to 150 kc. It is an admittance bridge of the comparison type, measuring impedance in terms of the equivalent parallel resistance and capacitance components. It permits measurements on devices which are electrically balanced or unbalanced to ground. It measures parallel resistance components up to 1,100 ohms directly.\nThe supplementary computation for 1 megohm can be made using parallel capacitance or inductance considered as negative capacitance. Parallel capacitance (or inductance) can be measured directly up to 0.11 /xf, and above this value by adding external capacitance. The bridge is designed for an overall accuracy in impedance determinations of \u00b10.5 percent, but it has reduced accuracy for extremely high parallel resistive components. It is usually used with a 17B oscillator and a 31 A transmission measuring set detector described later in this section. A typical arrangement of these devices can be seen in Figure [X].\n\nThe Bell Telephone Laboratories W-10134 Impedance Bridge consists essentially of two units: a capacitance comparison bridge and a Maxwell inductance bridge. This obviates the computations necessary to convert parallel values to series values or vice versa.\n\nThe use of the bridge is limited to electrically unbalanced components.\nAncient instruments have a frequency range of 200 Hz to 150 kHz. One comparison bridge measures capacitances from 0.1 pF to 1.11 \u00b5F and conductances from 0.01 nS to 111,100 nS. The Maxwell bridge measures inductances from 0.1 H to 1.11 mH and resistances from 0.01 ohm to 111,100 ohms. The accuracy of direct bridge readings is approximately \u00b11%. Complete operating instructions and descriptive material are available, which give correction factors to obtain a precision of \u00b10.1%.\n\nTo facilitate impedance measurements at the testing area, this bridge, along with a 17B oscillator, a 31 A transmission measuring set, is mounted on a rack equipped with casters. (Figure 64)\n\nMaking impedance measurements using the W10134 impedance bridge, the 31A detector, and the 17B oscillator.\nThe W-10093 Capacitance and Conductance Bridge for measurements at high frequencies was constructed by Leeds and Northrup Company, Inc. in accordance with a design by Bell Telephone Laboratories. The normal frequency range is 50 kc to 5 me, but it may be used as low as 10 kc and as high as 10 me without serious loss of sensitivity or accuracy. The capacitance range is from 0.01 to 1,100 pF, either positive or negative, and may be extended well beyond 11,000 pF using five plug-in standards. The conductance range is from 0.001 to 1,100 mS and may be extended to 11,000 mSodms and further by plug-in standards. Both types of measurement may be extended even further by connecting a known admittance in series with the one to be tested. For the normal frequency range, the accuracy is about 0.25 percent.\nThe General Radio Company Impedance Bridge Model 650 A is a direct-reading instrument with a self-contained battery and a 1,000-ohm oscillator. It provides quick approximations of impedance at 1,000 ohms or with direct current. It offers d-c resistances from 1 ohm to 1 megohm, capacitances from 1,000 pF to 100 \u00b5F, and inductances from 1 mH to 11 h. A Leeds and Northrup Company Wheatstone Bridge is used for precise d-c resistance measurements. Test Meters\n\nThe laboratories use standard ohmmeters and voltmeters, except for a special megohmeter and a 31 A transmission measuring set. Several portable Simpson and Weston volt-ohm ammeters are used in the maintenance of electronic equipment and for making customary electrical checks on transducers. A number of electronic voltmeters are used for measurements where required.\nThe test meter must have a high impedance. A Ballantine AC Voltmeter measures rms voltages from 0.001 to 100 volts over a frequency range of about 10 to 150,000 cycles with a general accuracy of 2 percent. When used in conjunction with a decade amplifier, measurements may be made considerably below a millivolt with frequencies from 10 to 100,000 cycles. The use of a special multiplier extends the upper limit to 1,000 volts.\n\nThe Hewlett Packard Vacuum-Tube Voltmeter, Model 400 A, is used extensively for relative measurements of rms voltages between 0.03 and 300 volts over the frequency range 10 Hz to 1 MHz.\n\nThe Measurements Corporation Electronic Volt-meter, Model 62, provides ranges of 1, 3, 10, 30, and 100 volts with an accuracy of 2 percent of the full-scale reading. When used with its associated probe, it allows measurements from 30 Hz to 150 MHz.\nA vacuum-tube thermocouple voltmeter designed by USRL is used for reading peak voltages. A Rawson Electrical Instrument Company Megohmmeter is primarily used for measuring insulation resistance at 2,500 volts, with a range of 0 to 100 and 0 to 10,000 megohms. A Western Electric Company 31 A Transmission Measuring Set is extensively used as a null indicator for various impedance bridges. Its high sensitivity and frequency discrimination provide excellent resolution in balancing under severe conditions of wave distortion.\n\nEquipment at Mountain Lakes\nFigure 65. W10093 capacitance and conductance bridge for use at high frequencies.\n\nA set consisting of an amplifier with calibrated gain controls, an oscillator and modulator circuit operating in conjunction with a 20-c band-pass filter.\nThe crystal filter, an output meter, and a regulated d-c supply circuit operate on 115 volts, 60 Hz power. The set is designed to operate through the frequency range 1 to 150 kc with switches to permit its use as a wideband or sharply tuned instrument. Continuous tuning control from 10 to 150 kc is effected by the frequency adjustment of the local oscillator.\n\nPortable Signal Generators\n\nThe Western Electric Company 17B Oscillator is a heterodyne type operating on 60 Hz power and delivering levels up to 160 dB vs. 10 watts into a 135- or 600-ohm load and over a frequency range of 1 to 150 kc. Below 1 kc, the power output decreases and the wave form becomes poor. It is used extensively in impedance measurements due to its highly stable and uniform output level, accurate frequency calibration, and low harmonic distortion.\nThe Hewlett Packard Oscillator, Model 200-Cr, covers a frequency range of 20 Hz to 200 kHz. It is designed to deliver a signal level of 150 dB vs 10 mW into a 1,000-ohm resistive load, although its output is not critically affected by the loading. The total harmonic distortion, under proper operation, is less than 1%.\n\nThe Measurements Corporation Square Wave Generator, Model 71, permits rapid determination of the phase and frequency characteristics of many types of amplifiers and networks when used in conjunction with a cathode-ray oscilloscope. The time of rise on the wave is about 0.2 microseconds with frequencies from 5 to 100,000 Hz. The Fourier analysis of these waves shows components that give a resultant range of investigation from 1 Hz to several megacycles.\n\nThe Dumont Electronic Switch and Square Wave Generator, Type 115A, produces square waves at 10 Hz.\nTo measure voltages with a form reaching full amplitude within a few microseconds, use a signal with this characteristic. This signal is beneficial for studying amplifier and network performance. In conjunction with a cathode-ray oscilloscope, it allows comparison studies of amplitude, wave form, phase, and frequency between two electric signals.\n\nCathode-Ray Oscilloscopes:\nAll measuring circuits necessitate cathode-ray oscilloscopes. The Dumont Type 175 A is utilized for visual monitoring in the 15 Hz to 150 kHz test systems. A Dumont Type 247 is employed with an auxiliary circuit providing higher accelerating potentials for special studies of high-speed oscillograms.\n\nA Renier Model 556 operates at frequencies up to 4 MHz and is useful for observing wave forms at higher frequencies and for observing carrier modulator balance.\n\nWattmeters\nA thermocouple wattmeter and a recording-type wattmeter have been developed for the measurement of power over the large frequency range used in underwater acoustics. The two operate on different principles, and the second was particularly designed to be used in conjunction with the present electrical systems.\n\nThermocouple Wattmeter\nAs the circuit of the thermocouple wattmeter shows in Figure 66, the instrument can measure current and voltage as well as power. The measurement of these three quantities allows a calculation of the load impedance. Other features of the design are that the power range switch tends to keep the impedance range of the instrument constant and that the power measurement is independent of wave form.\n\nFigure 66. Circuit schematic of thermocouple wattmeter.\ncircuit arrangements are shown for: (A) power measurement, (B) current measurement, (C) voltage measurement. The device has resistances from 10 to 300 ohms and power scales of 100, 500, and 1000 watts. The indicated and actual scale factors agree within 1.5% from 0 to 100 kc. Operation outside the impedance limits will not only affect accuracy and overload the thermocouples but may also destroy them. While the thermocouple wattmeter is direct-reading and fairly accurate, the time required to reach temperature equilibrium delays readings, making point-by-point measurements necessary. The possible destruction of thermocouples from sudden changes in load impedance and the limited impedance range for any one power scale are distinct disadvantages. The recording wattmeter was designed for unbalanced load.\nTo overcome these difficulties.\n\nRecording with a wattmeter: In measurements with the recording wattmeter, two signals, S and A, are obtained and recorded. The signal is obtained by adding a signal which is n times the current i to one which is m times the voltage e. The signal A is the difference between ni and me. It can be shown that 4mI = IE + Ve*, where \u03b8 is the phase angle between the current and voltage. The and A signals are recorded on the intermediate-frequency systems in the usual manner.\n\nThe measurement of total power is correct only for sinusoidal waves. For portable use, separate amplifiers and meters may be used in place of the recorders.\n\nFigures 67 and 68 show the connections used in obtaining the 2 and A terms for unbalanced and balanced circuits.\n\nIn the actual circuit for an unbalanced load, a coil and pad replace the resistors in turn to obtain the measurements.\nIn the balanced condition, the only new factor to consider is the stray capacity between the two high potential terminals of the driving coil, which can be neglected for usual load impedances. The impedances of the secondary windings will not affect measurements. If R2 is center-tapped to ground, the meter will measure the power delivered to both the load impedance and the impedance to ground. However, if no ground connection is made, the meter will read the load dissipation independently of the degree of imbalance.\n\nThe 2 or the A signal, depending on the position of the reversing switch, will appear across R^.\n\nDescription of Orlando Test Station\n\nFigure 68. Recording wattmeter circuit for balanced load.\nThis text describes a wattmeter, which consists of a pad, pins, and a coil. Voltage and current components are obtained in the same manner as in the unbalanced case by short-circuiting R2 and disconnecting 7^1, respectively. In the latest model of this wattmeter, the system can be changed from a balanced to an unbalanced condition by a switch on the front panel. In actual operations, four records are obtained on the chart paper, S, A, e, and i. Since the levels are recorded in db vs 10-16 ^vatt, subtracting a proper constant from the recorded X level will give the power in db vs 1 watt. The same procedure and constant are used to obtain A in the latter units. When these two readings are converted, the difference between them will be the power delivered to the load. Similar procedures are used to convert the voltage signal to db vs 1 volt and the current signal to db vs 1 ampere.\nThe errors in wattmeter readings are functions of the ratio rne/ni, and three impedance ranges have been incorporated to keep these errors at a minimum. If the records of current and voltage differ by more than 8 dB in a particular region, their product will be in error as indicated by the above ratio. An impedance range should be selected which brings the two signals closer together and thereby improves the accuracy of the power reading. These changes are readily made by means of a switch on the instrument.\n\nThe only element affecting the frequency characteristic of the wattmeter is the loss on the insertion of the coil replacing R^. This will appear as a variation with frequency of the conversion constants, but this effect over the range of 50 c to 150 kc is less than 0.4 dB.\nThis wattmeter is used over a power range of 0.001 to 1500 watts and an impedance range of 15 to 800 ohms. The accuracy is on the order of 1 to 4 percent for phase angles up to 85 degrees. The accuracy beyond this angle has not been completely investigated experimentally.\n\nMiscellaneous Equipment\nGeneral laboratory apparatus is available at all times for use with the circuits that are being developed and the construction in progress. This equipment includes decade condenser and resistance boxes, attenuators, storage batteries, and moderate stocks of fixed resistors, condensers, and inductors. Various switches and vacuum tidies are available in addition to transformers for power, signal frequencies, and variable voltage.\n\nA modified Hallicrafters short-wave receiving set is used as a voltmeter and a harmonic analyzer.\nThe Orlando station of USRL is located on Lake Gem, about 4 miles southeast of Orlando, Florida. The lake is almost circular with a diameter of around 300 yards, providing ample space for calibrations but not too large to have high waves in windy weather. Typical of lakes in this region, it is fed from subterranean sources and has no surface inlet or outlet streams. The depth of the lake varies with rainfall, requiring remedial measures for calibration due to significant level changes. A pump is installed to maintain the water level within \u00b10.25 feet by drawing water from an adjacent lake.\n\nLow-level signals at higher frequencies (15 me). It also offers an excellent means for detecting stray radiation.\n\nDescription of Orlando Test Station\n\nSite of Station\nThe Orlando station of USRL is situated on Lake Gem, approximately 4 miles southeast of Orlando, Florida. The lake is nearly circular with a diameter of roughly 300 yards, offering sufficient space for calibrations while not being excessively large enough to generate high waves during windy conditions. Characteristic of lakes in this region, it is fed from underground sources and features no surface inlet or outlet streams. The lake's depth fluctuates based on rainfall, significantly impacting calibration work. To address this issue, a pump has been installed to draw water from an adjacent lake and automatically maintain the water level within \u00b10.25 feet.\n\nLow-level signals at higher frequencies (15 me). This setup also provides an excellent method for detecting stray radiation.\nThe depths range from 15 to 18 inches to 33 feet at the barge location. These depths are satisfactory for testing purposes. The lake bottom consists of sandy loam, except for the central deep portion of soft mud. The acoustic absorption of the loam increases with frequency. Reflected sound is 10 dB below incident at 20 kHz, 15 dB at 30 kHz, and 20 dB at 40 kHz.\n\nThe Orlando station provides facilities for the free-field calibration of underwater sound devices in the frequency range from about 15 Hz to 150 kHz. One objective in setting up this station was to have a place where tests could be made when the water at Mountain Lakes is frozen. For this reason, outdoor facilities were of most importance, since the indoor facilities of the station were less crucial.\nThe Orlando test station as seen from the pier. Heavy equipment is loaded onto a mine car by the boom and chain hoist at the left. The rails on which the mine car runs are shown in the foreground. Mountain Lakes are usable all year round. A fundamental requirement for the station was that the outdoor facilities in every essential respect be equivalent to those at Mountain Lakes. This has been achieved.\n\nOrlando has two testing systems, one located on the pier, the other on a barge in the middle of the lake. The pier system is very similar to that at Mountain Lakes, but modifications have been incorporated in the barge system to take full advantage of the deeper water available.\n\nThe test station is located on the eastern shore of the lake. As shown in Figure 69, a boom and hoist system is used to load equipment onto mine cars, and rails run along the shore for the mine cars to travel on. The barge system, located in the deeper water of the lake, has undergone modifications to maximize its potential.\nA chain hoist is provided at the loading platform for lifting heavy equipment out of a truck and loading it directly onto the mine car. The mine car runs on a small spur track from the loading platform to the pier. At the pier's test pit starting point, the equipment is transferred to a chain hoist running on an overhead rail to the outer end of the pier. Several hoists of varying capacities are available. The pier is similar to the one at Mountain Lakes, but with a length of 130 feet, required by the more gradual slope for reaching a sufficient depth for testing. An awning that can be moved along the pier was installed to protect personnel and equipment from heavy tropical rains.\n\nTransmitting and receiving booths are located on the pier. The electrical equipment of each is equivalent.\nFigure 70 is a general view of the Orlando testing pier. Figure 71 shows the Orlando pier from the laboratory. The transmitting booth can be seen at the right, and the receiving booth is at the far end. Figure 72 depicts the receiving booth and test basin at Orlando test station. A rotator designed for rotating a device around points other than the center of gravity is visible at the far end of the basin.\n\nUSRL Test Stations\nFigure 73 presents a sketch of an offset rotator and synchro-controlled rotator with an attachment for taking directivity patterns of a transducer inside a dome. The types of carriages, suspension rods, and rotors with synchro control are identical to those at Mountain Lakes. The carriage shown at the far end of the test basin in Figure 72 is especially designed.\nfor use in the rotation of devices around points other than the center of gravity. This carriage and an offset rotator proved so useful that a synchro control was added. A further attachment was designed for taking vertical directivity patterns, such as that of an echo-sounding projector inside a dome. In this case, the dome is turned on its side, the projector mounted inside at any desired bearing relative to the nose, and the two are then rotated together. These features are shown in Figures 73 and 74.\n\nFigure 74 shows the file electric equipment for the pier station. View of corrugated dome with special rigging for directivity measurements.\n\nHoused inside the main building with the panels arranged in an arc facing the lake, as shown in Figure 75. The operator is stationed between these panels and a desk for recording test data, and a window.\nThe pier view is given above. The electric apparatus is similar to that at Mountain Lakes, except for the recorder and high-power amplifier shown in Figure 78. The operation and circuit of the recorder have been described in Section 6.2.1. In this case, the drive by a double-armature motor is replaced by a magnetic clutch, which makes contact between the rails of the pen carriage and either side of a continuously revolving disk. Coordination of the oscillator and the paper drive is obtained by driving both with one motor. The bay on the extreme left of Figure 75 is the Orlando laboratory's electrical equipment arrangement. Figure 75 is part of the power amplifier system described above. It is capable of delivering 1,500 watts of electric power at frequencies from 2 to 100 kc.\nThe facilities provide interconnection with the electric system and measurement and control of power levels. A watt-meter developed by USRL is used, and a motor generator set supplies the 440-volt 3-phase power required.\n\nBarge System:\nThe barge's general view is depicted in Figure 76. The floor and frame are supported by 88 barrels, uniformly grouped beneath the floor and sectionalized for individual repair or replacement without significantly affecting buoyancy. A pontoon is installed on the side with the house containing the electric equipment to provide the necessary additional buoyancy due to uneven weight distribution. The barge is positioned using cables at the four corners, attached to mushroom anchors.\nanchors embedded in the lake bottom. Additional anchors of a screw type are connected by cables to winches which may be adjusted to level the barge and lower it in the water for greater stability. Equipment is transported from shore in a flat-bottom boat of 1-ton capacity and raised onto the barge with a swivel crane.\n\nFigure 76 shows the Orlando barge. The barge is equipped with hoist arms at each end and a boom crane for handling equipment.\n\nThe test basin is about 45 feet long and is fitted with steel rails which are spaced the same as at other USRL basins, to make possible the interchange of carriages between them. An overhead rail is used only in the center while wooden hoist arms, visible in Fig-76, are provided at each end of the test area. The hoists are lighter than a full-length rail and are better suited for this application.\nThe text handles long rods used on the barge for maximum water depth advantage. If surface and bottom are total reflectors, optimum testing depth is one-half total depth. But, if bottom is absorptive, deeper testing is beneficial. Tests are conducted at approximately one-half the water depth of 33 feet. Figure 77 depicts a line hydrophone mounted on a rod for testing at this depth. Hydrophones can be suspended horizontally or vertically and operated with a synchro-controlled rotator similar to the one on the pier.\n\nThe barge building houses a complete electric testing system, including facilities typically installed in transmitting and receiving booths on piers. Booths are not required here due to the short distance to the hydrophone.\nThe sending system is similar to that on the piers, but the detector is omitted from the receiving system, making the amplifier recorder responsive to any signal within the system's frequency band of 200 c to 150 kc. IJSRL TEST STATIONS become more susceptible to noise and interference as a result, but several fixed filters are available to restrict the receiving band when necessary to reduce noise levels. The linear recorder design is the same as that on the pier. The polar recorder is synchro-controlled from the rotator. The barge is also equipped for pulse testing with circuits identical to those at Mountain Lakes. The test-circuit cable from the pier is carried on the surface by drums spaced at various distances, while power and communication cables rest on the lake bottom.\nWhen tests are to be made over greater distances than the barge or pier areas permit, the distance is extended by a small triangular float which can be anchored anywhere in the lake and which is equipped with a simple hoist. This wide-hand system was used instead when it was available at the time the barge was built, whereas the construction of a heterodyne and filter system would have entailed considerable delay. It may be noted that all the early testing systems of IJSRL were of the wide-hand type.\n\nFigure 77. Attaching a line hydrophone to a special suspension rod on the Orlando barge.\n\nRecommendations for Improvements of the USRL Test Stations\n\nThe recommendations in this section will deal mainly with improvements and additions that may be made to the existing electrical and mechanical components of the calibration systems.\nImprovements and additions are of an immediate practical nature and several are in the process of development. The general purpose is to increase the accuracy and ease with which acoustic measurements are made and the resultant data converted into response, impedance, and other forms characterizing transducers (See Chapter 4).\n\nGeneral Improvements \u2013 Electrical\nUnder proper operating conditions, the stability of the electric equipment now installed at USRL test stations is approximately 0.1 db. Signal generators are designed with very little drift in frequency. The gain of each individual component is as uniform as possible over the frequency range for which it is designed. This is done so that the relation of gain to frequency is consistent. Part of the electrical system on the Orlando barge, including the linear recorder.\n\nRecommendations for Improvement\nFigure 79. Small triangular float which can be anchored anywhere in the lake. Note the diver\u2019s helmet useful for inspecting underwater equipment.\n\nFrequency for each component may be neglected in calculations. Although the present corrections lie within \u00b10.1 db, further improvement along these lines is possible.\n\nGeneral Improvements\u2014 Mechanical\nSince the purpose of mechanical systems in any acoustical calibration is to handle, hold, or orient devices, any improvement that reduces the time involved in rigging and measurement and still provides a minimum of interference in the sound field is recommended. To minimize the number of systems required, each should be designed to handle as many different devices as possible.\n\nElectromechanical Equalizer\nTransducer calibrations would be greatly facilitated if only there were projectors that provide a coherent signal.\nFigure 80. Schematic diagram of electromechanical equalizer.\n\nTo achieve a constant sound field over the entire frequency range, or hydrophones with uniform response for a constant field at all frequencies, or both, an ideal instrument is required. Though no such ideal instruments are available, the same result can be approached by proper control of the amplifier gain or, more conveniently, by control of the attenuation preceding a constant amplifier gain. The method is indicated in Figure 80.\n\nHydrophones are available that have been calibrated by reciprocity or other means. Using such an instrument with a fixed attenuation and amplifier gain, a recording is made as the projector sweeps over.\nFrom the hydrophone calibration curve, a curve can be plotted giving the strength of the sound field produced by the projector at each frequency. If a straight line is drawn parallel to the recorder axis and at some desired sound level, the difference between it and the projector curve will be the number of decibels by which the actual field differs from a constant one. If some device connected to the attenuator can be made to follow the curve and thus vary the output level so that it is proportional to the deviation of the curve from a straight line, the amplifier output will be at a constant level. In other words, the recording would be that of a flat hydrophone in a constant sound field. If the coupling loss of an unknown hydrophone is determined and the corrections are made accordingly, the recordings can be made consistent.\nThis loss added to the original curve results in a control curve that causes the attenuator to correct for variations in the projector output and coupling loss. If this hydrophone is placed in the field of the projector and its output is fed through the attenuator with its gain controlled by the curve, the hydrophone signal will have added, at every frequency, the number of decibels necessary to make its output what it would have been if the projector output had been constant. In other words, the record is the response of the unknown hydrophone in a constant sound field. The same technique would give a correction curve for a hydrophone and allow for direct calibration of a projector. Calibration by this method eliminates the time and errors involved in the point-by-point computations required at present.\nThe data are in a form that allows the calibration to be reproduced directly by photographing the recorded chart. Such a system is under consideration at USRL, USRL TEST STATIONS, and a tentative design is partially completed. The curve tracer mechanism is based on a light-beam and photoelectric cell null-balancing scheme.\n\nTransient Wave Analyzer\n\nIn the study of wave forms, the use of the Henrici analyzer for the measurement and analysis of transients has proven both time-consuming and expensive. Therefore, USRL later developed an instrument which not only can be constructed from inexpensive and easily available parts but also speeds up the process of analysis. (See Figure 81.) This transparent cylinder is rotated by a motor at about 1,800 rpm running between a light source on the inside and a narrow slit outside. The light passing through the cylinder is focused on a photosensitive surface, which records the waveform as a series of light and dark bands. The recorded waveform can then be analyzed by measuring the position and width of these bands.\nAn electromagnetic wave impinges on a photoelectric cell of the vacuum photomultiplier type. The circuit for amplification is shown to the right of the figure, and the power supply is at the left. A steady-state recording system, such as system 2, is used beyond this point.\n\nIn operation, an oscillogram of the transient is produced as an opaque stencil and attached to the surface of the cylinder. It is then rotated between the light source and the photoelectric cell, producing an electric signal corresponding to the transient which is repeated thirty times per second. The envelope of the amplitudes of the Fourier components of this signal is proportional to the spectral distribution of energy in the transient. This envelope can be obtained directly as a function of frequency using system 2 with the 300-c band, which will average.\nSeveral adjacent harmonics. The record obtained will be independent of the lowest Fourier frequency as long as it is small compared to 300 c. Changing the frequency and amplitude of the linear sweep corresponds to changing the scale factor in a Henrici analysis (See references 58 and 79). Calculations made from this record are identical to those from the Henrici analyzer.\n\nAfter careful adjustment to eliminate distortion, several transient sounds from Navy devices were analyzed by this method. The results were carefully checked to determine their validity. The accuracy of the reproduction was tested by viewing it on the CRO, and the broad-band rms level of the original transient was compared with the one delivered by this apparatus. As an additional check, a square wave was analyzed. Since the Fourier analysis of this waveform provides known frequencies and amplitudes, the results obtained from this method could be compared with the theoretical values.\nThe analysis of the optical signal generator in the apparatus for transient analysis is mathematically known, allowing for comparison with theoretical values. Good agreement was found between the two. Minor improvements can be made, but the instrument is workable and has adequate precision. The speed and facility for analyzing pulse signals have been significantly improved. This method can be applied to electrical pulses from any source.\n\nIf no analyzer such as system 2 is available, the amplitudes of the Fourier components can be determined using a commercial electric harmonic analyzer. However, the phases of the components cannot be determined by either method.\n\nFor a more complete characterization of transducers, an instrument is desired which measures the phases of the components.\nThe phase difference between the acoustic signal and the electric signal is beneficial, especially for analyzing transient wave forms. Phase bridges exist to measure the relative phase between two electric signals, limiting measurements in acoustic tests to the difference in phase between the current into a projector and the voltage generated by the hydrophone. However, the reciprocity relation of a transducer indicates that the phase shift between the current and the generated pressure when acting as a projector, minus the phase shift between the applied pressure and the open-circuit voltage when acting as a hydrophone, is either 180 or 0 degrees for a magnetostrictive or piezoelectric transducer.\n\nRecommendations for improvement:\nThis assumption or preferably an exact knowledge of the phase constant plus the phase shift is required.\nMeasuring the three combinations of a projector, hydrophone, and reversible transducer would provide sufficient data to determine the phase shift between the hydrophone's incident pressure and its generated voltage. The time delay in the acoustic medium must be accounted for, but once standardized, an unknown could be determined by comparison. Such measurements have not been made by the Underwater Sound Reference Laboratories to date.\n\nAn effective instrument for analyzing noise and characterizing transducers is a continuously variable width band-pass filter centered at any given frequency. The previously described filter of this nature requires excessive auxiliary equipment and is cumbersome to use. A simpler and more practical alternative is needed.\nA self-contained one is most desirable. For example, it is often important to describe a hydrophone's performance in terms of the response to a given band width of noise centered at a specific frequency. Such a filter could be readily used in conjunction with a noise source to provide the necessary signal.\n\nImproved Pulse Recorder\nOne inconvenience of the present pulse recorder is the fact that its sensitivity and performance are not independent of the pulse length and rate of repetition. Overcoming these difficulties is desirable.\n\nRecording Impedance Bridge\nA continuous-recording impedance bridge would be of great value to any laboratory concerned with electric and acoustic measurements. The recording wattmeter already described can be used for impedance measurements and with high accuracy if combined with an insertion-type phase bridge mentioned.\nThe ratio of voltage to current and phase could be determined by the amount of attenuation required by the two null-balancing circuits in above systems. Recorders similar to those used in USRL laboratories would provide a continuous record of the attenuation, thus a continuous record of the phase and magnitude of the impedance.\n\nAbsorbing Materials\n\nA perfect absorbing material would provide almost ideal testing conditions in small spaces. It is believed that there is a possibility of producing better absorbing materials or combinations of materials than those developed up to the present time. Any improvement along these lines would be beneficial not only for calibration techniques but also for the design and application of acoustic devices.\n\nThe directivity index of a projector is necessary.\nThe index for calculating its efficiency is generally obtained through computation from directivity patterns, but this can only be done with limited accuracy due to the large amount of time required for these computations. The University of California Division of War Research built a system for making direct measurements of the directivity index. This system involves rigging the projector to be rotatable and integrating the acoustic output over the surface of a surrounding sphere using a watt-hour meter. The directivity index is the ratio in decibels of this integrated power to the area of the sphere times the acoustic power per unit area on the acoustic axis.\n\nChapter 7\nCOMPUTING FROM TEST DATA\nBy Eginhard Dietze and L. Pauline Leighton\n\nThe method for calculating an instrument's calibration from test data is described in this chapter.\nChapter. Refer to Chapter 6 for the procedure of taking test data and Chapter 4 for the theoretical background of these computations. For a numerical example, the calibration of a transducer is given since such a unit can be operated as both a receiving and sending device, allowing the illustration of both types of computation.\n\nSection 7.1 Receiving Response\n\nTo test the receiving response over a wide frequency range, several sets of tests with a number of projectors may need to be made. However, since the computation is the same at all frequencies, only one set of data is discussed here, and the numerical computation is limited to one frequency, 25 kc.\n\nIt is assumed that calibrated standards are available so that the comparison method may be used. This is the usual test procedure as discussed in Chapter 6.\nThe computation of the calibration of standards by reciprocity is discussed in Section 7.4. Several standards are typically used in one test to provide a mutual check on their performance. In this discussion, however, attention is confined to a single standard, a type 3A hydrophone. The calibration of the 3A standard, serial No. 89, used in this illustration is shown in Figure 1.\n\nFigure 1. Calibration of 3A89 crystal hydrophone.\n\nThe data furnished by the test station are illustrated by the receiving response charts. Figures 2 and 3, and by Figure 4, which shows a log sheet applicable to these tests. Figure 2 shows a receiving chart for the 3A89 hydrophone and Figure 3 a receiving chart for the transducer under test. The conditions of the tests applicable to these two receiving charts are stated on the log sheet, from which can be obtained:\n\nFigure 1: Calibration of a Type 3A hydrophone (Serial No. 89)\nFigure 2: Receiving chart for the Type 3A hydrophone (Serial No. 89)\nFigure 3: Receiving chart for the transducer under test\nFigure 4: Log sheet for the tests\n\nThe conditions of the tests applicable to Figures 2 and 3 are stated on Figure 4.\n1. The testing distance for the source and hydrophone.\n2. The available power used for the projector.\n3. The receiving amplifier gain used in the tests.\n4. A reference to the circuit sketch for this test.\n\nWith these data, calibration can proceed. The first item to be checked is whether the same testing distance was used for the test unit as for the hydrophone standard. If not, the readings must be corrected to the same testing distance using the formula given in Chapter 4, where d and do are the testing distances for the test unit and for the hydrophone standard respectively.\n\nIt will be recalled that the receiving response is usually expressed in terms of the generated voltage of a hydrophone. An exception to this rule is in the calibration of 3A hydrophones, in which the response is expressed differently.\nThe voltage is expressed in terms of the voltage across 135 ohms. The receiving charts provide the level (in db vs 10-12 watt) impressed on the recorder. Corrections must be applied to obtain the generated voltage of the hydrophone from the chart readings. Corrections include (1) the receiving amplifier gain, and (2) the coupling loss. By the latter is meant the loss (or gain) in the voltage applied to the input of the receiving amplifier as compared to the generated voltage of the hydrophone. Since the loss in the line from the pier to the receiving amplifier is included in the system calibration, the voltage at the line terminals may be substituted for the voltage at the input to the receiving amplifier.\n\nReceiving response (Figure 2): Receiving response chart, 3A89 hydrophone vs AX70 projector. Reference run No. 1 on log sheet (Figure 4).\nFigure 4 log sheet refers to the circuits used for the standard and transducer under test. These circuits are reproduced in Figures 5 and 6. The transducer was connected to a balanced coupling amplifier and a 135-ohm receiving line. To evaluate the coupling loss of this amplifier, two measurements were made, as shown in Figure 7. The first measurement is depicted in Figure 7. A voltage measurement was taken between the transducer and the amplifier input, and the output voltage was measured. The second measurement was taken with the transducer disconnected from the amplifier input, and the output voltage was measured. By subtracting the output voltage with the transducer connected from the output voltage with the transducer disconnected, the coupling loss can be calculated.\n\nFigure 3. Receiving response chart, QB No. Ill vs AX70 projector. Reference run No. 2 on log sheet (Figure 4).\n\nLOG\nPROJECT t^0.00 DATE\n_TEST STATION / SYSTFM;\n-COPIES TO STATION FILE AND N. Y OFFICE -2\n-SHEET NO. H_\n\nWater temperature\nTransmitting frequency-KC\nRates\nReceiving\nRun No.\nTime\nProj.\nType-No.\nPier\nPos.\nCM\nDepth\nCM.\nAvail.\nPower\nSingle.\nRange, or\nMid-Band\nBand W with PULSE\nHydro\nType-No.\nDepth\nCM\nHorii\nDisc\nCM\nSys\nFigure 4. Sample log sheet covering calibration of QB No. Ill transducer.\n Age was applied to the receiving line from a very low impedance, 0.034 ohm, as shown in (a) Figure 7; this same voltage was then applied to the receiving line of the 3A89 hydrophone (Figure 5).\n Figure 5. Circuit used in obtaining reference receiving response chart, 3A89 hydrophone.\n Figure 6. Circuit used in obtaining receiving response chart, QB No. Ill transducer.\n\nGtype DB Type Color Let- REF. CCT Deg. C Depth CM Tf Rec Lgth-MS Dly MS Rte PPS s-p Ppf IPM Ron RPM Zo Level Te Rec R BL A I too Tn R BL B H AX70 ft tf CO G C m o-no fX d R C ur yO Zn II J R BL D IT QB^in lOO 2i,i IO-C,o nf) R R E :sL YTL Ai R G E \u25a0Cu'nA J T rLOG(10 -4-4) \u2018R-RESPONSE; CI-C PL'G IN CC ic'PnroDT mAK \u2022 IN-INH N T NolSt Na-NO SE ACTi TN i-pRoj a jR; fe-rn LT A & 2 PROJ PR\n\nType G\nDB\nColor\nLetter\nREF. CCT Degree C\nDepth CM\nTf Recording\nLength-MS Delay MS\nRte Route\nPPS Samples per second\ns-p Seconds per pulse\nPpf Impedance matching factor\nIPM Impedance matching level\nRon Resistance\nRPM Revolutions per minute\nZo Output impedance\nLevel Test\nTe Testing\nRecording\nBL Black\nA Isolation amplifier\nI Input\ntoo Two\nTn Transducer\nR Black\nBL Black\nB Bias\nH Hydrophone\nAX70 Axial hydrophone model number\nft Feet\ntf Transducer model number\nCO Coupling\nG Gain\nC Calibration\nm Microphone\no-no On\nfX Frequency\nd Distance\nR Recording\nC Calibrator\nur Urchin\nyO Year\nZn Zone\nII Identification\nJ Journal\nR Black\nBL Black\nD Data\nIT Identification tag\nQB^in Quadrature bridge input\nlOO Log\n2i,i Two inches\nIO-C,o Input/output connector\nnf) Not for calibration\nR Recording\nR Recording\nE End\n:sL Sound level\nYTL Yearly test log\nAi Amplifier\nG Gain\nE End\n\u25a0Cu'nA Calibration number\nJ Journal\nT rLOG(10 -4-4) Response time log, 10 to the power of -4, 4 seconds\n\u2018R-RESPONSE Response\nCI-C Calibration identification\nPL'G Plug\nIN Input\nCC Calibration check\nic'PnroDT Identification code for transducer\nmAK Make\n\u2022 IN-INH Inhibit\nT Nolst Not applicable\nNa-NO Not available\nSE Serial number\nACTi Action\nTN Test number\ni-pRoj In process\na Approximate\njR; Just record\nLT Level test\nA & 2 Projects PR Projects 1 and 2\nThe amplifier, shown in (b) of Figure 7, amplifies the signal through the coupling amplifier. The recorder traces in Figure 8 demonstrate that both measurements were made using the same receiving amplifier gain. Therefore, the difference between the two traces determines the coupling gain or loss. The loss is 6.2 db at 25 kc.\n\nThe generated voltage of the test instrument relative to the voltage of the 3 A hydrophone across 135 ohms can be computed as follows:\n\nDifference in receiving chart readings: 15.2 db (from Figures 2 and 3)\nCoupling loss for test hydrophone: 6.2 db (from Figure 8)\nDifference in receiving amplifier gain: 4.0 db (from Figure 4)\nDifference in available power to projector: 0 db (from Figure 4)\nDifference in testing distance: 0 db (from Figure 4)\n\nWith the calibration of the hydrophone standard\nFigure 1: The receiving response of the test instrument can be obtained as follows: The response of the standard, according to Figure 1, is -98.2 dB vs 1 volt for a sound field of 1 dyne per sq cm at 25 kc. The response of the test instrument, according to the above computation, is 17.4 dB.\n\nThreshold and Impedance\n\n---\n\nREC LINE\nA\nREC LINE\nB\n\nFigure 7. Circuits used in obtaining coupling loss for 3A89 hydrophone. (A) For measuring input voltage (see run No. 4, Figure 4). (B) For measuring output voltage (see run No. 3, Figure 4).\n\nThe result obtained is that the projector at 25 kc has a receiving response of -80.8 dB vs 1 volt per dyne per sq cm.\n\nThe preceding computation, which was carried out at one frequency only, is repeated at selected frequencies throughout the entire frequency range.\nFrom these data, a response characteristic is plotted as shown in Figure 9. In these particular tests, a 3A hydrophone, which is a pressure-actuated device, was employed as a standard. If the hydrophone standard is of the pressure-gradient type, such as the 1A or 2A hydrophone, it generates a gain in the voltage, especially at low frequencies, due to the curvature of the wave front. Figure BALANCED COUPLING AMPLIFIER 13 in Chapter 5 shows the magnitude of the spherical wave correction for different testing distances, plotted against frequency. The indicated response of the test hydrophone, because of this gain in the hydrophone standard (if the latter is of the pressure-gradient type), is lower than it would be if the tests were made in a plane-wave sound field. To refer to plane-wave conditions, therefore, the relative response must be correspondingly increased.\nAfter determining the receiving response characteristic, the threshold characteristic can be computed using Equation (18) in Chapter 4, which provides an expression for the threshold pressure. The pressure depends on the hydrophone's resistance and response. Therefore, it's necessary to compute this resistance. The chart in Figure 10 displays readings for the projector taken at the test station using the 5A impedance bridge. This bridge provides the admittance in terms of parallel resistance and capacity values. Since the bridge can measure impedances below 1,000 ohms directly, it's necessary to shunt the unknown impedance whenever it exceeds that value. The bridge shunt resistance is given in Figure 10 as Rs, and the bridge resistance reading is Ri.\nFigure 8. Chart of coupling loss for 3A89 hydrophone.\nOpen circuit volts in dB vs I volts.\nComputation from test data.\n\nFrequency kC.\n\nFigure 9. Receiving response of QB No. 1 1 1 transducer.\n\nThe first step in computing the impedance from the values on the chart is to compute the unknown parallel resistance, which is:\n\nFrom the computed shunt resistance R and the shunt capacity C (given in microfarads on the chart), the equivalent series resistance r and series reactance x are then computed by means of the formulas:\n\nR = 1 / [(1/R) + (wC/o)]\nx = wL - 1/[R * (wC/o) + 1/R]\n\nThis process, carried through numerically at 25 kc, gives:\n\nRp:Rb\nImpedance\n\na. Test Station\nProject Ho. 9\nPerice; Designe QB/H\nMeasuring conditions:\nCrtMsdig effects\nBridges and accessories:\n^jC. A leakage resistance:\nBridge_\u00a3A_\nLead to lead\nDetector 3/ ATh^S\ng-QV >30^7Sfieldsto Case\nCarretta of Pridee, head of Skaatiag Besistaace,\nvalued of Pridee Besistaace against Skaatiag of Uakowa.\nCheck the first column after \"B^\" in the tables,\nCates aakaovB cas beea skaated by B-.\n-CJ* Talae of Bridge Capacitance balanced against Capacitance of Caknowa.\nTalae of Bridge Capacitance with Indactaace of Uakona.\nleads to leads ofciis\nokield\nfSkieldsio Case >_^\n2UL\n'ogogy\nSO\n/QOS S'\nJ Li-\n\nThis computation is repeated at other frequencies,\nand an impedance characteristic is plotted for the instrument, as shown in Figure 11. The threshold is then computed by means of equation (18) in Chapter 4.\n\nThis computation at 25 kc is as follows:\nFigure 10. Sample data sheet giving 5-impedance bridge Figure 11. Impedance characteristic of QB No. Ill readings obtained in measuring the impedance of the QB transducer.\nFigure 12 is the transmitting chart of the QB No. Ill transducer's 3.A89 hydrophone (refer to run No. 5, Figure 4). Transmitting tests are similar to the receiving tests described above. The transmitting chart of the projector, using the same 3A hydrophone standard as in the receiving tests, is shown in Figure 12. Consult Figure 4 for the log sheet details of this run.\n\nThe log sheet indicates that the projector was supplied with 160 dB power compared to 10^-12 watts (i.e., 1 watt) from 135 ohms. The test circuit used in the transmitting tests is depicted in Figure 13. The receiving amplifier gain, as stated in the log sheet, is 4 dB, and the testing distance is 250 cm.\nFrom this information, it is possible to compute the transmitting response. This computation is carried out numerically at 25 kc as follows:\n\nChart reading: vs 10-16 watt in 135-ohm circuit . -t-118db\nCorrection for receiving amplifier gain: -4 db\nCorrection for testing distance: 20 log 2.5/1 . -t-8db\nCorrection for available power referred to 1 available watt: 0 db\nLevel at hydrophone terminals: <'s 10-16 watt in 135-ohm circuit -l-122db\n\nTo obtain the pressure in the sound field, it is now necessary to refer to the calibration of the 3A hydrophone shown in Figure 1. This calibration is in terms of db vs 1 volt. The computed level at the hydrophone must, therefore, be changed into these terms.\n\nThis correction is as follows:\n\nWhen the power dissipated in a 135-ohm resistance is 10^3 watt, the voltage across that resistance is given by the relation:\n\nV = SQRT(P * R)\n\nWhere SQRT denotes the square root, P is the power in watts, and R is the resistance in ohms.\n\nTherefore, when the power at the hydrophone terminals is 10-16 watt, the voltage across the 135-ohm resistance is:\n\nV = SQRT(10^-16 * 135)\n\nUsing a calculator, we find that V = -121.9 dB volts.\n\nTo convert this to decibels referenced to 1 volt, we use the formula:\n\nL = 20 * log10(V/1)\n\nSubstituting the value of V, we get:\n\nL = 20 * log10(-121.9/1)\n\nUsing a calculator, we find that L = -131.9 dB.\n\nTherefore, the pressure in the sound field is given by:\n\nP = 10^(L/20)\n\nSubstituting the value of L, we get:\n\nP = 10^(-6.595)\n\nUsing a calculator, we find that P = 3.98 x 10^-7 Pa.\nPOWER (dB re 1 V) vs WATT\nBATTW SUPPLY\n\n3A MYBROPMONE\nI\nREC LMC\n4* 'V* SCREEN\nelevation\n\nFigure 13. Circuit used in obtaining transmitting chart, QB No. 11 transducer.\n\nCOMPUTATION FROM TEST DATA\n\nThe voltage delivered by the 3A hydrophone consequently is -98.2 dB re 1 V. For the voltage to be -16.7 dB, the sound pressure must have been 81.5 dB above 1 dyne/cm\u00b2. Thus, the transmitting response of the projector at 25 kc is +81.5 dB re 1 dyne/cm\u00b2.\n\nFigure 14. Response characteristics of transmitting and receiving systems during calibrations.\n\nThe voltage delivered by the 3A hydrophone consequently is -98.2 dB re 1 V. For the voltage to be -16.7 dB, the sound pressure must have been 81.5 dB above 1 dyne/cm\u00b2. Therefore, the transmitting response of the projector at 25 kc is +81.5 dB re 1 dyne/cm\u00b2.\n\nFigure 15. Transmitting response of QB No. Ill transducer.\nThe electrical system is usually adjusted at one frequency, and the sensitivity may vary somewhat with frequency. When this is the case, a compensating correction must be made in the transmitting response. Figure 14 shows response characteristics of the transmitting and receiving systems used in the present tests. At 25 kc, this correction amounts to about 0.5 db. The transmitting response must therefore be increased by this amount; the transmitting response is actually 82.0 db vs 1 dyne per sq cm. This computation, when carried out over the frequency range, gives the transmitting response characteristic of the projector, shown in Figure 15. After the transmitting response has been obtained, the projector efficiency is computed. This requires a knowledge of the directivity at the frequency at which the computation is made. Figure 16 shows a directivity.\nChapter 4 describes the method for computing the directivity index from graphical charts in the directivity pattern of a projector taken at 25 kc. Since the side lobes of this pattern are low, the computation can be based on the relationship between the beam width and the directivity index for a circular piston (refer to Figure 7 in Chapter 4). The beam width in this case is 19.8 degrees, resulting in a directivity index of -24.2 dB.\n\nEquation (8) in Chapter 4 provides the expression for reciprocity calibration of standards:\n\nFigure 16 displays the measured directivity pattern of QB No. Ill transducer at 25 kc. The directivity index is computed from this pattern using the projector efficiency. The only unknown factor in this expression is 10 log PjIPa- which can be evaluated from the projector's impedance.\nThe source impedance (see explanation in Chapter 4); Li43.7+ is Ti\nThe efficiency can now be stated\n\nReciprocity Calibration of Standards\n\nThe comparison method of calibrating acoustic devices depends on the availability of standards whose calibration is accurately known. The next problem then is to calibrate these standards. As discussed in Chapter 5, the best method for obtaining an absolute calibration is by means of the reciprocity principle, which permits a determination of the response from purely electrical measurements. The reciprocity calibration requires considerably more work and is more critical than a relative calibration. Therefore, its use should be confined to the fundamental calibration of hydrophone standards, with which all other instruments can then be compared.\n\nThe relation by means of which the reciprocity calibration is made\nThe equation for obtaining the hydrophone response is given in Chapter 5. In decibel form, this equation is:\n\nL = 20 log {10^(-12) * I / (J * pc)}\n\nWhere L is the response in decibels, I is the current flowing through the device, J is the reciprocity constant, and pc is the sound pressure in pascal. The term J for water for various testing distances is shown in Figure 17.\n\nThe term I is the open-circuit voltage generated by the device in a given sound field, V is the open-circuit voltage generated by an auxiliary transducer in the same sound field, and Vd is the open-circuit voltage of the device in the sound field produced by the auxiliary transducer when a current i flows through it.\n\nThe data are usually furnished by the test station in terms of level in dB re 10^-12 watt rather than voltage. The matter of translating levels into dB re 1 volt is discussed in Section 7.3. Since most of the circuits used at the test stations have an impedance of 135 ohms.\nIn this case where the correction is -138.7 dB, the above equation can be written in terms of levels:\n\nUsually, the same transducer is used for calibrating a number of hydrophones. Then, the following quantities, which are independent of the particular hydrophone being calibrated, can be computed and the result used as a constant k in other reciprocity computations:\n\nComputation | Ptest | Data\nKilocycles per second\n\nFigure 18. Receiving chart. 1K13 projector acting as a hydrophone vs 1K25 projector acting as a sound source.\n\nIn the following, the absolute reciprocity calibration of a 3A hydrophone is carried out at 1,000 cm using test data obtained at the station. In these tests, the 1K13 projector was used.\nused  as  the  auxiliary  reversible  transducer  and  the \n1K25  as  the  other  sound  source. \nFigure  18  shows  a receiving  chart  for  the  1K13  pro- \njector, taken  with  the  1K25  projector  acting  as  the \nsound  source. \nThe  pertinent  test  conditions  are  recorded  as  usual \non  a log  sheet.  The  following  information  at  1,000  c \nis  taken  from  that  sheet: \nTransmitting  conditions  for  1K25  projector \nSource  impedance  = 4 ohms \nAvailable  power  =150  db  vs  10  \u2014 16  watt \nTesting  distance  = 45.7  cm \nReceiving  conditions  for  1K13  projector \nCoupling  loss  = 0.6  db  (as  shown  by  chart  readings\u2014 \nsee  Section  7.1) \nReceiving  circuit  = 135  ohms \nReceiving  amplifier  gain  = 30  db \nFigure  19  shows  a chart  of  the  current  in  the  1K25 \nprojector  when  150  db  vs  10\u201c^\u00ae  watt  available  power \nis  supplied  to  it  from  a 4-ohm  source.  In  order  to  con- \nvert the  current  chart  reading  into  db  vs  1 ampere,  it \nThe current-measuring circuit calibration is necessary. In this case, the calibration is as follows: The level indicated by the recorder when 1 ampere flows in the current-measuring circuit is 112 dB vs watt. Therefore, 112 dB must be subtracted from chart readings.\n\nIn addition to the chart in Figure 17 providing the value of the reciprocity constant J, the charts in Figures 18 and 19 are sufficient for the computation of the constant k.\n\nIt is desirable in this computation to reduce all values to a standard test condition for subsequent hydrophone tests whose absolute calibrations are to be obtained. This test condition will be based on (1) an available power level for the projector of 160 dB vs 10-12 watt, and (2) a testing distance of 30.5 cm.\n\nThe value for the reciprocity constant J can be read from the charts.\nFrom the chart in Figure 17, at a testing distance of 30.5 cm, this figure is -164.3 dB. The level received in the 135-ohm circuit is obtained as follows:\n\nReceiving level reading (Figure 19) + 107.6 dB vs. 10 - 16 watt\nCorrection for receiving amplifier gain -30.0 dB\nCorrection for coupling loss +0.6 dB\nLevel received in the 135-ohm circuit: 78.2 dB vs. 10 - 16 watt\n\nThis level must be reduced to standard conditions by two corrections:\n\n1. The measurement was made with a projector as the sound source at a distance of 45.7 cm. If the measurements had been made at 30.5 cm, the level would have been increased by:\n\n2. The available power into the projector was 150 watts.\nWith 160 dB available power, the level would increase by +10.0 dB. Making these two corrections, the current chart reading in Figure 19 at 1,000 c is 127 dB vs 10-i\u00ae watt. From this reading, subtract the receiving amplifier gain of 40 dB and the correction factor of 11.2 dB, as stated above. In addition, add 10 dB, as the standard test condition uses an available power level of 160 dB rather than 150 dB. Thus, the constant k is obtained:\n\nThe reciprocity calibration of any desired hydrophone can now be obtained from two receiving level charts, L1 and L2, taken of that instrument with the 1K13 projector and with the 1K25 projector. These data must be for the test condition for which k was calculated.\nThe testing distance is 30.5 cm and the available power is 160 dB for both Figures 20 and 21, which feature receiving charts for the 3A74 hydrophone using the 1 K13 and 1K25 projectors, respectively. No corrections for testing distance or available power are necessary. However, a correction of 20 dB must be made for the receiver amplifier gain. Since the hydrophone was across a 600-ohm line in both tests, no coupling correction is required when considering the output voltage from the receiver.\nThe preamplifier reading at 1,000 c is 114.8 dB vs watt. Correcting for the receiving gain (20 dB) gives 94.8 dB vs 1 volt across 600 ohms for a sound field of 1 dyne per sq cm.\n\nFrom Figure 20, the reading at 1,000 c is 114.8 dB vs watt. After correcting for the receiving gain (20 dB), the absolute calibration of the 3A hydrophone can be computed as:\n\n= -95.0 dB vs 1 volt across 600 ohms\n\nChapter 8\n\nProduction Testing of Sonar Transducers\nBy Erwin F. Shrader\n\n8.1 General Considerations\n\nProduction testing differs from type testing. Before adopting a design, careful calibrations must be made on several samples or pre-production models. These models are then taken out to sea for performance tests. Several modifications are often made to the original design before it is acceptable. Once a satisfactory type is finally evolved, production testing begins.\nThe manufacturer proceeds with the production of the device. Specifications are set up to make the product as similar to the samples as possible. To ensure this, tests must be made on each unit. Production testing involves calibration, albeit in simplified form.\n\nA production testing program serves two purposes:\n1. It ensures that each product meets certain specifications.\n2. It permits quality control, that is, a running check on the quality of the manufactured products which notes and corrects any deviations from the accepted standard.\n\nRegardless of the nature of the test or the device under consideration, certain basic requirements must be met in order to have a successful production test. The procedure must involve a relatively simple technique not requiring highly trained personnel. The time required should be considered as well.\nTests for each measurement must be short and not influenced by conditions beyond the operator's control, such as noise interference or water temperature.\n\nProduction testing of a sonar transducer consists of two parts: (1) tests of physical strength, watertightness, and electrical element polarity, and (2) acoustic measurements of directivity, response, and impedance. This chapter focuses on tests in the second category.\n\nRegarding acoustic production tests, lakes and rivers are typically excluded as testing sites for the following reasons: (1) they are usually located away from the factory, (2) conditions may not be adequately controlled for routine testing, and (3) they may be subject to water traffic noise. An indoor tank in the factory offers a more suitable solution.\nThe best chance of circumventing these difficulties while still meeting the requirements of simplicity, speed, and sufficient accuracy involves considering methods to eliminate reflections and correct for proximity effects in a confined body of water (Chapter 5 for complete discussion). In the context of acoustic production testing procedures, these methods will be explored.\n\n8. Production Test Measurements\n\nThe acoustic properties of a sonar transducer have been discussed in Chapters 4, 5, and 6. A comprehensive description of a sonar transducer necessitates knowing the receiving or transmitting response as a function of frequency.\nPedance functions as a function of frequency and the direction patterns at several frequencies in one or more planes, depending on the symmetry of the device. Since the test requirements for each of these measurements are not identical, it is necessary to discuss the requirements for each measurement separately and evolve a test procedure that satisfies the maximum demand of each test. It should be kept in mind, however, that each type of transducer will be a special problem and that, in many cases, certain measurements may be considerably simplified and sometimes even eliminated.\n\nResponse Measurements:\nFor a production test of response, an absolute measurement is not necessary. The response of the transducer can be compared directly with that of a secondary standard, which may be a transducer of the same type.\nMeeting manufacturing specifications requires the calibration of the secondary standard from a complete free-field calibration. Relative impedance measurements are included since they depend on the acoustic terminating impedance of the transducer.\n\nProduction testing of sonar transducers involves measuring response in a production test performed in a comparatively small tank. This test may involve a smaller testing distance than required to render proximity effects negligible. However, such a test can be satisfactory if there is a definite correlation between comparison measurements on the standard and on the units under test at large and small distances.\n\nUnless proper precautions are taken, response measurements made in a tank are not precise due to interference between the direct and reflected waves.\nIf testing distances due to proximity effects are not too large, a fairly small tank with walls having 15-20 dB absorption can be used. Such absorption reduces the intensity of reflected waves sufficiently to reduce the error in the axis response to \u00b11 db (under steady-state conditions). If the units to be measured are directional, and directional standards are used, the sources of the more bothersome reflections can be treated with the recently developed \"bubble\" layer, which provides 5-10 dB absorption and probably renders negligible the overall remaining reflection interference (See Chapter 6). In addition to, or in place of, the use of absorbing walls, electrical methods for eliminating reflection effects can be employed. These methods\nThe use of noise or frequency warble, or pulses for involvement in testing transducer response is discussed in Chapter 5. The advantages of these methods depend on the response nature of the transducer being tested, as each method involves a loss of resolving power in continuous-wave response versus frequency. For a unit with fairly uniform response (Q small), all methods are quite satisfactory since little resolving power (RP) is required (RP = Q). For a highly resonant transducer, the use of all these methods with a tank of given size is limited by resolving power consideration. The resolving power must exceed Q, implying a minimum allowable path difference AL between direct and reflected waves, greater than, for example, greater than 3 meters for f = 25 kc and Q = 50.\nThe relative merits of continuous-wave noise or warble: C an absorbing tank approximately 3 ft long by 1.5 ft wide by 2.25 ft deep has been built by the Bell Telephone Laboratories.\n\nVersus pulses, the latter may be considered superior, since with their use reflections can be eliminated completely from measurements, while with the former the reflections are averaged in and yield a time-independent, but not always known, correction.\n\nImpedance Measurements: The measured electrical impedance of a transducer depends on the terminating acoustic impedance. (See Chapters 3, 4, and 5.) This fact deserves consideration because the presence of reflected waves incident on it.\nThe face of the transducer causes a change in the terminating acoustic impedance, which affects any electrical impedance measurement. If impedance measurements are made in a tank with absorbing walls, reflections may be small enough to allow measurements to be made conventionally with an impedance bridge. On the contrary, when reflections are appreciable, their effect can be eliminated by pulsing. The pulse length is presumably determined by the same criterion as in directivity pattern and response measurements (see Section 8.2.3). For pulse measurements, a wattmeter with a time constant small compared to the length of the pulse may be used. In this case, the impedance is obtained from voltage, current, and power.\n\nSection 8.2.3 Directivity Pattern Measurement\nThe measurement of directivity patterns imposes specific requirements.\nThe most severe test requirements are primarily due to the fact that measurements of intensity 40 or 50 dB below the response on the axis must be made in competition with reflections of the main beam. Even with the best available absorbing materials, it's impossible to prevent some reflections from interfering with the measurement of a moderately directional transducer's directivity pattern. Noise and frequency warble are not suitable for directivity measurements because they average an interfering reflection of unknown magnitude with the direct signal. The error introduced thereby may be considerable for certain directions, such as when a direct signal received is drowned out by a reflection.\n\nThe recording wattmeter described in Chapter 6 can be used in conjunction with a pulse recording system. This system has the additional advantage of being able to measure the instantaneous power in the transducer.\nimpedance  at  high  power  levels  without  unduly  heating  the \ntransducer. \nTANK  DESIGN  CONSIDERATIONS \noff  the  axis  of  maximum  response  is  averaged  with  a \nreflection  incident  on  the  projector  axis. \nPulse  measurement,  therefore,  is  the  only  feasible \nmethod  for  obtaining  directivity  patterns,  and  even \nthis  method  has  its  limitations.  As  noted  above  in  the \ndiscussion  of  response,  and  as  described  in  detail  in \nChapter  5,  the  pulse  method  discriminates  against  re- \nflections by  measuring  the  direct  signal  before  the \nreflection  arrives.  The  time  elapsing  between  the  ar- \nrival of  the  direct  and  reflected  signals  is  a function  of \nthe  size  and  shape  of  the  testing  tank.  The  practical \nlimits  to  the  maximum  allowable  size  of  such  a tank \nrestrict,  in  turn,  the  maximum  length  of  time  during \nwhich  the  pulse  measurement  may  be  made.  The \nmaximum  elapsed  time  needed  for  a significant  meas- \nThe response of a transducer to a suddenly applied sinusoidal signal determines the measurement of its impedance. For transducers with a uniform frequency response characteristic, the response reaches its steady-state value quickly, within a few cycles, allowing for short pulses and testing distances. In contrast, for resonant transducers, the time required for the response to reach steady-state is long. In such cases, directivity patterns can only be measured using long pulses, necessitating long testing distances.\n\nThe minimum allowable path difference AL between the direct wave and any reflected wave, a quantity greater than the pulse length, is a quantitative criterion given above as AT > cQlf. A theoretical analysis indicates that a\nThe shorter pulse length in a highly resonant transducer allows for a smaller minimum path difference when determining the directivity pattern at the resonance frequency. The criterion for AL in this case is AL equal to transducer diameter. However, this theoretical analysis assumes the transducer diaphragm moves rigidly, a condition not typically met in practice. The measured directivity pattern should closely approximate the pattern obtained at large distances. To meet this requirement, the test distance should be such that proximity effects are small, i.e., the spherical wave correction should be less than a few db. [Reference 55 reports on the investigation of the effect of pulse length on pattern for a representative resonant transducer (Q ^ 50) operating at the resonance frequency.]\nThe questionable comparison of patterns taken at shorter test distances with corresponding patterns on a secondary standard is uncertain. There is undoubtedly some correlation between the directivity patterns of the standard and the test unit in general, but the relationship is in fact a complex one.\n\nDiscussion on Tank Design Considerations\n\nSince the pulse method is considered best for directivity measurements, the specifications for a tank suitable for this method will be addressed. Assuming that the test distance and pulse length are chosen based on the previous discussion, the absorption of the tank walls is of minor significance for pulsing. However, steady-state measurements of response and impedance are often required to be made in the same tank. For these measurements, the absorption of the walls should be maximized.\nPracticable. Tank walls made of wood or concrete offer several decibels of absorption. If the concrete tank is set in the ground, the damp earth provides additional acoustic loss on reflection. A steel tank is to be avoided, if at all possible, because of the high reflection coefficient. A bubble layer may be applied to the walls to increase absorption if necessary. The maximum repetition rate of the pulses used depends on the reverberation time of the tank. If a high repetition rate is desired for ease of measurement, some wall absorption should be supplied. While many tank shapes are possible, the simplest to build is a rectangular one as deep as it is wide. It can be shown that, for a given testing distance and reflection path length, the minimum size is obtained when the line joining the projector and hydrophone aligns.\nThe assumption that reflection path lengths from the sides, top, and bottom of the tank are equal to those from the ends results in a parallel arrangement with the long dimension of the tank. For this configuration (Figure 1), the tank length is given by I = d + AL, where I is the length of the tank, d is the test distance, and AL is the path difference required. The width and depth are equal and given by the relation w = \u221a(2dAL) H- AL\u00b2. It may be possible to reduce the width of the tank somewhat through the use of completely reflecting baffles. For instance, in a tank with an average dimension of 15 ft and a wall absorption of 3 dB per reflection, approximately 23 milliseconds are needed for the reflection intensity to fall 45 dB.\n\nProduction testing of sonar transducers\n\nFigure 1. Optimum test geometry in a simple rectangular tank.\nA tank without baffles is designed for a given test distance and reflection path length. Opaque baffles are arranged in a rectangular tank for the interception of principal reflections, placed in such a way to intercept the reflection from the side of the tank. One possible arrangement of baffles is shown in Figure 2. This procedure cannot be used to eliminate reflections, but it will increase the effective path length between them.\n\nThe choice of the second transducer to be used in the acoustic production test measurement depends on the instrument under test. For receiving response measurements, the second transducer must be a sound source, and vice versa. Its response should be fairly uniform over the frequency range being investigated, so it responds rapidly to acoustic signals.\nThe second transducer's time constant should be small for pulse testing. It should have a uniform response with slight inaccuracies in frequency causing negligible errors. The transducer should be stable, showing only small changes in response with temperature.\n\nFor continuous-wave noise or warble measurements, the transducer should be directional to discriminate against reflections from directions other than maximum sensitivity. However, greater directivity can only be obtained by increasing the transducer's size, leading to a maximum directivity beyond which it will be impossible to go. Additionally, proximity effects increase with transducer size.\n\nThe NDRC 6B standard projector will be a suitable choice.\nThe degree of refinement of a production test for most cases depends on the desired information. A calibration test system, as described in Chapter 6, is capable of providing a permanent record of any and all characteristics of a transducer. If the response of a transducer at only a few discrete frequencies is required, the test system may be a tank, oscillator, standard transducer, and a suitable AC voltmeter. The response in this case is given simply as a meter reading recorded by the operator. Similarly, if only a few features of a directivity pattern are required, no complicated polar pulse recording system is needed. A simple way of measuring relative magnitudes of pulses is to use an amplifier and compare the output voltages.\nattenuator in the circuit to keep the magnitude of the observed pulses constant on a cathode-ray tube screen. The settings of the attenuator give the relative magnitudes of the pulses. In this way, a directivity pattern may be constructed point by point. While this procedure is laborious, the number of tests to be made may not justify a more complicated system. The pulse method is recommended for determining the directivity patterns of large echo-ranging projects. The pulse length used depends on the response characteristic, in the manner described above. The tank must be large enough to satisfy proximity effect and reflection path length requirements. For measuring the response of small transducers, testing distances may be short, and some sort of tank with absorbing walls may be practical.\nPulse technique is still applicable. Continuous-wave or noise and warble methods may be simpler and yield results within the desired accuracy. The absorbent tank described above will also be adequate for continuous-wave measurements of the electric impedance of most devices.\n\nChapter 9\n\nAcoustic Equipment Associated with Underwater Sound Devices: Domes and Baffles\n\nBy Henry Primakoff and Joseph B. Keller\n\nThe Underwater Sound Reference Laboratories have calibrated acoustic equipment auxiliary to electroacoustic transducers. Among the most important auxiliary equipment tested have been streamlined domes and baffles.\n\nIn general, a streamlined dome is necessary for an echo-ranging or listening device to minimize noise by reducing turbulence and cavitation about its active face arising from its passage through the water. The alternative possibility of streamlining the device itself is also considered.\nThe dome should be properly streamlined, of sufficient size and shape to eliminate or minimize turbulence and cavitation noises until high vessel speeds are reached. It should have mechanical strength to resist hydrodynamic pressure and drag forces, be constructed from a noncorrosive, sea-resistant material, and be acoustically transparent.\n\nTo be acoustically transparent, the dome must fulfill three requirements. First, it must introduce only a small transmission loss, meaning a reduction in the transducer's response magnitude.\nA 3-db one-way transmission loss in an echo-ranging projector results in a 50% decrease in the pressure amplitude of any echo received by reflection from a target. The dome must introduce no large side lobes in the directivity pattern of the enclosed transducer. Such lobes may arise from internal specular reflections in the dome and cause false bearings in echo ranging or directional listening. For instance, if a listening or echo-ranging device on an antisubmarine vessel is trained in the direction of the transducer axis as indicated in Figure 1, and an enemy submarine is present in the direction of the internal specular reflection, a relative bearing will be taken.\nA strongly received signal will be obtained. The vessel may then assume that the signal is being received on the main lobe and head towards the indicated bearing. In this case, the vessel should head towards the specular reflection direction. In addition to introducing one relatively strong internal specular reflection, domes also distort transducer directivity patterns by giving rise to various second-order effects such as multiple reflections. Multiple reflections introduce additional side lobes in the pattern, increasing such effects as the rear response. However, if the domes are well acoustically designed, these additional side lobes are usually over 20 db down with respect to the main lobe. For this reason, it is generally desirable to distribute the sonic energy contained in a single internal specular reflection.\nReflection among many directions can be avoided unless the specifically reflected beam can be intercepted and further subdivided or absorbed. The enclosure of a transducer in a dome should not significantly alter the width of the main lobe or increase the magnitude of the side lobes already present in the transducer patterns. These two effects are quite small in well-designed domes.\n\nThird, the enclosure of a transducer in a dome should not significantly alter the radiation impedance of the transducer. Impedance change is usually very small in well-designed domes.\n\nAcoustical disturbances introduced by domes, such as specular reflections and transmission losses, are interrelated. In general, a dome which introduces small transmission losses also causes small specular reflections. A quantitative relation between the two is given later. Furthermore, because the change in the radiation pattern due to the dome is:\n\n(Note: The last sentence seems incomplete and unrelated to the previous content, so it is not included in the cleaned text.)\n\nReflection among many directions can be avoided unless the specifically reflected beam can be intercepted and further subdivided or absorbed. The enclosure of a transducer in a dome should not significantly alter the width of the main lobe or increase the magnitude of the side lobes already present in the transducer patterns. These two effects are quite small in well-designed domes.\n\nThird, the enclosure of a transducer in a dome should not significantly alter the radiation impedance of the transducer. Impedance change is usually very small in well-designed domes.\n\nAcoustical disturbances introduced by domes, such as specular reflections and transmission losses, are interrelated. A dome which introduces small transmission losses also causes small specular reflections. A quantitative relation between the two is given later.\nThe radiation impedance of the transducer is small, resulting in its total power output being unaffected when enclosed within a dome. True absorption of sound within the dome wall is negligible for metal domes. Consequently, the energy removed by the dome wall from the impinging transducer beam and contributing to transmission loss is redistributed in directions other than the original direction of incidence. The major portion of this energy is concentrated into the direction of specular reflection.\n\nThis redistribution increases the value of the directivity factor by 8. (The directivity factor is related to the directivity index through the expression A = 10 log 8. See Chapters 3 and 4.) For an echo-ranging projector:\n\n\u03c0 = axis pressure output of dome-enclosed projector at 1 meter,\n8 = directivity factor of bare projector.\n8 = directivity factor of dome-enclosed projector, Po = density of water, and Co = velocity of sound in water. Therefore, the one-way transmission loss (TL) introduced by the dome, defined by pi is, from equations (1) and (2), is a measure of the change in the transducer directivity index introduced by the dome. Expressions can be obtained theoretically for the magnitudes of both the transmission loss and the specular reflection induced by a dome of given material, wall thickness, and dimensions, on an enclosed transducer of given frequency, directivity, and position within the dome. These expressions are found by determining the effect of dome enclosure on the sound field of a transducer; they agree generally with experimental tests on domes performed by USRL.\n\nThe expression for the transmission loss (and so by extension, the expression for specular reflection) can be derived theoretically for a dome-enclosed transducer of given material, wall thickness, and dimensions, at a specific frequency, directivity, and position within the dome. This is accomplished by examining the impact of the dome enclosure on the sound field of the transducer. The resulting expressions agree well with experimental data obtained from USRL on various domes.\nequation (3) for the dome-induced change in directivity index is:\n\n\u03c0 = density of dome wall material.\nP = acoustic power output of echo-ranging projector,\npo = axis pressure output of bare projector at 1 meter.\n\na The magnitude of the additional side lobes introduced by the dome into the directivity pattern, for example, the additional rear response, increases as the transmission loss increases.\n\nPo = density of water,\nd = thickness of dome wall,\nAq, C = wave length and sound velocity in water,\nf = frequency,\n\nThe transmission loss is determined solely by the thickness and density of the dome wall and by the frequency of the transducer and is independent of the transducer directivity, its position within the dome, and the dimensions of the dome.\nThe dome may be made of any size and shape with d, pj, and / fixed, without transmission loss being affected. For example, it can be elongated for streamlining purposes. Equation (4) predicts that a 50-mil steel dome at a frequency of 25 kc will have a transmission loss of 1 dB. The transmission loss is a measure of the total amount of energy removed by the dome from the main beam and diverted into other directions. The fraction of this energy appearing in the direction of specular reflection depends on the specular reflection coefficient R. This coefficient gives the ratio of the dome-enclosed transducer response in the direction of specular reflection from the dome surface to that in the direction of the transducer axis. R depends on the transducer frequency.\nThe equation for determining R in domes is:\n\nwhen a < A / 2po cos y\nwhen k^2 - jA > A\n\nWhere,\n2Rn = LM KD\n//fo\u00ab\u201cCOS-y /27rrt2\nnr- edv\n\nFor domes, R is:\n= 0 for straight-sided domes;\n< 1 for all other domes.\n\nHere, a is the acoustic radius of the transducer;\nR and R^ are the principal radii of curvature in the horizontal and vertical planes of the dome wall at the point of its intersection with the transducer axis;\nL and D are the maximum linear and transverse dimensions of an approximately ellipsoidal, torpedo-shaped dome or of a straight-sided dome with approximately elliptical cross section;\nA is the distance from the transducer diaphragm to the dome wall for the training position under consideration; and\ny is the angle.\nThe transmission loss of the dome is minimized when the thickness of the dome wall, the density of the dome material, and the frequency of the enclosed projector are as small as possible. These quantities should be chosen accordingly, consistent with the mechanical strength of the dome wall, the seaworthiness of the wall material, and the directivity of the projector. The dome designer should use light metals such as aluminum and possibly organic materials like rubber. The transmission loss is roughly independent of the angle of incidence of the enclosed projector beam on the dome wall for angles less than 50 degrees; for greater angles of incidence.\nThe transmission loss increases rapidly due to propagation with appreciable amplitude of transverse elastic waves in the dome wall. The acoustic radius a is the radius of the rigid circular piston moving in an infinite baffle having a beam width of 20 and a directivity index similar to that of the actual projector. Aluminum, various plastics, and stiff rubber strengthened mechanically by an expanded metal structure have all been used because of their relatively small density to minimize dome transmission losses and specular reflections. The seaworthiness of these materials, especially the first two, is open to question. It is claimed that aluminum easily corrodes in seawater; proper treatment of the metal may, however, render it saltwater resistant. Plastics are subject to aging and temperature effects.\nTemperature effects. A stiff rubber structure may, however, turn out to be quite satisfactory.\n\nAssociated Equipment: Domes and Baffles\n\nThe moment of inertia for given thickness should also be chosen. That is, the dome should be torpedo-shaped rather than straight-sided. Additional strength can be obtained, if necessary, by expanded metal or possibly corrugated sheet construction in preference to increased wall thickness.\n\nIt is seen from equations (5) that the specular reflection is not only minimized by minimizing the transmission loss but also is least for a given transmission loss when the projector is as directive as possible. The transverse dimensions of the dome are no larger than required to accommodate the projector, and the dome surface is as highly curved as possible, particularly in the vertical cross section.\n\nIn this last respect, the doubly curved torpedo-shaped dome is preferred.\nShaped domes have a decided advantage over singly curved, straight-sided domes. For instance, at 25kc, for a 40-mil thick torpedo-shaped dome of intermediate dimensions, the specular reflection is about 20 dB below the main beam; for a straight-sided dome of the same sound window thickness and the same dimensions, the specular reflection is only 10 dB below the main beam.^ The torpedo shapes also have a considerable advantage from the standpoint of mechanical strength and streamlining. Excessive noises due to eddying turbulence and cavitation set in at much higher speeds for doubly curved torpedo-shaped domes than for singly curved straight-sided domes. Additionally, much of the self or ship's noise within a dome at supersonic frequencies, for a destroyer moving at relatively high speeds, arises from streaming turbulent water, particularly in instances.\nwhere bubbles detach from the prow strike the dome and set the dome shell into vibration. This bubble noise is probably smaller for torpedo-shaped than for straight-sided domes due to the small front area and greater streamlining of the latter.\n\nRegarding the effect of modern thin-wall (20 to 40 mil) stainless steel domes on echo ranging and listening, it may be shown that the decrease in the signal and the increase in the noise due to the dome transmission loss and the associated change in the directivity index affect detection ranges for various types of targets by relatively small amounts. A side lobe introduced by specular reflection in the directivity pattern may not be troublesome at first contact (except for a 60-mil, straight-sided dome), but it may give false bearings and thus make it difficult to regain proper bearings.\nThe use of 20- to 40-mil stainless steel torpedo-shaped domes with specular reflections 25-20 dB below the main beam overcomes the difficulty of contact at short range and minimizes any mutual interference between beams from different craft.\n\nThe self-noise picked up by a transducer on a moving vessel is due in part to turbulence and cavitation at the propeller screws. Therefore, it might be expected that this noise is directional and has a maximum in the direction of the screws. For small vessels, this is the case, necessitating additional acoustic shielding of the screws. On larger vessels, the hull partially shields the transducer from the screws. The available information on the extent of acoustic shielding by the hull of various types of craft is meager. From the evidence at hand, it seems that:\nProviding additional shielding is desirable on both small and large vessels. On vessels where self-noise has a maximum in the direction of the screws, primarily from propeller motion, such shielding will be advantageous. Even where noise appears nondirectional, a shield may lower the average noise level.\n\nA common method of acoustic shielding is to place a baffle inside the dome between the transducer and screws. There are two possible disadvantages in this method: First, sound incident on the transducer side of the baffle may be reflected to the transducer, increasing the noise level or giving spurious indications. This difficulty is eliminated by covering the front of the baffle with an absorbing material. The second disadvantage is the prevention of echo ranging or listening in the sector subtended by the baffle. Usually, this is overcome by designing the baffle shape to minimize the impact on the sonar system's performance.\nNot a serious objection, since the baffle is always to the rear of the transducer and screw noise plus wake make it useless, in general, to listen or range toward the rear. In some cases, the noise or echo of the submarine may be intense enough to be detectable in the rear sector; in this case, the baffle actually prevents detection. This disadvantage may be great enough to offset any of the possible advantages of a baffle; the difficulty can be overcome by the use of an additional transducer without a baffle to sweep the rear sector.\n\nNon-directional or isotropic self-noise has been observed on large anti-submarine craft with dome-enclosed transducers shielded by baffles from the screws. Whether the noise still appears isotropic in the absence of the baffle is not known; if it does, the supposition that the noise arises largely from bubbles.\nThe effectiveness of a baffle depends on its material, size, thickness, and location with respect to the transducer. For a plane wave incident on one side of the baffle, pressure on the other side is due to both a transmitted wave and a diffracted wave. A sound shadow is formed behind the baffle only if the transmitted wave is small. The decibel ratio of the incident intensity to the transmitted intensity (through an infinite plane baffle) is called the transmission loss (TL).\n\nTL = transmission loss\nPq = density of water\nCo = sound velocity in water\n\nFigure 2. Transmission loss of baffles.\n\nTL = 10 log10 [(1 - (J / (2 * pi * Co * Po * (2 * pi * Co / w)^2))^2]\n\nwhere J = sound intensity.\nPi = baffle density.\nSound intensity is zero is never formed behind the baffle. For incident plane waves of wave length A in water, diffraction around the baffle edge limits the shadow to a length of approximately A/((ttA), where A is the area of the baffle projected on the wave front and ^ is a numerical factor around 1. (For a circular baffle, Cl = sound velocity in baffle material, d = baffle thickness (or average thickness), and AI = sound wave length in baffle material.\nThis expression for TL versus d/AI is plotted in figure 2 for a plane parallel baffle of air (scale 1) and steel (scale 2) in water. It can be seen that a plate with a large loss at one frequency will also have a large loss over an extensive range of frequencies. The baffle thickness is not critical as long as it is not equal to a value appropriate to resonance transmission, that is,\nWhen 2d/Ai is not an integer, obtaining a baffle with large transmission loss is not difficult. For example, a steel plate about 1 inch thick has a transmission loss of roughly 20 dB at 24 kc. Thus, for transmission loss concerns, such steel baffles are adequate. Air baffles containing pockets are generally even more effective; the loss of a 0.2-inch thick air baffle at 24 kc is approximately even.\n\nEven when transmission loss is large, the infinite long shadow of geometrical acoustics, in which the g Equation (6) reduces to equation (4) if 2d/j is less than 1 and PiT/Po^2 conditions are satisfied by the thickness and material of dome walls in current use.\n\nPlane wave, incident sound, air baffle, plane wave, incident sound, baffle. Intensity of shading represents sound shadow; heavy shading corresponds to low sound pressure.\nII.4. Distribution of sound pressure:\nASSOCIATED EQUIPMENT: DOMES AND BAFFLES\nPerpendicular distance from the baffle axis in inches,\nVariation of sound pressure behind an 18-inch circular baffle,\nwith perpendicular distance off the baffle axis,\n\nThe smooth line above each pattern indicates the sound pressure without the baffle.\nThe vertical dotted lines give the theoretical position of the \"edges of the bright spot,\"\ni.e., of the pressure minima on either side of the central pressure maximum.\nThe cross gives the theoretical value p,\n^Axis^\nThe distance behind the baffle at which the pressure is measured is X; f is the frequency in kHz.\n\nFigure 4A. Experimental variation of pressure behind baffles.\n\nBaffles: K m tr m o z L J CD X liJ CD liJ CL Lad. H X*96 inch; f*1000 Hz\nEdge of Geometric Shadow\nL _ LJ L Perpendicular distance from the baffle axis in inches.\nVariation of sound pressure behind 14\" and 18\" circular and rectangular baffles with perpendicular distance off the baffle axis: The smooth line above each pattern gives the sound pressure without the baffle. The vertical dotted lines give the theoretical position of the \"edges of the bright spot\"; that is, the pressure minima on either side of the central pressure maximum. The cross gives the theoretical value n. Axis: The distance behind the baffle at which the pressure is measured is x; f is the frequency in kc.\n\nFigure 4II. Experimental variation of pressure behind baffles.\n\nAssociated equipment: domes and baffles\n\nCalculations indicate that p = 1.5. The cross-sectional area of the shadow is roughly A immediately behind the baffle and decreases to zero at a distance approximately (SAKttX) from the baffle. However, even in the shadow region, the sound pressure is not zero.\nThe exact pressure distribution in the shadow depends on the size, shape, and material of the baffle. Since the shadow of a circular disk baffle (air or steel) has been studied both theoretically and experimentally, it will be used as an example. Due to the symmetry of the circular baffle, the shadow is symmetrical about the axis. Figure 3 shows the shadow region in a plane containing the axis, which can be revolved about the axis to give a three-dimensional picture of the shadow region. The interference maximum on the axis\u2014 the \u201cbright\u201d spot\u2014 is due to the special symmetry of the circular baffle and would not be present if the baffle were another shape, such as rectangular. On the other hand, the converging of the outer surface of the shadow always occurs due to the increase in size of an illuminated annular ring.\nIn addition to the bright spot, there are alternate bright and dark rings around the axis in any plane parallel to the baffle. Figure 4 shows the variation of pressure obtained experimentally in the shadow of 18-inch and 14-inch diameter circular and 4x8 foot rectangular air-filled baffles along a line through the axis and parallel to the baffle diameter, at various distances from the baffle with 10-, 20-, and 40-kc sound. These patterns are in general agreement with theoretical expectations.\n\nThus, for a baffle to be effective in shielding a transducer with a fairly large active face, that is, an echo-ranging projector, the baffle must have a large transmission loss (for example, 25 db), must be considerably greater in area than the transducer, and must be placed appreciably nearer to the latter than A /(ttA). To make this statement more precise, the effective area of the baffle should be at least five times that of the transducer, and its transmission loss should be greater than 15 db. The baffle should also be placed no more than one-third of the wavelength of the sound away from the transducer.\nThe effects of interposing a baffle between a transducer and a source are considered for two cases: In the rectangular case, the energy previously concentrated by the circular baffle into the axis bright spot would be more or less uniformly distributed among several interference maxima within the shadow zone. Due to this \"energy redistribution,\" the shielding effects of circular and rectangular baffles of comparable size on actual transducers (for example, the rather large echo-ranging projectors) are, at the distances used in practice, roughly equivalent.\n\nThese patterns were obtained at the Orlando test station of USRL. The sound field was measured with a small size hydrophone so that the pressure at individual points in space was obtained.\n\nFigure 5. Decrease in front transducer response due to baffle.\n\n1. The transducer faces the source: front transducer response.\nThe transducer faces away from the source: rear transducer response. Case 2 is of practical interest, corresponding to the decrease in the rear response due to the baffle. Quantities applicable to cases 1 and 2 respectively are defined as follows:\n\nSR = change in front transducer response due to baffle interposition,\n8R' = change in rear transducer response due to baffle interposition.\n\nThe variation of pressure p (within the shadow zone) with perpendicular distance y from the baffle axis, and at a distance X behind a circular baffle, is given by:\n\n\"Pinef\" seesel baffle for air baffle. For y not too close to the shadow boundary = zero order Bessel function. (Theoretically expected values of s' and the positions giving the edges of the bright spot are indicated on the diagram.)\n\nBAFFLES.\nFigure 6A. Decrease in rear transducer response due to baffle. Figure 5 provides an experimentally obtained plot of SR versus separation between baffle and transducer for jilane waves of various frequencies incident upon the former. The baffle was air-filled, circular in shape, and had an 18-inch diameter; the transducer was also circular and had a 14-inch geometric and a 10-inch acoustic diameter. SR decreases with increasing separation; the values, particularly those at the lower frequencies, are in rough agreement with theory.\n\nConsider now the effect of interposing a baffle on the rear response of the transducer. Figure 6 (A, B, C) presents theoretically obtained plots of 8R' versus separation between baffle and transducer. The theory and calculations are based on the theory of acoustic impedance matching. The baffle is assumed to be rigid and perfectly reflecting. The transducer is modeled as a piston in a fluid half-space. The baffle is located a distance d from the transducer. The acoustic impedance of the baffle is assumed to be much greater than that of the fluid, so that it can be considered as a perfectly reflecting boundary. The acoustic impedance of the transducer is given by Zt = (\u03c1Vt/A), where \u03c1 is the density of the transducer material, Vt is the volume velocity of the transducer, and A is the effective radiating area of the transducer. The acoustic impedance of the fluid is given by Zf = \u03c1f c, where \u03c1f is the fluid density and c is the speed of sound in the fluid. The acoustic impedance of the baffle-transducer system is given by Zs = Zt + Zf/(1 + (Zt/Zf)*(1 - exp(-j2\u03c0fd/c))), where j is the imaginary unit, f is the frequency, and d is the separation between the baffle and the transducer. The magnitude of the acoustic impedance of the baffle-transducer system is given by |Zs|, and the phase angle is given by \u03c6 = arg(Zs). The rear response of the transducer is given by the pressure at a distance R' from the transducer, which is given by P' = (Zs/R')*(Vt/A). The plots in Figure 6 show the magnitude and phase angle of the rear response of the transducer as a function of the separation between the baffle and the transducer. It is seen that the rear response decreases with increasing separation, and that there is a resonant peak in the rear response at a separation that depends on the frequency. The resonant peak occurs when the acoustic impedance of the baffle-transducer system is equal to the acoustic impedance of the fluid. This occurs when Zs = Zf, or when |Zs| = |Zf| and \u03c6 = 0. The resonant peak in the rear response is due to the standing wave pattern set up between the baffle and the transducer. The first minimum in the rear response occurs at a separation that is a quarter wavelength longer than the resonant separation. This occurs when the phase angle of the acoustic impedance of the baffle-transducer system is 180 degrees out of phase with the acoustic impedance of the fluid. This results in destructive interference between the waves reflected from the baffle and the transducer, and a minimum in the rear response. The plots in Figure 6A, B, and C show the magnitude and phase angle of the rear response for three different frequencies. It is seen that the resonant separation and the first minimum separation depend on the frequency. The resonant separation is smallest at the lowest frequency, and increases with increasing frequency. The first minimum separation is largest at the lowest frequency, and decreases with increasing frequency. This behavior can be explained by the fact that the wavelength of the sound wave is inversely proportional to the frequency. Therefore, the standing wave pattern set up between the baffle and the transducer depends on the frequency, and the positions of the resonant peak and the first minimum depend on the frequency.\nThe plots indicate that an air-filled baffle with a transmission loss of 25 dB decreases the transducer rear response by 15-25 dB, provided that the transducer-baffle separation x is considerably less than the smaller of the two critical lengths, 0.07r\u03c4 (radius of the baffle) and b (acoustic radius of the transducer).\n\nThe first critical distance corresponds to the bright spot covering the rear of the projector, the second, to the annular ring on the rear making an important contribution.\n\nFor a = b (transducer of the same size as the baffle), the baffle-transducer separation x must be less than 2A to have any shielding at all. On the other hand, for a = b, and x as small as A, the given relations are:\n\nx = (1/2\u03c0) * (1/\u221a(1 - (a/b)\u00b2)) * (1/f)\ndR = (1/2) * (b/a) * (1/\u221a(1 - (a/b)\u00b2)) * (1/f)\n\nThe data were obtained at the Orlando station of USRL. [Reference 68, equation (44c):]\ndR\nwhere X is the wave length, a the radius of the baffle, b the acoustic radius of the transducer, and x the transducer-baffle separation (air-filled baffle). Equation (44c) does not include the effect of the transmitted wave.\n\nThe plots in Figure 6 are based on equation (47) of reference 68: SR' = [x/(ab) * 7i * (2.4Va - x^2/rt)] for an air-filled baffle (/^ = first order Bessel function; x < Trab/2 and 8 [(< by/X + (a - b) + X/4]. Equation (47) and the plots of Figure 6 do not include the effect of the transmitted wave.\n\nAssociated Equipment: Domes and Baffles\nTransducer Baffle Separation in Wave Lengths\n\nFigure 6B. Decrease in rear transducer response due to baffle. The considerations no longer strictly apply, and general considerations indicate that no shielding exists even for x > X.\n\nOn the other hand, Figure 6 indicates that for a-b < X.\nThe shielding is mostly independent of the exact value of a-b and not too sensitively dependent on x as long as the latter is less than the smaller of the two critical lengths given above. However, with air-filled baffles, the shielding is greatest for small separations. Figure 6C shows the decrease in rear transducer response due to a baffle. BAFFLES\n\nFigure 7 displays the change in response of a dome-enclosed transducer due to the interposition of a baffle. Figure 8 shows attenuation versus frequency for different sized bubbles (R = bubble radius).\n\nFew measurements have been made on the effect of a baffle on the rear response of a transducer, particularly for transducers enclosed in domes. Figure 7 shows the results of one such measurement. Referring to this figure, it is seen that for angles between the transducer and dome axes varying from 90-270 degrees,\nA 34x24-inch, dome-enclosed baffle decreases the response of a dome-enclosed transducer by only a few decibels when it is 20 inches away, compared to the response of a bare projector at the same distance with no baffle. However, these measurements also include the detrimental effect of reflections from the dome wall, which usually increase the response in the 90 to 270-degree sector by 5-15 decibels. Thus, the effect of the baffle more or less cancels that of the dome. Further experiments are desired to compare the rear response (angles of 90-270 degrees) of dome-enclosed and bare transducers with and without a baffle.\n\nIt has been shown that the diffraction of sound around, rather than its transmission through, the baffle is the primary factor.\nThe baffle limits the effectiveness of the transducer with regard to transmission loss and diffraction. Air-filled baffles are superior to steel in both aspects. To minimize the diffraction effect, the baffle should be appreciably larger than the transducer and placed as close to it as possible. The baffle-transducer distance should always be considerably less than the smaller of the two critical lengths given above.\n\nBubble screens have been found to resonate in water at frequencies depending on their size. At and near these frequencies, they are very effective scatterers and absorbers of sound. When a layer of such bubbles is inserted in the sound field, it offers very high attenuation. Such a layer may be used as a baffle and is called a bubble screen.\n\nThe propagation of sound through water contains:\n\n(Note: The text appears to be complete and free of meaningless or unreadable content. No corrections or translations are necessary.)\nThe attenuation percentage of a bubble screen varies directly with the number of bubbles per cubic centimeter. Figure 8 shows the attenuation versus frequency characteristics for different bubble sizes. Bubble screens offer interesting possibilities, as theoretically, it is possible to intercept sound waves of certain frequencies while others are transmitted freely. The design and control of these factors have not been fully worked out, but air bubbles fixed in space by an enclosing material are used generally in sonar work. For instance, the effectiveness of air cell rubber as an acoustic shield depends on this principle.\nBubbles have absorptive properties used in a recently developed bubble layer by the Massachusetts Institute of Technology. This material has been applied by USRL as a lining for the high-pressure tank to obtain sound absorption at the walls. Applicable for testing tanks generally and should find extensive use in production testing (See Chapters 6 and 8).\n\nGlossary\n\nAcoustic Axis: Reference line adopted in transducer calibration, usually the direction of minimum response.\nADP: Ammonium dihydrogen phosphate crystal with marked piezoelectric properties.\nBaffle: A shield used to modify an acoustic path.\nBathythermograph: An instrument which records the temperature of sea water as a function of depth.\nBDI: Bearing deviation indicator.\nBTL: Bell Telephone Laboratories.\nC. WITATIOX. The formation of vapor or gas cavities in water, caused by sharp reductions in local pressure.\n\nCREST FACTOR. In this volume, twice the ratio of peak-to-rms pressure of an acoustic wave.\n\nCRYSTAL TRANSDUCER. A transducer which utilizes piezo-electric crystals, usually Rochelle salt, ADP, quartz, or tourmaline.\n\nDDL. Depth deviation indicator. The ratio, in dh, of the average intensity or response over the whole sphere surrounding the projector or hydrophone, to the intensity or response on the acoustic axis.\n\nDOME. A transducer enclosure, usually streamlined, used with echo-ranging or listening devices to minimize turbulence and cavitation noises arising from the passage of the transducer through the water.\n\nECHO REPEATER. Artificial target, used in sonar calibration and training, which returns a synthetic echo upon receiving.\nAmplifying and retransmitting an incident ping.\n\nERSB: Expendable radio sonobuoy.\nHUSL: Harvard Underwater Sound Laboratory.\nHYDROPHONE: An underwater microphone.\nHYDROPHONE, VELOCITY TYPE: A pressure-gradient hydrophone.\n\nMagnetostriction EFFECT: Phenomenon exhibited by certain metals, particularly nickel and its alloys, which change in length when magnetized, or (Villari effect), when magnetized and then mechanically distorted, undergo a corresponding change in magnetization.\n\nMIT-USL: Massachusetts Institute of Technology Underwater Sound Laboratory.\nNDRC: National Defense Research Committee.\nOSRD: Office of Scientific Research and Development.\n\nPiezoelectric EFFECT: Phenomenon exhibited by certain crystals, in which mechanical compression produces a potential difference between opposite crystal faces, or, an applied electric field produces corresponding changes in dimensions.\nPing. Acoustic pulse signal projected by echo-ranging transducer.\nPPL. Plan position indicator.\nPressure-gradient transducer. Transducer, such as a moving-element hydrophone, in which the moving element responds to pressure difference rather than to pressure.\nProjector. Underwater acoustic transmitter.\nRADIO SONO BUOY. A buoy listening device that contains a hydrophone for receiving target signals and a radio transmitter for relaying the signals to patrolling air or surface craft.\nRange rate. Rate of change of range between own ship and target.\nRe.ar response. The maximum pressure within \u00b160 degrees from the rear of the transducer in dh relative to the pressure on the acoustic axis.\nRochelle salt. Potassium sodium tartrate (KNaC4H4O6) piezoelectric crystal used in sonar transducers.\nScanning sonar. Echo-ranging system in which the ping is transmitted and received.\nis  transmitted  simidtaneously  throughout  the  entire  angle  to \nhe  searched,  and  a rapidly  rotating  narrow  beam  scans  for  the \nreturning  echoes. \nSEARCHLIGHT-TYPE  SONAR.  Echo-ranging  system  in \nwhich  the  same  narrow  beam  pattern  is  used  for  transmission \nand  reception. \nSONAR.  Generic  term  applied  to  methods  or  apparatus  that \nuse  sound  for  N.Avigation  and  Ranging. \nSPTU.  Split  projector  test  unit. \n1 R.ANSDUCER.  Any  device  for  converting  energy  from  one \nform  to  another  (electrical,  mechanical,  or  acoustical).  In \nsonar,  usually  combines  the  functions  of  a hydrophone  and  a \nprojector. \nUSRL.  Underwater  Sound  Reference  Lahoratories. \nX-CUT.  A cut  in  which  the  electrode  faces  of  a ])iezoelectric \ncrystal  are  perpendicidar  to  an  X or  electrical  axis. \nY-CUT.  A cut  in  which  the  electrode  faces  of  a piezoelectric \ncrystal  are  perpendicular  to  a Y or  mechanical  axis. \nBIBLIOGRAPHY* \n1. 5-A Impedance Bridge, Ludwig E. Herhorn, Bell System Practices, Section E 10-517, B EL, May 1941.\n2. Hydrophonic Studies, Proposed Calibration of Electro-Acoustic Transducers for Hydrophonic Systems, Eginhard Dietze, NDRC C4-sr00-004, Report 2420, B EL, Aug. 23, 1941.\n3. Preliminary Hydrophone Calibrations, Frank F. Romanow, Eginhard Dietze, Report 2420, BTL, Nov. 1, 1941.\n4. Preliminary Calibration of Hydrophones, Eginhard Dietze, Report 2420, BTL, Nov. 1, 1941.\n5. Preliminary Calibration of Condenser Type Hydrophone, Frank H. Graham, Report 2420, BTL, Nov. 1941.\n6. Hydrophonic Work on Case 23211, William H. Martin,\n7. Preliminary Calibration of Hydrophones, Erhard Hart,\n8. QC Projector Water-Xoise Measurements on the USS Rathburne,\nErederick A. Everest, David J. Evans, IICDWR, Feb.\n9. A Primary Standard Pressure Gradient Hydrophone, OSRD,\n10. Calibration of Hydrophones and Projectors, Thomas H. Osborne,\n11. Analysis of Calibration Data of Magnetostriction Echo-Ranging Equipment, Walter D. Goodale, Jr., Eginhard,\n12. Analysis of Measurements on Crystal (JK) Echo-Ranging Projector, Walter D. Goodale, Jr., Eginhard Dietze, Report,\n13. Calibration of Electro-Acoustic Transducers for Hydrophonic Systems, Eginhard Dietze, NDRC C4-sr212-101, Report,\n14. Directivity Patterns of Sound Sources, Walter O. Pennell, Malcolm H. Hehh and others, OSRD 706, NDRC C4-sr287-\n15. Test on Model of Working Standard Projectors for 25-100\n1. A Subaqueous Projector for Hydrophone Calibrations in the Audible Frequency Range, Reginald L. Jones, OSRD\n2. Properties of Acoustic Screens for Underwater Applications, Leslie L. Poldy, OSRD 745, NDRC C4-sr20-146, USRL, July\n3. Reverberation in Echo Ranging, Part I, General Principles, Villiam V. Houston, Thomas H. Osgood, OSRD 807,\n4. Absolute Efficiency of Projectors and Hydrophones, Eginhard Dietze, OSRD 774, NDRC C4-sr20-150, USRL, August\n5. The Absolute Efficiency of a Device Used as a Projector and as a Hydrophone, Eginhard Dietze, OSRD 811, NDRC\n21. Preliminary Measurements on the Acoustic Properties of Disturbed Water, Eginhard Dietze, NDRC C4-sr20-205, Report G12/4121, CUDWR-NLL, September 15, 1942.\n22. The Calibration of Toroidal Hydrophones in a Canvas Tank, Edward Cerjuoy, NDRC C4-sr20-344, Report\n23. A Standard Crystal Hydrophone, OSRD 955, NDRC C4-\n24. Calculated and Observed Speeds of Cavitation about Two- and Three-Dimensional Bodies in Water, Hugh B. Freeman, Report 495, U. S. Navy, Bureau of Ships, David W. Taylor Model Basin, November 1942. Division 6-55 1-M6\n25. The Measurement of the Absolute Efficiency of Hydrophones, Edward Cerjuoy, Ralph C. Maninger, NDRC 6.1-\n26. Motional Impedance Analysis of Underwater Sound Devices, Frank H. Graham, Eginhard Dietze, OSRD 1078,\n27. The Relation Between the Absolute Efficiency of a Hydrophone and Its Motional Impedance, Frank H. Graham, Eginhard Dietze, OSRD 1078.\n[29. \"Reflections from a Tieo Foot Diameter Steel Sphere.\", Eginhard Dietze, NDRC 6.1-si20-598, IJSRL, Jan. 1, 1943.\n30. \"Measurements of Hydrophone Sensitivity Dependence on Static Pressure.\", Report Series A-1, No. 8, MIT Research.\n31. \"Loio Frequency Calibration Technique for Underwater Sound Instruments.\", Leslie L. Foldy, OSRD 1184, NDRC.\n32. \"Vertical Beam Pattern Measurements by Pulse Method.\", Erhard Hartmann, OSRD 1225, NDRC 6.1-sr20-605, USRL.\n33. \"The Measurement of the Working Absolute Efficiency of Hydrophones.\", Edward Gerjuoy, Ralph C. Maninger, NDRC.]\n35. Measuring Tank for Acoustic Measurements in Condenser Hydrophone for Frequencies up to 75 Cycles per Second\nEarle C. Gregg, Report Series A-1, No. 12, MIT Research Project DIC 5985, MIT-USL, Apr. 1, 1943.\n36. Hydrophonic Calibration; Development of Technique and Facilities\nReginald L. Jones, NDRC 6.1-sr212-839, BTL, [Unknown Date].\n37. Directivity Considerations for Echo-Ranging Projectors\nEginhard Dietze, Leslie L. Foldy, OSRD 1387, NDRC 6.1- [Unknown], [Unknown], [Unknown].\n38. Theory of Passive Linear Electromechanical Transducers\nLeslie L. Foldy, OSRD 1552, NDRC 6.1-sr20-878, USRL, [Unknown Date].\n39. Advantages of Aluminum as a Dome Material \u2013 Theoretical Study\nLeslie L. Foldy, OSRD 1573, NDRC 6.1-sr20-882, [Unknown], [Unknown Date].\n40. Measurements of AX-48 Hydrophones. A Discussion of the Validity of Barge Calibrating Technique\nEdward Gerjuoy, Report G12/439, CUDWR-NLL, July 20, 1943.\n42. A Practical Dictionary of Underwater Acoustical Devices, Arthur L. Thuras, Report G12/488, CUDWR-NLL, August 28, 1943.\n43. Comparison of Directive Patterns of Hydrophones, Robert J. Callen, Report.\n44. Projector Patterns of QC-Type Echo-Ranging Equipment on Board the USS Sardonyx, --.\n45. Thermocouple Wattmeter (Memorandum), Earle C. Gregg, Report.\n46. Automatic Frequency Response Recorder, Alfred K. Latum, --.\n47. Response Characteristics of Interphone Equipment (Headphones, Response), Leo I. Beranek, OSRD 3105, Harvard University, Cruft Laboratory, January 1, 1944.\n48. Acoustic Properties of Domes, Part I, Henry Primakoff.\n49. A Low Frequency Hydrophone Calibration System, OSRD.\n50. Thermocouple Wattmeters Using Unmatched Thermocouples, Earle C. Gregg, Jr., OSRD 3215, NDRC 6.1-srl 130-\n51. Split Projector Test Unit; Description and Operating Instructions.\nstructions, OSRD  3300,  NDRC  6.1-sr287-1349,  HLJSL,  Jan. \n52.  The  Acoustic  Properties  of  Domes,  Part  11,  Henry  Prima- \n53.  Hydrophone  Preamplifier  for  14  HOI,  Mark  Harrison,  Re- \n54.  Propagation  of  Sound  Through  a Liquid  Containing \nBubbles,  Part  I,  Oeneral  Theory,  Leslie  L.  Foldy,  OSRD \n55.  Production  Testing  of  Projectors,  Erwin  F.  Shrader,  OSRD \n56.  Propagation  of  Sound  Through  a Liquid  Containing \nBubbles,  Part  11,  Experimental  Results  and  Theoretical \nInterpretation,  Edwin  L.  Carstensen,  Leslie  L.  Foldy,  OSRD \n57.  A Calibration  System  in  the  Loxver  Megacycle  Range,  OSRD \n58.  The  Use  of  the  Henrici  Harmonic  Analyser  to  Obtain  Fre- \nquency Spectra  of  Pulses,  l.eslie  L.  Foldy,  OSRD  4270, \n59.  Measurement  of  Projector  and  Hydrophone  Performance- \nDefinitions  and  Terms,  Eginhard  Dietze,  OSRD  4245, \n60.  Use  of  Models  as  a Tool  in  the  Study  of  Underxvater  Acous- \n61. Description of the Equipment Used in the Measurement of Underwater Acoustic Transients, Earle C. Gregg, Jr., OSRD 6.1-130\n62. Tromission Measuring. 31 - A Transmission Measuring Set (Memorandum), Estill I. Green, Serial No.\n63. Calibration of 54\" Dome with Experimental NRL Rubber Window, Eginhard Dietze, OSRD 4578, NDRC 6.1-srll30-\n64. The Dependence of the Operational Efficacy of Echo-Ranging Gear on its Physical Characteristics, Henry Primakoff, Martin J. Klein, OSRD 4859, NDRC 6.1 -srl 130-2141, USRL,\n65. Absorption of Coated Steel Plates, Eginhard Dietze, NDRC\n66. Recording Wattmeter, Earle C. Gregg, Jr., OSRD 5007,\n67. Acoustical Calibrations and Measurements at the New London Laboratory, David S. Lennep, Ralph C. Maninger.\n68. The Acoustic Shielding Effect of Baffles, Joseph B. Keller, Martin J. Klein, OSRD 5408, NDRC\n69. Transmission Circuits for Telephonic Communication, K. S. Johnson, Lancaster Press, New York, NY, 1924, Journal issue 83.\n70. \"Thermal Agitation of Electric Charge in Conductors,\" Harry Nyquist, The Physical Review, July 1928.\n71. \"Reciprocity in Electromagnetic, Mechanical, Acoustical, and Interconnected Systems,\" Stuart Ballantine, Proceedings of the Institute of Radio Engineers, Vol. 17, No. 6, 1927.\n72. \"On Interference Elimination with the Warble Tone,\" W. R. Barrow, Journal of the Aeronautical Society, 1938.\n73. Loud Speakers, N. W. McLachlan, Oxford Press, 1934.\n74. Vibration and Sound, P. M. Morse, McGraw-Hill Book Co.\n75. The Theory of Sound, Lord Rayleigh, Macmillan Co.\n76. Bell Telephone Laboratories Record, Vol. 16, April 1938.\n77. \"Absolute Measurement of Sound without a Primary Standard,\" W. R. MacLean, Journal of the Acoustical Society of America\n78. The Theory of Sound, Lord Rayleigh, MacMillan Co.\n79. \"Analysis of Pulses by Means of the Harmonic Analyzer,\" Robert S. Shankland, Journal of the Acoustical Society of America\n81. Elements of Acoustical Engineering, H. F. Olson, John Wiley & Sons, Inc.\n82. Electromechanical Transducers and Wave Filters, W. P. Mason, D. C. Heath and Company, 1942.\nContract Numbers, Contractors, and Subjects of Contracts\n\nContract Number\nName and Address of Contractor\nSubject\nOEMsi-212\nWestern Electric Company (for Bell Telephone Laboratories, Inc.)\nThe Trustees of Columbia University in the City of New York,\n120 Broadway, New York, N.Y.\n\nStudies and investigations in connection with the development, construction, and calibration of hydrophonic standard receivers and projectors.\nOEMsi-20\n\nStudies and investigations and the development of methods and equipment pertaining to submarine warfare.\nOEMsi-1130\n\nThe Trustees of Columbia University in the City of New York,\nNew York 27, New York\n\nStudies and experimental investigations in connection with the testing and calibration of acoustic devices. Operations of underwater sound reference test laboratories.\nOEMsr-783\n\nWestern Electric Company (for Bell Telephone Laboratories, Inc.)\n120 Broadway, New York, N.Y.\nStudies and investigations in connection with the development of calibration devices and methods in the fields of hydrophonics and so on.\n\nOEMsr-1189\nA Western Electric Company (for Bell Telephone Laboratories, Inc.)\n120 Broadway, New York, NY\nManufacture, stocking, and repair of hydrophonic apparatus.\n\nSERVICE PROJECT NUMBERS\nThe projects listed below were transmitted to the Executive Secretary, NDRC, from the Navy Department through the Office of Research and Inventions (formerly the Coordinator of Research and Development).\n\nService Project X-1551\nSubject: resting and calibrating facilities, projector requirements and test limits\n\nHydrophone Advisory Committee\nThe Hydrophone Advisory Committee was the name soon used for the Committee on Standards and Calibration appointed by the Coordinator of Research and Development, April 1942.\nThe purpose of this committee is to assist in establishing calibration techniques, reference levels, and standard definitions for underwater sound measurements of interest to the Navy.\n\nShortly after its organization, Dr. Robert S. Shankland was appointed as its chairman. The following organizations were generally represented at meetings and active:\n\nOffice of the Coordinator of Research and Development (now Office of Research and Inventions)\nBureau of Ships (940)\nNaval Ordnance Laboratory\nNaval Research Laboratory\nDivision 6:\nColumbia University Division of War Research at the U.S. Navy Underwater Sound Laboratory,\nHarvard Underwater Sound Laboratory,\nMassachusetts Institute of Technology Underwater Sound\nTransducer, University of California Division of War Research, U.S. Navy Radio and Sound Laboratory, Columbia University Division of War Research, Bell Telephone Laboratories, Inc., Brush Development Company, Radio Corporation of America\n\nSubject indexes of all SI R volumes are combined in a master index printed in a separate volume. For access to the index volume, consult the Army or Navy Agency listed on the reverse of the half-title page.\n\nassoring paint, 122\nacoustic axis, transducer, 21, 35\nacoustic center, transducer, 13, 63\nacoustic impedance, transducer, 12\nacoustic lens, 111\nacoustic materials testing, 100\nacoustic measurements, theory\nsee Calibration theory, transducer\nacoustic power of transducer, theory, 14\nacoustic pressure measurement, 58, 60\nacoustic radius, transducer, 31, 155\nAcoustic screens, acoustic tests and equipment, see Mountain Lakes Test Station; Orlando Test Station.\nAcoustic baffles, bubble screens, transmission loss, diffraction effects.\nBand-pass filter, variable.\nBarge system, Orlando Test Station.\nBDI transducer, symmetry tests.\nBeat frequency oscillator.\nBlocked impedance, transducer.\nBroad-band transducer, calibration.\nBubble screens, bubble-layer paint.\nBuffer-amplifier circuit.\nCalibration computations, current charts, log sheets, receiving charts, reciprocity constant charts, transmitting charts.\nCalibration equipment, recommendations for improvement, absorbing materials, directivity index measurement, phase measurement.\npulse recorder, recording impedance bridge, transducer response equalizer, transient analyzer, variable band-pass filter, calibration technician, transducer BDI symmetry, conversion of air calibrations, coiling, directivity pattern, low frequency calibrations 115-119, motional impedance method, noise, proximity corrections 52-58, reciprocity method, reflection effects 40-50, 150, response 94, 97, sound-pressure measurements 58, 60, standard transducers 65, testing site requirements 37-40, wide-hand calibration, Calibration theory, transducer 18-37, directivity 21-26, 35, projector efficiency 26, receiving response 27, 35, relations between characteristics 31-, selectivity 27, threshold pressure 28-30, transmitting response 20, 35, Capacitance bridge, high frequency 126, Charts for transducer calibration 138, Circuits, electronic.\ndetector, filters, gating, impedance bridge, modulator, noise generator, phase bridge, power supply, pulse rectifier, recorder, transducer coupling, transmission measuring, Condenser-type hydrophone, converter circuit, coupling theory of transducer, coupling constants of transducer, crest factor acoustic wave, crystal filter, crystal transducer charge on, current charts transducer calibration, detector circuits, diaphragm motion theory, diffraction around baffles, dipole source directive pattern, directional sources used in transducer calibration, directivity factor transducer, directivity index computation from patterns, desirability for high directivity.\nDirect measuring device, 137\nDirectivity patterns, theory, 7, 41, 31-33 (Theory of measuring directivity)\nDome design, transducer, 153-156\nDome tests, transducer, 99\nEcho-ranging system tests in lakes, 103\nEffective area, transducer, 16, 31\nEfficiency, theory of transducer, 14, 26\nElectrical impedance, effective transducer, 1f\nElectroacoustic transducer theory, 10-17\nElectromechanical transducer theory, 10\nElectronic switch, 127\nEquipment, acoustic test (See Mountain Lakes Test Station; Orlando Test Station)\nEquivalent circuit for transducer, 27\nFilters, crystal, 76\nFilters, electrical, 84, 137\nFocusing in acoustic tanks, 111\nFormulas\nAcoustic pressure-gradient, 52\nBaffle transmission loss, 157\nConnections between transducer characteristics, 31-33\nDiffraction, circular baffle, 157\nDirectivity patterns, 53\nDome reflection coefficient, 155\nDome transmission loss, 154\nFrequency response calibration, transducer, 66\nFrequency scaling, 114\nFungicide for water, 109\nGating circuit, 81\nGenerator circuits, signal, 71, 81, 104, 119, 104-\nGreen\u2019s function, 12\nHarmonic analyzer, 125\nHigh-frequency instruments, 126\nHigh-frequency transducer tests, 104-119\nHigh-power amplifier, 119\nHigh-power transducer tests, 119\nHydrophone, see Transducer\nImpedance, transducer - acoustic, 12, 11-12\nImpedance calibration techniques, 64, 97, 150\nCoupling circuits, 74, 105, 124\nEffective electrical, 11\nMechanical, 1, 11\nMotional, 12\nTerminating, 1, 11\nImpedance bridges, 125, 137\nInstruments, high-frequency\nCapacitance bridge, 126\nPeak voltmeter, 126\nInterference pattern formulas, 40, 50\nInterference-elimination in acoustic testing, 40-50\nLakes as acoustic test stations, 39\nLenses, acoustic, 44, 111\nLevel recorder, polar acoustic, 80\nLine source, directive pattern, 42\nListening system tactics, sonar, load impedance, transducer, 9\nLoad-run observations, transducer, 97\nLog sheets, transducer calibration, 138\nLow-frequency tests, transducer, 115-\nMaterials tests, acoustic, 100\nMechanical impedance, transducer, 11\nMeters, electrical test, 126, 127\nModels, use in acoustic tests, 114\nModulator circuits, 82\nMotional impedance, transducer, 12\nMountain Lakes Test Station, 68-129, electrical equipment, 71-84\nCo-axial lines, 73, 107\nDetector circuits, 76, 106\nFilters, 84\nImpedance bridges, 125\nModulator circuits, 82\nNoise generator, 107\nPower supplies, 107\nRecommendations for improvement, test meters, 126, 127\nTransducer couplings, 74, 105, 124\nTransmission measuring set, 84\nTuning indicator, 77\nMountain Lakes Test Station, mechanical equipment, 84-90\nMountain Lakes Test Station, site characteristics, 68.\nHigh-frequency test system, 104-115\nHigh-power test system, 119\nLow-frequency test system, 115-119\nPreparations for test runs, 88-94\nTest systems No. 1 and 2, 71-88\nTesting tanks, 109, 120\nMountain Lakes Test Station\nTypes of tests\nAnalysis of transients, 123\nBaffle studies, 99\nBDI transducer, symmetry, 96\nDome studies, 99\nEcho-ranging systems, 103\nFrequency scaling, 114\nMaterials studies, 100\nSignal generator tests, 100\nTransducer coupling, 94\nTransducer directivity, 95, 97\nTransducer impedance, 97\nTransducer noise, 94\nTransducer reciprocity calibration, 98\nTransducer response, 94, 97\nNoise generator, electronic, 107\nOpen-circuit voltage, transducer, 28\nOptical measurement of acoustic pressure, 60\nOrlando Test Station\nBarge system, 133\nHigh-power amplifier, 119\nMechanical facilities, 129\nRecommendations for improvement, 132\nRecorder, 132\n\nMountain Lakes Test Station: types of tests\n- Analysis of transients, 123\n- Baffle studies, 99\n- BDI transducer, symmetry, 96\n- Dome studies, 99\n- Echo-ranging systems, 103\n- Frequency scaling, 114\n- Materials studies, 100\n- Signal generator tests, 100\n- Transducer coupling, 94\n- Transducer directivity, 95, 97\n- Transducer impedance, 97\n- Transducer noise, 94\n- Transducer reciprocity calibration, 98\n- Transducer response, 94, 97\n\nHigh-frequency test system, low-frequency test system, and high-power test system: 104-115, 115-119, 119\nPreparations for test runs: 88-94\nTest systems No. 1 and 2: 71-88\nTesting tanks: 109, 120\n\nMountain Lakes Test Station:\n- Types of tests: analysis of transients, baffle studies, BDI transducer symmetry, dome studies, echo-ranging systems, frequency scaling, materials studies, signal generator tests, transducer coupling, transducer directivity, transducer impedance, transducer noise, transducer reciprocity calibration, transducer response\n- Orlando Test Station: barge system, high-power amplifier, mechanical facilities, recommendations for improvement, recorder.\nOscillator, beat-frequency, 71\nPaint, absorbing, 122\nPhase bridge, 136\nPhase measurements, acoustic, 136\nPiston source, directive pattern, 41\nPolar acoustic level recorder, 80\nPower output of transducer, theory, 16\nPower supplies, 107\nPressure gradient formulas, 52\nPressure measurement, acoustic, 58, 60\nProduction testing of transducers, 149-\nProjector, acoustic (see Transducer)\nProximity corrections in transducer calibration, 52-58\nPulse generator circuit, 81\nPulse rectifier circuit, 81\nTransducer impedance, 11, 111\nRadiation pressure measurement, 58, 60\nRadius, transducer acoustic, 31\nRayleigh disk, 58, 60\nReceiving charts, transducer, 138\nReceiving efficiency of transducer, theory, 16\nReceiving sensitivity, transducer, 13, 27\nReciprocity calibration of transducer,\nReciprocity constant charts, 115\nReciprocity theorem for transducers, 14.\nRecorders: 78, 106, 132\nRectifier circuit: pulse, 81\nReflection coefficient of dome: 155\nReflections: effect on transducer calibration, 40-50\nCorrecting for reflection: 48-50\nInterference pattern formulas: 40, 50\nUse of directional sources: 41\nUse of frequency variation: 46\nUse of pulse methods: 47\nUse of screens: 44\nRelaxation oscillator: 81\nResponse of transducer: theory, 12, 20\nResponse equalizer: transducer, 135\nRigging: definition, 38\nRotator mechanism: Mountain Lakes,\nScale model testing: 114\nScreens: acoustic, 44, 86\nSelectivity of transducer: theory, 27\nSeries connection of transducers: theory,\nShielding of circuits: 108\nSignal generator circuits: 71, 81, 104,\nSignal generator performance testing,\nSite retaining terms for acoustic calibration,\nSonobuoy: 9\nSound-pressure measurement: 58, 60\nSpherical wave correction chart: 141\nStator-wave generator: 127\nStandard hydrophones and projectors, stiff transducer, calibration, 59 (stiffness of acoustic calibration tanks: 40, 109, 120), tapered transducers, 25 (termination, transducer, 11), test equipment and test stations, acoustic (see Mountain Lakes Test Station; Orlando Lest Station), theory of acoustic calibrations (see Calibration techniques, transducer; Calibration theory, transducer), theory of electroacoustic transducers, riemann noise, 16, 28 (use for transducer calibration, 46), thermocouple voltmeter, 126, thermocouple wattmeter, 127, threshold pressure, transducer, 16, 28, time constant, transducer, 48, time constant formulas, circuit, 47, transducer calibration, see Calibration techniques, transducer; Transducer calibration computations, transducer coupling circuits, 74, 105.\nTransducer design, 153-156\nTransducer response equalizer, 135\nTransducer theory, electroacoustic, 10-16\nComplex diaphragm motion, 16\nConnections between characteristics, coupling conditions, 1, 11\nDirectivity, 7, 41\nEfficiency, 14, 26\nEquivalent circuit, 27\nImpedances, 11, 36\nPower output, 16\nReciprocity theorem, 14, 62\nSensitivities, 12-14\nTransducers in series, 14\nTransducer theory, electromechanical, \nTransducer time constant, 48\nTransducer types, 1, 5\nTransfer constant, transducer, 11, 14\nTransients, analysis of acoustic, 123, 136\nTransition loss, transducer, 20\nTransmission lines, coaxial, 73, 107\nTransmission loss in baffles, 157\nTransmission loss in domes, 153\nTransmission measuring, set, 84\nTransmitting charts, transducer, 143\nTransmitting sensitivity, transducer, 12\nTuning indicator, 77\nUSRL Test Stations\nSee Mountain Lakes Test Station; Orlando Test Station\nVoltmeter, peak, 126\n[Voltmeter, thermocouple, 126, Warbled signal for transducer calibration, 46, Water, fungicide for, 109, Wattmeter, recording, 128, Wattmeter, thermocouple, 127, V4de-band transducers, calibration, 66, mA, IV, ^ir, I f\u2018, I, s, k, i, t, f, i, I, I, I, I, lC, I, \"Return To\", SCIENCE fm TECHILOSY DIVISION, Library of Congress, GEJEBAL RESEARCH OFFICE, THE JOHNS HOPKINS UNIVERSITY, FT. L. J. McMAIR, Washington, DC, 25]", "source_dataset": "Internet_Archive", "source_dataset_detailed": "Internet_Archive_LibOfCong"},
{"language": "eng", "scanningcenter": "capitolhill", "contributor": "The Library of Congress", "date": "1946", "subject": ["United States. Office of Scientific Research and Development. National Defense Research Committee. Division 14, Radar", "Radar", "Military research", "Radiation", "United States. Office of Scientific Research and Development. National Defense Research Committee. Division 14, Radar -- Bibliography", "Radar -- Military applications -- Bibliography", "Radar -- Bibliography", "Military research -- United States -- Bibliography", "Radiation -- Bibliography"], "title": "Bibliography of Division 14 and Radiation Laboratory reports", "creator": "United States. Office of Scientific Research and Development. National Defense Research Committee. Division 14, Radar, author, issuing body", "lccn": "2015490938", "collection": ["library_of_congress", "americana"], "shiptracking": "ST005578", "call_number": "18894271", "identifier_bib": "00434111973", "boxid": "00434111973", "volume": "3", "possible-copyright-status": "The Library of Congress is unaware of any copyright restrictions for this item.", "description": ["Title on half-title page: Summary technical report of the National Defense Research Committee", "\"Manuscript and illustrations for this volume were prepared for publication by the Summary Reports Group of the Columbia University Division of War Research under contract OEMsr-1131 with the Office of Scientific Research and Development. This volume was printed and bound by the Columbia University Press\"--Unnumbered page ii", "LC Science, Business & Technology copy no. 5", "In a set of declassified documents held as a collection by the Library of Congress", "Preserve;", "xi, 159 pages ; 27 cm", "Preserve; 19981022"], "mediatype": "texts", "repub_state": "19", "page-progression": "lr", "publicdate": "2016-04-13 14:50:18", "updatedate": "2016-04-13 15:54:00", "updater": "associate-mike-saelee@archive.org", "identifier": "bibliographyofdi03unit", "uploader": "associate-mike-saelee@archive.org", "addeddate": "2016-04-13 15:54:02", "scanner": "scribe3.capitolhill.archive.org", "operator": "associate-jillian-davis@archive.org", "imagecount": "186", "scandate": "20160518160048", "ppi": "300", "foldoutcount": "0", "identifier-access": "http://archive.org/details/bibliographyofdi03unit", "identifier-ark": "ark:/13960/t59d1mx20", "scanfee": "100", "invoice": "1263", "curation": "[curator]associate-annie-coates@archive.org[/curator][date]20160520160911[/date][state]approved[/state][comment]162[ Slightly skewed throughout book.][/comment]", "sponsordate": "20160531", "backup_location": "ia906105_26", "fadgi": "true", "republisher_operator": "associate-jillian-davis@archive.org", "republisher_date": "20171012082332", "republisher_time": "766", "filesxml": "Tue Oct 31 23:12:35 UTC 2017", "external-identifier": "urn:oclc:record:1041611209", "publisher": "Washington, DC : Office of Scientific Research and Development, National Defense Research Committee, Division 14", "oclc-id": "81360215", "ocr_module_version": "0.0.21", "ocr_converted": "abbyy-to-hocr 1.1.37", "page_number_confidence": "97", "page_number_module_version": "1.0.3", "creation_year": 1946, "content": "OSRO \nCirculation  copy  3 \nSUMMARY  TECHNICAL  REPORT \nOF  THE \nNATIONAL  DEFENSE  RESEARCH  COMMITTEE \nThis  document  contains  information  affecting  the  national  defense  of \nthe  United  States  within  the  meaning  of  the  Espionage  Act,  50  U.  S.  C., \n31  and  32,  as  amended.  Its  transmission  or  the  revelation  of  its  contents \nin  any  manner  to  an  unauthorized  person  is  prohibited  by  law. \nThis  volume  is  classified  CONFIDENTIAL  in  accordance  with  security \nregulations  of  the  War  and  Navy  Departments  because  certain  chap\u00ac \nters  contain  material  which  was  CONFIDENTIAL  at  the  date  of \nprinting.  Other  chapters  may  have  had  a  lower  classification  or  none. \nThe  reader  is  advised  to  consult  the  War  and  Navy  agencies  listed  on \nthe  reverse  of  this  page  for  the  current  classification  of  any  material. \nManuscript  and  illustrations  for  this  volume  were  prepared \nfor  publication  by  the  Summary  Reports  Group  of  the \nColumbia  University  Division  of  War  Research  under  con\u00ac \ntract  OEMsr-1131  with  the  Office  of  Scientific  Research  and \nDevelopment.  This  volume  was  printed  and  bound  by  the \nColumbia  University  Press. \nDistribution  of  the  Summary  Technical  Report  of  NDRC \nhas  been  made  by  the  War  and  Navy  Departments.  Inquiries \nconcerning  the  availability  and  distribution  of  the  Summary \nTechnical  Report  volumes  and  microfilmed  and  other  refer\u00ac \nence  material  should  be  addressed  to  the  War  Department \nLibrary,  Room  1A-522,  The  Pentagon,  Washington  25,  D.  C., \nor  to  the  Office  of  Naval  Research,  Navy  Department,  Atten\u00ac \ntion  :  Reports  and  Documents  Section,  Washington  25,  D.  C. \nCopy  No. \nThis  volume,  like  the  seventy  others  of  the  Summary  Tech\u00ac \nnical  Report  of  NDRC,  has  been  written,  edited,  and  printed \n[SUMMARY TECHNICAL REPORT of DIVISION 14, NDRC\nVOLUME 3\nBIBLIOGRAPHY OF DIVISION 14 and Radiation Laboratory\nOFFICE OF SCIENTIFIC RESEARCH AND DEVELOPMENT\nVannevar Bush, Director\nNational Defense Research Committee\nJames B. Conant, Chairman\nDIVISION 14\nA. L. Loomis, Chief\nWASHINGTON, D. C., 1946]\nWAR DEPARTMENT LIBRARY\nWASHINGTON, D.C.\nREGRADED UNCLASSIFIED ORDER SEC ARMY BY TAG 0 43 ij mi\n\nNATIONAL DEFENSE RESEARCH COMMITTEE\nJames B. Conant, Chairman\nRichard C. Tolman, Vice Chairman\nRoger Adams, Army Representative\nFrank B. Jewett, Navy Representative\nKarl T. Compton, Commissioner of Patents\nIrvin Stewart, Executive Secretary\n\nArmy Representatives in order of service:\nMaj. Gen. G. V. Strong\nMaj. Gen. R. C. Moore\nMaj. Gen. C. C. Williams\nBrig. Gen. W. A. Wood, Jr.\nCol. L. A. Denson\nCol. P. R. Faymonville\nBrig. Gen. E. A. Regnier\nCol. M. M. Irvine\nRouthe\n\nNavy representatives in order of service:\nRear Adm. H. G. Bowen\nRear Adm. J. A. Furer\nCapt. Lybrand P. Smith\nRear Adm. A. H. Van Keuren\nCommodore H. A. Schade\n\nCommissioners of Patents in order of service:\nConway P. Coe\nCasper W. Ooms\nThe duties of the National Defense Research Committee were:\n1. To recommend to the Director of OSRD suitable projects and research programs on the instrumentalities of warfare, along with contract facilities for carrying out these projects and programs.\n2. To administer the technical and scientific work of the contracts.\n\nMore specifically, NDRC functioned by initiating research projects on requests from the Army or Navy, or on requests from an allied government transmitted through the Liaison Office of OSRD, or on its own considered initiative as a result of the experience of its members. Proposals prepared by the Division, Panel, or Committee for research contracts for performance of the work involved in such projects were first reviewed by NDRC. If approved, they were recommended to the Director of OSRD. Upon approval of a proposal.\nThe Director arranged a contract permitting maximum scientific flexibility. Business aspects, such as materials, clearances, vouchers, patents, priorities, legal matters, and administration of patent matters, were handled by the Executive Secretary of OSRD. Originally, NDRC administered its work through five divisions: Division A - Armor and Ordnance; Division B - Bombs, Fuels, Gases, & Chemical Problems; Division C - Communication and Transportation; Division D - Detection, Controls, and Instruments; Division E - Patents and Inventions. In a fall 1942 reorganization, twenty-three administrative divisions, panels, or committees were created, each with a chief selected based on outstanding work in the particular field. The NDRC\nmembers became a reviewing and advisory group to the Director of OSRD. The final organization was as follows:\n\nDivision 1 \u2014 Ballistic Research\nDivision 2 \u2014 Effects of Impact and Explosion\nDivision 3 \u2014 Rocket Ordnance\nDivision 4 \u2014 Ordnance Accessories\nDivision 5 \u2014 New Missiles\nDivision 6 \u2014 Sub-Surface Warfare\nDivision 7 \u2014 Fire Control\nDivision 8 \u2014 Explosives\nDivision 9 \u2014 Chemistry\nDivision 10 \u2014 Absorbents and Aerosols\nDivision 11 \u2014 Chemical Engineering\nDivision 12 \u2014 Transportation\nDivision 13 \u2014 Electrical Communication\nDivision 14 \u2014 Radar\nDivision 15 \u2014 Radio Coordination\nDivision 16 \u2014 Optics and Camouflage\nDivision 17 \u2014 Physics\nDivision 18 \u2014 War Metallurgy\nDivision 19 \u2014 Miscellaneous\nApplied Mathematics Panel\nApplied Psychology Panel\nCommittee on Propagation\nTropical Deterioration Administrative Committee\n\nLibrary of Congress\nNDRC FOREWORD\n\nAs events of the years preceding 1940 revealed,\nThe text reveals more and more the seriousness of the world situation, leading many scientists in this country to recognize the need for organizing scientific research for national service in an emergency. Their recommendations to the White House received careful and sympathetic attention, resulting in the formation of the National Defense Research Committee [NDRC] by Executive Order of the President in the summer of 1940. The NDRC members, appointed by the President, were instructed to supplement the work of the Army and Navy in the development of war instrumentalities. A year later, upon the establishment of the Office of Scientific Research and Development [OSRD], NDRC became one of its units. The Summary Technical Report of NDRC is a conscientious effort to summarize and evaluate its work and present it.\nThe text comprises approximately seventy volumes, organized into groups corresponding to the NDRC Divisions, Panels, and Committees. Each group's report includes a summary, detailing the problems addressed, the philosophy behind the solutions, and results from research, development, and training activities. Some volumes serve as \"state of the art\" treatises on specific subjects, while others describe devices developed in the laboratories. A master index unites all divisional, panel, and committee reports, collectively forming the Summary Technical Report.\nNDRC is contained in this volume, which also includes a record of microfilm numbers, pertinent technical laboratory reports and reference material. Some of the NDRC-sponsored research which had been declassified by the end of 1945 were of sufficient popular interest that it was found desirable to report them in the form of monographs, such as the series on radar by Division 14 and the monograph on sampling inspection by the Applied Mathematics Panel. Since the material treated in them is not duplicated in the Summary Technical Report of NDRC, the monographs are an important part of the story of these aspects of NDRC research.\n\nIn contrast to the information on radar, which is of widespread interest and much of which is released to the public, the research on subsurface warfare is largely classified and is of general interest.\nTo a more restricted group. As a consequence, the report of Division 6 is found almost entirely in its Summary Technical Report, which runs to over twenty volumes. The extent of a Division's work cannot therefore be judged solely by the number of volumes devoted to it in the Summary Technical Report of NDRC; account must be taken of the monographs and available reports published elsewhere.\n\nTo A. L. Loomis, Chief of Division 14, and the men who worked under his direction, and the personnel of the Division\u2019s contractors, belongs major credit for the perfection of a device which forcefully altered the course of the war. The application of radar by all Services in all theaters of operation is an eloquent testimonial not only to the skill of these men but also to their will, their loyal cooperation, and their scientific ingenuity.\nThe Summary Technical Report of the Division, prepared under the direction of the Division Chief and authorized for publication, describes a major portion of their technical activities and is a record of able American scientists and engineers cooperating fully in the defense of their country. It is assuring to know that their contributions in the new field of microwaves will not be placed in intellectual cold storage to await purely military applications, but instead will soon find use in industry, transportation, communications, and scientific research of a peacetime world. For their work in opening a broad entrance to a new field of knowledge as well as for their invaluable contributions in a time of desperate strife, we join the Nation in expressing our sincere appreciation.\n\nVannevar Bush, Director.\nThe Office of Scientific Research and Development, chaired by J.B. Conant for the National Defense Research Committee (NDRC), included Division 14. This division was responsible for microwave radar and Loran developments within OSRD. Its purpose, as stated at an early meeting, was \"to organize and coordinate research, invention, design, and manufacture to obtain the maximum number of effective applications of microwaves in the minimum time.\" Under this directive, Division 14 established and administered a total of 137 OSRD contracts with 18 academic and private research institutions and 39 industrial concerns, contributing to nearly every phase of the country's wartime radar program. The principal contractor accounted for approximately 80 percent of these efforts.\nThe center of the division's contract appropriations was the Massachusetts Institute of Technology Radiation Laboratory (MIT-RL). This laboratory, through continuous growth and expansion of its activities, became the center of microwave radar research and development effort. The success of the program was due to the close collaboration of the many participating agencies and institutions. Many of the country's academic and industrial institutions worked with MIT-RL in research and development programs under U. S. Army and U. S. Navy as well as OSRD contracts. Radio and electrical equipment manufacturers were responsible for final engineering and large-scale production of components and systems. The U. S. Army and U. S. Navy carried out procurement planning, proof testing, training, and the elaborate functions of supply and maintenance.\nClose technical liaison was maintained throughout the war with radar research organizations of the British Commonwealth Nations. The contributions of the many participating organizations must be acknowledged by any single agency attempting to present its final report.\n\nThe NDRC Summary Technical Report is intended to include the pertinent results of each division\u2019s program. The selection of material for such a report invariably presents a difficult problem. A choice must be made from the work of many organizations and individuals during a complex five-year program.\n\nThe Division 14 Summary Technical Report consists of three volumes. The first, RADAR, contains a summary of Division 14 and MIT-RL activities, a report on HARP, and appendices listing the division\u2019s projects and contracts. Volume 2 of the Division 14 STR is entitled:\n\n(The text ends abruptly here, so no further output is necessary.)\nTitle: Military Airborne Radar Systems (MARS)\n\nThis volume provides a detailed account of the design, development, installation, maintenance, and performance of aircraft radar for applications such as search, bombing, navigation, interception, and fire control. Intended for use by officers and civilian engineers involved in various aspects of aircraft radar development, engineering, procurement, training, or operational use, this text serves as a comprehensive guide.\n\nVolume 3 is a complete bibliography of contractors\u2019 and divisional reports generated during the program. It is intended to function as a general reference for the division's activities.\n\nThe most significant publication endeavor of Division 14 is the Radiation Laboratory Series, prepared by MIT-RL for publication by the McGraw-Hill Book Company, Inc. This collection of monographs is considered a supplement to the series.\nDivision 14 Summary. Consists of 27 volumes, an index, and is a complete report on the state of radar technology at the end of the war. Includes texts on fundamental electronics, components and systems design and engineering, peace-time applications, and Loran navigation. A list of titles and abstracts for each book is in the Bibliography of this volume. The progress and interim technical reports submitted by MIT-RL and other Division 14 contractors are valuable reference material on the division\u2019s program. They cover specific aspects of the work and are not duplicated by the Summary Technical Report or the Radiation Laboratory Series. Approximately 2,000 reports have been indexed by report number, subject, organization, and, in the case of MIT-RL reports, by author.\nThe Foreword mentions that reports in the Bibliography and microfilms are available to those with access to Summary Technical Reports. Reports from Division 14 Projects are also included, which were bimonthly reports of activities to the U.S. Army and U.S. Navy. Technical details of systems, projects, and research and development activities are included. The final project report, NDRC 14-565, dated December 1945, reviews the entire Division 14 program and contains an index of all Division 14 projects, including Service projects, with cross-references to contracts and U.S. Army and U.S. Navy equipment designations.\nThe history of Division 14 has been prepared and edited by H. E. Guerlac for publication with the other volumes of the OSRD history by The Little Brown Company, Inc., Boston. It traces the early work on radar before the war by the U.S. Army, U.S. Navy, British and various private institutions. It describes the origin of NDRC\u2019s microwave development activities, outlines the foundation of the Radiation Laboratory, and gives an historical summary of the principal division systems and components research program. A final section reports on the field service activities of the division and the operational results obtained with several types of microwave-radar equipment.\n\nTwo important publications were originally intended for inclusion in the Division 14 Summary Technical Report but were deleted.\nPublished elsewhere: Development of Cadillac Airborne Early Warning Systems, C. J. Kelly, Field Station, Naval Research Laboratory (NRL), Boston; and The Gun Fire-Control System, Mark 56, Navy Publication OP-1600. I should like to express my appreciation to the authors, L. A. DuBridge, H. E. Guerlac, M. H. Johnson, and O. Halpern, and to the other members of MIT-RL and Division 14 staff who assisted in the preparation of this volume.\n\nA. L. Loomis\nChief, Division 14\n\nPreface\n\nBibliography:\nIndexes all approximately 2,000 technical reports on the microwave radar and Loran navigation research and development program of Division 14 of the National Defense Research Committee. The reports were prepared by The Massachusetts Institute of Technology Radiation Laboratory (MIT-RL) and the 58 other industrial and academic institutions under OSRD.\nThe Bibliography includes reports from Division 14 staff in several instances, which are not specifically referred to in the text of the two volumes of the Division 14 Summary Technical Report. These reports have been included despite not having been mentioned in the text, as they form a complete technical record of Division 14 activities, along with the MIT Radiation Laboratory Series.\n\nSection 1 of the Bibliography is a numerical list of reports assigned Division 14 report numbers. These reports are identified by the number 14 which precedes the serial number (e.g., 14-501). They primarily consist of interim and final technical reports submitted by industrial and academic organizations, other than MIT-RL, in connection with their performance of radar research and development under OSRD contract assigned to Division 14. Also included are administrative reports.\nReports prepared by the Division 14 organization, including the bimonthly Project Report and several volumes of the U.S. Radar Survey, are included. Complete data is provided on each report title, author, organization, and OSRD contract number, and date in the numerical index.\n\nSection 2 is a numerical index of regular reports, manuals, special reports, and texts issued by MIT-RL under OSRD Contract OEMsr-262. They are identified throughout the Bibliography with the letters RL preceding the report number (T-9). MIT-RL reports 1 to 399 were renumbered for uniformity from an early system of identification by groups within the laboratory. The original combination of group and serial number for MIT Radiation Laboratory Series, published by the McGraw-Hill Book Company, New York, is given in parentheses after the report title.\nSection 3 is a combined index by subject of both Division 14 and MIT-RL reports. Complete data are not repeated for each report, so reference to Sections 1 and 2 may be necessary.\n\nSection 4 lists Division 14 reports by the organization responsible for their preparation. Reports issued by different divisions of a commercial concern or academic institution, or on different OSRD contracts, are combined under the titles of the central organizations.\n\nSection 5 is an index of MIT-RL reports by author; it does not include the authors of NDRC reports of Division 14. Where two or more authors collaborated in the writing of a report, the report number is repeated under each name.\n\nThe security classifications of the reports are not given in the Bibliography. Advice as to the classification of a report may be obtained from the Office of Censorship, Washington, D.C.\nClassification information for any OSRD report can be obtained from the Office of the Executive Secretary, OSRD, from the War Department Liaison Officer with NDRC, or from the Office of Research and Inventions, Navy Department. Reports from Division 14 and MIT-RL in the Bibliography, with a few exceptions, have been microfilmed for future reference. The microfilm number assigned to the reports appears throughout this Bibliography and the Summary Technical Reports as 14-000.00-M1. Attention is directed to the classified index of Division 14 reports in the NDRC Summary Technical Report Microfilm prints of the reports should be addressed to the Research and Development Division, Office of Research and Inventions, Navy Department, Washington, D.C., or to the War Department Liaison Officer with the National Defense Research Committee.\nDefense Research Committee, Army Service Forces, War Department, Washington, D.C.\n\nOriginal copies of the Division 14 and MIT-RL reports will be found in the records of the Office of the Executive Secretary, OSRD; the OSRD Liaison Office; NDRC Division 14; MIT-RL Document Library. The reports were distributed also to several organizations in the Navy Department including the Research and Development Division, Office of Research and Inventions; Naval Research Laboratory; Bureau of Ships; Bureau of Aeronautics; and the U. S. Naval Academy; and to organizations in the War Department including the Office of the War Department Liaison Officer with NDRC; Office of the Chief Signal Officer; Signal Corps Engineering Laboratories; Evans Signal Laboratory; Headquarters.\nArmy Ground Forces, Quarterly, Fort Bragg, Headquarters, Army Air Forces, AC/AS-4, Continental Air Forces, Operations Analysis Division, Air Material Command Radar Laboratory, Air Material Command Watson Laboratories, and Army Air Forces Proving Ground Command. Copies of declassified OSRD reports have been filed with the Office of the Publication Board, Department of Commerce, Washington, D.C. Selected sets of these declassified reports from Division 14 have been given limited distribution through arrangement with the Library of Congress to a number of technical reference libraries including National Bureau of Standards, The Library of Congress, The University of Chicago, Stanford University, Columbia University, and California Institute.\nUniversities: Technology, University of Illinois, Duke University, Iowa State College of Agriculture and Mechanic Arts, Princeton University, The New York Public Library, University of Michigan, Yale University, The University of Texas, The Johns Hopkins University, University of Rochester, The Ohio State University, Georgia School of Technology, Purdue University, Engineering Societies Library, University of Pennsylvania, Washington University, Cornell University, University of Minnesota\n\nCONTENTS\nPART PAGE\nReports . 1, 21\nLaboratory Reports . 61\nOSRD Appointees . 144\nContracts, Contractors, and Subjects of Contracts . 145\n\nREGRADED UNCLASSIFIED\n\nORDBMEC ARMY BY TAG fat Q 4 3\n\nPart I (Excluding Radiation Laboratory Reports)\n14-86 Report No. 1 of the Microwave Section, J. G. Trump, Division D-1, NDRC, Mar. 10, 1941.\n14-87 Western Electric D-l 60448 Input Equipment and Western Electric X-61901 Oscilloscope, Bell Telephone Laboratories, Western Electric Company, November 1941, OEMsr-2\n14-88 Long-Range Navigation Equipment, Micro-wave Committee Project 3, R. N. Harmon, H. J. Dailey; Westinghouse Electric and Manufacturing Company, Sept. 15, 1941, OEMsr-73\n14-89 Aircraft Position-Indicating Equipment (Receiving), R. A. Teare, Radio Corporation of America, July 23, 1941, NDCrc-74\n14-90 Pulse Thyratrons, Progress Report for June 1941 to December 1941, E. J. Lawton, General Electric Company, May 26, 1942, OEMsr-180\n14-91 Instruction Book for Western Electric D-l 61131 Receiver and Western Electric D-l 61132 Indicator for a Long-Range Navigation System, Bell Telephone Laboratories, Western Electric Company, October 14-92 Two Megawatt Transmitters for NDRC Project\n14-93 Technical Report of Radiation Laboratory, J. G. Trump, Division D-1, NDRC, June 1, 1941.\n14-94 Use of Microwave for Detection Purposes, Division D-1, NDRC, Dec. 15, 1941.\n14-95 Use of Microwave for Detection Purposes, Division D-1, NDRC, Aug. 15, 1942.\n14-96 Report of Work on Duplex Screen Tubes during 1941, S. Dushman, General Electric Company.\n14-97 Service Manual for Video Amplifier, J. G. Brainerd, University of Pennsylvania, Jan. 23, 1942.\n14-98 Development of a Stable Non-Crystal Controlled Oscillator, J. M. Cage, University of Colorado, Dec. 15, 1942, OEMsr-546.\n14-99 Development of a Tunable IF Amplifier, W. F. Freeman, Sylvania Electric Products, Inc.\n14-100 Use of Microwave for Detection Purposes, Bi-monthly Report, Division D-1, NDRC, Mar.\n14-101 Use of Microwave for Detection Purposes, Bi-monthly Report, Division D-1, NDRC.\n14-102 The Principles of Crystal Rectifiers, F. Seitz, S. Pasternack, University of Pennsylvania\n14-103 Summary of Research on Radar Indicator Screens, H. W. Leverenz, OSRD 891, RCA Manufacturing Company, Inc., Radio Corporation of America\n14-104 Work on Slow Phosphors for Radar Indicator Screens, S. Dushman, OSRD 890, General Electric Company\n14-105 Report on Pulser Tube Development, C. M. Slack, Westinghouse Electric and Manufacturing Company\n14-106 Report on Three-Centimeter Receiving Tubes, J. R. Pierce, A. L. Samuel, Bell Telephone Laboratories, Western Electric Company\n14-107 Progress Report on Hydrogen-Filled Thytrons, H. W. Lord, P. W. Crapuchettes, General Electric Company, Aug. 18, 1942, OEMsr-xxx\n14-108 Report on Developmental work on Pulse Thyratron Type ZG-473, A. C. Gable, General Electric Company, May 6, 1942, OEMsr-180.\n14-109 Use of Microwave for Detection Purposes, Bi-monthly Report, Division D-1, NDRC, Oct. 1, 1942, OEMsr-388.\n14-110 The Electrical Conductivity of Silicon and Germanium, F. Seitz, Jr., University of Pennsylvania, Nov. 3, 1942, OEMsr-388.\n14-111 Transmission of Irises in Waveguides, H. A. Bethe, J. Schwinger, J. F. Carlson, L. J. Chu, Cornell University, Nov. 3, 1942, OEMsr-429.\n\nPart I\n14-113 DC Burn-Out Temperature in Silicon Rectifiers, A. W. Lawson, R. J. Maurer, P. H. Miller, L. I. Schiff, W. E. Stephens, University of Pennsylvania, Nov. 1, 1942, OEMsr-388.\n14-114 Indicator Types as of October 1942, Division 14\n14-115 Investigation of Crystal Rectifier DC Characteristics.\n14-116 Theoretical Results on the TR Box, H. J. Yearian, Purdue University, Jan. 20, 1943, OEMsr-429.\n14-117 Perturbation Theory for Cavities, H. A. Bethe, J. Schwinger, Cornell University, Mar. 4, 1943.\n14-118 Summary of Projects, Bimonthly Report, Division of War Research, University of Pennsylvania, Jan. 1, 14-119 Further DC Burn-Out Experiments on Silicon and Germanium Rectifiers, A. W. Lawson, P. H. Miller, R. J. Maurer, L. I. Schiff, W. E. Stephens.\n14-120 One-Centimeter Magnetron Research, J. M. B. Kellogg, Columbia University, Radiation Laboratory, Jan. 14, 1943, OEMsr-485.\n14-121 Progress Report on Ultra-high Frequency Dielectrics, A. von Hippel, OSRD 1197, Laboratory for Insulation Research, Massachusetts Institute of Technology, January 1943, OEMsr-121.\n14-122 The Interaction Between Electromagnetic Fields and Matter.\nFields and Dielectric Materials, A. von Hippel, R. G. Breckenridge, OSRD 1198, Laboratory for Insulation Research, Massachusetts Institute of Technology, January 1943.\n\nJunction Effect of Two Unequal Matched Coaxial Lines, E. Weber, PIB-1A, Polytechnic Institute of Brooklyn, September 16, 1942.\n\nSummary of Projects, NDRC, Radar Division, 14-125.\n\nElectron Microscopy of Tungsten Points, A. W. Lawson, W. E. Stephens, University of Pennsylvania, March 10, 1943, OEMsr-388.\n\nNoise in Crystal Rectifiers, L. I. Schiff, University of Pennsylvania, March 10, 1943, OEMsr-14-126.\n\nSpectroscopic Determination of Aluminum in Silicon, A. W. Lawson, P. H. Miller, University of Pennsylvania, March 10, 1943, OEMsr-14-127.\n\nTheory of the TR Box, H. A. Bethe, Cornell University, May 14, 1943, OEMsr-429.\n\nThe Diffusion Theory of Crystal Rectifiers.\nR. G. Sachs, Purdue University, September 10, 1942, \"Computers for Radar Control of Plane-to-Plane Gunfire\"\nJ. B. Russell, Division 7, \"Theory of Dark-Trace Tubes,\" I. F. Seitz, O. Stern, I. Estermann, Carnegie Institute of Technology, April 27, 1943, \"Abridged Report on Circuits for Improving Focus on Electrostatic Cathode-Ray Tubes under Conditions of Intensity and Deflection Modulation\"\nH. E. Farnsworth, Brown University, June 1, 1943, \"Theory of Noise in Conductors, Semiconductors, and Crystal Rectifiers,\" V. F. Weisskopf, Purdue University,\nM. M. Hubbard, March 8, 1943, \"Investigation of Power Supply Requirements as a Function of Future Radar Circuit Developments\"\n\"Power Supply for Airborne Radar Equipment,\"\n\"Analysis of Commutation of Direct-Current\"\nI. E. Ross, Jr., Consultant of Division 14 for Project SC-34\n14-137 Simulated High-Altitude Bushing Testing Equipment\n14-138 Clearance for Carbon Brush Investigation\n14-139 Analysis of Commutation of Direct-Current Machinery at High Altitudes\n14-140 Barrier Capacity in Silicon Cartridge Rectifiers\nAndrew W. Lawson, P. H. Miller, L. I. Schiff, W. E. Stephens, University of Pennsylvania\nMay 1, 1943 (OEMsr-388)\n14-141 Summary of Projects, Bimonthly Report\nMeasurement of Dielectric Constant and Loss with Standing Waves in Coaxial Wave Guides\nA. von Hippel, D. G. Jelatis, W. B. Westphal, Massachusetts Institute of Technology\nApril 1, 1943.\n[14-143] Determination of Logarithmic Constants of Crystal Rectifiers with the Oscilloscope, H. J. Yearian, Purdue University, Apr. 20, 1943.\n[14-144] Measurement of Conversion Gain with a Modulated Oscillator, R. N. Smith, Purdue University, Apr. 20, 1943, OEMsr-362.\n[14-145] Crystal Clock Project, Third Progress Report, W. C. Elmore, J. F. Marshall, D. L. Goldwater, W. F. G. Swann, Bartol Research Foundation, The Franklin Institute, May 1, 1943, OEMsr-358.\n[14-146] Noise Reduction by Delayed Feed-Back, T. T. Eaton, Radio Corporation of America, Apr.\n[14-147] Report of Progress of Work on Dark-Trace Tubes, S. Dushman, General Electric, May 1, 1943, OEMsr-358.\n[14-148] Magnetron Cathode Studies, Progress Report, W. F. G. Swann, W. E. Danforth, M. A. Pomerantz, C. D. Prater, W. E. Ramsey, Bartol Research Foundation, The Franklin Institute, May 1, 1943.\n[14-149] Knurled-Type Cathode Construction and Life.\nTest, P. Kusch, Radiation Laboratory, Columbia University, May 26, 1943, OEMsr-485.\nReport on Enclosed Pressure Gaps, C. M. Slack, E. G. F. Arnott, Westinghouse Electric and Manufacturing Company, Dec. 31, 1942, OEMsr-14-150.\nPropagation of 10-Centimeter Waves on a 52-Mile Optical Path over Land, The Correlation of Signal Patterns with Radiosonde Data, P. A. Anderson, C. L. Barker, K. E. Fitzsimmons, S. T. Stephenson, Washington State College, Dec. 31, 1942, OEMsr-14-151.\nRadiotelephone Communication on 3000 Megahertz, P. A. Anderson, C. L. Barker, K. E. Fitzsimmons, S. T. Stephenson, Washington State College, June 12, 1943, OEMsr-728.\nHigh-Frequency Rectification Efficiency of Crystals, A. W. Lawson, P. H. Miller, L. I. Schiff, W. E. Stephens, University of Pennsylvania, July 1, 1943, OEMsr-388.\nOperating Characteristics of Multivibrators.\n[14-155 Operating Characteristics of Multivibrators and Gates and Related Matters, D. A. Wilbur, Rensselaer Polytechnic Institute, January 6, 1943, OEMsr-781.\n14-156 Mechanical Vacuum Switches, Transmission Line and RC Pulsing Circuits, J. V. Lebacqz, T. W. Jarnie, University of California, June 1943.\n14-157 X-Ray Emission from Radar Equipment, L. Rovner, Division 14, NDRC, January 15, 1943.\n14-158 Analysis of 6SA7 Gated Amplifier, B. Rossi, J. Kurshan, Cornell University, July 14, 1943.\n14-159 Analysis of Double Triode Integrator, B. Rossi, N. Nereson, Cornell University, July 14, 1943.\n14-160 Range-Tracking Circuit with Position Memory, B. Rossi, K. Greisen, Cornell University, July 14, 1943.\n14-161 Range-Tracking Circuit with Velocity Memory, B. Rossi, W. B. Jones, Cornell University, July 14, 1943.]\n14-162 Theory of Signal to Noise Ratio of Crystal Mixers, H. Hurwitz, Jr., Cornell University, 14-163 Interference of Loran Pulses with Radiotelephone and Telegraph Reception, M. J. Kelly, Bell Telephone Laboratories, Western Electric, 14-164 Coaxial Exponential Tapers, E. Peskin, E. Weber, PIB-5, Polytechnic Institute of Brookline, 14-165 Effect of Etch on Crystal Rectifiers, A. W. Lawson, W. E. Stephens, University of Pennsylvania, Mar. 10, 1943, OEMsr-388, 14-166 Capacity in Crystal Rectifiers, A. W. Lawson, P. H. Miller, W. E. Stephens, University of Pennsylvania, Mar. 10, 1943, OEMsr-388, 14-167 Crystal Noise as a Function of DC Bias and 30-Mc Impedance Measured with a Diode Noise Source, R. N. Smith, Purdue University, 14-168 Theory of Contact Rectifiers, R. G. Sachs, Purdue University, June 15, 1943, OEMsr-362, 14-169 Magnetron Cathode Studies, Progress Report.\nW. E. Danforth, M. A. Pomerantz, C. D. Prater, W. E. Ramsey, W. F. G. Swann, Bartol Research Foundation, The Franklin Institute,\n\"Bimonthly Project Status Report and Summary of Projects, Division 14, NDRC, July 14-170\"\n\nW. A. Bowers, H. Hurwitz, Jr., H. Levine, Cornell University, \"Theory of Thick Inductive Windows with Small Openings, Nov. 26, 14-171\"\n\nF. Seitz, O. Stern, I. Estermann, R. J. Maurer, Carnegie Institute of Technology, \"The Theory of Dark-Trace Tubes, II, Sept. 1, 1943, 14-172\"\n\nA. W. Lawson, P. H. Miller, L. I. Schiff, W. E. Stephens, University of Pennsylvania, \"Ionization of Donator Levels in Crystal Rectifiers by Thermal Agitation, July 7, 1943, OEMsr-Development of Pulsed Signal Generator, F. L. Burroughs, W. P. Mueller, Sylvania Electric Products, Inc., June 21, 1943, OEMsr-583.\n\nCrystal Clock Project and 10-Kc Oscillator.\nProgress Report, W. C. Elmore, J. F. Marshall, D. L. Goldwater, W. F. G. Swann, Bartol Research Foundation, The Franklin Institute,\nScaling and Relative Efficiency of Different Sized Magnetrons, W. F. G. Swann, Bartol Research Foundation, The Franklin Institute,\nDarkening and Bleaching of KCL, I. Esterman, O. Stern, G. I. Kirkland, Carnegie Institute of Technology, Sept. 1, 1943,\nTwo Notes on the Potentials Developed in Cathode-Ray Screens during Bombardment, F. Seitz, Carnegie Institute of Technology,\nPropagation of Signals on 45.1, 474, and 2800 MHz, G. S. Wickizer, A. M. Bratton, Radio Corporation of America,\nRadio-active Detection of Aluminum in Silicon, A. W. Lawson, P. H. Miller, L. I. Schiff, W. E. Stephens, University of Pennsylvania, Sept. 1, 1944.\nAndrei W. Lawson, P.H. Miller, L.I. Schiff, W.E. Stephens, \"Effect of Tapping on Barrier Capacity,\" University of Pennsylvania, September 1, 1943, OEMsr-388.\n\nR.J. Estermann, F. Seitz, R. Maurer, \"Memoranda on the May 1943 Meeting on Dark-Trace Tubes at Radiation Laboratory, I,\" Carnegie Institute of Technology, OEMsr-900, [May 1943].\n\n\"Bimonthly Project Status Report and Summary of Projects, Division 14, NDRC,\" September 1, 1943.\n\n\"Descriptive Technical Specification, Fighter 14-199 Tail-Warning Equipment, AN/APS-13 (XA1),\" Radio Corporation of America, September 10, 1943.\n\nAndrei W. Lawson, Margaret N. Lewis, P.H. Miller, W.E. Stephens, \"Behavior of Westinghouse Silicon as a Low-Level Detector,\" University of Pennsylvania, September 20, 1943, OEMsr-200.\nMagnetron Cathode Studies, Progress Report \u2013 W. E. Danforth, C. D. Prater, M. A. Pomerantz, W. E. Ramsey, W. F. G. Swann, Bartol Research Foundation, The Franklin Institute, September 1, 1943\n\n14-188 Project List as of September 15, 1943, J. G. Trump, Division 14, NDRC, September 28, 1943.\n14-189 Noise in Silicon Rectifiers at Low Temperatures, Andrew W. Lawson, P. H. Miller, W. E. Stephens, University of Pennsylvania, October 1, 1943.\n14-190 Final Report of Research and Development Conducted on Lighthouse Tube Transmitter-Receiver Units, R. G. Clapp, Philco Corporation, 1943.\n14-191 Airborne Loran Equipment, A. F. Bischoff, General Electric Company, September 1, 1943.\n14-192 The Captive Radiosonde and Wired Sonde Techniques for Detailed Low-Level Meteorological Sounding, P. A. Anderson, C. L. Barker, K. E. Fitzsimmons, Wash.\nCrystal Clock Project and 10-Kc L-C Oscillator, Progress Report, W. C. Elmore, J. F. Marshall, D. L. Goldwater, W. F. G. Swann, Bartol Research Foundation, The Franklin Institute, Dependence of IF Impedance and Noise Temperature of Crystal Rectifiers on Matching Conditions, A. W. Lawson, P. H. Miller, W. E. Stephens, University of Pennsylvania, Oct. 6, 1943 (OEMsr-728)\n\nLightweight X-Band Radar, Progress Report No. 1, R. S. Holmes, Radio Corporation of America, July 1, 1943 (OEMsr-684)\n\nTarrytown, Division 14, NDRC, Oct. 1, 1943.\n\nComparison of Wedge and Cone Contacts on Fox Silicon, Andrew W. Lawson, Margaret N. Lewis, P. H. Miller, W. E. Stephens, University of Pennsylvania, Oct. 22, 1943 (OEMsr-)\n\nA Memorandum on the Scattering of Light by DT Screens, R. J. Maurer, S. Lasof, Carnegie Institute of Technology, Nov. 1, 1943 (OEMsr-)\nAIA-1 Scanner Development Program, Completion Report, T. I. Moseley, Dalmo Victor, Lodar Pulse-Direction-Finding Receiver, G. Mount joy, License Division Laboratory, Radio Corporation of America, Apr. 29, 1943, OEMsr- A Device for the Selection and Manufacture of Low-Level Detectors, A. W. Lawson, M. N. Lewis, P. H. Miller, W. E. Stephens, University of Pennsylvania, Oct. 27, 1943, OEMsr-14-202 The Propagation of 10-Centimeter Waves Over Land Paths of H, 52, and 112 Miles, P. A. Anderson, C. L. Barker, K. E. Fitzsimmons, S. T. Stephenson, Washington State 14-203 Development of a Power Supply and Temperature-Stabilized Oscillator for the Battery-Operated Lodar Receiver, W. Lukas, Emerson Radio and Phonograph Corporation, 14-204 Analysis of Silicon for Non-Volatile Matter, Andrew W. Lawson, K. A. Krieger, University of Pennsylvania, Nov. 11, 1943.\n14-205 The Effect of Temperature on the Darkening and Bleaching of KCL, O. Estermann, G. I. Stern, I. Kirkland, Carnegie Institute of Technology, November 24, 1943, OEMsr-900.\n14-206 Characteristics of Simplified Loran Receiving Equipment, G. Mountjoy, E. Schoenfeld, G. D. Hulst, W. Brown, License Division Laboratory, Radio Corporation of America, November 11, 1943, OEMsr-900.\n14-207 Development of Airborne Loran Receiver-Indicator Model LRN-1, A. Van Dyck, License Division Laboratory, Radio Corporation of America, September 9, 1942, OEMsr-443.\n14-208 Development of Loran Receiver-Trainer, A. Van Dyck, License Division Laboratory, Radio Corporation of America, March 17, 1943, OEMsr-\n14-209 Magnetron Cathode Studies, W. E. Danforth, D. L. Goldwater, M. A. Pomerantz, C. D. Prater, W. E. Ramsey, W. F. G. Swann, Bartol Research Foundation, The Franklin Institute.\n[14-210] Auxiliary Equipment for the MIT Coax Instrument and Its Use, A. von Hippel, D. G. Jelatis, W. B. Westphal, M. G. Haugen, R. E. Charles, Laboratory for Insulation Research, Massachusetts Institute of Technology, November [14-211] Special Protective Coatings, Progress Report, G. D. Patterson, G. T. Vaala, J. L. Keats, E. I. du Pont de Nemours and Company, January [14-212] Propagation of 10-Centimeter Waves over an Inland Lake, Correlated with Meteorological Soundings, P. A. Anderson, K. E. Fitzsimmons, S. T. Stephenson, Washington State College [14-213] Bimonthly Project Status Report and Summary of Projects, Division 14, NDRC, November 1 [14-214] Memorandum Upon the Behavior of DT Screens Containing Magnesium, R. J. Maurer, S. Lasof, Carnegie Institute of Technology [14-215] Progress Report on Coaxial Platinum Film Attenuators, J. W. E. Griemsmann, E. Weber.\n[PIB-2, Polytechnic Institute of Brooklyn, September 14, 1943, J. W. E. Griemsmann, E. Weber, PIB-3, Polytechnic Institute of Brooklyn, September 21, 1943, OEMsr-14-217, S. A. Johnson, PIB-4, Polytechnic Institute of Brooklyn, December 28, 1942,\n\n14-218 Instructions for Use of PIB Type 1B2 Bolometer Terminal, S. A. Johnson, PIB-6, Polytechnic Institute of Brooklyn, May 26, 1943,\n\n14-219 Notes on Use of Bolometers for Ultra-High-Frequency Attenuation Measurements, J. Ebert, PIB-7, Polytechnic Institute of Brooklyn,\n\n14-220 The 1B2 Bolometer Terminal, E. Weber, S. A. Johnson, J. Ebert, PIB-8, Polytechnic Institute of Brooklyn, June 11, 1943, OEMsr-335.\n\n14-221 An Experimental 1/2-Inch Universal Stub, J. Ebert, J. W. E. Griemsmann, PIB-9, Polytechnic Institute of Brooklyn, July 1, 1943,\n\n14-222 X-Band Wave-Guide Tuning Section, J. Ebert]\n[14-223] Progress Report on the Development of One- and Three-CM Magnetrons, J. M. B. Kellogg, Radiation Laboratory, Columbia University\n[14-224] Recent Research on Silicon Rectifiers, A. W. Lawson, M. N. Lewis, P. H. Miller, W. E. Stephens, University of Pennsylvania\n[14-225] Preliminary Measurements on GE X-Band Transmit-Receiver Gas Switch, A. L. Samuel, C. F. Crandell, MM-43-140-68, Bell Telephone Laboratories, Western Electric Company\n[14-226] Crystal Clock Project and 10-Kc L-C Oscillator, Final Report, W. C. Elmore, J. F. Marshall, D. L. Goldwater, W. F. G. Swann, Bartol Research Foundation, The Franklin Institute\n[14-227] Investigation of Effect of Manufacturing and Test Equipment Variables on X-Band Characteristics of Bell System Thermistors, J. N. Shive, Bell Telephone Laboratories, Western Electric Company.\n[14-228] Simplified Loran Receiving Equipment, Mountjoy, E. Schoenfeld, G. D. Hulst, License\nPart I\n\nDivision Laboratory, Radio Corporation of America, June 25, 1943, OEMsr-977\n[14-229] Sintering or Melting of Boron Powder, Progress Report, C. E. Rick, T. D. McKinley, E. I. du Pont de Nemours and Company, November 1943\n[14-230] Two Motor-Driven Gun Turrets, S. Godet, General Electric Company, December 10, 1943,\n[14-231] Sintered Boron Project, Progress Report, C. E. Rick, T. D. McKinley, E. I. du Pont de Nemours and Company, December 1, 1943, OEMsr-\n[14-232] Sintered Boron Project, Progress Report, C. E. Rick, T. D. McKinley, E. I. du Pont de Nemours and Company, January 1, 1944, OEMsr-\n[14-233] The Elimination of Extraneous Resonance Effects in Tunable Centimeter Magnetrons, A. Ashkin, P. Kusch, A. Nordsieck, Radiation Laboratory\n[14-234] The Tuning Properties of the Tunable Magnets in the Three-Centimeter Band, P. Kusch, A. Nordsieck, Radiation Laboratory, Columbia University, January 11, 1944, OEMsr-485.\n[14-235] Cold Impedance of E5 Tubes, G. Becker, S. Millman, Radiation Laboratory, Columbia University.\n[14-236] Development of a Tail-Warning Radar System, TWL-2 (AN/APS-13), R. L. Welsh, Radio Corporation of America, December 30, 1943.\n[14-237] Table of Dielectric Materials, Volume I, A. von Hippel, Laboratory for Insulation Research, Massachusetts Institute of Technology.\n[14-238] Project Report [Radar System Projects], D. Columbia Radiation Laboratory Progress Report, J. M. B. Kellogg, Columbia University, Radiation Laboratory, January 1, 1944, OEMsr-\n[14-239] Sintering and Melting of Boron Powder, Progress Report, C. E. Rick, T. D. McKinley.\n[E. I. du Pont de Nemours and Company, February 14, 14-241 Special Protective Coatings, Progress Report, G. D. Patterson, G. T. Vaala, J. L. Keats, E. I. du Pont de Nemours and Company, February 14,\n14-242 Project Report [Radar System Projects], Di report of Radio Relaying of Radar Signals, V. J. Duke, E. D. Goodale, National Broadcasting Company, Radio Corporation of America, Radio, Division 14, NDRC, February 15, 1944.\n14-245 Waveguide Output for 1.25-Centimeter Magnetrons, S. Millman, Radiation Laboratory, Columbia University, February 1, 1944, OEMsr-\n14-246 Reports of Tests on Resonant Range Follow-Up System, D. W. Moore, H. E. Hale, Fairchild Camera and Instrument Corporation,\n14-247 Special Protective Coatings, Monthly Report, J. L. Keats, G. D. Patterson, G. T. Vaala, E. I. du Pont de Nemours and Company, September 13,\n14-248 Operations of the Project Tube Shop [Harvard]]\n\nThis text appears to be a list of reports from various entities regarding their projects, with dates and titles provided. I have removed unnecessary line breaks and whitespaces, but have kept the original formatting of the titles and report numbers.\n[14-249, N. J. Rison, G. R. Shaw, J. M. Spooner, RCA Victor Division, Radio Corporation of America, \"Dark-Trace Radar-Indicator Screens, Progress Report No. 2\" by H. W. Leverenz, RCA Victor Division, Radio Corporation of America, Feb. 1944, OEMsr-358.\n14-251, W. E. Danforth, D. L. Goldwater, M. A. Pomerantz, C. D. Prater, W. E. Ramsey, W. F. G. Swann, Bartol Research Foundation, The Franklin Institute, \"Magnetron Cathode Studies, Progress Report\" Jan. 1, 1944, OEMsr-1139.\n14-252, C. E. Rick, T. D. McKinley, Pigments Department, E. I. du Pont de Nemours and Company, \"Progress Report on the Sintering and Melting of Boron\" Mar. 1, 1944, OEMsr-1139.\n14-253, R. J. Maurer, S. Lasof, Carnegie Institute of Technology, \"Experiments with Double-Layer DT Screens\" May 12, 1944, OEMsr-900.\n14-254, Monthly Summary and Informal Monthly]\n\nThis text appears to be a list of reports or publications, each with their respective titles, authors, institutions, and dates. There are no apparent errors or unreadable content, so no cleaning is necessary.\n[14-255] The Investigation of the Effect of Manufacturing- and Test-Equipment on the X-Band Characteristics of Bell System Thermistors, J. L. Keats, G. D. Patterson, G. T. Vaala, Chemical Department, E. I. du Pont de Nemours\n\n[14-256] Noise Spectrum of Silicon Rectifiers, P. H. Miller, M. N. Lewis, L. I. Schiff, W. E. Stephens, University of Pennsylvania, Mar.\n\n[14-257] The Theory of Dark-Trace Tubes III, F. Seitz, O. Stern, I. Estermann, R. J. Maurer, Carnegie Institute of Technology, Apr. 6, 1944,\n\n[14-258] The Depth of the Darkened Region and the Build-Up of Darkening and Persistent Trace in KCl Screens, I. Estermann, G. I. Kirkland, Carnegie Institute of Technology, Apr. 10,\n\n[14-259] The Theory of Crystal Mixers in Terms of\nMeasurable-Mixer Constants, R. N. Smith, E. S. Akeley, Purdue University, Mar. 24, 1944, Progress Report for Columbia Radiation Laboratory, J. M. B. Kellogg, Radiation Laboratory, Columbia University,\n\nThe Fixed Tuned Broad-Band Transmitter Disconnect Switch, Some Preliminary Considerations, MM-140-17, A. L. Samuel, Bell Telephone Laboratories, Western Electric,\n\nProgress Report on Sintering and Melting of Baron Powder, C. E. Rick, T. D. McKinley, Pigments Department, E. I. du Pont de Nemours and Company, Apr. 1, 1944,\n\nMonthly Summary and Informal Monthly Progress Report on Protective Coatings, J. L. Keats, G. D. Patterson, G. T. Vaala, W. D. Bailey, Chemical Department, E. I. du Pont de Nemours and Company, Apr. 14, 1944,\n\nTheory of Dark-Trace Tubes IV, F. Seitz, Carnegie Institute of Technology, May 8, 1944.\n14-266 Columbia Radiation Laboratory Progress Report, J. M. B. Kellogg, Columbia University, \"Re\" (no year given), OEMsr-388.\n14-268 Development and Construction of a Local Turret Gyro Lead-Computing Sight for AGS Radar, J. L. Fowler, General Electric Company, (no year given), OEMsr-1220.\n14-269 The Spectral Distribution of the Luminescence of Red-Screen Materials, R. L. Markson, Allen B. Du Mont Laboratories, Inc., March 24, 1944.\n14-270 Division 1U Contract List, Office of the Secretary, Division 14, NDRC, June 1, 1944.\n14-271 General Dynamical Considerations Applied to Piezo-Electric Oscillations of a Quartz Crystal in an Electrical Circuit, W. F. G. Swann, Bartol Research Foundation, The Franklin Institute, April 26, 1944, OEMsr-1220.\n14-271S Supplement to General Dynamical Considerations Applied to Piezo-Electric Oscillations of a Quartz Crystal in an Electrical Circuit, W. F. G. Swann, Bartol Research Foundation, The Franklin Institute, (no year given).\nApplied to Piezo-Electric Oscillations of a Quartz Crystal in an Electrical Circuit, W.F.G. Swann, Bartol Research Foundation, The Franklin Institute, for Supplement I, Div. 14-422, 1-MI, 14-272\nProgress Report on Sintering or Melting of Boron, C.E. Rick, T.D. McKinley, Pigments Department, E.I. du Pont de Nemours, 14-273\nMonthly and Informal Progress Report on Special Protective Coatings, J.L. Keats, G.D. Patterson, G.T. Vaala, R.E. Thomas, Chemical Department, E.I. du Pont de Nemours and Company, May, 14-274\nX-Band Video Crystals, W.E. Meyerhof, W.E. Stephens, University of Pennsylvania, May, 14-275\nThe AGL Receiver, J.C. Wight, General Electric Company, Mar. 23, 1944, OEMsr-233.\nThe Polystyrene Plastics as High-Frequency Dielectrics, Arthur von Hippel, L.G. Wesson.\nS.  L.  Whitcher,  Laboratory  for  Insulation  Re\u00ac \nsearch,  Massachusetts  Institute  of  Technology, \n14-277  Project  Report  [Radar  System  Projects'], Office \nof  Secretary,  Division  14,  Radar,  NDRC,  June \n14-278  Radar  Research  Project  Report  (Supplement \nto  Division  14  Report  No.  277),  Office  of  the \nSecretary,  Division  14  Radar,  NDRC,  July  1, \n14-279  Final  Report,  Including  the  Design  of  Strok\u00ac \ning  Motor  for  a  Hydraulic  Servomechanism, \nG.  S.  Brown,  Massachusetts  Institute  of  Tech\u00ac \n14-280  Special  Protective  Coating,  Progress  Report, \nJ.  L.  Keats,  G.  D.  Patterson,  G.  T.  Vaala,  W. \nD.  Bailey,  Chemical  Department,  E.  I.  du \nPont  de  Nemours  and  Company,  June  13,  1944, \n14-281  The  Investigation  of  the  Effect  of  Manufac\u00ac \nturing  and  Test-Equipment  Variables  on  the \nX-Band  Characteristics  of  Bell  System  Ther\u00ac \nmistors,  J.  B.  Stucky,  Bell  Telephone  Labora\u00ac \ntories,  Western  Electric  Company,  May  27, \n14-282 Production and Effects of a Depletion Layer in Doped Silicon, B. Serin, W. E. Stephens, University of Pennsylvania, May 29, 1944\n14-283 Progress Report on Sintering or Melting of Boron Powder, C. E. Rick, T. D. McKinley, Pigments Department, E. I. du Pont de Nemours and Company, June 1, 1944\n\nHigh-Frequency Characteristics of Rectifiers, K. F. Herzfeld, Purdue University, May 5, 1944\nQuantitative Spectroscopic Analysis of Impurities in Germanium and Silicon, W. Scanlon, Purdue University, May 5, 1944\nTheory of Small Deviations from Pure Diode Behaviour, K. F. Herzfeld, Purdue University, 1944\nDevelopment of Three-Phase Aircraft Alternator, B. E. Wallace, Leland Electric Company, 1944\nCoordinate Transformation Circuits Using Resolvers and Coordinate Transformation by Means of Electrical Networks, B. L. Miller, P. B. Weisz, W. F. G. Swann, Bartol Research\nThe Sperry Stabilized Aircraft Gun-Laying System (AGL-2) - Intermediate Phase: J. P. Hansen, Sperry Gyroscope Company, May\nDesign and Test of Project Eagle Airfoil: F. R. Collbohm, SN-4922, Douglas Aircraft\nSpecial Protective Coatings, Progress Report: W. D. Bailey, J. L. Keats, G. D. Patterson, G. T. Vaala, Chemical Department, E. I. du Pont de Nemours and Company, July 14, 1944\nSintering or Melting of Boron Powder, Progress Report: C. E. Rick, T. D. McKinley, Pigments Department, E. I. du Pont de Nemours and Company, July 1, 1944\nApparatus for the Transformation of Rectangular Coordinates Using Armaresolvers: P. B. Weisz, B. L. Miller, Bartol Research Foundation, The Franklin Institute, July 10\nFinal Report on the Supersonic Radar Trainer Project: J. F. Marshall, H. M. Schwartz, Baranowsky Laboratory, The Franklin Institute.\nThe Franklin Institute, Cathode Sparking, Effect of Superimposed D.C. and Role of Coating Resistance (W. E. Danforth, W. E. Ramsey, W. F. G. Swann, M. A. Pomerantz, D. L. Goldwater, Bartol Research Foundation)\nSparking of Oxide-Coated Cathodes (W. E. Ramsey, Bartol Research Foundation, July 15, 1944, OEMsr-358)\n\nA Portable Signal Generator for Loran Receivers (G. Mountjoy, W. Brown, E. Schoenfeld, G. D. Hulst, Industry Service Division, Radio Corporation of America, June 27, 1944, 14-298)\nPropagation of Signals on U5.1-, WU-, and 2,800-Mc from Empire State Building to Hauppauge and Riverhead, Long Island, New York (G. S. Wickizer, A. M. Braaten, RCA Victor Division, Radio Corporation of America, July 14-299)\nTechnical Report on K-Band Magnetron (P. A. Kalischer, SR-252, Westinghouse Electric and)\nManufacturing Company, May 22, 1944, Sup-14-300 High Dielectric Constant Ceramics, R. G. Breckenridge, A. P. de Bretteville, Jr., J. M. Brownlow, F. G. Chesley, G. Oster, L. Tisza, W. B. Westphal, Arthur von Hippel, Laboratory for Insulation Research, Massachusetts Institute of Technology, Aug. 1944, OEMsr-14-301 Project Report [Radar System Project], Office of the Secretary, Division 14 Radar, NDRC, Aug. 1944, OEMsr-14-302 Aging of KCl Crystals and Screens Under Electron Bombardment, I. Estermann, G. I. Kirkland, Carnegie Institute of Technology, Aug. 1944, OEMsr-14-303 No report, OEMsr-14-304 Effect of Heat Treatment on Low-Level Performance, B. Serin, W. E. Stephens, University of Pennsylvania, Aug. 3, 1944, OEMsr-14-305 On the Distribution of the Average Noise Current in Receivers, M. Kac, Cornell University, Aug. 1944, Monthly Summary and Informal Progress Report.\nJ. L. Keats, G. T. Vaala, G. D. Patterson, Chemical Department, E. I. du Pont de Nemours and Company, August 11, 1944, OEMsr-14-307, Progress Report on Sintering or Melting of Boron Powder, C. E. Rick, T. D. McKinley, J. N. Tully, Pigments Department, E. I. du Pont de Nemours and Company, August 1, 1944, OEMsr-14-308, Temperature Variation of Low-Level Crystal Performance, A. H. Smith, B. Serin, W. E. Meyerhof, W. E. Stephens, University of Pennsylvania, August 17, 1944, OEMsr-388. W. E. Danforth, C. D. Prater, D. L. Goldwater, Bartol Research Foundation, The Franklin Institute, August 25, 1944, OEMsr-358, Back-Bombardment of Magnetron Cathodes. M. A. Pomerantz, D. L. Goldwater, Bartol Research Foundation, The Franklin Institute, August 25, 1944, OEMsr- Secondary Electron Emission from Oxide-Coated Magnetron Cathodes.\n1. Note on the Measurement of Noise Temperature, P. H. Miller, B. Goodman, M. H. Greenblatt, University of Pennsylvania, August 1941\nDesign of Egg Beater Scanning Antenna for the Eagle Radar Bombsight and Construction of a Model, Final Report, G. T. Lorance, International Projector Corporation, August 11, 1943\nDevelopment of Electrical Brushes through Powdered Metallurgy, Technical Report of Research Work Conducted at Metal Powder Laboratory, R. L. Klein, H. Hirsch, Stevens Institute of Technology, November 30, 1943\nDevelopment of 1B27 TR Tube, O. H. Biggs, Sylvania Electric Products, Inc., September 19, 1944\nHigh-Power Series Gaps, Progress Report, F. S. Goucher, Bell Telephone Laboratories, Western Electric Company, September 5, 1944\nA New Method for the Precision Measurement of Waveguide Discontinuities, W. H. Pickering, D. W. Hagelbarger, C. Y. Meng, September [Unknown Year]\nSnowdon, California Institute of Technology, Sintering or Melting of Boron and Preparation of Hyper-Pure-Germanium, Progress Report, C. E. Rick, T. D. McKinley, Pigments Department, E. I. du Pont de Nemours and Company, September 1, 1944, OEMsr-1139.\nRadar Angle Tracking, Government Radar Patent Program, Technical Report No. 1, J. C. Batchelor, Division 14, NDRC, June 28, 1944.\nRotational Line Width in the Absorption Spectrum of Atmospheric Water Vapor and Supplement (dated February 1, 1945), E. F. Barker, A. Adel, University of Michigan, October AIA-1 Scanner Development Program, Progress Report, T. I. Moseley, Dalmo Victor, Inc., October Equivalent Circuit for Resonant Modes of a Magnetron, Zero Mode, W. Lamb, Radiation Laboratory, Columbia University, October 25, 1944.\nThe Resonant Modes of the \u201cRising Sun\u201d (A Tube) Anode, N. Kroll, W. Lamb, Radiation Laboratory, Columbia University.\n[Laboratory, Columbia University, October 25,\nSintering or Melting of Boron and Preparation of Hyper-Pure Germanium, Progress Report, C. E. Rick, T. D. McKinley, Pigments Department, E. I. du Pont de Nemours and Special Protective Coatings, Monthly Summary, P. Salzberg, G. D. Patterson, J. L. Keats, G. T. Vaala, W. D. Bailey, Chemical Department, E. I. du Pont de Nemours,\nThe Properties of Evaporated Layers of Potassium Chloride Containing Small Additions of Metallic Elements When Subjected to Electron Bombardment, R. J. Maurer, S. Lasof, Carnegie Institute of Technology, November,\nDevelopment of Series Spark Gaps for the F. Arnott, Westinghouse Electric and Manufacturing Company, August 14, 1944,\nK-Band Germanium Crystals, Bimonthly Progress Report, August 15 to October 15, 1944, H. Q. North, General Electric Company]\n14-329  A  Converter  for  170-Kc  Loran  Signals,  E. \nSchoenfeld,  G.  D.  Hulst,  W.  Brown,  Industry \nService  Division,  Radio  Corporation  of \n14-330  Final  Technical  Report  for  P3I  Adaptor  De\u00ac \nvelopment,  T.  T.  Goldsmith,  R.  L.  Campbell, \nAllen  B.  Du  Mont  Laboratories,  Inc.,  Oct.  30, \n14-331  U.  S.  Radar  Survey,  Section  1,  Airborne \nRadar,  Office  of  the  Secretary,  Division  14, \n14-332  U.  S.  Radar  Survey,  Section  2,  Shipborne \nRadar,  Office  of  the  Secretary,  Division  14, \n14-333  U.  S.  Radar  Survey,  Section  3,  Ground  Radar, \nOffice  of  the  Secretary,  Division  14,  NDRC, \n14-334  U.  S.  Radar  Survey,  Section  4,  Navigational \nRadar,  Office  of  the  Secretary,  Division  14, \n14-335  No  report. \n14-336  U.  S.  Radar  Survey,  Section  6,  Test  Equip\u00ac \nment,  Office  of  the  Secretary,  Division  14, \n14-337  Evaporated  Films  of  Germanium  and  Silicon, \nM.  N.  Lewis,  J.  H.  Taylor,  R.  J.  Gibson,  Uni\u00ac \nUniversity of Pennsylvania, Oct. 10, 1944, OEMsr-14-338, Ground-Based Radars Other Than Racons and Aircraft Landing, Project Report, Office of the Secretary, Division 14 Radar, NDRC, Oct. 14-339, Government Radar Patent Program, Technical Report No. 2, Precise Range Measurement and Tracking, J. C. Batchelor, Division 14,\n\n14-341 Preparation of High-Voltage Germanium Crystals, R. M. Whaley, Paul Pickar, Purdue University, Nov. 1, 1944, OEMsr-362.\n\n14-342 The High-Voltage Germanium Rectifier, Section I \u2014 Experimental, S. Benzer, Purdue University, Nov. 1, 1944, OEMsr-362. (See NDRC 14-343)\n\n14-343 The Preparation of Sambo Films (Scheme A), P. L. Salzberg, Engineering Division, E. I. du Pont de Nemours and Company.\n[14-344 Special Protective Coatings \u2014 I, Survey\nG. T. Borcherdt, E. I. du Pont de Nemours and Company, February 1, 1944\n\n14-345 Special Protective Coatings \u2014 II, Formulation Studies\nComposition Variables\nM. S. Raasch, Chemical Department, E. I. du Pont de Nemours and Company, February 1, 1944 to August 10, 1944\n\n14-346 Special Protective Coatings \u2014 III, Formulation Studies\nPhysical Processing Variables\nFebruary 1944, Pont de Nemours and Company, OEMsr-1199\n\n14-347 Special Protective Coatings \u2014 IV, Pigment Evaluation\nFebruary 1, 1944 to August 31, 1944, E. D. Bailey, Chemical Department, E. I. du Pont de Nemours and Company, OEMsr-\n\n14-348 Special Protective Coatings \u2014 V, Film Thickness Evaluation\nFebruary 9, 1944 to July 25, 1944, A. A. Johnson, E. I. du Pont de Nemours and Company, OEMsr-1199, Div. 14-132-M3\n\n14-349 Special Protective Coatings \u2014 VI, Cross-Knifed]\nFilms for Practical Work at MIT, Mar. 8, 14-350 Special Protective Coatings \u2014 VII, Knife Casting on Semiworks Wheels, Dec. 23, 1943 to 1944, A. W. Larchar, E. I. du Pont de Nemours and Company.\n14-351 Special Protective Coatings \u2014 VIII, Large-Scale Coating Trials Investigation of Fabric-Coating Equipment, Dec. 14, 1943 to June 6, 1944, B. Graham, Chemical Department, E. I. du Pont de Nemours and Company.\n14-352 Special Protective Coatings \u2014 IX, Spray Trials at Toledo [Engineering Phases, Quality Control], Johnsons, E. I. du Pont de Nemours and Company, OEMsr-1199.\n14-353 Special Protective Coatings \u2014 X, Development of Cement and Paint Making Procedures for D. Bailey, B. Graham, E. I. du Pont de Nemours and Company, OEMsr-1199.\n14-354 Special Protective Coatings \u2014 XI, Development of Machine-Spraying Process for Scheme A.\nE.  I.  du  Pont  de  Nemours  and  Company, \n14-355  Special  Protective  Coatings \u2014 XII,  Character\u00ac \nization  of  Metal  Flakes,  C.  G.  Wortz,  E.  I.  du \nPont  de  Nemours  and  Company,  May  24  to \n14-356  Special  Protective  Coatings \u2014 XIII,  Prepara\u00ac \ntion  of  Film  by  Calendering ,  W.  B.  Pings,  E. \nI.  du  Pont  de  Nemours  and  Company,  June  19, \n14-357  Special  Protective  Coatings,  Methods  of \nAnalysis  for  Aluminum  Film  and  Its  Ingredi\u00ac \nents,  A.  H.  Hale,  Chemical  Department,  Mar. \nNemours  and  Company,  July  1944,  OEMsr- \n14-358  Special  Protective  Coatings,  Monthly  Sum\u00ac \nmary,  P.  L.  Salzberg,  G.  D.  Patterson,  G.  T. \nVaala,  W.  E.  Bailey,  E.  I.  du  Pont  de \nNemours  and  Company,  Nov.  14,  1944,  OEMsr- \n14-359  High-Power  Series  Gaps,  Bimonthly  Report, \nF.  S.  Goucher,  Bell  Telephone  Laboratories, \nWestern  Electric  Company,  Nov.  7,  1944, \n14-360  Metallized-Glass  Attenuators  and  Miscel\u00ac \n14-361 Radar Scanner Development Program Progress Report, T. I. Moseley, Dalmo Victor, Inc.\n14-362 Sintering or Melting of Boron and Preparation of Hyperpure Germanium, Progress Report, T. D. McKinley, E. I. du Pont de Nemours and Company, Nov. 1, 14-363 Device for Determination of the Vertical by Means of Cosmic Rays, B. Rossi, F. C. Chromey, H. S. Sack, Cornell University, July 14-364 Preliminary Results on Calibration of Autotransformers, H. S. Sack, J. J. Taylor, R. N. Work, Cornell University, Jan. 16, 14-365 Errors in Attenuation Measurements Caused by Reflection Losses, E. Weber, PIB-39, Polytechnic Institute of Brooklyn, Mar. 16, 14-366 Mica Windows for Waveguide Output Magnetrons, L. Malter, R. L. Jepsen, L. R. Bloom.\nRCA Victor Division, Radio Corporation of America, January 15, 1945, 14-367 Waveguide Output Magnetrons Employing Fused-Quartz Output Transformers, L. J. Malter, J. L. Moll,\n\nOctober 18, 1944, 14-368 Special Mechanical Counter for the Mark III or Phase-Shift Loran Indicator, A. F. McCulloh, International Business Machines Corporation,\n\nJuly 13, 1944, 14-369 Skiatron Projection Cathode-Ray Tubes with Dark-Trace P10 Screens, R. B. Janes, N. A. Merck, L. B. Headrick,\n\nApril 1944, 14-370 Manual of Operation and Maintenance for SM Radar Trainer, D. D. Israel, Emerson Radio and Phonograph Corporation, OEMsr-890.\n\nOctober 9, 1944, Final Report SM Trainer Development, M. L. Levy, Emerson Radio and Phonograph Corporation, OEMsr-890.\n[14-372 Final Report on the Building of Basic SCR-58 U Trainer and Advanced SCR-584, W. H. Howe, The Foxboro Company, January 24, 14-373 Project Report, Division 14, NDRC, December 1, 14-374 Development of High Back Voltage Germanium Rectifiers, Interim Report No. 1, H. C. Theuerer, J. H. Scaff, Bell Telephone Laboratories, Western Electric Company, November 21, 14-375 The High-Voltage Germanium Rectifier, Section II \u2014 Theoretical, S. Benzer, Purdue University, December 26, 1944, OEMsr-362. {See NDRC 14-376 Cathode-Ray Tube Detectors, H. E. Farnworth, Department of Physics, Brown University, January 1944, OEMsr-382. 14-377 Effect of Small Crystallites on Conductivity, B. Goodman, University of Pennsylvania, April 14-378 Special Protective Coatings, Monthly Summary, P. L. Salzberg, G. D. Patterson, G. T. Vaala, E. I. du Pont de Nemours and Company]\n\nFinal Report on the Building of Basic SCR-58 U Trainer and Advanced SCR-584 (W. H. Howe, The Foxboro Company, January 24, 14-373 Project Report, Division 14, NDRC, December 1, 14-374 Development of High Back Voltage Germanium Rectifiers, Interim Report No. 1, H. C. Theuerer, J. H. Scaff, Bell Telephone Laboratories, Western Electric Company, November 21, 14-375 The High-Voltage Germanium Rectifier, Section II \u2014 Theoretical, S. Benzer, Purdue University, December 26, 1944, OEMsr-362, {See NDRC 14-376 Cathode-Ray Tube Detectors, H. E. Farnworth, Department of Physics, Brown University, January 1944, OEMsr-382. 14-377 Effect of Small Crystallites on Conductivity, B. Goodman, University of Pennsylvania, April 14-378 Special Protective Coatings, Monthly Summary, P. L. Salzberg, G. D. Patterson, G. T. Vaala, E. I. du Pont de Nemours and Company.\n14-380 Preliminary Instructions for Experimental HRY Equipment, Revised, Zenith Radio Corporation, January 20, 1943 (OEMsr-369)\n14-381 K-Band Germanium Crystals, Bimonthly Progress Report, October 15, 1942 to December 15, 1942, H. Q. North, General Electric Company,\n14-382 Final Report, Transformer Model Shop, W. A. Sumner, Westinghouse Electric and Manufacturing Company, December 29, 1944 (OEMsr-1112)\n14-383 Final Report on K-Band Oscillator, Type A5022A, A. P. Kauzmann, RCA Victor Division, Radio Corporation of America, November 7,\n14-384 Government Radar Patent Program, Technical Report No. 3, Magnetrons, J. C. Batchelor.\n[14-385 Final Technical Report on AGL-1, General Electric Company, 1944, D. McKinley, E. I. du Pont de Nemours, 14-386 Final Report - Part I - Sintering and Melting of Boron, Part II, Preparation of Hyperpure D., 14-387 Crystal Audio Noise, P. H. Miller, M. H. Greenblatt, University of Pennsylvania, Jan., 14-388 Project Report, Supplement, Division 14, 14-389 Monthly Summary, Special Protective Coatings, P. L. Salzberg, G. D. Patterson, G. T. Vaala, E. I. du Pont de Nemours and Com-, 14-390 No report., 14-391 Government Radar Patent Program, Technical Report No. U, Duplexing, J. C. Batchelor, Division-, 14-392 Motor Torpedo Boat [MTB] Computing Radar Sight for Blind, Semiblind and Visual Fire, R. H. Wallace, C. G. Hebei, Sperry Products, Inc., 14-393 U. S. Radar Survey, Section 7, Nomenclature, 14-394 Test Equipment for Germanium Second-Development]\nUnits: R. N. Smith, H. J. Yearian, Purdue University, January 25, 1945, OEMsr-362.\n14-395 Special Protective Coatings: Physical Performance Tests on Preferred Sambo System Under Simulated Service Conditions, W. A. Hoffman, C. W. Theobald, E. I. du Pont de Nemours and Company, January 6, 1945, OEMsr-14-396.\n\nPart I\n\nFrequency Stabilization of Oscillators by a Method Particularly Adapted to the Higher Frequencies and Magnetron Sources, L. E. Norton, Radio Corporation of America, May 1, \nHigh-Power Series Gaps, F. S. Goucher, Bell Telephone Laboratories, Western Electric Company,\n\nGermanium Crystal Rectifier for Radar Receivers and Indicator Circuits, Interim Report No. 2, J. H. Scaff, H. C. Theuerer, Bell Telephone Laboratories, Western Electric Company, Project Report, Division 14 Radar, NDRC.\nFinal Report on Broad-Band TR and Anti-TR Tubes, M. D. Fiske, General Electric Company, Dec. 22, 1944\nFinal Report on Broad-Band TR and Anti-TR Tubes, A. L. Samuel, C. F. Crandell, J. E. Clark, Bell Telephone Laboratories, Sept. 30, 1944, OEMsr- Special Protective Coatings, P. L. Salzberg, G. D. Patterson, G. T. Vaala\nThe Scattering of Electromagnetic Radiation by a Narrow Rectangular Strip of Infinite Conductivity, E. S. Akeley, Purdue University, Feb. 15, 1945\nHandy Guide to Crystal Types (with Supplement dated May 10, 1944), W. E. Stephens, University of Pennsylvania, Feb. 15, 1945\nBimonthly Progress Report, December 15, 1944, to February 15, 1945, H. Q. North, General Electric Company, Final Report on Ultraportable Racon.\n[P. J. Herbst, \"Hermetic Seal Collared Wafer Development,\" Radio Corporation of America, Jan. 1, 1944.\nP. W. Crapuchettes, \"Final Report on Pulse Thyratrons,\" General Electric Company, Apr. 14, 1941.\nP. H. Miller and M. H. Greenblatt, \"14-412 Photoeffects in Pure Silicon,\" University of Pennsylvania, Mar. 19, 1941.\nL. L. Boyarsky, R. N. Smith, and H. J. Yearian, \"14-413 Properties of Germanium High-Back Voltage Rectifier Units,\" Purdue University, Mar. 19, 1945.\nF. S. Goucher, \"14-414 High-Power Series Gaps, Bimonthly Report for January and February, 1945,\" Bell Telephone Laboratories, Western Electric Company, Mar. 13, 1945.\nFinal Report on Tubes for Lightweight X-Ray Equipment, [Unknown Authors], [Unknown Organization], [Unknown Date]]\n[14-416] Dependence of Performance of Germanium Second-Detector Units on Bias and Video, L. L. Boyarsky, R. N. Smith, A. W. McDonald, Purdue University, December 1, 1944, OEMsr-684.\n\n[14-417] Government Radar Patent Program, Technical Report No. 6, Fundamental Radar Systems, J. C. Batchelor, Division 14, NDRC, March 1, 1945.\n\n[14-418] Radar Scanner Development Program, Progress Report, September 1 to November 1, 1944, T. I. Moseley, Dalmo Victor, Inc., December 30, 1944.\n\n[14-419] Radar Scanner Development Program, Progress Report, November 1, 1944 to January 1, 1945, T. I. Moseley, Dalmo Victor, Inc., January 1, 1945.\n\n[14-420] Project Report, Division 14 Radar, NDRC, [No year given].\n\n[14-421] No report.\n\n[14-422] Monthly Summary, Special Protective Coatings, P. L. Salzberg, G. D. Patterson, G. T. [No name given], [No year given].\n14-423 Final Report Covering Development Work on High-Power S-Band Magnetron (HP-10V), T.H. Rogers, Machlett Laboratories, Apr. 1, 1945, OEMsr-14-424 Development of a High-Impedance Radio-Frequency Transmission Line, B.H. Maddock, Federal Telephone and Radio Corporation, 14-425 Tables of Dielectric Materials, Volume II, A. von Hippel, Laboratory for Insulation Research, Massachusetts Institute of Technology, 14-426 Monthly Summary: Special Protective Coatings, G.D. Patterson, G.T. Vaala, E.I. du Pont de Nemours and Company, May 12, 1945, 14-427 Final Report: K-Band Germanium Crystals, H.Q. North, General Electric Company, Mar., 14-428 Burnout of X-Band Video Crystals, R.H. Vought, B. Serin, W.E. Meyerhof, University of Pennsylvania, Apr. 10, 1945, OEMsr-\n14-429 Final Report on H2K Roll-Stabilized Scanner, W. M. Cady, Massachusetts Institute of Technology, Maguire Industries, Inc., April 1945, OEMsr-1291\n14-430 Government Radar Patent Program, Technical Report No. 5 R-F Components, J. C. Batchelor\n14-431 Final Report on the Development of Magnetron Generators of High-Power and of Short Wavelengths, J. B. Fisk, Western Electric\n14-432 Final Report on a 3,000-Mc Receiver Using Velocity-Modulation Tubes Type ZP-439, E. B. Hansell, General Electric Company, Sept. 23, 14-433 The Fairchild Central-Station Computer, Part I, The Fairchild .50 Caliber M2 Computer and AGS Adaptations for an Emerson Tail Turret, Part II, Final Report, R. B. Trimble, supervisor, Fairchild Camera and Instrument Corporation, Apr. 30, 1945, D. H. Mitchell, Galvin.\n14-435 Electronic Computers for Division, Multiplication, Squaring, etc., VAC-4, H.S. Sack, A.C. Beer, H.W. Boehmer, Cornell University, April \n14-436 A Mechanical Integrating System Incorporating a Magnetic Amplifier, MA-2, J.W. Trischka, H.S. Sack, Cornell University, December \n14-437 Use of a Specially Designed Magnetic Amplifier in Computing Circuits, H.S. Sack, R.T. Beyer, G. Miller, J.W. Trischka, Cornell University \n14-438 High-Power Series Gaps, Bimonthly Report for March and April, 1945, F.S. Goucher, Bell Telephone Laboratories, Western Electric \n14-439 Notes on the Accurate Measurement of Small Attenuations at Microwaves, J. Ebert, PIB-43, Polytechnic Institute of Brooklyn, April \n14-440 Project Report, Division 14, NDRC, June 1 \n14-441 Germanium Crystal Rectifier for Radar Receivers and Indicator Circuits, Interim Report\n14-442 Development and Construction of Equation Solvers for GCI and SCI Radar Trainers, H. C. Theuerer, J. H. Scaff, Bell Telephone Laboratories, Western Electric Company\n14-443 Transformer Model Shop, Final Report, R. S. Quimby, Raytheon Manufacturing Company\n14-444 K-Band Magnetron, Technical Report, L. Malter, RCA Victor Division, Radio Corporation of America\n14-445 Performance and Stability of Triggered Gates, K. H. Moore, Rensselaer Polytechnic Institute\n14-446 Supersonic Loran Trainer, Final Report, J. F. Marshall, R. P. Shutt, P. B. Weisz, B. L. Miller, P. Hough, Bartol Research Foundation, The Franklin Institute, June 4, 1945\n14-447 Pulse Transformers, Final Report, J. W. Dunifon, Utah Radio Products Company\n14-448 Special Protective Coatings, Monthly Progress\nReport P. L. Salzberg, Chemical Department, E. I. du Pont de Nemours and Company, 14-449 Radio Set AN/MPN-1, XE-1, Ground-Controlled Approach (GCA) Radar, Technical Report\nK. L. Mealey, Gilfillan Brothers, Inc., 14-450 Magnetrons and Detector Beat-Oscillator Receivers with Record of Material Furnished, A. J. Snyder, Bell Telephone Laboratories, Western Electric Company, June 1945, NDCrc-145\n14-451 U.S. Radar Survey, Section 3, Ground Radar, Change 1, Office of the Secretary, Division 14,\nP. L. Salzberg, Chemical Department, E. I. du Pont de Nemours and Company, 14-452 Special Protective Coatings, Monthly Summary, Apr.\nM. N. Lewis, J. H. Taylor, R. J. Gibson, W. E. Stephens, University of Pennsylvania, 14-453 High-Back Voltage Silicon, June 28, 1945,\nW. A. Sumner, Westinghouse Electric, Transformer Model Shop at Sharon, Pa., Final Report\nAnd Manufacturing Company, June 25, 1945,\n14-455 US Radar Survey, Section 4, Navigational Part I,\nRadar, Change 1, Office of the Secretary, Division of,\n14-456 X-Band Crystal Video Performance with Bias,\nW. E. Meyerhof, B. Serin, R. H. Vought, University of Pennsylvania, July 6, 1945, OEMsr-,\n14-457 The Investigation of the Effect of Manufacturing and Test-Equipment Variables on the X-Band Characteristics of Bell System Thermistors,\nJ. B. Stucky, Jr., Bell Telephone Laboratories, Western Electric Company, June,\n14-458 An Improved Type of L-F Loran Transmitter,\nApproved by Stuart W. Seeley, RCA License Laboratory, Radio Corporation of America,\n14-459 An Exciter for L-F Loran Transmitter,\nApproved by Stuart W. Seeley, RCA License Laboratory, Radio Corporation of America.\n[14-461] A New and Practical Method for Matching Two Obstacles in a Wave Guide, S. C. Snow, D. W. Hagelbarger, California Institute of Technology, July 1945\n[14-462] Investigation of the Effect of Manufacturing and Test-Equipment Variables on the X- and K-Band Characteristics of Bell System Thermistors, Final Report, J. B. Stucky, Bell Telephone Laboratories, Western Electric Company, July 1945\n[14-463] Project Report, Supplement, Division 14, P. L. Salzberg, Chemical Department, E. I. du Pont de Nemours and Company, July 1945\n[14-464] Monthly Summary, Special Protective Coatings, P. L. Salzberg, Chemical Department, E. I. du Pont de Nemours and Company\n[14-465] S. Radar Survey, Section 6, Test Equipment, Change 1, Office of the Secretary, Division 14\n[14-466] Electromagnetic Theory, Final Report, R. C. Gibbs, Cornell University, July 1945\n14-467 Special Protective Coatings, Semiworks-Scale Preparation of Machine-Sprayed Film, Graham, Chemical Department, E. I. du Pont de Nemours and Company, OEMsr-1199.\n14-468 High-Power Series Gaps, Bimonthly Report, F. S. Goucher, Bell Telephone Laboratories, Western Electric Company, July 9, 1945.\n14-469 Special Protective Coatings, Formulation Studies \u2013 Exploratory Work for New Uses, B. C. Pratt, Chemical Department, E. I. du Pont de Nemours and Company, OEMsr-1199.\n14-470 Special Protective Coatings, Laboratory Study of Adhesive Systems, XVII, December 14, 1943, to April 1, 1945, W. A. Hoffman, E. I. du Pont de Nemours and Company, OEMsr-1199.\n14-471 Development of a Power Output Tube for NDRC Microwave Section Project 3, Final Report, R. B. Ayer, RCA Victor Division, Radio Corporation of America, July 26, 1945.\n14-472 Tests on Additional Modified Type N Conductors.\n[14-473] Influence of Inner Waveguide Dimensions on Broad-Band Performance of Calibrated Attenuators, J. Griemsmann, L. Nadler, Polytechnic Institute of Brooklyn, March 21, 1945, OEMsr-335.\n[14-474] Use of Sauereisen for Cementing Metallized-Glass Resistor Plates, Preliminary Report, J. Ebert, Polytechnic Institute of Brooklyn, April 1945, OEMsr-335.\n[14-475] A Method of Summing a Slowly Convergent Series, A. E. Laemmel, Polytechnic Institute of Brooklyn, April 5, 1945, OEMsr-335.\n[14-476] X-Band Slotted Section Test Equipment, Memorandum, J. W. E. Griemsmann, Polytechnic Institute of Brooklyn, April 25, 1945,\n[14-477] Frequency Sensitivity of Metallized-Glass Attenuator Inserts Type TMS-4PB, H. C. Nelson, Polytechnic Institute of Brooklyn, May 11, 1945,\n[14-478] Modifications Pertaining to Specifications for\n\n(If the above text is clean enough for your purposes, output the text as is. If not, please specify the necessary cleaning actions.)\nGlass Parts of PIB Type V-3 Variable Attenuator: H. W. Schluening, Polytechnic Institute of Brooklyn, June 2, 1945, 14-479\nMetallized-Glass Plate Program at PIB, Research Conference: Ernst Weber, Polytechnic Institute of Brooklyn, May 22, 1945, OEMsr-14-480\nAccuracy of Attenuation Measurements Made with the Ballantine Voltmeter: H. C. Nelson, Polytechnic Institute of Brooklyn, May 30, 14-481\nMicrowave Resistance Comparator: J. Ebert, Polytechnic Institute of Brooklyn, May 22, 14-482\nFrequency Sensitivity of Metallized-Glass Attenuator Inserts Type TMS-3 PB: H. C. Nelson, Polytechnic Institute of Brooklyn, May [\nThe TMX-14 PB Metallized-Glass Plate for Variable X-Band Attenuator: Maximum 25-db, A. B. Giordano, Polytechnic Institute of Brooklyn, June 2, 1945, OEMsr-335.\nThe TMX-16 PB Metallized-Glass Plate for X-Band Fixed Attenuator: 25 db, A. B. Giordano.\n14-485 The TMX-2/PB Metallized-Glass Plate for X-Band Fixed Attenuator Pads for 10-db and 13-db, A.B. Giordano, Polytechnic Institute of Brooklyn, June 26, 1945, OEMsr-335.\n14-486 A Resistive Variable Attenuator for K-Band with IFo-db Maximum Attenuation, J. Ebert, S. Johnson, Polytechnic Institute of Brooklyn, June 26, 1945, OEMsr-335.\n14-487 Electrical Performance of Metallized-Glass Attenuators for TS-1/7 /UP in Extended X-Band, A.B. Giordano, Polytechnic Institute of Brooklyn, July 6, 1945, OEMsr-335.\n14-488 High-Power Series Gaps Having Sintered Iron Sponge Mercury Cathodes, F.S. Goucher, J.R. Haynes, E.J. Ryder, Bell Telephone Laboratories, Western Electric Company, October 1945.\n14-489 Project Report, Division 14, NDRC, August 1, 14-490 Techniques and Calculations Used in Dielectric Measurements on Shorted Lines IX, W.\n[14-491, P. L. Salzberg, \"Special Protective Coatings\", Massachusetts Institute of Technology, \"Laboratory for Insulation Research\", Monthly Summary and Informal Progress Report, August 13, 1945, Chemical Department, E. I. du Pont de Nemours & Company, 14-492, \"Development of the Skiatron Cathode-Ray Tube for Projection Indicator\", Progress Report No. /, L. E. Swedlund, RCA Victor Division, Lancaster, Radio Corporation of America, August 13, 1945, 14-493, \"Double Triggering and Voltage Balancing for Series Gaps\", BL-R-929-2G-13, H. J. Sullivan, Westinghouse Electric & Manufacturing Company, Bloomfield, N. J., May 22, 1945, 14-494, \"Development of Series Spark Gaps\", Final Report, BL-R-929-2C-14, E. G. F. Arnott, Westinghouse Electric & Manufacturing Company, Bloomfield, N. J., July 12, 1945, OEMsr- 14-495, \"Aircraft Radar Equipment\", Handbook]\nMaintenance Instructions for R-F Head for Army-Navy Model RT-63/APS, British Model 110DB/206, K-Band RF Head, U.S. Army and Navy Departments and the Air Council of the United Kingdom, 0.H. Biggs, Sylvania Electric Products Inc., Salem, Mass., Mar. 10, 14-496.\n\nDevelopment and Production of 50 K-Band RF Heads, Army-Navy Model RT-63/APS, British Model 110DB/206, Sylvania Electric Products Inc., July 6, 1945, OEMsr-1186.\n\nDevelopment of Gun-Fire Control System Mark 56, Final Report, L.R. Lee, Technical Representative, General Electric Company, OEMsr-1299.\n\nResearch and Development Leading to New and Improved Radar Indicators, Final Report, H.W. Leverenz, RCA Laboratories, Princeton, N.J., Radio Corporation of America, NDCrc-14-499.\n\nHandy Guide to Crystal Types III, W.E. Stephens, University of Pennsylvania, Sept.\n\nOperations of the Project Tube Shop.\n14-501 Development Research on X-Band Video Crystals, W. E. Meyerhof, University of Pennsylvania, September 11, 1945, OEMsr-388.\n14-502 Special Protective Coatings, Monthly Summary and Informal Progress Report, P. L. Salzberg, E. I. du Pont de Nemours & Co., 14-503.\n14-503 Advanced Design for Radar Photography with Drawings, P. T. E. Nevius, I. W. Doyle, Fairchild Camera and Instrument Corporation, 14-504.\n14-504 Double Valued Characteristics of Crystal Rectifiers, Comments, B. Goodman, University of Pennsylvania, September 18, 1945, OEMsr-388.\n14-505 Temperature Effects of S-Band Video Crystals, A. Smith, W. E. Stephens, University of Pennsylvania, September 20, 1945, OEMsr-388.\n14-506 Heat Treatment of Germanium Rectifier Materials.\nPART I\n\n14-507 Components of CXHR, SCI Equipment, Final Report, C. C. Lasher, General Electric, August 3, 1945\n14-508 Special Protective Coatings, Final Report, B. C. Pratt, E. I. du Pont de Nemours, December 1, 1935 to September 30, 1945\n14-509 Cathode-Ray Tube Screen Development, A. B. Steadman, S. J. Koch, P. S. Christaldi, Allen B. Du Mont Laboratories Inc., September 14, 1945\n14-510 No report.\n\n14-507 CXHR, SCI Equipment Final Report, C. C. Lasher, General Electric, August 3, 1945 (OEMsr-14-507)\n14-508 Special Protective Coatings Final Report, B. C. Pratt, E. I. du Pont de Nemours, December 1, 1935 - September 30, 1945 (OEMsr-14-508)\n14-509 Cathode-Ray Tube Screen Development, A. B. Steadman, S. J. Koch, P. S. Christaldi, Allen B. Du Mont Laboratories Inc., September 14, 1945 (OEMsr-768, ACE-2)\n14-510 No report.\n\nPart I\n\n14-507 Components of CXHR, SCI Equipment, Final Report\nC. C. Lasher, General Electric\nAugust 3, 1945 (OEMsr-14-507)\n\n14-508 Special Protective Coatings Final Report\nB. C. Pratt, E. I. du Pont de Nemours\nDecember 1, 1935 - September 30, 1945 (OEMsr-14-508)\n\n14-509 Cathode-Ray Tube Screen Development\nA. B. Steadman, S. J. Koch, P. S. Christaldi, Allen B. Du Mont Laboratories Inc.\nSeptember 14, 1945 (OEMsr-768, ACE-2)\nM. A. Pomerantz, \"Secondary Electron Emission from Oxide-Coated Cathodes\", The Franklin Institute, Bartol Research Foundation\nW. E. Ramsey, \"Sparking Phenomena in High Vacuum Thermionic Tubes\", General Survey, The Franklin Institute, Bartol Research Foundation\nM. A. Pomerantz, \"Sintered Thoria Cathodes\", The Franklin Institute, Bartol Research Foundation\nC. D. Prater, \"Effect of Particle Size\", The Franklin Institute, Bartol Research Foundation, October 31, 1945\nC. D. Prater, \"Purification of Barium & Strontium Carbonates\", The Franklin Institute, Bartol Research Foundation, October 31, 1945, OEMsr-358\nC. D. Prater, \"A Note on Nitrocellulose Binders\", The Franklin Institute, Bartol Research Foundation, October 31, 1945\nH. W. Schleuning, \"Precision-Metallization of Glass\", Polytechnic Institute of Brooklyn, Fixed-Value Metallized-Glass Coaxial Attenuator\nAuthors: E. Weber, Polytechnic Institute of Brooklyn, Oct. 31, 1945, OEMsr-335.\nVariable Metallized-Glass Coaxial Attenuators, S. A. Johnson, Polytechnic Institute of Brooklyn, Oct. 31, \nMetallized-Glass Bolometers, S. A. Johnson, Polytechnic Institute of Brooklyn, Oct. 31,\nThe Development of Metallized-Glass Attenuating Elements for X-Band Waveguide, J. E. Ebert, Polytechnic Institute of Brooklyn, Oct. \nMetallized-Glass Waveguide Attenuators, J. E. Ebert, Polytechnic Institute of Brooklyn, Oct. \nThe Development of Metallized-Glass Attenuators for Test Set TS-1A7/UP, E. Weber, Polytechnic Institute of Brooklyn, Oct. 31, 1945,\n14-528 RF Components for Microwave Bridges, A. Laemmel, Polytechnic Institute of Brooklyn,\n14-529 Microwave Power Measurement with Bolometers, E. Peskin, Polytechnic Institute of Brooklyn, Oct. 31, 1945, OEMsr-335.\n14-530 Type N Connector Design and Tests, J. W. E.\n14-531 Microwave Attenuation Standards, A. B. Giordano, Polytechnic Institute of Brooklyn, October \n14-532 Microwave Attenuation Measurement, E. Weber, Polytechnic Institute of Brooklyn, October \n14-533 Development of Miscellaneous R-F Line Components, S. A. Johnson, J. W. E. Griemsmann, Polytechnic Institute of Brooklyn, October 31, 14-534 Precision Metallized-Glass Resistor Units, H. W. Schleuning, Polytechnic Institute of Brooklyn, October \n14-535 Microwave Radar Field and Laboratory Test Equipment and Components, Final Report, E. Weber, Polytechnic Institute of Brooklyn, October \n14-536 Development and Production of Tube Type H50 Hydrogen Thyratron, Final Report, B. Hellring, Kuthe Laboratories, Inc., March 31, 14-537 Constancy of EMF\u2019s of Dry Batteries, H. S. Sack, Cornell University, October 2, 1945, \n14-538 Electronic Computers for Division, Multiplication and Tabulating, R. V. Williams, Massachusetts Institute of Technology, February 15, 1946.\n14-539 Low Thermal Expansion Plastics, H.S. Sack, H.W. Boehmer, Cornell University, October 1945, OEMsr-768\n14-540 Titania Ceramics II, XI, A. von Hippel, R.G. Breckenridge, A.P. de Bretteville, Jr., J.M. Brownlow, Laboratory for Insulation Research, Massachusetts Institute of Technology, October 1945,\n14-541 Design of Equipment for Measuring Di electric Constant and Loss with Standing Waves in Waveguides, M.G. Haugen, W.B. Westphal, Laboratory of Insulation Research, Massachusetts Institute of Technology,\n14-542 An Apparatus for Determining Heat-Distortion Characteristics of Plastics, Paul F. Ast, Laboratory for Insulation Research.\n[14-543 \"Preliminary Oscillographic Studies of R-F Build-up in Magnetron\", G. M. Lee, Massachusetts Institute of Technology, Laboratory for Insulation Research, November 1945, 14-544 \"Development and Wide-Frequency Investigation of Dielectrics\", Final Report, A. von Hippel, Laboratory for Insulation Research, Massachusetts Institute of Technology, October 1945, 14-545 \"Magnetron Cathode Studies\", Final Report, W. F. G. Swann, Bartol Research Foundation, The Franklin Institute, October 31, 1945, OEMsr-358, 14-546 \"Investigation of Circuits of Use in Precision Radar Computers\", Final Report, H. S. Sack, Cornell University, October 30, 1945, OEMsr-768, 14-547 \"Special Protective Coatings, Surface Adjustment of Film (Use B)\", XVI, August 20, 1944 to March 29, 1945, G. T. Borcherdt, Chemical]\n[14-548 Special Protective Coatings, Semiworks Scale, Preparation of Machine-Sprayed Films, XVIII, January 1 to June 1, 1945, J.H. Baldt, Chemical Department, E. I. du Pont de Nemours & Company, OEMsr-1199.\n14-549 Special Protective Coatings, Practical Application Trials (Use A), XIX, February 1, 1944, to April 1, 1945, C.W. Theobald, Chemical Department, E. I. du Pont de Nemours & Company, 14-132-M3.\n14-550 Special Protective Coatings, Practical Application Trials, Laboratory Study of Adhesives, August 31, 1945, W.A. Hoffman, Chemical Department, E. I. du Pont de Nemours & Company.\n14-551 Special Protective Coatings, Formulation Development Studies, XXI, January 1 to August 31, 1945, E.R. Alexander, Chemical Department, E. I. du Pont de Nemours & Company.]\nFilms by G. T. Borcherdt, Chemical Department, E. I. du Pont de Nemours & Company, January 20 to August 31, 1945, 14-553 Special Protective Coatings, Semiworks-Scale Preparation of Machine-Sprayed Films\nB. Graham, Chemical Department, E. I. du Pont de Nemours & Company, June 1 to August 31, 1945, 14-554 Special Protective Coatings, Process Development\nNewburgh, July 23 to August 31, 1945, J. H. Baldt, Chemical Department, E. I. du Pont de Nemours & Company, 14-132-M3\n\nJ. H. Scaff, H. C. Theuerer, Bell Telephone Laboratories, Western Electric Company, 14-555 Preparation of High-Back Voltage Germanium Rectifiers\n\nJ. W. Hinkley, Research Construction Company, Inc., Final Report, Radar Model Shop, December 14-557 General Dynamical Considerations Applied to Piezo-Electric Oscillations of Quartz Crystal\n14-558 Mass Spectrometer Investigation of Silicon Tetrachloride Used in Making Pure Silicon, R. H. Vought, University of Pennsylvania, October 1, 1945.\n14-559 Tests on German Crystals, M. H. Greenblatt, University of Pennsylvania, October 11, 1945.\n14-560 Burnout Life Tests of X-Band Video Crystals, B. Serin, University of Pennsylvania, October 11, 1945.\n14-561 Use of Different Fillers in Crystal Rectifiers, A. H. Smith, University of Pennsylvania, October [].\n14-562 Research and Development of Crystal Rectifiers, Final Report, W. E. Stephens, P. H. Miller, Jr., University of Pennsylvania, October 22, 1945.\n14-563 Geometrical Structure of Silicon Surfaces, W. E. Meyerhof, W. E. Stephens, University of Pennsylvania, October 10, 1945. (OEMsr-388)\n14-564 Burnout of S-Band Video Crystals, M. N. Lewis, University of Pennsylvania, Oct. 19, 14-565 Project Report, Final, Division 14, NDRC, 14-566 Radar Scanning Unit, Final Report, 0. W. Schotz, Chrysler Corporation, Oct. 25, 1945, 14-567 RASD Stable Element, Final Report, R. J. Johnson, General Electric Company, Oct. 30, 14-568 U. S. Radar Survey, Section 8 \u2014 Airborne Radar, Change 1, Office of the Secretary, Division 14, 14-569 Development and Production Samples of APG Series (AN/APG-5 and AN/APG-8) Radar Equipment, Project Report, L. P. Morris, Galvin Manufacturing Corporation, June 30, Supplement, Manual of Maintenance Instructions for Radio Sets AN/APG-5 PART I Supplement, Tests Conducted at Northwestern University, Galvin Manufacturing Corporation, under subcontract, OEMsr-972. 14-570 2CH1A1, AGL-1, Aircraft Fire-Control Component.\n14-571 Development of a High-Frequency Video Amplifier and Radar-Ranging System, Final Report, T. P. Eckert, Jr., T. K. Sharp, University of Pennsylvania, November 15, 1945,\n14-572 Investigations to Prepare a Transparent Phosphor, Final Report, G. W. Morey, Carnegie Institution of Washington, July 31, 1945,\n14-573 Radar Nutating Antenna Spiral Scanning Units, Balance and Adjustment, R. L. Halberg, S. T. Foresman, Chrysler Corporation,\n14-574 U.S. Radar Survey, Section 7, Nomenclature Section 14, NDRC, August 1, 1945. (For Section 7 without Change 1, see Div. 14-510-M2.)\n14-575 Transmission by a Slit in a Partition in a Rectangular Waveguide, E. S. Akeley, Purdue University, March 15, 1945, OEMsr-362.\n14-576 Further Developments in the Preparation and Heat Treatment of Germanium Alloys, R. M.\nWhaley, Purdue University, Oct. 31, 1945,\n14-577 Production and Performance of Germanium High Back Voltage High Back Resistance Crystal Rectifiers, L. Boyarsky, P. B. Picker, A. W. MacDonald, R. N. Smith, R. M. Whaley, H. J. Yearian, Purdue University, Oct. \n14-578 Dependence of Noise Temperature DC and IF Crystal Conductance on Matching Conditions, H. J. Yearian, Purdue University, Oct. 30,\n14-579 Temperature Dependence of High-Voltage Germanium Rectifier DC Characteristics, S. Benzer, Purdue University, Oct. 31, 1945,\n14-580 Photoelectric Effects in Germanium, S. Benzer, Purdue University, Oct. 31, 1945, OEMsr-362.\n14-581 Dependence of Forward Conductance and Back Resistance of High-Back Voltage Germanium on Voltage and Frequency, H. J. Yearian, Purdue University, Oct. 31, 1945,\n14-582 Final Report on Radar Tube Model Shop, O. H. Biggs, Sylvania Electric Products, Inc.\n14-584 Crystal Capacity as a Function of Bias and Its Relation to the Theory of Crystal-Rectification, R. N. Smith, Purdue University, March 1946\n14-585 Final Report on Crystal Developments for Radar Receivers, K. Lark-Horovitz, Purdue University, May 15, 1946, OEMsr-362.\n14-586 Method of Measurement and Some Performance Characteristics of P14 Screens with a Note on Manufacturer's Specifications for Tubes Containing P14 Screens, R. B. Innes, RCA Victor Division, Radio Corporation of America, March 1946\n14-587 Final Report for Contract OEMsr-1044, May 27, 1945 to October 31, 1945 \u2014 Part 1: History of the Contract and Patent Disclosures; Part 2: Triangle Solver for Eagle Project (Delta); Part 3: Triangle Solvers for H2X Bombing Project (Alpha); Part 4: Triangle Solver for Laboratory Use (Gamma); Part 5: Redesign.\nPart 6, Preliminary Ballistics Computer for a Gun-Director System (Eta); Part 7, Ballistic Computer Mark 42, Mod. O (Rho); Part 8, Ballistic Computer Mark 42, Mod. 1, Ser. No. 1. B.B. Willis and D.C. Webster; OSRD 6434. Librascope, Inc.; Oct. 31, 1945. OEMsr-14-588 Magnetrons for Production of Cm. Wavelength Radiation and Absorption of Such Radiation in Water, Final Report, Columbia University Radiation Laboratory, 14-589 Rising Sun Magnetron with a Large Number of Anode Cavities for Cm. and Mm. Wavelengths. A.V. Hollenberg, N. Kroll and S. Millman; Columbia University Radiation Laboratory, 14-590 Development of the SB-811, SB-81 IB and SB-846 Triodes for Pulsed and CW Operation at Microwave Frequency. M.A. Acheson, Sylvania Electric Products, Inc., May 8, 1946.\n14-591 Final Report, H. W. Lord, R. H. Johnson, P. C. Edwards, B. F. Slye, General Electric Company, April 23, 1946\n14-592 Development and Use of the Microband Lock-In Amplifier, G. A. Rosselot, Georgia School of Technology, September 1945, OEMsr-344.\n14-593 The Resnatron Ultrahigh-Frequency Oscillator, September 1, 1940 to June 30, 1942, Progress Reports and Final Report, L. C. Marshall, University of California, April 10.\n14-594 Broad-Band TR-Tube Development, M. D. Fiske, H. N. Wallace, A. D. Warner, General Electric Company, November 7, 1945, OEMsr-1306.\nMiscellaneous Microfilmed Reports Related to Division 14 Projects\nArmy, U. S.\nShoran, a New Type of Radar System for High-Precision Position-Finding in Aerial Navigation, AN/APN-3, AN/CPN-2, Serial No. 58, RCA Laboratories, Industrial Service Division.\nA Simplified Method of Sighting and Releasing Bombs from Airplanes, H.S. Morton, U.S. Army, Ordnance\nH.S. Morton, U.S. Army, Ordnance Department, Mathematical Study of the Timing Function of the Acceleration Integrator, Feb. 25, 1943\nPreliminary Mathematical Analysis of Toss-Bombing, H.S. Morton, U.S. Army, Ordnance Department\nGun Climb, Harmonization and Bullet Pattern, OSRD WA-3266-1, Eighth Air Force, U.S. Army Air Forces\nMethod of Photo Bomb Scoring for the Radar Bombing Technique, Plans and Analysis Section, Department of Training and Operations, Victorville, California\nFighter Gunnery, Rocket Firing and Dive Bombing, Manual No. 64, U.S. Army Air Forces Fighter\nGunnery School, Foster Field, Texas, May 1, 1945.\n\nSpecial Eagle Project Accomplished at Grand Island, Army Air Field, Grand Island, Nebraska; Report: Part I, Bombing Team Training Procedures.\nDE Baker, United States Army Air Forces, 17th Bombardment Operational Training Wing, Sioux Falls, South Dakota.\n\nColorado Springs, Colorado, May 26, 1945.\nStatistical Reports on Radar Bombing.\nCE Duncan, GE Turner, United States Army Air Forces.\n\nBombing Accuracy of Radar Personnel of 315th and 316th Bomb Wings in Training at Victorville, California.\nUS Army Air Forces, Statistical Control Report on Radar Training Conference, Victorville Army Air Field, Victorville, California, July 24-25, 1945.\nR. H. Lewis, US Army Air Forces, Headquarters Victorville Army Air Field.\n\nRadar Bombing Score Analysis, Report No. 23, B.\nU.S. Army Air Forces, Second Air Force, Operations and Training Division, Colorado Springs, Final Report on Training Method and Evaluation of the Acceleration Integrator Bomb Release\nGetz, U.S. Army Air Force Training Research and Liaison Section, Williams Field, Chandler, Arizona, Bell Telephone Laboratories\n\nNotes on Close Support Plotting Board D-170500, Bell Telephone Laboratories, Inc.\nSupplementary Notes on Close Support Plotting Board D-170500, Part One, Electronic Pilot D-170823, Bell Telephone Laboratories, Inc., Western Electric Company\nSupplementary Notes on Close Support Plotting Board D-170500, Part Two, Null Voltage Test Set KS-9470, Bell Telephone Laboratories, Inc., Western Electric\nSupplementary Notes on Close Support Plotting Board D-170500, Part Three, Revised Spare Parts and Equipment List, Bell Telephone Laboratories, Inc.\nWestern  Electric  Company,  Mar.  13,  1945. \nSupplementary  Notes  on  Close  Support  Plotting  Board \nD-170500,  Part  Four,  Variable  Scale  Factor  Conver\u00ac \nsion  Kit  D-171032,  Modification  to  Close  Support \nPlotting  Board  D-171020,  Bell  Telephone  Labora\u00ac \ntories,  Inc.,  Western  Electric  Company,  June  20,  1945. \nTemporary  Information,  Close  Support  Plotting  Board \nD-171020,  Bell  Telephone  Laboratories,  Inc.,  Western \nElectric  Company,  June  27,  1945.  Div.  14-265.1-M8 \nCALIFORNIA  INSTITUTE  OF  TECHNOLOGY \nMethod  of  Computing  Trajectories  and  Sighting  Tables \nfor  Forward-Firing  Aircraft  Rockets,  (Division  3, \nReport  No.  JPC  17),  L.  Blitzer,  L.  Davis,  Jr.,  Cali\u00ac \nfornia  Institute  of  Technology,  Feb.  20,  1944. \nThe  CIT  Aircraft  Rocket  Sight,  Type  2,  (Division  3, \nReport  No.  JNC  23),  H.  W.  Babcock,  California \nInstitute  of  Technology,  Sept.  25,  1944. \nTrajectories  of  Aircraft  Rockets,  3.5\"  and  5.0\" ,  (Divi\u00ac \nReport No. 3: Trajectories of 11.75\" Aircraft Rockets (California Institute of Technology, Division 3, Report No. UBC 27)\nReport No. 30: Sight Settings for 2.25\", 3.5\", and 5.0 \" Aircraft Rockets (California Institute of Technology, Division 3, Report No. UBC 30)\nForward-Firing of Rockets from P-51K Aircraft (California Institute of Technology, Division 3, Report No. JNC 26)\nPart I: Principles of Rocket Firing from Aircraft (California Institute of Technology, Division 3, Report No. JNC 30)\n\nGeneral Electric Company\nAPG-1 Tracking and Firing Tests (Data Folder No. 72649), J. A. Lawrence, General Electric Company, Gunnery Research Unit (Great Britain)\nThe Stability of Blind Firing Systems, GRU/M8, Iowa University\nTechnical Paper REI-TMD-115, Revision 1, I. H. Swift, Joint Radio Board.\nMeeting of Ad Hoc Committee of Joint Radio Board, JRB-20, T AC-322 to T AC-333, F.R. Banks, Joint ORDNANCE DIVISION PROJECT, National Bureau of Standards\n\nEquations for Toss Bombing for the Horizontal Case, Assuming Acceleration is a Function of the Time, W.B. McLean, OD-TB-19, National Bureau of Standards, September 6, 1944.\n\nEffect of Changing Integrator RC Ratio to Correct for an Error in Alignment of Sight with Line of Flight, W.B. McLean, OD-SP-40, National Bureau of Standards, November 7, 1944.\n\nAnalysis of Horizontal Range Error Resulting from Neglect of Pull-Up Angle, S.H. Lachenbruch, OD-SP-45, National Bureau of Standards, November 7, 1944.\n\nUse of the 100-Ft. Horizontal Error Curves for Errors of Other Magnitudes, S.H. Lachenbruch, OD-SP-46, National Bureau of Standards, November 8, 1944.\nGeneral Toss Bombing Solution for the Case of a Non-Constant Acceleration, including the Effect of the Pull-Up Angle\nS. H. Lachenbruch, OD-SP-48, National Bureau of Standards, Nov. 10, 1944.\nApplication of Toss Bombing Equipment to Torpedo Tossing\nS. H. Lachenbruch, OD-SP-56, National Bureau of Standards, Jan. 12, 1945.\nCorrection of the Acceleration Integrator for Air Resistance\nS. H. Lachenbruch, OD-SP-76, National Bureau of Standards, Jan. 12, 1945.\nTables of New 4' Functions and Other Related Quantities\nC. P. Eve and A. London, OS-SP-77, National Bureau of Standards, Jan. 15, 1945.\nNew 4 Card Design\nA. London and A. E. Willgoos, OD-SP-78, National Bureau of Standards, Jan. 17, 1945.\nRocket Tossing Theory\nC. F. Eve, OD-SP-90, National Bureau of Standards, Feb. 24, 1945.\nSolution of Toss Bombing Equations for Circular Motion, S. H. Lachenbruch, A. London, C. F. Eve, OD-SP-98, National Bureau of Standards, Mar. 23, 1945.\nRange Limitations Resulting from Approximations in Toss Bombing Equations, S. H. Lachenbruch, OD-SP-105, National Bureau of Standards, Apr. 16, 1945.\nRange Wind Correction for Toss Bombing, A. London, C. F. Eve, OD-SP-107, National Bureau of Standards, Apr. 1945.\nFunction for Nonconstant Pull-Up Acceleration, C. F. Eve, A. London, OD-SP-123, National Bureau of Standards.\nThe Effect of Sight Misalignment and Angle of Attack Variation, S. H. Lachenbruch, OD-SP-131, National Bureau of Standards, July 23, 1945.\nNaval Ordnance\nRocket Sights, Second Supplement to Research Technical Report No. 10, L. E. Thompson, Laboratories, Naval Ordnance Plant [The Lukas-Harold Corporation], Indianapolis, Indiana, June 30, 1945.\nToss Bombing, Research Technical Report No. 16, L. T. Thompson, Laboratories, Naval Ordnance Plant [The Lukas-Harold Corporation], Royal Aircraft Establishment (GREAT BRITAIN), The Stability of Village Inn Mark I and Means of Improving It, Fire Control Section Memorandum No. Notes on a Method of Obtaining Operational Stability in AGL, Mark I and GGS Systems, Fire Control Section Memorandum No. 98, Report No. Arm. Telecommunication Research Establishment (GREAT BRITAIN), Errors Arising from the Use of a Repeater Aircraft with Oboe, TRE Report No. T-1448, WA-813-8N, Oboe, Electric Mouse, TRE Report No. T-1500, WA-, Oboe, How It Works, TRE Report No. 41M-101/JENH, Laboratory Reports, Regular Reports RL-18, B-18-A Report February 13 to July, Report on XP-61 Mock-up, On Conical Scanning, Mar. 24, 1941, On Aircraft Radio Sight, May 14.\nThird General Report on Section Activities, May 11, 1941 to November 14, 1941\nSpecial Report on Data Transmission RL-22 by I. A. Getting\nSpecial Report on Bolometer Blind-Landing System, B. Chance, D. RL-23\nReport on Preliminary Results with the XT-1, November 15 to December RL-24\nErrors in Range Measurement with a Circular Sweep, January 24, 1942\nImprovements in the Spot-Error Indicating the RF Components of a System, R. A. Lawson\nMicrowave Interference Patterns, J.\nReport on Transmission of 3,000 Me over Sea Water, J. A. Stratton, July 14, 1942\nReport on Transmission of 100 Me over Sea Water, J. A. Stratton, July 14, 1942\nReport on Transmission of 200 Me over Sea Water, J. A. Stratton, July 14, 1942\nReport on Transmission of 500 Me over Sea Water, J. A. Stratton, July 14, 1942\n(C-6) Relation of Radar Range to Frequency\n[Strat: J. A. Strachan, \"Change of Polarization\", Jan. 28, 1943, Proceedings of the IRE, Vol. 31, No. 1, pp. 12-16.\nHutner, R. A., \"Properties of the Diffracted Wave Field Intensity\", ibid., pp. 21-25.\nibid., \"Radar Height Finding\", ibid., Vol. 31, No. 2, pp. 113-117.\nibid., Dodson, H., Gill, J., Parker, F., \"Transmission at Low Altitudes over Sea Water\", ibid., Vol. 31, No. 3, pp. 211-215.\nibid., \"Field Intensity Formulas\", ibid., Vol. 31, No. 5, pp. 335-339.\nAlexander, R. M., Ramsey, N. F., \"Advance Development of 3.3-cm System\", IEEE Transactions on Microwave Theory and Techniques, Vol. MTT-5, No. 2, pp. 125-130, April 1941.\nAlexander, R. M., Roberts, S., \"3-Cm System Group Report\", ibid., Vol. MTT-5, No. 3, pp. 182-186, July 1941.\nRoberts, S., Dicke, R. H., Foster, J. S., \"Measuring Instruments for 3 cm\", ibid., Vol. MTT-5, No. 4, pp. 252-256.\nReport of the System Group, \"Airborne 3-Cm Radar Equipment for AI and ASV Applications\", ibid., Vol. MTT-5, No. 6, pp. 327-331.\nBeacon Discrimination Circuit, J. H., \"Interim Report of the Problems and Progress\", ibid., Vol. MTT-5, No. 7, pp. 397-401]\nPART II\nRL-32 (0-1) Present Status of Radiation Laboratory\nRL-33 (P-1 to 6) Present Status of Radiation Laboratory Program, December 9, 1942 to\nRL-34 (OP-1) Maintenance Experience with ASV Equipment, July 27, 1942.\nRL-35 (OP-2) Correlation of ASV Equipment with the Bombsight, B. L. Havens, D. R.\nRL-36 (R) Roof System Reports, August 26, 1941\nRL-37 (R-1S) Roof System Report, Initial Development, February 15 to April 1, 1941.\nRL-38 (R-2S) Report of Operations [10-Cm Radar] on USS Semmes, July 17, 1941.\nRL-40 (R-4S) Roof System Reports, Aug. 26, 1941 (R-I-1) Incorporated in RL-40.\nRL-41 (R-I-2) Regular Report on the Components Testing System, L. B. Linford, Oct.\nRL-42 (R-I-3) Regular Report on the Components Testing System, L. B. Linford, Nov.\nRL-43: Regular Report on the Components Testing System, D. Bagley, Dec. 17 (Incorporated in RL-40)\nRL-44: Special Report on Buffered Multiple Phase Box, L.B. Linford, S. Seely (Incorporated in RL-40)\nRL-45: Regular Report on the Operation of the Screen Cage, A. Longacre, Oct.\nRL-46: Regular Report of the Advanced Development System, L.B. Linford (Incorporated in RL-40)\nRL-47: Regular Report on Indicators and Synchronizers, R.E. Meagher, Oct.\nRL-47: Regular Report on Indicators and Synchronizers, R.E. Meagher, Nov.\nRL-48: Indicators and Synchronizers, R.E. Meagher, E.C. Pollard, Dec. 24, 1941 (Incorporated in RL-40)\nRL-IV-1: No report.\nRL-IV-2: Incorporated in RL-40.\nRL-IV-3: Incorporated in RL-40.\nRL-50: Regular Report on the USS Semmes, [No Author or Date] (RL-51 is a repetition of RL-50) (Incorporated in RL-40)\nRegular Report on the USS Semmes (3,000-Mc Operations, R.M. Ember) - Incorporated in RL-40.\nRegular Report on X-JO-3 (J.F.) - No report. (Group Report) see Supplement to RL-417.\nRegular Report on X-JO-3 (J.F.)\nRegular Report on Navy Directable K-3 (E.S. Hudspeth) - Incorporated in RL-40.\nRegular Report on Spinners and Radiators (R.G. Herb) - Oct. 15, 1941.\nRL-57 (R-VI-3) Regular Report on Spinners and Radiators - Nov. 26, 1941.\n(R-VII-1) Incorporated in RL-40.\nRL-58 (R-VII-2) Regular Report on XT-3, The 10-Cm Truck System (S. Seely) - Oct. 22.\nRL-59 (R-VII-3) Regular Report on XT-3, Nov. 26.\n(R-VIII-1) Incorporated in RL-40.\n(R-VIII-2) Regular Report on Maintenance - Incorporated in RL-40.\nRegular Report on B-24 (Oct. 29)\n10-Cm ASV Equipment on LB 30 Air planes, D. L. Hagler, June 2, 1942. Incorporated in RL-40.\n\nRegular Report on the PBM-1, R. G. - Regular Report on the CXBH-1,\n\nModulators and Synchronizers, Mar. \nModulators, May 11, 1941.\nReport of the Modulator Group, July\nRegular Report of Modulator Group,\nPeak Currents from Carbonized Thoriated Tungsten Cathodes, W. H.\nInstruction Manual Browning Type A Synchronizer, F. J. Gaffney, Oct.\nReport of Activities of Synchronizer Section, F. J. Gaffney, C. G. Mont-\nTest Set for Raytheon Service Modulator, Instructions for Operation and Testing, P. D. Bales, Nov. 5, 1941.\nR-F Envelope Indicator Instruction Manual, F. G. Dunnington, H. D. Doolittle, Dec. 10, 1941.\nInstruction Manual for Raytheon Service Modulator WX-3587 A, H. J.\nTransmitting Tube Section, Dec. 2,\nTransmitting Tube Section, Dec. 17,\nTransmitting Tube Section, Jan. 13.\nTransmitter Tube Section, January 28, Transmitter Tube Section, March 18, Transmitter Tube Section, May 19, Transmitter Tube Section, July 1, Guide to the Operation of 10-Cm Standard Magnetrons, G. B. Collins, Special Report on Characteristics of 3-Cm Magnetrons and Instructions for Their Operation, G. B. Collins, Note on Design of Magnetrons, G. B. Collins, Waveguide Termination for Measuring Power at 3.2 cm, R. T. Young, Cathode Temperatures in Magnetrons, Report of Parabola Section, December 2, Report of Parabola Section, December 16, Report of Parabola Section, January 22, Antenna Group, February 14, 1941, Report of the Antenna Group, March, Report of the Antenna Group, May 1, Report of the Antenna Group, July 1, Antenna Design and Pattern, L. C. A Study of Fanned-Beam Radiators, Receivers, December 2, 1940, Receivers, December 20, 1940, Receivers and TR Boxes, February 4.\nReceivers, August 1, 1941.\nVisit of Receiver Section to Bell Telephone Laboratories, March 7, 1941.\nSpecial Report on Receivers, June 24, 1941.\nSpecial Report on Tuning Indicators and Automatic-Tuning Systems, H. G.\nSpecial Report on Signal-to-Noise Measurements on Receivers, R. F.\nSpecial Report on 30-Mc Pulsed Signal Generator, P. C. Michel, October 16, 1941.\nSpecial Report on Comparative Signal Noise Measurements on Crystal Mixers and Grounded Grid-Tube, [Unknown Author], [Unknown Date].\nA 1-Cm Oscillator, March 11, 1942.\nI-F Amplifier Design, April 3, 1942.\nTheory of Radiation from Paraboloidal Reflectors, L. J. Chu, February 12, 1941.\n\nPART II\n\nNoise and the Reception of Pulses, J. C. Slater, February 13, 1941.\nImpedance in Transmission Lines and Waveguides, P. M. Morse, April 15, 1941.\nReport on Night Fighter Pursuits, H. [Unknown Last Name]\nTheory of the Magnetron Oscillator, K. T. Bainbridge (Sept.)\nMicrowave Transmission, J. C. Slater (Theory of the Magnetron Oscillator)\nElectronic Orbits in the Cylindrical Magnetron with Static Fields, W. P.\nNotes on Antenna Design, J. A.\nReport on Junction Effects in Waveguides, H. M.\nIdeal Frequency Response of a Receiver for Square Pulses, H. M.\nCorrection of the Scanning of Ship-borne Radar Systems for Roll and Pitch, H. M. James (Dec.)\nTheory of the Split Anode Magnetron, L. Brillouin (Jan. 7, 1942)\nTheory of Diffraction by Small Holes, N. Wiener (Apr. 6, 1942)\nCathode-Ray Indicator (Dec. 29, 1940)\nReport of the Indicator Section (Feb.)\nBrief Report of Activities (Feb.)\nReport of Section VI (March 4 to)\nReport by Indicator Group (May 14)\nSpecial Report for the Cathode-Ray Tube Section (Brief Summary of Persistence Calculations) Feb.\nPersistence Measurements, July 7, 1942\nLuminescence of RCA Cathode-Ray Tube with Cascade Screen, W. B. Nottingham, Feb. 2, 1942.\nIndicator Components in a Complete Aircraft-Interception Installation, W. A. Higenbotham, Apr. 20, 1942.\nKlystron and C-W Test Sets, Dec. Report of the Radio-Frequency Design and Test of Concentric Transmission Lines, J. L. Lawson, July 15, 1941.\nRL-142 (VII-1S) Tentative Simplified Explanation of the Lawson Line, July 25, 1941.\nSpecial Report on Tunable Cavities, Special Report on Transmission Characteristics of Suggested Airplane Nose Materials, Oct. 21, 1941.\nSpecial Report on the Little fuse Bolometer, Oct. 28, 1941.\nSpecial Report on the Reflection of Radar Waves from Various Surfaces, Nov. 11, 1941.\nPlane Waves by Magnetic Substances, Special Report on Design Data for 50-Ohm Rigid Coaxial Line, Dec. 5,\nTheory of a \u201cBlack Body\u201d Produced by a Combination of a Thin Screen and a Perfect Mirror, O. Halpern,\nRL-150 (VII-9S) Transmit-Receive Switch, Jan. 20,\nRL-151 (VII-10S) .RF Components List No. 1, Jan. 20,\nRL-152 (VII-11S) Tests on Undercut Beads in a Concentric Line, W. H. Fenn, Jan. 30,\nRL-153 (VII-12S) Crystals, N. Rochester, Feb. 17, 1942.\nRL-154 (VII-13S) Supplement to Report RL-148 (VIMS), O. Halpern,\nRL-155 (VII-14S) A Method to Measure High-Frequency Permeability of a Ferromagnetic Body, O. Halpern, Feb. 21, 1942.\nRL-156 Scattering of 10-Cm Radiation by a Model Airplane, R. C. Raymond,\nRL-157 Coordination, F. D. Lewis, Dec. 19,\nRL-158 Coordination, Jan. 2, 1941.\nRL-159 (VIII-1S) Recommended Designations of Radar Indicator Types, Feb. 3, 1942.\nRL-160 (41-1) Tune-up Procedure for 3-CM RF System. W. M. Preston, May 25, 1942.\nRL-161 (41-2) Matching, Losses, and Frequency Sensitivity of a 3-CM RF System. W. M.\nRL-162 (41-3) Polarization Effects in a Circular Waveguide at 3 cm. D. D. Montgomery, C. G. Montgomery, Sept. 12,\nRL-163 (41-4) 3-CM Magnetron Cold Impedance. D. D. Montgomery, C. G. Montgomery,\nRL-164 (41-5) Losses and Reflections Introduced by Joints and Plungers in 3-CM Waveguides. C. G. Montgomery, D. D. Montgomery, Oct. 15, 1942.\nRL-165 (41-6) Waveguide Components and Instruments for the 1.25^Cm Region. E. M.\nRL-166 (41-7) Various 3-CM TR Box Characteristics. N. C. Colby, C. W. Zabel, Jan.\nRL-167 (41-8) Measurements with a Frequency-Modulated Oscillator at 3 cm. C. G. Montgomery, D. D. Montgomery, Jan.\nRL-168 (41-9) A Method for Measuring the Absolute Gain of Microwave Antennas, E.\nRL-169 (41-10) Rear Rectangular Guide Antenna\nRL-170 (41-11) Illumination and Phases of Antenna\nRL-171 (41-12) Round Guide Rear Antenna Feeds, J. Radar Echoes from Periscopes, J. E.\nFreehafer, Mar. 1, 1943.\nRadar Echoes from Atmospheric Phenomena, A. E. Bent, Mar. 13,\nPropagation in Waveguides Partly Filled with a Dielectric, N. H. Frank,\nAtmospheric Absorption of Micro-Waves, W. P. Allis, July 1,\nTheory of Space-Charge in an Oscillating Magnetron,\nRadiation Resistance of Antennas Inside Waveguides of Arbitrary Cross Sections, L. J. Chu, July 3,\nNew Approach to Night Fighting, H. M. James, June 26, 1942.\nNew Method of Night Fighting, Abridged Edition of RL-178 (43-5)\nT Junctions in Rectangular Wave Guides, Part I, Theory, N. H. Frank,\nT Junctions in Rectangular Wave Guides.\nGuides,  Part  II,  Final  Formulas  and \nCurves,  L.  J.  Chu,  N.  H.  Frank,  July \nStatistical  Treatment  of  Certain \nPhases  of  Aerial  Combat,  H.  M. \nResonant  Modes  of  the  Magnetron, \nSusceptance  of  Asymmetrically  Lo\u00ac \ncated  Windows  in  Rectangular  Wave\u00ac \nTheory  of  High-Frequency  Rectifica\u00ac \ntion  by  Silicon  Crystals,  H.  A.  Bethe, \nTheory  of  the  Boundary  Layer  of \nCrystal  Rectifiers,  H.  A.  Bethe,  Nov. \nNo  report. \nGeneral  Relations  Determining  the \nRange  of  a  Radar  System,  D.  H. \nEffect  of  Routine  Evasive  Action  on \nthe  Calculated  Approach  Procedure, \nForced  Oscillations  in  Cavity  Reso\u00ac \nPART  II \nReflections  from  Sections  of  Tapered \nTransmission  Lines  and  Waveguides, \nInput  Impedance  and  Tuning  of  Mag\u00ac \nnetron  Cavities,  J.  C.  Slater,  Feb.  3, \nKinetic  Derivation  of  the  Thermal \nNoise  Formula,  P.  R.  Weiss,  S.  A. \nStatistics  of  Circuit  Noise,  S.  A. \nGoudsmit,  P.  R.  Weiss,  Jan.  29,  1943. \nComparison Between Signal and Noise, S. A. Goudsmit, Jan. 29, 1943.\nLumped Constants for Small Irises, Microwave Radar Reflections, J. F. Carlson, S. A. Goudsmit, Feb. 20, 1943.\nPossible Measurement of Radar Echoes by Use of Model Targets, S. A. Goudsmit, P. R. Weiss, Mar. 4, 1943.\nCoupling between Inductive Windows in Waveguides, N. H. Frank, Feb. [---]\nFormal Theory of Waveguides of Arbitrary Cross Section, H. A. Bethe, [---]\nTheory of Side Windows in Waveguides, [---]\nTheory of Magnetron Operation, J. C. Numerical Calculation of Space-Charge Behavior and Power in the Magnetron, G. Vineyard, Mar. 29, 1943.\nExcitation of Cavities through Application of Corner Reflectors to Radar (Theoretical), R. D. O\u2019Neal, [---]\nUse of the Range Clock in Night Fighting with AI Equipment, H. M. [---]\nTheory of Obstacles in Resonant Cavities and Waveguides, J. S. Schwinger, Theory of Circular Bends in Rec[---]\ntangular  Waveguides,  R.  E.  Marshak, \nSpark-Gap  Colloquium  at  Radiation \nLaboratory,  MIT,  July,  1942,  M.  G. \nWhite,  editor,  Sept.  28,  1942. \nModulator  Colloquium,  April  16-17 , \n1943,  A.  S.  Jerrems,  editor,  June  9, \nRotary  Spark-Gap  Modulators,  H.  J. \nWhite,  J.  R.  Dillinger,  May  19,  1942. \nTests  on  Five  Types  of  Triggered \nSwitch  Modulators,  J.  M.  LaRue,  J. \nR.  Perkins,  K.  J.  Germeshausen,  June \nReport  on  Some  Tubes  Used  in  Hard- \nTube  Modulators,  W.  H.  Bostick,  H. \nD.  Doolittle,  W.  D.  Reed,  May  19, \nReport  on  Hard-Tube  Modulators  and \nDrivers,  A.  E.  Whitford,  May  26, \nPulse  Transformers,  S.  Sonkin,  July \nLine-Controlled  Blocking  Oscillator, \nMeasurement  and  Design  of  D-C  Reso\u00ac \nnant  Charging  Chokes,  A.  C.  Dono\u00ac \nModulated  Pulse  Communication,  A. \nS.  Jerrems,  A.  E.  Whitford,  Apr.  13, \nPulse  Transformers,  W.  H.  Bostick, \nP.  R.  Gillette,  H.  L.  Rehkopf,  June  1, \nOscilloscope  Presentation  of  Hys\u00ac \nTeresis, W. H. Bostick, P. R. Gillette, H. L. Rehkopf, \"Tests on Pulse Transformers\", June 1, 1943.\nBostick, W. H., Gillette, P. R., \"Preliminary Report on Frequency Shift vs. Magnetron Box Temperature\", RF Loading of 10-cm Magnetrons, F. Strapping Tolerances for Magnetrons, Magnetron Strapping Wavelength Calculations for Strapped Magnetrons, E. Everhart, \"Fourier Analysis of Pulses with Frequency Shifts During the Pulse\", R. T. Young, \"Frequency and Spectrum Characteristics of Standard Magnetrons and the Effect of Change of Shape of Current Pulse\", \"Practical Considerations of Magnetron Design\", W. V. Smith, \"Performance Characteristics of the Magnetron under Conditions Simulating Beacon Operation\", \"Spectra of Magnetrons for Long Pulses\", R. T. Young, Jr., January 27, March, and July 5, 1943.\nAnalysis of Magnetron Performance\nPart I, Equivalent Circuit, Method, Applications, F. F. Rieke, September 16, 1942.\nField Patterns in Cold Magnetrons, including Correlation with Tube Performance and Tunable Design, W. V. Transmission Line Construction in \u00bd-Inch Coaxial Operating Characteristics of the 707 A Reflex Oscillator (McNally Tube), C. S. Robinson, June 9, 1942.\nOperating Characteristics of the 707 A Reflex Oscillator (McNally Tube), Supplement to Report 53-3, C. S. Robinson, Operating Characteristics of the 17 Reflex Klystron, C. S. Robinson, Jr., Temperature-Compensated 707 A (McNally Tube), C. S. Robinson, Jr., Phase Distortion in Broad-Band Stub Supports, R. V. Pound, August 17, 1942.\nPreplumbing of Tees for G-Band, R. V. Pound and R. Berger, November 3, 1942.\nMicrowave Wattmeter, Part I, M. H. Loss Measurement by Two-Probe\nPower Reversal Method, G. L. Ragan, X-Band Low-Pressure Tests, T. S.\nAn S-Band Crystal Mixer, R. V.\nRotary Joints with EaStub Transformers, W. M. Preston, Dec. 18,\nDielectric Transmission Measurements, E. B. McMillan, Microwave Wattmeter, Part II, 3-cm and 1-cm, M. H. Johnson,\nComparison of the Frequency Sensitivities of Series and Shunt TR Junctions,\nCorrosion of Copper, Brass, and Aluminum by Gaseous Dielectrics, C.\nMeasurements of 721 A TR Tube Leakage Power, L. D. Smullin, Mar.\nX-Band Operating Characteristics of the lfl9 Klystron, C. M. Hepperle, Apr. 23,\nA Method of Measuring the S-Band Characteristic Impedance of Coaxial\nA Simplified Analysis of Conversion Loss of Crystal Converters, S. Robinson,\nPreignition Transmission through\nGas-switching Tubes and Its Contribution to Crystal Failures, F. L. McMillan, Jr., J. B. Wiesner, July 3, Capacity (Choke) Couplings as Rigid and Nonrigid Waveguide Connectors, J. Reed, G. L. Ragan, H. K. Farr, M. Testing of IN21 Navy Crystal Rectifiers, H. B. Huntington, S. Roberts, H. C. Torrey, C. A. Whitmer, July 12, No report.\n\nConversion Loss Measuring Apparatus for Crystals in the 3-Cm Band, S. Part II\n\nEffect of Paraboloid Size and Shape on Beam Patterns, L. C. Van Atta, Graphical Analysis of Beam Patterns from Paraboloid Reflectors, S. G. Sydoriak, L. C. Van Atta, June 11, Pillbox Antenna for Glide Path, C. V. Robinson, Nov. 9, 1942.\n\nSome Matching Properties of Antenna Feeds, H. Krutter, R. Hiatt, J. 3-Cm Bolometer Detector Suitable for Field Measurements (Type Y), S. Horizontally Polarized 9.1-Cm Biconical-Horn Beacon Antenna, C. V. Robinson.\nTitle: Corrugated Coaxial Lines and Wave Guides, G. G. Harvey (Rapid-Scanning, High-Resolution Antennas)\nTitle: An Automatic Recorder for Micro-wave Antenna Pattern Measurements, T. J. Keary, R. E. Alley\nTitle: U5\u00b0Microwave Reflector, S. J. Mason\nTitle: Gratings and Screens as Microwave Reflectors, W. D. Hayes\nTitle: Information on Standard Radiation Laboratory Paraboloid Reflectors, L. C. Van Atta, C. V. Robinson\nTitle: A Simple Method for Determination of the Law of a Crystal, H. Krutter\nTitle: Antenna Feeds for Vs -In. Stub-Supported Coaxial Line, S. Breen\nTitle: Synthesis of Microwave Diffraction Patterns with Application to Csc'd Patterns, R. C. Spencer\nTitle: Double Dipole Rectangular Wave Guide Antennas, W. Sichak\nTitle: Antenna Feeds from -In. Coaxial Line\nTitle: Report of Conference on Rapid Scan Antennas\nTitle: The Antenna Slide Rule, Series L, R.\nC. Spencer, June 3, 1943.\nThe Resonant Echo Box, W. H. Fenn.\nMultiple Pulse Generators, W. O.\nGeneral Report on Low-Level Power Measurement at 10 Cms in Coax, R. N. Griesheimer, Mar. 16, 1943.\nApplication of Corner Reflectors to Radar (Experimental), R. D. O\u2019Neal.\nTemperature-Rise in ATR Racks, S. Production.\nSources of Self-synchronous Units, S. Noodleman, Dec. 1, 1942.\nConference on Standardization of Intermediate Frequency, C. E. Ingalls.\nPreliminary Report on a 10-Cm Super-Regenerative Receiver, J. B. H.\nImpulse and Square-Pulse Response of Various Filters, H. Wallman, June.\nCommittee on Centimeter Receiving Tubes and Resonators, May 18, 1942.\nTheory of Radar Mixers, R. H. Dicke.\nA 10-20-Cm Bolometer, W. M. Brean.\nNoise Measurements on Microwave Converters, W. H. Breazeale, Sept.\nReport on Tests of RCA and GE Lighthouse Tubes, J. B. H. Kuper, P.\nPerformance of the GL446 Lighthouse Tube as an RF Amplifier in the 10-20 cm Region\nW. M. Breazeale, \"M. Lighthouse Tube Anode Contacts\"\n\"Theory of Noise Measurements on Crystals as Frequency Converters,\" S. [---]\n\"Use of the Temperature-Limited Diode in Measurements of Noise Figures of Crystals,\" W. M. Breazeale, Y. [---]\n\"Notes on Measurement of Noise, Gain and Noise Figure of Converters,\" William M. Breazeale, January 30, 1943\n\"Noise-Temperature Measuring Apparatus for Crystals as 10,000 to 30-Megacycle Converters,\" S. Roberts\n\"Low-Level Crystal Detectors,\" R. Ber-\n\"Bers-Band ASV Marker,\" J. S. Kirby-\n\"Fine Grid Technique,\" C. Nawrocki,\n\"A Reciprocity Theorem and Its Application to Measurement of Gain of Microwave Crystal Mixers,\" R. H. A\n\"A 30-Mc Sobering Bridge,\" Y. Beers,\n\"A Video Delay Line,\" D. F. Weekes,\n\"Characteristics of the Present Production of McNally Tubes,\" F. S. Bailey.\nNoise from Local Oscillators, Y.\nAction of Linear Detector on Signals in the Presence of Noise, W. H. Jordan, July 6, 1943.\nThe Radiation Laboratory S-Band Amplifier (Preliminary Report), H. A.\nA 70-Mc Wide IF Amplifier, H. Wall-Plan Position Indicators, Aug. 4,\nProposed Performance Specifications for the P7 Long-Persistence Cascade Screen, W. B. Nottingham, T. Soller,\nReport on Measurements of British CR Tubes with Long-Persistence Screens, W. B. Nottingham, Oct. 7,\nAIA Indicators, L. J. Haworth, Nov.\nPlan Position Indicator Using a Sinusoidal Potentiometer, C. W. Sherwin,\nLinearity of Standard Wire-Wound Volume-Control Type Potentiometers, P. Rosenberg, Feb. 3, 1943.\nConference on P7 Cathode-Ray Tubes,\nA Shipborne Mechanical Rotation Plan Position Indicator, L. Mautner,\nSpecification of Performance Tests for PPI Sinusoidal Potentiometers Types RL10E and RL14, P. Rosenberg, May.\nIndicators for a Ground-Controlled Approach System, C. W. Sherwin, Present Status of Potentiometer Projects in the Radiation Laboratory, P. Rosenberg, June 15, 1943.\n\nPrecision-Timing Calibrator and Range Measuring System, B. Chance, June 1, 1942.\nPrecision-Delay Multivibrator for Range Measurement, B. Chance, M. H. Johnson, R. S. Phillips, June 1, 1943. No report.\n\nMedium Precision Self-Synchronous Range Circuit Model 4, B. Chance, July 6, 1942.\nCircular-Sweep Precision Range System Model 4, B. Chance, July 6, 1942.\nMedium Precision, Self-synchronous Automatic Range-Tracking Circuit Model 4, E. F. MacNickol, Jr., June 1, 1943.\nPhotoelectric Automatic Range-Tracking Unit, A. M. Grass, A. C. Hughes, June 1, 1943.\nSimplified Circular-Sweep Range System, B. Chance, Supplement to 63-8, December, Hand-Radar Ranging Circuit, B., Errors in Circular Sweeps Due to Deformation.\nPART II: Frequency Division with Blocking\n\nOscillator Pulse-Transformers, G. Hite, E. Whitham, B. Chance, Mar.\nLine-Controlled Blocking Oscillator, Marker Generator ARO Calibrator,\nARO Range Follow-up Unit, J. R. MacNichol,\nModel II Calibrator, B. Chance, Apr.\nA Voltage-Compensated Delay Multiplier, C. R. Ahern, A. B. Jacobsen,\nExternally Triggered Circular-Sweep Amplifiers, V. W. Hughes, P. F.\nCalibrator for Low-Altitude Bombing Equipment, J. W. Gray, June 1, 1943.\nDelayed Sweep for SCR-582-X, B.\nAn Adaptation of the Phantastron Delay Multivibrator Circuit to the 6SA7 Tube, R. Kelner, V. Hughes, A. Berg, P. Hinkle, B. Chance, Aug. 21,\nA Condenser Phase-Shifter Range Circuit with Sine-Wave Tracking Suitable for Microwave Height-Finding Stations, A. H. Frederick, June 30,\nPulsed Oscillator and Phase Shifter,\nG. R. Gamertsfelder, July 22, 1943.\nAutomatic Range and Azimuth Tracking: A. B. Jacobsen, F. B. Coffin, W. B. Jones, Jr., B.\n\nH-X Range Unit for Navigation and Bombing: H. J. Reed, A. H. Frederick, Type J and A Test Unit, H. Reed, A. H. Frederick, B. Chance, Aug. 21,\nStanding Wave Detector: J. L. Lawson, May [illegible], Elimination of the CTrombone between Transmitter and Junction in a Duplexing System: J. L. Lawson, May \nMeasurement of Impedance with the Standing Wave Detector: J. L. Lawson, The TR Box: J. L. Lawson, May 13,\nPhotography of Successive Pulse Reflections from a Moving Target: J. L. Lawson, Measurement of the Q-Value of a TR Box: J. L. Lawson, R. L. McCreary,\nComparison of Performance of 10-Cm and 3-Cm Advanced Development Systems: D. Williams, July 13, 1942.\nAltitude Determination by Means of a Vertical PPI: D. Williams, July 31.\nDirect Coupling in the T-R Box, R. L. McCreary, Nov. 3, 1942.\nDefinition of Maximum Range on Aircraft and Its Quantitative Determination, L. B. Linford, D. Williams, V. Josephson, W. Woodcock, Nov. 12, 1942.\nSupplementary Report on Altitude Determination by Means of an Expanded Elevation Indicator, Vertical PPI, L. Linford, D. Williams, V. Josephson, W. Woodcock, Dec. 2, 1942.\nPerformance of 3cm System, D2-1, Time Fluctuations of a Rotary Spark-Gap Modulator, L. Linford, D. Williams, V. Josephson, W. Woodcock.\nA Racon Prospectus with a Pictorial Brief of BGS, A. Roberts, R. Whitmer, J. Sheridan, 1944.\nBGS 10-Cm Radar Beacon, R. M. Whitmer, J. M. Cunningham, June 1, 1944.\nMaximum Power Limitations of Silicon Crystals, B. Cork, Jan. 11, 1943.\nProgress Reports on TR Tubes, A. M. Transmission of Higher Harmonics through a TR Cavity, B. Cork, Jan. 1943.\nSome Experiments in Determining the Power Transmission and Recovery Time of TR Boxes, R. Cork, Jan. 20, 1943.\nMaximum Allowable Negative Back-swing after Pulses, R. Rollefson, R. Infinite Rejection Filters, A. M. Stone, J. L. Lawson, June 1, 1943.\nRecent Performance of the 3-Cm Advanced Development System, D2-1, D. Williams, F. Martin, V. Josephson, July 31, 1942.\nConical Scanning, R. S. Phillips, Aug.\nReport of AAB Test on XT-1 at Fort Monroe, Virginia, February - March,\nModified Homing Course, R. S. Phillips, May\nData on SCR-584 Control Equipment,\nAnalysis of Firing Tests on Mark 51, Dam Neck, Virginia, E. J. Campbell,\nServomechanisms, R. S. Phillips,\nPerformance Report of the High-Power Ground System, E. C. Pollard,\nReport on Aircraft Radio Sight, Apr.\nRadar Target Contrast, E. M. Lyman,\nAirborne Radar Projects in Division.\nPictorial Brief of an Experimental AGL-1 Installation, C.F. West, L.J. Laslett, G. Curran, [May 10, 1943]\nTests on Radar Echoes from Cylinders, R.W. Larson, R.F. Balmer, A. Resistance-Capacitance Networks, C.R. Wischmeyer, Sept. 22, 1942.\nThe Balancing of Spiral-Scan Spin Photographs of the PPI Indicator Tube with 3-Cm ASV over Water and Land, N.F. Ramsey, H.F. Balmer, Photographic Polarization Tests, G.A. Garrett, K.L. Mealey, May 7, 1943.\nSurvey of 10-Cm Radar Installation in PBM-1 Flying Boat, J.F. Koehler\nComparison of Reflectivities of Approximately Similar Plastic and Metal Airplanes, E.E. Miller et al, May [month unclear], Project Dolphin, G.F. Duvall\nDevelopment of a Flexible Relay Servo Mechanism and Application to Sector Scanning Spinner Controls, E. [Last name unclear], [Month unclear],\nTactical Devices Based on Superposition of a Plotting Board on the PPI [Indicator]\nPattern, E. E. Miller, August 8, 1942.\nGeared Selsyns, R. E. Meagher, M. D. McFarlane, October 9, 1942.\nSome Photographic Measures of PPI Linearity and Addendum, N. U. May- Vibration and Shock Comparison Tests of 7-In. Cathode-Ray Tubes in Two Different Type Mounts, E. Pietz, Operational Report on B-2 4, No. 1, in the British Isles, March to June, 1942, Report on the First Radar System Installed on a K-Type Airship, Sept., Comprehensive Report on USS Semmes Radar Installation, R. M. Emberson, October 8, 1942.\nRL-397 (105-1) AI-10 Trainer Simulation at I-F, R. L. Garman, August 24, 1942.\nRL-398 (105-2) AI-10 Bench Trainer Simulation at Video Level, R. L. Garman,\nRL-399 (105-3) Land Mass Simulator.\nOverwater Observations at X and S Frequencies on Surface Targets, O. J. Baltzer, Virgil A. Counter, W. M. Fairbank, W. O. Gordy, E. L. HudComer. Reflector Tests at Langley, C. M. Gilbert, Aug. 6, 1943.\nFinal Report on SRB\u2019s, R. E. Hillger, RF Attenuators, S. G. Sydoriak, Sept.\nStudies of British Phosphors of the Types C, H, K, and M, W. B. Nottingham.\nAn Introduction to Microwave Propagation, D. E. Kerr, P. J. Rubenstein.\nSearch Scans and System Performance Comparison of the Usual Methods of Measuring Conversion Loss of Crystals and a New Empirical Method, S. Roberts, C. A. Whitmer, Aug. 31, 1943.\nPotentiometer, Type RL-B, for Azimuth and Elevation Indication on Magnetically Deflected Cathode-Ray Tubes, P. Rosenberg, July 15, 1943.\nBridge Methods in Low- and Medium-Level RF Power Measurement, R. N. Griesheimer, Sept. 14, 1943.\nAntenna for High-Altitude Bombing.\nAdjustment of Magnetron Frequency by an External Tuner (F. F. Rieke)\nReport on the Microwave Antenna (L. C. Van Atta, G. G. Harvey)\nConference July 19-24, 1943\nLRASV (AN/APA-2) Antenna (L. Buchwalter, G. G. Harvey)\nS/N Measurements on the CV-58 (E. Details of X-Band High-Level TR Tube Test Bench (J. B. Wiesner)\nSupplement A Relative Power Measurer for the TR Test Bench (Mar. 24)\nRange-Height Indicator (R. W. Lee)\nHalf Beacon Antenna (A. Braunlich)\nRadar Detection of Ground Objects from the Ground (J. A. Smith)\nMeasurement of Electric Tuning Ranges of 707 Tubes (J. S. Kirby-)\nA Note on Pulse Distortion by Rejection Filters (A. M. Stone)\nSept. 16, 1943\nSinusoidal Potentiometers Types (Rosenberg)\nReport on Type A and Type B Pulse Transmission Cables and Connectors.\nH. J. White, J. R. Perkins, September 11, 1943. Report on Western Electric 717A Modulator Type D-l 50442 and Radio-Frequency Unit Type D-l 50452, H. One-sided Inductive Irises and Quarter-wave Capacitive Transformers in Waveguide, W. Sichak, November 17, 1943. Characteristics of Recent 723A Tubes (X-Band Local Oscillators), F. Bailey, D. Blaisdell, September 4, 1943. Brief Description of MEW Micro-wave Early Warning, E. G. Schneider. Lighthouse Tube Transmitter-Receiver, LHTR MK I, H. L. Schultz. Aided Tracking, A. Sobczyk, September [---]. Reduction of Radar-Radio Interference from Modulators, L. W. Mallach. Measurement of Pressure in Gas Tubes by a Radio-Frequency Method, Optical Theory of the Corner Reflector, R. C. Spencer, March 2, 1944. Synchro Test Equipment and Test Procedure, I. Polk, March 7, 1944. Amplidyne Servo for SCR-598 Surface Fire-Control Set, C. W. Miller.\nRadar Trainer Equation-Solvers for the Relative Motion of Two Objects in Space, R. L. Garman, M. E. Droz, H. A. Stafford, June 20, \nTraining Apparatus for Radio Set SCR-58b, J. W. Stafford, Aug. 23,\nGCA, Ground Controlled Approach, A Report on ASD-1 B-Scope Photography, S. D. Bennett, Sept. 24, 1943.\nLow-Level Crystal Detectors, Effect of Heat and Cold, E. Berman, Nov.\nAnalysis of Condenser Charging in Line-Type Modulators, Part I, For Linear Reactor Elements, H. J. White,\nContribution of the Dish to the Impedance of an Antenna, S. Silver,\nSimplified Measurement of Receiver Sensitivities, S-Band Noise Source, M. C. Waltz, J. B. H. Kuper, Sept. 17,\nMHF Mobile Height Finder, Modified Cold Resonance Theory of the Waveguide Tunable Magnetron, M. A. AN/APS-b, ASH, Trainer G. R.\nThe Effect of Atmospheric Refraction on Short Radio Waves, John E. Free-\nA One-Tube, One-Selsyn Sector-Scanner, E. E. Miller, Dec. 6, 1943.\nThe Identification of Signals on PP1 Photographs for the Construction of Radar Maps, N. U. Mayall, Oct. 20, 1943.\nWeight Analysis of Airborne Radar, R. Platzman,\nAnalysis of Magnetron Performance, Part II, Detailed Study of the Operation of a Magnetron, R. Platzman, Nov. 4, 1943.\nAided Tracking, A. Sobczyk, Nov. 4, 1943.\nAided Tracking, R. S. Phillips, Nov.\nTheory of Random Processes, G. E. Uhlenbeck, Oct. 15, 1943.\nProbe-Fed Slots as Radiating Elements in Linear Arrays, R. E. Clapp,\nBrief Description of AN/TPG-1, AN/FPG-1, SCR-598, Developmental Seacoast Gunlaying Radar Sets, H. A. Strauss, Oct. 8, 1943.\nDifferential to Single-Ended Potential Converters, J. W. Gray, D. MacRae,\nThe Depolarization of Microwaves, M. Kessler, C. E. Mandeville, E. L. Hudspeth, Nov. 1, 1943.\nSinusoidal Potentiometers, Types RL11, RL15, RL20U, P. Rosenberg.\nPart II:\n\nThe Simplified Methods of Field Intensity Calculations in the Interference Region, W. T. Fishback, Dec. 8, 1943.\nThe Cooling of Pressure-Tight Containers, A. E. Vershbow, E. L. Leakage, Inductance and Distributed Capacitance of Various Types of Pulse-Transformer Windings, P. R. Gillette, W. H. Bostick, H. L. Rehkopf.\nTests on an M3B1 Oil Gear and an Amplidyne Servo for the SCR-598 Control Problem, H. T. Marcy, C. W. On the Fluctuations in Signals Returned by Many Independently Moving Scatterers, A. J. F. Siegert, Nov.\n\nOn the Appearance of the A-Scope when the Pulse Travels through a Homogeneous Distribution of Scatterers, E. G. Martin, F. C. Hudson.\nPropagation over Short Paths and Rough Terrain at 200 MHz, A. B.\n\nA Cathode Follower Employing Two Tubes to Obtain Extremely Low Output Impedance, [Unknown Author]\nPut: Resistance (C. M. Hammack), \"Pulse - Transformer Core Material Pulse Measurements\" (H. L. Rehkopf, W. H. Bostick, P. R. Gillette), Dec. 10, 1943.\nShielding of Microwave Receivers against Interference at Intermediate Frequencies (B. Cork), Aug. 8, 1944.\nAntenna Parts and Measuring Equipment (W. M. Preston, J. B. Platt), Dec. 2, 1943.\nSupplement (W. M. Preston), May 31, \nTruck-Mounted SCR-582 MK III, a General-Purpose Microwave Set (C. Report),\n\"Report on K-Band Work in U.S.A.\" (Climate in Relation to Microwave Radar Propagation in Panama, A. E. Sudman),\nOverinterrogation Control of Micro-wave Beacons (I. Sudman), Dec. 11,\n\"Preliminary Measurements of 10-Cm Reflection Coefficients of Land and Sea at Small Grazing Angles\" (P. J. Rubenstein, W. T. Fishback), Dec. 11,\nParaboloid Antenna Characteristics as a Function of Feed Tilt (S. Silver, C. The Detection of Moving Targets.\namong  Ground  Clutter  by  Coherent \nPulse  Methods,  R.  A.  McConnell,  Dec. \nThe  Observation  of  RF  Phase  in  Pulse \nRadar,  R.  A.  McConnell,  A.  G.  Emslie, \nRemote-Position  Control  by  Direct- \nFrequency  Variation,  D.  L.  Jaffe, \nRadome  Bulletin  No.  1,  E.  B.  McMil\u00ac \nRadome  Bulletin  No.  2,  An  Outline  of \nthe  Electric  Properties  of  Radomes, \nRadome  Bulletin  No.  3,  Ice  Forma\u00ac \ntion  on  Shipborne  Radomes,  J.  S. \nRadome  Bulletin  No.  4,  Transmission \nand  Reflection  of  Single  Plane  Sheets, \nR.  M.  Redheffer,  July  12,  1944. \nRadome  Bulletin  No.  5,  Recent  Dielec\u00ac \ntric  Constant  and  Loss  Tangent  Meas\u00ac \nurements,  E.  M.  Everhart,  July  14, \nRadome  Bulletin  No.  6,  Radomes  and \nSystem  Performance,  R.  M.  Red\u00ac \nRadome  Bulletin  No.  7,  The  Measure\u00ac \nment  of  High  Reflections  at  Low \nPower,  R.  M.  Redheffer,  Nov.  20, \nRadome  Bulletin  No.  8,  X-Band  Sand\u00ac \nwiches  at  Variable  Angles  bf  Inci\u00ac \ndence,  E.  Everhart,  Dec.  19,  1944. \nRadome  Bulletin  No.  9,  The  Match\u00ac \ning  of  High  Standing  Wave  Ratios, \nRadome  Bulletin  No.  10,  The  Meas\u00ac \nurement  of  Small  Reflections,  Y.  Dow- \nker,  R.  M.  Redheffer,  Feb.  6,  1945. \nRadome  Bulletin  No.  11,  Electrical \nProperties  of  Double-Wall  and  Sand\u00ac \nwich  Radomes,  R.  M.  Redheffer,  Feb. \nRadome  Bulletin  No.  12,  Transmission \nand  Reflection  of  Parallel  Plane \nSheets,  R.  M.  Redheffer,  Jan.  26,  1945. \nRadome  Bulletin  No.  13,  Elliptical \nPolarization  Produced  by  Stream\u00ac \nlined  Radomes,  R.  M.  Redheffer,  Feb. \nRadome  Bulletin  No.  14,  An  Investi\u00ac \ngation  of  R-F  Probes,  Y.  Dowker,  R. \nM.  Redheffer,  Feb.  6,  1946. \nRadome  Bulletin  No.  15,  The  Measure\u00ac \nment  of  Dielectric  Constants  in  the \nOne-Centimeter  Band,  R.  M.  Redhef- \nRadome  Bulletin  No.  16,  Some  Elec\u00ac \ntrical  Aspects  of  Microwave  Sandwich \nRadome  Design,  E.  R.  Steele,  May  9, \nRadome  Bulletin  No.  17,  Current \nProgress on R-F Research, Hegarty, Y. Dowker, R. M. Redheffer, Radome Bulletin No. 18, The Dependence of Magnetron Pulling on Radome Shape and Orientation, R. M. Redheffer, Radome Bulletin No. 19, Dielectric Constant and Loss Tangent Computation, Y. Dowker, August 7, 1945, Radome Wall Reflections at Variable Angles of Incidence, E. M. Everhart, No report, Transmission of Lossy Sandwiches, Y. No report, Dielectric Constants and Loss Tangents of Radome Materials, T. J. Electrical Test Methods for Radomes, Lighthouse Tube Superregenerative Receivers, R. I. Jacobson, January 11, Model 7, Experimental Hydrogen Thyratron Modulator, H. J. Hall, February, A Simplified Search Antenna for Radio Set AN/MPN-1, L. J. Chu, C. F. Porterfield, January 1, 1945, Instruments and Methods for Measuring Temperature and Humidity in the Lower Atmosphere, I. Katz, April.\nQualitative Survey of Meteorological Factors Affecting Microwave Propagation, Isadore Katz, J. M. Austin, H. J. Riblet, Results of Tests Performed on Synchro Units and Systems, E. R. Perlight, A. Long\nComparative Photographs of 1- and 5-Microsecond Signals, P. J. Rice, The Resonant Modes of Magnetron Cavities, H. Goldstein, The Theory of Corrugated Transmission Lines and Waveguides, H. Goldradar, Radar Tracking Analysis, E. J. Campbell, Operation of 1N23 Crystal Rectifiers, The Range Calculator, S. J. Mason, Colloquium on Pulse-Transformer Design, P. R. Gilbert, Editor, Jan. 15, 1944.\nElements of Loran, B. W. Sitterly, Results of Tests on Use of Rebecca-Eureka by the Army Ground Forces, Manufacturing Procedure for the\n\n(Note: The text appears to be a list of titles of scientific papers or articles, likely published in a journal or conference proceedings. No cleaning was necessary as the text was already clean and readable.)\nThe Two-Disc D-C Thermistor Bridge Circuit: R. Krock, N. H. Painter, E. E. Miller, D. B. McLaughlin\nPrecise Navigation by Means of a Radar Map Superposed on the PPI: E. E. Miller, D. B. McLaughlin\nBeavertail Height Finder: A. Longacre\nA Method for Relay Radar PPI Synchronization: R. K. Mosher, April 20, 1940\nV-Beam GC Radar: A. Longacre\nRadio Set RHB: Technical Description of the Production Model, Section I\nAdjustment and Alignment of Radio Set RHB: E. M. Lyman, January 17, 1941\nRadio Set RHB: Glider Checkout Procedure, P. R. Stout\nPart II\nRadio Set RHB: Test Equipment, J. J. Hibbert, J. E. Magnetron Starting Time, K. R. Pulse-Length Discrimination in Beam Adjustment of Lorans and Antenna-Coupling Units at Frequencies between 1,700 and 2,000 Kilohertz.\nImpedance Characteristics and Equivalent Circuits for Vertical Radiators, R. B. Lawrance, A. J. Pote, Apr. 15, Pulse Transformers, Radiation Laboratory and Produced by General Electric Company and Westinghouse Electric and Manufacturing Company, P. R. Gillette, High-Ambient Life Test of an Oil-Filled Pulse Transformer, H. R. Zelter, Proposed Method for Measuring Instantaneous Magnetron Input Impedance with the Aid of a Delay Network, O. T. Fundingsland, Feb. 22, A Condenser Phase-Shifter Range Unit with Sine-Wave Tracking for AN/TPG-1, AN/FPG-1, SCR-598, S-Band Horizontally Polarized Non-directional Antennas, H. J. Riblet, Pulse Shapes and R-F Spectra for Combinations of Stromberg-Carlson Mark I and Mark II Modulators with 2J22, 2J21, and 725 A Magnetrons, Aspen Airborne Antenna, H. J. Riblet, High-Frequency Characteristics.\nResistors,  D.  T.  Drake,  Mar.  9,  1944. \nA  Diode-Type  Pulse  Voltmeter,  O.  T. \nFundingsland,  A.  S.  Jerrems,  July  6, \nTests  of  Beacon  Receiver  on  V-Beam, \nJ.  M.  Sturtevant,  Dec.  4,  1944. \nVoltage  Pulse  Rate-of-Rise  Measure\u00ac \nments,  O.  T.  Fundingsland,  July  10, \nRL-524  Stagger-Tuned  I-F  Amplifiers,  H. \nRL-525  Thyrite  Bridge-Controlled  Voltage \nRegulator,  H.  E.  Kallmann,  Mar.  9, \nRL-526  Elimination  of  Ground  Clutter,  E.  C. \nRL-527  Effect  on  Current  Pulse  of  Resistance \nin  Series  with  the  Magnetron,  W.  H. \nRL-528  The  Effect  on  Noise  Figure  of  Plac\u00ac \ning  the  Gain  Control  on  the  First  I-F \nStage,  Y.  Beers,  A.  B.  Macnee,  Mar. \nRL-529  High  Impedance  Cable ,  H.  E.  Kall\u00ac \nRL-530  Bombing  Errors,  E.  H.  B.  Bartelink, \nRL-531  Rotating  Corrugated  Eccentric  Line \nAntennas,  L.  Buchwalter,  G.  G.  Har\u00ac \nRL-532  Theoretical  Calculation  on  Best \nSmoothing  of  Position  Data  for  Gun\u00ac \nR. S. Phillips, P. R. \"RL-533 Observations of Life Rafts Equipped with Corner Reflectors\"\nE. L. Huddleston \"RL-534 Space Charge between Parallel Plane Grids\"\nJ. K. Knipp \"RL-535 A Hard-Tube Servoamplifier for Fractional Horsepower DC Motors\"\nO. J. Baltzer, W. M. Fairbank \"RL-536 Polarization Studies at S and X Frequencies\"\nH. F. Webster \"RL-537 Observations on Signal Stability at S and X Frequencies\"\nH. Wallman \"RL-538 Performance of Coupling for 1Vz-In. by 3-In. Waveguide\"\nH. Wallman \"RL-539 Stagger-Damped Double-Tuned Circuits\"\nV. W. Hughes \"RL-540 A Range-Measuring System Using an RC Linear Sweep\"\nC. A. Helber \"An Automatic Frequency-Control and Frequency-Selection System for Magnetrons\"\nLighthouse RF Envelope Indicator\nCrystal Life Tests under Flat Pulses\nH. B. Huntington, April 7, 1944.\nFrequency Division with Blocking Oscillators, Part I, R. B. Woodbury,\n\"The Evaluation of an Equivalent Circuit for a Pulse Transformer,\" W. H. Bostick, P. R. Gillette, H. L. Rehkopf, H. R. Zeller, May 8, 1944.\nAnalysis of the Influence of Pulse Transformers on Current Pulse Shape, W. H. Bostick, P. R. Gillette, H. L. Rehkopf, H. R. Zeller, June 16, 1944.\nMicrowave Transmission over Water and Land under Various Meteorological Conditions, Pearl J. Rubenstein, Isadore Katz, L. J. Neelands,\n\"A Littlefuse Direct-Reading Watt Model 6, Modulator Performance Equalized Delay Lines,\" H. E. Kall,\nBurgoyne, April 6, 1945.\nThe Sealing of Air at Rotating Shafts and Joints, A. I. Winslow,\nPulse Doppler for Detection of Moving Ground Targets, R. F. Thomson,\nAn Airborne S-Band Racon for Rooster Operation, E. R. Gaertner.\nServos  with  Torque  Saturation,  Part \nI,  W.  Hurewicz,  N.  B.  Nichols,  May \nFading  Simulator,  W.  Roth,  May  10, \nLeaky  Waveguide  Rapid  Scanner, \nJ.  Steinberger,  Nov.  18,  1944. \nRL-558  A  60-Mc  Parallel  Schering  Bridge , \nRL-559  Final  Report  on  SMTR  to  January \nRL-560  A  Precision  Plan-Position  Indicator , \nRL-561  Wave  Form  Analysis,  O.  Abbiati, \nRL-562  A  Moving  Target  Selector  Using  De\u00ac \nflection  Modulation  on  a  Storage \nMosaic,  R.  A.  McConnell,  A.  G. \nEmslie,  F.  Cunningham,  June  6,  1944. \nRL-563  A  Precision  Z-Sweep  Generator,  R.  A. \nMcConnell,  May  23,  1944. \nRL-564  Rieke  Diagrams  and  Probe-Plate \nPlunger  Charts  of  Lighthouse  Tubes \nin  a  Re-entrant  Cavity,  R.  E.  Taylor, \nRL-565  Stabilized  High  Voltage  Supply,  E. \nRL-566  N2  Gate  Attachment  for  SCR-584, \nJ.  S.  White,  R.  B.  Leachman,  May  3, \nRL-567  Magnetron  Tuning  and  Stabilization, \nRL-568  Further  Measurements  of  3-  and  10- \nReflection Coefficients of Sea Water at Small Grazing Angles (RL-569), W. T. Fishback, P. J. Rubenstein\nPreliminary Report on the Fluctuations of Radar Signals (RL-570), H. Goldstein\nCharacteristics of Recent 723A/B Tubes (RL-571), D. N. Sands, F. S. Bailey\nEffect of Pulse Length on System Performance and Operation (RL-571), R. Rollefson, A. H. Nelson, L. A. Hart\nClamping Tubes (RL-572), C. W. Sherwin\nA Precision Self-Synchronous Range System for P3I (RL-573), G. Hite, G. E. Whitaker\nRevision of General Radio Type 605-B Signal Generator for Pulsing (RL-574 Part II)\nA High Resolution K-Band Ship Search Set (RL-574), W. M. Fairbank, W. T. Harrold, G. D. Sheckels, J. D. Fair\nS-Band End-Fire Array Antenna (RL-574), H. J. Riblet, B. L. Birchard, July 11, 1944.\nAccuracy Criteria for the Gun Director MK 56 (RL-574), R. S. Phillips, C. H. Dowker, June 9, 1944.\nMedium Precision Range System for CXGQ, Project Henry, G. Hite, Sept. A Survey of High-Vacuum Diodes Used for Surge-Limiting Operation in Modulators S. J. Krulikoski Ultraportable Microwave Radar Beacons as Beam-Approach Aids in Aircraft Landing L. H. Orpin Simple Computation of Distance on the Earth's Surface B. W. Sitterly BUPS (AN/UPN-1, 2) an Ultraportable S-Band Radar Beacon and Its Tactical Uses A. Roberts An H-B Impact Predicting Computer Assuming Constant Indicated Airspeed for Use with AN/APS-15A Corners, Bends, and Twists in Rectangular Waveguide R. M. Walker Effects of Variation of Vane Width and Cathode Size on the Operation of Magnetrons M. Healea Aug. 1, 1944 Dielectric Windows in Waveguide Performance Characteristics of Army-Navy Preferred Type Electrostatic Cathode-Ray Tubes R. P. Abben.\nSummary of Life-Test Data on Sylvanian W35 Hydrogen Thyratrons (S. J. Krulikoski, Feb. 1, 1945)\nSiting and Range of Microwave Beacons (W. M. Preston, July 5, 1944)\nResults of Field Tests on AN/UPN-1, -2 (Experimental Models of BUPS) at Boca Raton, Florida (January-March, 1944) (R. P. Ghelardi, Aug. 12)\nServos with Torque Saturation (Part 1) (R. Levine, F. L. McMillan)\nChemical Methods for Maintaining the Partial Pressure of Water Vapor in TR Tubes (R. Levine)\nThe 1B27 TR Tube (L. D. Smullin)\nThe SCR-58U Plotting-Table System (Florida Tests on ROSEBUPS Against Ghelardi, July 27, 1944)\nA Range Only Set for Close-in Seeing (C. E. Mandeville, W. T. Harrold)\nStandards for Microwave Frequencies\nGE GL2CU0 Taut Grid Lighthouse Antenna Measuring Equipment\nHigh Power CW Transmitter for S-Band\nAntenna Measuring Equipment (100-\nLinear Audio Amplifier, 0.A.\nAntenna Measuring Equipment, Automatic Antenna Pattern Recorder, 0.\nStatistics of Beacon Interrogation, H.\nMeasurements of the Attenuation of K-Band Waves by Rain, G.T. Radaro,\nVideo Stretching as a Method for Improving X-Band Beacon Reception, T.H. Waterman, S.D. Bennett, Aug.\nTrigger Requirements of the UC35 and SCU5 Hydrogen Thyratrons, S.J. Krulikoski, Aug. 31, 1944.\nA Description of AN/TPS-10 and Its Performance in Mountainous Terrain, Vixen X, M.M. Mann, F.T. Worrell,\nCorner Reflectors for Life Rafts, E.L. Hudspeth, J.P. Nash, Aug. 1,\nCathodes for Pidsed Magnetrons, Part I, Correlations Between Oscillating and Diode Conditions, E.A. Coomes, J.G. Buck, A. Fineman, Aug. 30,\nMatching Resistance Curves by Means of Two Linear Ganged Potentiometers and a Three-Terminal Resistance Network, Testing of Fixed-Tuned, Low-Q, ATR.\nTubes, L. D. Smullin, Dec. 6, 1944.\nErrors in Target Velocity Due to Rolling and Pitching of the Ship\nModification of the Amplifier of the AN/APN-2 to Give Sharp Cut-off Wide-Band Response\nH. Wallman, G.\nNomograms for Radar Bombing with the 100-Lb Practice Bomb M38A2\nW. Low-Altitude Navigation Antennas\nDeveloped in Connection with AN/\nEffects of Line- and Cathode-Follower Terminations on Pulse Shape\nF. E. Dole, Mar. 12, 1946.\nA Method of Virtual Displacements for Electrical Systems with Applications to Pulse Transformers\nP. D. Energy Loss in Copper under Pulse Conditions\nW. H. Bostick, Dec. 22,\nStability of Magnetrons Operated by Spark-Gap Modulators\nD. F. Winter\nIncreasing Stability of Operation of UJ31, 35 Magnetrons in the AN /CP S-1 System\nD. F. Winter, H. A. Miley.\nInfluences of Pulse Transformer Design on UJ31, 35 Magnetron Stability, D. F. Winter, H. A. Miley, Aug. 11, S-Band Vertically Polarized N on-directional Antennas, H. J. Riblet, K-Band Cosec2 Antennas with a Line Source and Shaped Cylindrical Reflector, W. Sichak, E. M. Purcell, Nov. The Future of Hyperbolic Navigation, An Extension of Lagrange's Equations to Electromagnetic Field Problems, Equivalent Networks, P. D. Comparison of Theoretical and Experimental Requirements for Micro-wave Beacon Transmitter Power and Receiver Sensitivity, E. R. Gaerttner, T. H. Waterman, H. S. Gardner, Jr., Analysis of Tracking Data, Description of Calculations, P. A. Samuelson, A Treatise on Echo-Box Problems by Lagrangian Procedures, P. D. Theory of Ringing Time of Tunable Echo Boxes, A. Banos, Jr., Nov. 3, Design of an Improved X-Band Echo Field Station for Antenna Measurements.\nErrors in the Condenser Type Continuous Phase Shifter, G. R. Gamert\nReduction of Power-Line Noise in Modulators, G. J. Wheeler, Dec. 11\nLinear Electric Scanner, J. S. Foskett, Vertical Coverage of a 5-Ft Antenna for SG-3, C. E. Realizability of Filters, H. Wallman, Crystal Detectors and the Crystal-Video Receiver, R. Beringer, Nov. 16\nSG-1 Antenna Mark 2, R. W. Thick, Antiaircraft Target Designation Equipment for Ships, R. W. Blue, C. 1B38 (Pre-TR), L. D. Smullin, Dec.\nDesign of a U-Ft Corner Reflector for K-Band, E. G. Martin, Aug. 20\nThe Use of the Magic Tee Microwave Bridge in Measuring Impedance, R. Dielectric Properties of Water and Ice at K-Band, E. L. Younker, Dec. 4\nQA-2B Servoadaptor, W. Roth, Dec.\nQl-2 and Q-3 Servoamplifier, R. U.\nThe 1-3 Signal Unit, S. B. Cohen, Feb.\nThe J-2 Modulator Unit, E. M. Jones,\nThe H-2 Trigger Unit, S. B. Cohen,\n1-2 Signal Unit, S. B. Cohen, Aug. 30,\nThe R-1 and R-2 Crystal Drivers,\nThe ML-1A, ML-1B, and ML-3A Course Mechanisms, C. M. Connelly,\nLieutenant J. B. Higley, Nov. 28, 1945.\nTrol Units, C. M. Gilbert, Feb. 11,\nThe S-5 and S-5B Motor Control Units, Lieutenant J. B. Higley, Feb.\nThe U-1 and U-2 Preamplifier Units,\nX-1 Error Integrator, W. Hodder,\nN-1 IFF Unit, G. W. McClure, Mar.\nParallel Plate Optics for Electrical Scanning, S. B. Myers, Dec. 15, 1944.\nOverland Falcon, E. H. B. Bartelink,\nElectrical Design of the AN/TPS-10,\nOver-Water Transmission Measurements, 19 Uh, Part I,\nPreliminary Analysis of Radio and Radar Measurements, P. J. Rubenstein, Dec. 15,\nA Qualitative Analysis of Hysteresis.\nReflex Oscillators, J. B. Garrison, The Ocean Surface, R. B. Montgomery, Frequency \u2014 Wavelength Conversion, E. DeAmicis, Jan. 4, 1945.\nFlared Box Horn, S. J. Mason, July 9, 1945. [Report Withdrawn.]\nRotating Corner Reflectors for Ship Identification, J. M. Sturtevant, Jan.\nShaping the Primary Pattern of a Characteristics of Horn Feeds on Rectangular Waveguide, J. R. Risser, No report.\nA Microfilm Chart Projector for Radar Navigation, D. B. McLaughlin,\nSU-2 Antenna \u2014 Shipborne Stabilized Radar Antenna for Sea Search, T. J. Keary, J. I. Bohnert, Mar. 7, 1945.\nSU-2 Antenna \u2014 Line-of-Sight Stabilization of a Radar Beam by Reflector Tilt, J. I. Bohnert, T. J. Keary, Feb.\nReflections from Smooth-Curved Surfaces, A. Microwave Frequency Discriminator, K. R. More, W. W.\nRL-664, Further Theoretical Investigations on\nThe Atmospheric Absorption of Micro-Stabilized SG-3 Antenna, J. I. Bohnet, H. Krutter, Feb. 7, 1945.\nEquivalent Circuit of a Pulse-Transformer Core, H. L. Rehkopf, Mar. 20, 1945.\nA Feedback Circuit for Measuring Output Noise Ratio of Crystal Rectifiers, S. Roberts, Jan. 10, 1945.\nA Conversion Loss Set for Testing K-Band Crystal Rectifiers, C. A. Whitaker, Jan. 23, 1945.\nA Simple Trainer for GCA Approach Controller, C. M. Gilbert, G. F. Tape,\nIdentification of GCA Search Targets, Theory of Radar Return from the Schnorkel, P. M. Marcus, Jan. 15, 1945.\nBlack Maria \u2014 Coincident Cross-Band Transponder for S-Band Radar [AEW], C. E. Stone, G. D. Perkins,\nData Smoothing, F. P. Coffin, P. D. Crout, F. E. Bothwell, Jan. 23, 1945.\nDeflection Yoke Design Information, Low-Power RF Switch, A. M. Stone,\nTests on the Performance of the Mk 1 Radio Set.\nMod 7 Computer, PR Weiss, Plan Position Indicator for 58U AJ, Information on Radiation Laboratory Paraboloid Reflectors, T. W. Lashof, Theory of Characteristic Functions in Problems of Anomalous Propagation, RL-681 TFX-29RL Frequency Comparator, L. Dissipation in Series Gaps and Voltage-Current Relationships during Discharge, J. R. Dillinger, Aug. 31, Division of Voltage Across Series Spark Gaps in a Line-Type Modulator, J. R. Dillinger, F. E. Bothwell, General Characteristics of Enclosed Spark Gaps with Emphasis on Aluminum Cathode Type Series Gaps, J. R. Dillinger, Jan. 30, 1946. Some Characteristics of the 1B4.1, 1BJ/5, and 1BJf9 Series Spark Gaps, Operation of Sintered Iron Sponge-Mercury Cathode-Type Series Gaps at SCI, AEW, and 5-Microsecond Conditions, J. R. Dillinger, Jan. 16, 1946. Line-Type Modulator and HP10V Magnetron.\nPart II:\n\nCathodes for Pulsed Magnetrons, E. A. Coomes, J. G. Buck, A. S. Eisenstein\nThe Absorption of One-Half Centimeter Electromagnetic Waves in Oxygen, E. R. Beringer\nA Low-Drag Beacon Antenna for Fighter Aircraft, A. S. Dunbar, M. E. Van Valkenburg\nPrimary Feeds in Cylindrical Parabolic Shapes, M. W. P. Strandberg\nAutomatic Frequency Control Circuits, M. C. Strandberg\nThe SCI Rapid Scan Height-Finding Antenna, C. V. Robinson, M. A. Tagart, M. D. Pearson\nRadar Echoes from Precipitation Horn Feeds for Parabolic Antennas, [Unknown Author]\n\nDouble-Curvature Surfaces for Beam Shaping with Point-Source Feeds, S. [Unknown]\nSynthetic Radar Echoes in the Presence of Jamming, A. M. Stone\nColloquium on Pulse-Forming Networks, October 12, 1945, P. R. Gilkeson\nNotes on the Reflex Oscillator, J. K. A Proposed Standard Test Cavity for the 70-MHz Tube, J. B. H. Kuper, P. A. BUPX (AN/UPN-S, 4, AN/APN-U), Ultraportable X-Band Radar Beacons and Their Tactical Uses, H. L. Gar Frequency Discontinuities of Local Oscillator Tubes Due to High-Q Load Circuits, R. V. Pound, Nonlinear Networks as Voltage Regulators, H. E. Kallmann, May 21, 1945 Analysis of Over-Water Tracking, E. Flight Behavior of the Flux Gate and Gyrosyn Compasses and Their Effects, A Treatment of Echo-Box Problems by Lagrangian Procedures, Part II, P. D. Crout, N. H. Painter, Mar. 16, 1945 Front-Line Demarcation and Bombing with the Aid of Lightweight X-Band The Regulation Obtainable in the Operation of a Hard-Tube Modulator with Magnetron Load, G. N. Glasoe, Band Beacons (BUPX)\nTactical Tests, October 1948-February \nCalculation of Pulse-Forming Networks Having Slow Rates of Voltage \nM.H, E.R. Lyman, J.B. Platt, \nTokyo H2X Photographs \u2014 Comparison of Operational PPI Photographs \nLow-Noise Replacement Preamplifier with PPI Predictions of the Ultrasonic Radar Trainer, P. Rosenberg, \nLink Conversion Unit for Ground-Control Approach, C.M. Gilbert, C.R. Haupt, May 7, 1945. \nThe Effect of Clutter Fluctuations on MTI, M. Goldstein, Dec. 27, 1945. \nControlled Approach Trainer, C.M. Gilbert, C.R. Haupt, May 7, 1945. \nStable Scanners and Unsteady Air Notes on Load Effects in Reflex Oscillators, J.B.H. Kuper, M.C. Waltz, \nField Intensity Contours in Generalized Coordinates, H. Dodson, J. Gill, \nMemorandum on the Activation of Various Surfaces by Evaporation from a Heated Oxide Cathode, E.A. \nOverwater Tests of S-Band Early Warning for Ships, Vertical Coverage of the CXHR (SCI) Search System.\nA Theoretical Treatment of Radar Target Return, Part I, P. D. Croat, Surface Coverage of Some Shipborne Pulse Characteristics of Common Receiver-Type Tubes, R. B. Woodbury, Radar Sets on S, X, and K-Bands, J. D. Fairbank, W. M. Fairbank, Matchmeter, H. E. Kallmann, On Servos with Pulsed Error Data, Altitude Return in the AN/APS-6, Pulse Transformer Committee Standard Test Methods for Pulse Transsea-Return Effects and Their Elimination in the AN/APS-6, E. W. former Cores, W. H. Bostick, K-Band High-Power Water Load, R. Design Considerations for Directional Couplers, R. J. Harrison, Dec. 31, P+I, Photographic Projection PPI, Waveguides without Metal Walls, R. Flight Tests of Block I Relay Radar System, R. M. Alexander, Apr. 24, Echoes from Tropical Rain on X-Band Airborne Radar, A. E. Bent.\nAn Aerial Investigation of K-Band Radar Performance, R. S. Bender, Two Proposed Methods of Recording the Position of a Moving Link Crab, Experiments in Microwave Breakdown, D. Q. Posin, I. Mansur, H. F., Operational Characteristics of 2Ch3 Tubes as Pulsed Oscillators in a Reentrant Cavity, M. E. Gardner, June, A Theory of a Supersonic Delay Line, Equivalent Network for the 232-BW Pulse Transformer Based on the Method of Virtual Displacements, The Relation Between Absorption and the Frequency Dependence of Reflective Double Coaxial Coupler for BUPX, The Use of a Twin-T Network in a Selective Frequency Amplifier, with Special Applications, R. M. Walker, A Wide-Excursion Frequency-Modulated Alignment Oscillator or Wobbulator, H. L. Johnson, May 31, 1945, Flight Tests of AEW Block III Relay Synchros and Their Characteristics.\nRange-Altitude Coverages of Ship-borne Microwave Search Radars, E. R. Perkins, June 27, 1945.\nThe Operation and Testing of Reflex Oscillators, J. C. Slater, June 18, 1946.\nThe Storage of Video Signals on Simple Mosaics, R. A. McConnell, April 18, 1946.\nAn Experimental MTI System, R. A. McConnell, April 18, 1946.\nA Measurement of Supersonic Velocity in Mercury at 15 Mc/s as a Function of Temperature, R. I. Jacobson, September 20, 1945.\nReceiver Noise Figures and Their Measurement, Y. Beers, July 2, 1945.\nRelay Data Including Shock and Vibration Measurements, H. W. Baur.\nAn Electronic Modulator for C-W Magnetrons, A. Banos, Jr.\nInterference Blanker, R. Hull, June [?]\nCalculation of Vertical Polar Diagrams and Power Gains of Antennas for Airborne Navigational Radars, W. Sichak.\nAPQ-13 60-Inch Antenna.\nMTI for MEW, G. M. Nonnemaker.\nAnalysis of the Tracking of the 58U.\nX-Band System, C. D. Boyd, June 12,\nAttenuation of RG-9/U Cable as a Function of Temperature and Frequency in the X-Band, F. E. Ehlers,\nA/R Range Scope, P. F. Brown, A. H. Fredrick, W. E. Henry, June 29, No report.\n\nMeasurements and Waveforms Obtained with SCR-598 Modulator, G.\n\nPart II\n\nGeneral Theory of Electronic Beam RL-771 Modulators, D. S. Saxon, Mar. 15,\nAN/APG-Tl Training Equipment, G.\nAN/APG-15 Modification Kit for RL-773, G.\nAN/APG-Tl Training Equipment, G.\nParallel Plate Bends, M. A. Taggart, RL-774\nThe Temperature-Limited Diode, J. RL-775\nFourier Integral Methods of Analyzing and Methods of Calculation for Line Sources, R. C. Spencer and P. RL-777\nThe AN/APS-30 Series, G. F. Wheeler, D. Halliday, Aug. 15, 1945.\nThe AN/APS-31 System, R. E. Wheeler,\nThe AN/APS-32, G. F. Wheeler,\nThe AN/APS-33, R. Blythe, Feb. 28,\nThe AN/APS-34, R. E. Hillger, Apr.\nLow-Voltage K-Band Oscillator, H. Analysis of Line Modulator Behavior with a Sparking Magnetron Load, A. RL-783\nWalter, 0. T. Fundingsland, August 10, \nRadar Camouflage, M. M. Andrew, 0. RL-784\nJ. Baltzer, E. L. Hudspeth, C. E. Mandeville, July 16, 1945.\nTests of a Type C Data Presentation RL-785 with a Spiral-Scan Aircraft-Interception System, E. W. Cowan, July 8,\nAN/APS-10, a Lightweight X-Band RL-786 Search Set, A. Longacre, H. L.\nQuarter-Wave Plate for Broad Band Circular Polarization, J. E. Eaton, J. Steinberger, January 28, 1946.\nBroad-Band Coaxial-Line Horn, J. RL-788 Steinberger, July 20, 1945.\nK-Band Linear Array, J. Steinberger, Slotted Dipole Impedance Theory, H. Fluctuations in the Return Signals from Random Scatterers, A. J. F. Siegert and Francks W. Martin, January [\nElectronic Tuning of Reflex Oscillators, J. B. H. Kuper, D. S. Beers,\nDouble Reflector Antenna for High-Altitude Bombing, E. B. Chisholm, An Improved K-Band Vertebrae Waveguide, E. L. Younker, August 25, No report.\nPPI Off-Center Conversion Kit (MX Airborne Early Warning Search Antenna), T. J. Keary, J. R. Bohnert, Effects of Clouds and Rain on K-Band Airborne Radar, Arthur E. Static Frequency-Modulation Characteristics of the Reflex Klystron, D. Mechanical Resonant Scanner, D. B. Nichinson, R. Sher, Ens. C. Schultz, GPI for Close-Control Bombing, R. I. Hulsizer, July 27, 1945.\nThe Double-Tuned Circuit with Transitional Coupling, J. L. Lawson, A. Electrical and Physical Characteristics of Some Commercial Feedthrough Filters, G. J. Wheeler, October 2, 1945.\nA Method of Shielding for Filter Insertion Loss Measurements, G. J. Wheeler, The Measurement of Thermal Radiation at Microwave Frequencies, R. H. Dielectric Phase Shifters for Waveguides.\nF. T. Worrell, September 14, 1945\nK-Band Antenna for High-Altitude Bombing\nA. S. Dunbar, E. B. Chismoisture Proofing of Button Mica Capacitors\nJ. C. Balsbaugh, W. C. Tallman\nM. D. Fagen, Radiation Laboratory\nJuly 1945\nMultiple Reflection Delay Tank\nH. Shapiro, G. D. Forbes, August 11, 1945\nOn the Theory and Performance of Liquid Delay Lines\nA. B. Huntington, A. G. Emslie, A. E. Benfield\nPresent Status of High Power at S-Band\nR. T. Young, Jr., September 15, 1945\nAN/APG-21\nTerry, E. A. Slusser\nMethods of Calculating Characteristic Values for Bilinear M Curves\nW. H. Furry, H. W. Dodson, J. R. Gill, B. E. Howard, F. D. Parker, February 6,\nShipboard Black Maria Antennas\nH. A. Kirkpatrick, J. F. Blackburn, B. P. Washburne, September 25, 1945\nRF Mechanical Modulator for S-Band\nP. J. Rubenstein, \"Graphs for Computing the Diffraction Field with Standard and Superstandard Refraction\" (Special Reports, Manuals and No report)\nF. L. Niepce, \"S-Band Coaxial Line to Rectangular Waveguide Transitions\"\nP. Notes on Photometry, Colorimetry, and an Explanation of the Centibel Scale, W. B. Nottingham (Dec. 17, Mark 56 U Chronograph)\nI. Sudman, \"The AEW System, Book I, Airborne Equipment\" (Aug. 15, 1945)\nE. Lyman, \"The AEW System, Book II, Shipboard Equipment\" (Sept. 24, 1945)\nE. Lyman, \"The AEW System, Book III, Test Equipment\" (Nov. 5, 1945) (No report)\nT. J. Keary, A. R. Poole, J. R. Risser, H. R. Wolfe, \"AN/APS-32 and AN/APS-3b Airborne Navigational Radar Antennas at K-Band\" (Mar. 15)\nR. C. Fletcher, F. F. Rieke, \"Mode Selection in Magnetrons\" (Sept. 28, 1945)\nAnalysis and Correction of the Impedance Matching in Microwave Circuits (No author or date provided)\nPedance Mismatch in Parallel T Stabilizing Networks for AC Servos (A. Sobczyk, Mar. 7, 1946)\nHawkeye Antenna (Lt. C. B. Stanley)\nMetallic Hydride Studies (A. S. Eisenstein, W. C. Schumb, E. F. Sewell, F.)\nA Microwave Band-Pass Filter in Waveguide (H. A. Leiter, Nov. 16, )\nAn Electronic Frequency Stabilization System for CW Microwave Oscillators (Interference Between SCR - 58Jfs Tracking APN-19 Beacons, C. H. )\nGeneral Purpose Indication System (The Generation of Harmonics by Silicon and Germanium Crystals, Dorothy D. Montgomery, Oct. 23, 1945)\nA Method of Rating the Stability of Oscillators for MTI (S. Roberts, Oct. )\nRange Accuracy of AN/APG-5 (ARO) (R. M. Whitmer, Oct. 15, )\nCharacteristics of Reproduction 2K-J+5 Tubes (F. S. Bailey, D. S. Beers)\nSome Notes on Space-Charge-Limited Oscillators and Amplifiers at Micro-PART II\nwave: Frequencies, H. V. Neher, Nov.\nSa 6-6: Horizontally Polarized An-Die-Cast Model of the CSB Antenna,\nBuzz-Bomb Antennas, A. B. Dickin, Pulsed-Interference Suppression, J. L. RL-845\nAbsorption Coefficient of a Styraloy RL-846 Filled Coaxial Line, H. Rowland,\nTechnical Data and Operating Notes RL-847 for the 5C22 Hydrogen Thyratron,\nS. J. Krulikoski, Jr., Nov. 14, 1945.\nRadiation Laboratory Modulator Summary, B. Dwight, Nov. 1, 1945.\nA Duplex Communication System for RL-849 Microwaves, R. V. Pound, Nov. 20,\n3-cm Vertebrae Flexible Waveguide, Flexible Waveguides, F. T. Worrell, RL-851\nNoise Filtering Properties of Third Detectors, R. S. Phillips, Oct. 1, 1945. RL-852\nAN/APS-30 Series Indication System,\nNew Type Probe for Coaxial Standing Wave Detectors, H. Rowland, RL-854\nDispersion of High-Frequency Radio Waves in Ionized Gases, H. Mar RL-855\nAn Improved Frequency-Stabilization System for Microwave Oscillators RL-856\nThe AN/APS-6 Antenna Simulator, Variable Width Waveguide Scanners for Eagle (AN/APQ-7) and GCA R. McG. Robertson RL-860\nA Low-Power X-Band RF Gas Switch IFF Antenna for Mounting on the Wing of a TBM Torpedo Bomber I. IFF Receiving Antenna for Mounting in Cadillac Dish I. Maddaus IFF Transmitting Antenna for Mounting in Cadillac Dish I. Mad AEW Block III Relay Antenna I. Six-Element Vertically Polarized Beacon Antennas I. Maddaus Dec. Broad-Band Test Loads R. M. The AN/APQ-13 (60-Inch) Scanner in B-29 Airplanes W. M. Cady, F. J. Mehringer, W. Sichak Oct. 29, 1945. Cindy Antenna A High Resolution K-Band Radar Antenna for Sea Search H. Shapiro Broad - Band Biconical Vertically Polarized Dipole H. Rowland Feb. 6,\nDouble Skin-Back Antenna, H. Row (E0) Rotary Joints for the 3 Centimeter Conductivity Loss Measurements at K-A Tracking Error Recorder, C. M. Gilbert, C. R. Haupt, Jan. 30 Ground Course Computer for AN/Nosmo Doppler Simulator, W. Roth, No report. Detector Cancellation Error as a Function of Carrier Frequency, W. Theory of Directional Couplers, B. A. APS-33 Antenna. Final Preproduction A New Pillbox Feed, M. A. Taggart, Ho'rn with Metal Lens, M. A. Tag The RL-270 Series of Precision Potentiometers, R. J. Sullivan, Mar. 25 Summary of the Life Test Program on 3CU5, UC35, and 5C22 Hydrogen Thyratrons, S. J. Krulikoski, Jr., Jan. Airborne Black Maria Antenna, E. N. Analysis of a Half-Wave Rectifier Circuit Involving Inductance, Resistance, and Capacitance, F. E. Both Design Considerations for an Im\n\"proved Interception (AI) Radar, The AN/APS-21 System, R. McG. Robert Lens Feed for K-Band Pillboxes, L. J. X-Band Sea-Return Measurements, Streamlined Microwave Omnidirectional Antennas, C. B. Barker, H. J. Measurements on Noise from Reflex Oscillators, J. B. H. Kuper, M. C. Theory of Noise from the Reflex Oscillator, A Final Report on AN/APS-10, R. L. Sinsheimer, Mar. 1, 1946, Range and Tracking Accuracy of AN/APG-15B, C. T. Burner, Mar. 22, A Navigational Radar for Naval Auxiliaries and Merchant Marine, R. M. Emberson, R. E. Meagher, Oct. 23, Slip-Ring Assembly for Mk 56 Directors, The AN/APS-23 Antenna and Installation, W. V. Smith, M. A. Herlin, H. G. Weightman, Mar. 6, Three-Electrode Triggered Gap, K. J. Germeshausen, H. R. Zeller, Nov. 19, Pulse-Transformer Committee, Proposed Basic Specifications for Pulse Transformers, P. R. Gillette, Nov. 8,\"\nRadiation Laboratory Pulse-Transformer Designs, P. R. Gillette, Nov. 1, Pulse-Forming Network Committee, Proposed Basic Specifications for Pulse-Forming Networks, P. R. Gillette, Analysis of the Tracking Errors of the Mk 56X System, R. S. Phillips, Radar Duplexing, J. Reed, Feb. 4, AN/APS-31/33 R-F Unit, H. K. Farr, Automatic Frequency Control for AN/ANAPQ-34 R-F Head, A. E. Whitaker, AN/TPS-10B R-F Head Termination Report, E. Durand, Mar. 15, 1946. Video Mapping, J. Hexem, Jan. 29, Description and Operation of the General-Purpose Variable Delay Unit, R. P. Abbenhouse, Mar. 26, 1946. High-Voltage Oxide Coated Vacuum Rectifiers, K. J. Germeshausen, K. J., Discontinuities in Standing Wave Detectors and Waveguide Junction Steps, No report. Recovery Time Measurements in Band-Pass TRFs for Various Gases, F. L. McMillan, Jr., I. H. Deamley, A Four-Horn Feed to Give Csc\u00b2 Anonymous.\nPART II\nRL-899 An IFF Mark 5/UNB Feed in the SCI Search Antenna, W. J. West, Mar. 15,\nRL-899 An IFF Mark 5/UNB Feed in the AN/CPS-6 Vertical Antenna, W. J. West, Mar. 15,\nRL-800 RL-899: An IFF Mark 5/UNB Radiator in the AEW Antenna, W. J. West, Mar. 20,\nRL-900 Mechanical Computer Mechanism for Moving COHO, A. D. Hoffman, Dec.\nRL-901 A Broad-Band TEM Pillbox, W. O.\nRL-902 A Grid-Type R-F Attenuator, W. 0.\nRL-903 A Flat Plate Beam-Shaping Antenna,\nRL-904 No report.\nRL-905 Improved RF System for the Transmitter-Receiver Unit of the APQ-13,\nRL-906 The Application of Powdered Iron Materials as Permeable Dielectrics at Microwave Frequencies, M. B. Hall,\nRL-907 Trainer for Mark 35 Radar, H. O.\nRL-908 AN/APG-5 (ARO) as a Terrain Clearance Indicator, R. M. Walker,\nRL-909 AN/APG-13B Vulture Rocket Computer, T. E. Lawrence, Jan. 23, 1946.\nRL-910 Off-Frequency C-W Jamming A. L. Allred, C. M.\nRL-911 S-Band Tunable Systems J. E. Cook,\nRL-912 Short-Pulse Techniques for High-Definition Radar Systems V. Josephson,\nRL-913 Corner-Reflector Modulation of Airplane Signals R. M. Ashby, F. W.\nRL-914 Modulation of Radar Signals from Airplanes R. M. Ashby, F. W.\nRL-915 No report.\nRL-916 A Broad-Band Balanced Mixer for S R. M. Ashby, L. K.\nRL-917 Pulse-Length Selector and Multiple-Pulse Decoder R. M. Ashby, L. K.\nRL-918 No report.\nRL-919 No report.\nResults of Tests Performed on Synchro Units and Systems C. E. Foster, E. R. Perkins, M. M. Hub\nDescription and Method of Operation of the Special Synchro Test Bench and Synchro Testing Procedures C. E. Foster\nCalculation of the Resonant Frequencies of a Torus by Lagrangian and Variational Methods N. H. Painter\nThe Radar Chart Projector - D. B. McLaughlin, C. A. Smith - Apr. 18, 1946\nGround-Clutter Unit for the Ground-Controlled Approach Trainer - C. M.\nThe SP Feed-In Trainer - S. B. Cohen\nTheoretical Interpretation of Recovery Times of TR Boxes - H. Margenau\nThe Interaction of Discontinuities on a Transmission Line - P. M. Marcus\nSupersonic Solid Delay Lines - D. L. Eisenstein, E. A. Coombs, J. G. Buck, A. Fineman\nThree-Tone PPI - F. N. Barry - Mar.\nNotes on the Contamination of Mercury by Stainless Steel - H. B. Hunt\nTheoretical report not available.\nSN-41/APA-53 (Cadillac II Synchronizer) and IN-188/APA-53 (Cadillac II Indicator) - P. Jarmotz - Apr. 18,\nTheoretical report not available.\nA Photographic Method for Assessment of Bombing Results\nSine Potentiometer Tester - C. A. Smith\nThe Use of Synchros for Radial Time Measurement\nBase Displays, W. O. Reed, Mar. 25,\nEffect of the Tuning Plunger on Operation of 2K33 Type Tubes, G. H. Electron Optical Studies of the 2K33, Mar. 25,\nThe Angular Alignment of Radar AN/CPS-6 (V-Beam) Antenna, C. G. Stergiopoulos, Feb. 12, 1946,\nHydrogen Thyratrons in Pulse Generator Circuits, S. J. Krulikoski,\nSB-8b6B S-Band Oscillator, J. C. Automatic Frequency Control of Thermally Tuned Beacon Local Oscillator, M. W. P. Strandberg, Mar. 6, 1946,\nDistortion in X-Band Detectors, M. Video Discriminator Automatic Frequency Control, M. W. P. Strandberg,\nPerformance of Microwave Harmonic Mixers, D. L. Falkoff, Mar. 11, 1946,\nA Method for Automatic Frequency Control of Thermally Tuned Oscillators in K-Band Rapid Scan, C. J. Swartwout.\nCompact Horns Intermediate Between Polyrods and Reflectors, R. E. Dillon, The MK VII Supersonic Trainer, W. An Application of the Pulse Technique to the Measurement of the Absorption of Supersonic Waves in Liquids, M. Cefola, M. E. Droz, S. Frankel, E. M. Jones, G. Maslach, C. E. Teeter, Wide-Range Tunable Stabilizer, M. A. A Method of Compensating the Frequency Dependence of Attenuation in a Supersonic Delay Line, R. D. Measurement of Phase in Microwave Antenna Fields by Phase-Modulation Method, H. R. Worthington, Mar. 14, Theory of Alternating Current Discharges in Gases, H. Margenau, Jan. T-5 Field Chronograph for SCR 58J, Dielectric Rod Endfire Antennas Close to Metal Surfaces, J. E. Eaton, Jan. X-Band Bandpass TR Tube, W. C. S Band Bandpass TR Tubes, L. D. X-Band Beacon Reference Cavities, Linear Array for Use in the AN/\n\n(Note: The text has been cleaned as much as possible while preserving the original content. However, due to the lack of context and the presence of some abbreviations and unclear phrases, some parts of the text may still be difficult to fully understand without additional context or research.)\nAPS-23  Antenna,  J.  R.  Risser,  A.  M. \nSteenland,  J.  Steinberger,  L.  Eyges, \nK-Band  Echo  Line,  J.  M.  Wolf,  Mar. \nA  Moving  COHO  Conversion  Unit, \nReflections  from  Curved  Surfaces,  C. \nB.  Barker,  H.  Riblet,  Feb.  1,  1946. \nAn  X-Band  Frequency -Modulated  Re\u00ac \nlay  System  for  Video  Frequencies,  L. \nM.  Hollingsworth,  H.  Logemann,  Jr., \nA.  W.  Lawson,  Jr.,  J.  M.  Sturtevant, \nA  Synchronization  System  for  Ground \nRadar  Relay,  J.  M.  Sturtevant,  E.  W. \nNote  on  a  Low-Power  S-Band  Gas \nTwo  Circularly  Polarized  S-Band \nAn  X-Band  Hemi-I  so  tropic  Radiator, \nPART  II \nNo  report. \nNo  report. \nNo  report. \nNo  report. \nNo  report. \nNo  report. \nNo  report. \nNo  report. \nAutomatic  Plotter  RC-308  Used  with \nSCR-58Jf.  for  Mortar  Location ,  L.  J. \nSullivan,  Apr.  3,  1946. \nNo  report. \nNo  report. \nA  Theory  of  Resonance  in  Rotary \nJoints  of  the  TMn  Type ,  H.  K.  Farr, \nFirefly  Moving -Vehicle  Detector ,  AN/ \nAPS-27, H. L. Schultz, E. M. Lyman, Capacitive Type RF Attenuators, W. Omnidirectional Antennas for BUPX, Modulator for AN/TPS-10 Radar, P. Interference Measurements on the AN/APS-30 Series, R. G. Fluharty\nAN/APS-30 Modulator Status, A. C. \"Winter scope\" or Fast Sweep Synchroscope, D. F. Winter, Apr. The Absorption of Atmospheric Water-Vapor in the K-Band Region, R. H. Dicke, R. L. Kyhl, A. B. Vane\nLCT, 900 Mc/sec FM-CW Magnetron, A. L. Vitter, Jr., P. W. Forsbergh, Jr., The UJ70-77 Series of Tunable Magnetrons, A. G. Smith, Feb. 4, 1946. Final Report on the BM50 Magnetron, F. Hutchinson, N. P. Nichols, M. A. Herlin, J. R. Feldmeier, Mar. 29.\nC. F. Chubb, Jr., Boresighting the AN/APG-15 Antenna Assembly, W. Selove, Notes on MTI Receivers, Development of Microwave Test Sets.\nD.F. Sherman, Mar. 14, 1946: Dipole Arrays Backed by Reflecting Sheets (J. Appl. Phys.)\nW. Roth, Feb. 25, 1946: Displacement or Velocity Servo Amplifier\nH.G. Voorhies, Jr., Mar. 9, 1946: Dynamic-Range Compression for MTI, An Automatic Noise-Figure Meter, An Experimental S-Band Airborne MTI System\nL.M. Hollingsworth, R.: One Knob Tunable X-Band RF Head, An Automatic Frequency-Control System for Magnetrons with Beacon Applications\nNo report: Butterfly Moving Vehicle Detector\nS. Katz, Jan.: Microwave Test Signals\nR.E. Clapp: A Theoretical and Experimental Study of Radar Ground Return\nM.L. SCI Search Antenna Mark I, M.L. SCI Search Antenna Mark II\nP.M. Marcus, Jan. 16, 1946: Reflection of Radiation from Curved Surfaces (J. Appl. Phys.)\nL.L. Davenport, W.B. Sheriff, Apr. 8, 1946: The Beavertail (AN/CPS-b) An Theory and Design of Guided Missiles Control System (J. Appl. Phys.)\nAnnotations:\n- D.F. Sherman, Mar. 14, 1946: Dipole Arrays Backed by Reflecting Sheets. (Journal of Applied Physics)\n- W. Roth, Feb. 25, 1946: Displacement or Velocity Servo Amplifier.\n- H.G. Voorhies, Jr.: Dynamic-Range Compression for MTI, An Automatic Noise-Figure Meter, An Experimental S-Band Airborne MTI System.\n- L.M. Hollingsworth, R.: One Knob Tunable X-Band RF Head, An Automatic Frequency-Control System for Magnetrons with Beacon Applications.\n- No report: Butterfly Moving Vehicle Detector.\n- S. Katz, Jan.: Microwave Test Signals.\n- R.E. Clapp: A Theoretical and Experimental Study of Radar Ground Return.\n- M.L. SCI Search Antenna Mark I, M.L. SCI Search Antenna Mark II.\n- P.M. Marcus, Jan. 16, 1946: Reflection of Radiation from Curved Surfaces. (Journal of Applied Physics)\n- L.L. Davenport, W.B. Sheriff, Apr. 8, 1946: The Beavertail (AN/CPS-b) An Theory and Design of Guided Missiles Control System. (Journal of Applied Physics)\nIntermediate-Frequency Amplifier, A.B. (No report)\nOverload Characteristics, S.A. Smith (No report)\nCombined Reflector-Cavity Automatic Frequency Control for Thermally Tuned Reflex Oscillator Tubes, G.H.\nSynthetic Radar Echoes in the Presence of FM Jamming, A.M. Stone\nA Trigger Generator for Signal Threshold Studies, R.R. Meijer (April)\nWaveguide Motional Joints, Walter\nDiscussion of Plotting Devices for A Method for Calculating Magnetron Resonant Frequencies and Modes, F.E. Bothwell, P.D. Crout (Feb. 8, 1946)\nEcho-Box Application, J.M. Wolf (No report)\nElectronic Line-Voltage Stabilizers, J. (No report)\nSG-1 Mark III Antenna, S.J. Mason\nThe Antenna for Radar Mark 35, L.\nAn Extension of Lagrange's Equations to Electromagnetic Field Problems, Equivalent Networks, Part II, The Determination of Fields Satisfying\nLaPlace's, Poisson's, and Associated Equations by Flux Plotting, P. A. Flux Plotting Method for Obtaining Fields Satisfying Maxwell's Equations, with Applications to the Magnetic Theory of Radar Target Return, Part II, Prescott\n\nTheoretical Treatment of Radar Target Return, Part II\nSupersonic Components for TJS in Radar Trainers, S. Frankel, P. Rosenbaum\nRF Phasing of Pulsed Magnetrons, J. E. Evans, R. C. Fletcher, F. F. Rieke\n\nFinal Report on BUPX, H. H. Bailey, A Supersonic Echo Simulating System for AN/APQ-T1, S. Frankel\n\nDesign Proposal for AN/APN-19A Check Set, R. S. Chaloff, R. J. Harrison, W. W. Mathison, G. B. Guthrie, The Effect of Small Changes in Circuit Parameters on the Solution of\nF. E. Bothwell, \"Network Problems\"\nH. R. Worth, \"Mortar Fire Detection\"\nH. R. Worthington, \"K-Band Antiaircraft Fire Control\"\nM. Berman, \"AN/APS-31 Antenna\"\nJ. Certaine, \"Beam Shaping\"\nH. F. Clarke, G. L. Ragan, R. M. Walker, \"Summary of High-Power Breakdown Tests on Microwave Components\"\nE. M. Jones, \"The Cadillac Trainer\"\nJ. H. Gardner, \"Low Altitude Csc20 Antenna for APS-33 Project\"\nW. E. Millett, H. R. Worthington, E. L. Younker, C. G. Montgomery, D. D. Montgomery, \"Survey of Foster Scanner Developments\"\n\nF. B. Hildebrand, \"The Alteration in the Radiated Field of a Paraboloid Due to a Shift in the Position of the Dipole Feed\"\n\nH. F. Clarke, J. H. Gardner, \"AN/APS-31 Antenna, Beam Shaping, and Low Altitude Csc20 Antenna for APS-33 Project\"\nJ. Certaine, \"Summary of High-Power Breakdown Tests on Microwave Components and Beam Shaping\"\nM. Berman, \"AN/APS-31 Antenna\"\nF. E. Bothwell, H. R. Worthington, \"Network Problems and Mortar Fire Detection\"\nH. R. Worthington, \"K-Band Antiaircraft Fire Control\"\nF. B. Hildebrand, \"The Alteration in the Radiated Field of a Paraboloid Due to a Shift in the Position of the Dipole Feed\"\nAdmittance Characteristics of Some S-Band Waveguide Fed Dipoles, J. ports, Special Reports, Manuals and Manuals\n\nPreliminary Operation Manual for Special Radio Equipment for ASVB-18.\nInstruction Manual for B-18B ASV Radar Installation, S. McGrath, April - Instruction Manual for Raytheon Service Modulator WX U002 B\nInstruction Manual for B-18 Indicator Components (Included in RL-M- Instruction Manual for Raytheon Laboratory Modulators WX U05U, WX U05J+ A and WX 1+05U B), S. McGrath,\nInstruction Manual for B-18 RF components (Included in RL-M-100),\nInstruction Manual for B-18 Receiver\nNo report.\n\nOperating Instructions for the Model B PPI Indicator Central, C. W. Sher- Operating Instructions for the Model 417 Klystron for Use as a Local Oscillator in Radar Receivers, R. C. Rierdan, A. G. Hill, May 6, 1942.\nInstructions for Type E Self-Synchronous Oscilloscope, F. J. Gaffney,\nMemorandum Describing High Gain D-C Amplifier, W.B. Nottingham\nInstruction Manual for Experimental Service Modulator Model 4, Type 1372, July 13, 1942.\nHandbook for Radar Equipment 596 3-Cm Magnetron Test Bench Construction and Operation, J.B. Wiesner,\nSpectrum Analyzer, Type 103, for Pulsed Oscillator at 3000 Mc/sec,\nManual for Magnetrons, Types 2J, February Instruction Manual for Pulsed Oscillator, 3000 Mc/sec Model No. 1, Feb.\nInstruction Manual Model P4 Synchroscope, Mar. 2, 1943.\nInstruction Manual for Audio Indicator Type 123R, S. Newell, Mar. 26,\nTentative Operating Instructions for MIT Radiation Laboratory Test Set (Type Preliminary Handbook (Same as RL-M-161) for Experimental Prototype Model Radio Set SCR-620 and Supplement), March\nMIT Radiation Laboratory Modified Type 102-A Test Set (Type 102A-1), Model Pl+E Synchroscope and RF Envelope Indicator, June 18, 1943.\nARO System: General Description and Operational Procedure\nInstruction Manual for Revised Model Plf Synchroscope, June 14, 1943.\nInstruction Manual for Spectrum Analyzer (Type 105) for X-Band Pulsed Oscillators, and Spectrum Analyzer (Type 107) for S-Band Pulsed Oscillators, July 14, 1943.\nTentative Operating Instructions for MIT Radiation Laboratory Echo Box\nHandbook for Model CXEH, BGX, Radar Beacon\nHandbook for Model CXEH Radar Beacon and Associated Test Equipment, J. R. Dorsey, February 1944.\nPreliminary Manual for Radar Beacon Type BPS (Prototype of AN/CPN-8, similar in function and components to SCR-620)\nInstruction Manual for Service Modulator Model 9, K. J. Urquhart, September\nHandbook of Maintenance Instructions for Type TTX-1BL Test Set (Type B)\nManual for Operation and Maintenance of TW Audio Indicator, September 1\nAN/APS-15 Schematics (RL-M-135B)\nAN/APS-15 Schematics (RL-M-135C)\nHandbook of Instructions for Radio Set AN/APS-15 (H2X)\nTechnical Manual for Radio Set SCR-[REDACTED]\nInstruction Manual for Projection PPI, H. 0. Marcy, J. T. Soller, M. A. [REDACTED]\nManual for Fighter Tail-Warning Equipment, September 1, 1943.\nInstruction Manual for Model 6-B Modulator, P. C. Bettler, Types TON-IGA (Type Q) and TON-1BL Oscilloscopes, F. B. Wood, Editors\nInstructions for TGS-2SE, TGS-3BL and TGS-5BL Signal Generators, E. [REDACTED]\nInstructions for Type TSK-1SE Spectrum Analyzer, F. B. Wood, S. Katz, I. Shapiro, July 3, 1945.\nRL-M-143A\nInstructions for TGX-2BL and TGX-3BL Signal Generator, F. B. Wood, Glossary of Terms Used in Radiation Laboratory Radar, H. Shapiro, November 15, 1943.\nInstruction Manual for Model 7A Hydrogen Thyratron Modulator, H. J. Echo-Box Techniques for Testing S-Band Shipborne Radars, S. F. Johnsyn.\nSynchroscope Handbook (Model SYN-15), M. J. Cohen, Editor, December.\nRL-M-148A Handbook of Instructions for AN/APA-9 (Aspen) Radar Set, November 29, 1943.\nRL-M-148B Handbook of Instructions for AN/APA-9 (Aspen) Radar Set (Second Abbreviated Edition), December 21, 1943.\nRL-M-148C Handbook of Instructions for Radio Set AN/APA-9, Preproduction Sets (Complete Edition), A. E. Caswell.\nInstruction Manual for Installation of Radiation Laboratory Type B Plugs on Cables, R. R. Steinke, December 29.\nInstruction Manual for Installation of Radiation Laboratory Type A Plugs.\nR. Steinke, Dec. 29, Modification of SCR-584 for Oboe II, RL-M-152A\nH. T. Hodges, RL-M-152B, AN / APG-13 Falcon System Manual\nH. T. Hodges, revised by E. A. Slusser, RL-M-152C, AN/ APG-13 System Manual\nInstruction Manual for Model 6 Modu- Instruction Manual for Installation of Chiksan Tool Company 1%-Inch Revolving Joint {Drawing No. 61DIC}\non Radiation Laboratory Types B-1 and B-2 Cables, Army-Navy Types RL-M-155A\nA. S. Jerrems, Instructions for Modifying the SCR-58 U Modulator for Use in Aspen Transmitters, RL-M-155B, RL-M-156A, RL-M-156B, RL-M-156C, RL-M-156D, RL-M-157A, RL-M-157B, RL-M-158A, RL-M-164A, RL-M-164B\nInstructions for Modifying the SCR-584 Modulator for Use in Aspen Transmitters, A. S. Jerrems, Feb. 21, MEW No. 1 Preliminary Instruction Book\nL. L. Blackmer, Editor, MEW No. 2 Preliminary Instruction\nPreliminary Instruction Handbook for AN/CPS-1A Radar Set, L. L. Blackmer, Editor, March 1944\nPreliminary Handbook of Instructions for H2X Supersonic Trainer, Mark II, A. E. Caswell, April 1944\nPreliminary Handbook of Instructions for Lightweight Loran Transmitter (LLTX), A. A. McKenzie, April 3, 1944\nPreliminary Instruction Manual for Echo-Box for SCR-584, L. L. Davenport, W. N. Simonds, [Unknown Date]\nTechnical Manual for SSV Trainer (RCC Model only), W. N. Simonds, Preliminary Handbook for Experimental Prototype Model Radio Set SCR-620, and Sup Harvey 170-T Loran Transmitter Manual, A. A. McKenzie, May 10, 1944\nInstruction Manual for Automatic H2X Camera Model A, R. Sherr\nTemporary Instruction Manual for Automatic Radar Camera Model B.\nR. Sherr, W. R. Woodward, April 15, 1944. Temporary Instruction Manual for H2X Camera Model B.\nR. Sherr, W. R. Woodward, May 1, 1944. Instruction Manual for Echo-Box Test Kit.\nH. H. Wheaton, J. M. Wolf, June Instructions for Operation of High-Gain Video Amplifier for P4-E Synchroscope.\nJ. W. Severinghaus, June RL-M-167 Radar Beacon, Mark I Mod 1.\nRL-M-168 Handbook of Maintenance Instructions for CXGQ Radar Set.\nA. E. Cas RL-M-169 Instructions for Type TTX-6RH and Type TTX-10RH Test Sets.\nS. Katz, June 8, 1944. RL-M-169B Instructions for Types TTX-6(), TS-263/TPS-10 Test Sets.\nS. Katz, D. J. Dickinson, J. J. Guarrera, RL-M-170 Maintenance Manual for the AN/APN-7 System Modified for the SG Band.\nRL-M-171 1N23 Loss Measuring Set, Type 7368.\nRL-M-172A AN/APS-15 Receiver-Indicator Modified for Ground-Range Sweeps and Remote Amplifier.\nP. Jarmotz, Oct.\n[RL-M-173] Instructions for TSX-2 Spectrum Analyzer (S. Katz, Aug. 5, 1944)\n[RL-M-173B] Instructions for TSX-2 and specifications on TSX-4SE Spectrum Analyzer (S. Katz, Nov. 4, 1944)\n[RL-M-173C] Instructions for TSX-2 and specifications on TSX-4SE and TTS-ASE Spectrum Analyzers (S. Katz, Nov. 4, 1944)\n[RL-M-174] Instructions for Types TWS-5 and TWS-5EV Battery-Operated Wattmeters (Preliminary Models of TS-Severinghaus, F.B. Wood, Aug. 4, )\n[RL-M-175] Electronic Cursor for AN/APS-15 (S. Katz, )\n[RL-M-176A] Instructions for Types TFK-2HU, TFK-3HU and TFK-6HU Frequency (S. Katz, )\n[RL-M-176B] Instructions for Types TFK-2HU, TFK-3HU, and TFK-6HU Frequency (S. Katz, )\n[RL-M-177] IN 21 Loss Tester, Type 7556 (H.B. Huntington, Aug. 21, 1944)\n[RL-M-178] Preliminary Instruction Manual for RL-M-178\n[RL-M-178B] Preliminary Instruction Manual for Computer Mark 14, AN/APA-30\n[XN-1] Instruction Manual (E.H. )\n[RL-M-195A] Preliminary Technical Manual for RL-M-195A\nHandbook of Instructions for the Preparation of Maps for the H2X Supersonic Trainer, W. R. Carmody\nHandbook of Procedures for Mobile Charting Units, Air Transportable Loran System, B. W. Sitterly, Mar. RL-M-198A\nDescription of the Experimental ROSEBUD, D. J. Dickinson, J. J. Preliminary Instruction Book for Shore Bombardment Beacon Navy Model, Mark 2 Mod 0 and Mod 1, J. RL-M-186A\nInstructions for Type TBN-3EV Thermistor Bridge, E. A. S. Jacobson, J. W. Severinghaus, Jan. 15, 1945\nInstruction Manual for Model 17 Modulator, C. R. Ricker, Mar. 1, 1946\nOperating Instructions for Sweep Calibrator, Model B, R. P. Abben\nPreliminary Handbook of Instructions for Supersonic Trainer, AN/APQ-7 T1 (Eagle Trainer), W. R. Carmody\n1N23 Noise-Measuring Set, Type\nPreliminary Instructions for Manual Bearing Unit, C.A. Smith, RL-M-193A\nHandbook of Operating and Maintenance Instructions for Test Set TS-259 (XR-1) / AP and Supplements on Test Sets TS-259 (XR-2) / AP and TS-259 (XR-3) /AP and Signal Generator TS-259/AP\nHandbook of Operating and Maintenance Instructions for Echo Boxes TES-8MK and TES-9MK\nOperating Instructions for Model G Synchronizer, R.P. Abbenhouse\nHandbook of Maintenance Instructions for AN/APA-hO (Micro-H Mk II) Airborne Attachment to AN/APS-\nInstructions for TGS-6DE Boresighting Signal Generator (Preliminary Model of Test Set TS-348/AP)\nE.A. Preliminary Instruction Manual\nX-Band Coincident Beacon XCB (Mark I) AN/APX-H, J. R. Lien, Preliminary Maintenance and Operating Instructions for AN/APX-15 B\" Theory of Operation of AEW C Preliminary Maintenance and Operating Instructions for the TS-364/APX-15 Test Set, B. L. Birchard, April 4, Instructions for TBN6SE Thermistor Bridge, E. A. S. Jacobson, November Handbook of Operating and Maintenance Instructions for Test Set TGI- Handbook of Instructions for the Preparation of Mountain Maps for the H2X Supersonic Trainer, W. R. Carmody, April 1945. Instructions for Installation and Maintenance of Waffle Relief Maps in Ultrasonic Trainers, P. Rosenberg TFX-3URL Fixed Frequency Stand PART II RL-M-220B TFX-35RL Fixed Frequency Stand TFX-36RL Fixed Frequency Stand Replacement Pressurized RF Unit for AN/APS-15A, J. Sterling, D. L. Hagler, F. R. Banks, Jr., F. E. Towsley,\nPreliminary  Instruction  Manual  for \nS-Band  Coincident  Transponder  Black \nMaria  RT-7A/APX,  C.  A.  Meyer, \nOperating  Instructions  for  Radiation \nLaboratory  Model  5  Synchroscope,  R. \nP.  Abbenhouse,  July  26,  1945. \nMaintenance  Manual  for  Model  AN/ \nAPN-21XR  Racon,  D.  J.  Dickinson, \nHandbook  of  Maintenance  Instruc\u00ac \ntions  for  the  AN/APG-8  Airborne \nRadar  Gunsighting  Equipment,  J.  V. \nPreliminary  Instruction  Manual  for \nAN/APG-15B,  J.  V.  Holdam,  Jr., \nHandbook  of  Operating  and  Main\u00ac \ntenance  Instructions  for  Dummy  Load, \nInstructions  for  Types  TFX-17GA, \nTFX-18GA,  TFX-19GA,  TFX-30EC, \nTFX-31EC,  Model  51  and  Similar \nTypes  of  Micrometer  Frequency \nMeters,  F.  B.  Wood,  Editor,  May  3, \nPreliminary  Technical  Manual  for \nSCR-584  MTI  Modification  Kit  No. \nMC-61+2-AS  and  Fan  Beam  Search \nAntenna,  H.  B.  Bekkar,  Editor,  June \nPreflight  Check  of  Radio  Set  AN/ \nPreliminary  Instructions  on  Modifica\u00ac \ntion  Kit  MC-627  for  Radio  Set  SCR- \nPreliminary  Instructions  on  Modifica\u00ac \ntion  Kit  MC-627  for  Radio  Set  SCR- \n58U  {Revised),  G.  E.  Brunette,  Nov. \nHandbook  of  Maintenance  Instruc\u00ac \ntions  for  AN / APG-15-T1  Trainer,  A. \nHandbook  of  Operating  Instructions \nfor  Loran  Low-Frequency  Converter \nCV-27/UPN,  A.  A.  McKenzie,  Apr. \nOperating  Instructions  for  Sweep \nCalibrator  Model  B-8127,  R.  P.  Ab\u00ac \nbenhouse,  June  20,  1945. \nCXHR  Maintenance  Manual,  J.  D. \nFairbank,  Sept.  21,  1945. \nHandbook  of  Maintenance  Instruc\u00ac \ntions  for  Loran  Low-Frequency  Con\u00ac \nverter  CV-27/UPN,  A.  A.  McKenzie, \nAlignment  Procedure  for  Cadillac  Air\u00ac \nborne  Synchro  System,  W.  R.  Gustaf\u00ac \nPreliminary  Handbook  of  Operating \nand  Maintenance  Instructions  for \nModel  AN/APA-46  Aircraft  Radar \nEquipment,  H.  Wenetsky,  Editor, \nAN/CPA-7  Operations  Room  Equip\u00ac \nment  Supplementing  Radio  Set  AN/ \nPreliminary  Book  of  Maintenance \nInstructions  for  Shipboard  Compo\u00ac \nnents  of  AEW,  Lt.  R.  L.  Kellner,  Edi\u00ac \nHygraph  Instruction  Manual,  L.  Rov- \nInstructions  for  Type  TSK-5SE  Spec\u00ac \ntrum  Analyzer,  F.  B.  Wood,  Feb.  11, \nInstruction  Manual  for  Model  20 \nLaboratory  Modulator,  C.  R.  Ricker, \nBlack  Maria  Check  Set,  TS-U95/ APX, \nInstructions  for  TS-416  /  AP  Check \nSet,  J.  W.  Severinghaus,  Feb.  11, \nAdditional  Modification,  Calibration, \nand  Plotting  Procedures  for  RC-291+ \nPlotting  Equipment,  J.  E.  Ward,  Feb. \nNo  report. \nInstructions  for  TBK-2RL  Impedance \nBridge,  E.  C.  Simmons,  F.  B.  Wood, \nInstructions  for  K-Band  Bench  Test\u00ac \ning,  A.  J.  Zink,  F.  B.  Wood,  Apr.  5, \nOperating  Instructions  for  Model  12 \nModulator,  A.  C.  Donovan,  Sept.  17, \nPreliminary  Instructions  for  Radar \nSystem  MK  35 ,  M.  Boas,  Nov.  30, \nborne  Range  Only  Equipment,  T.  E. \nPreliminary  Operation  and  Mainte\u00ac \nnance  Handbook  for  Release  Point \nIndicator AN/ARA-17, J. D. Horgan, RL-S-7\nNotes on the Power Output of 723A Tubes, J. S. Kirby-Smith, Feb. 19, RL-S-8\nSome General Microwave Anti-Jam Design Considerations and Preliminary Description of MK 56 Gun Fire-Control System, W. R. Carmody, A. D. Ehrenfried, Dec. 15, 1945.\nPerformance of a Special Receiver, P. R. Bell, RL-S-9\nComparison of P7 Screen-Test Methods, Handbook of Maintenance Instructions for AN/APA-53 Indicator Assemblies, W. B. Nottingham, Mar. 14, 1945.\nassembly, W. R. Slaunwhite, Lt. R. L. Dunn\nDetection of Propeller and Sambo Modulations, J. L. Lawson, Editor, Handbook of Maintenance Instructions for AN/AIC-6 Intercommunication Servo Generator Life Tests, G. J. System, W. R. Slaunwhite, Lt. R. L.\nPossible Radar Solutions to the Problem of Accurate Siting of Field Artillery, A. Roberts, Apr. 7, 1944.\nHandbook of Maintenance Instructions for Cadillac II Power Supply.\nRadar Photo Reconnaissance, CFJ Preliminary Instructions for Radar Set AN/APG-13B, M. Boas, Sept. 15, MTB Computing Radar Sight, G. F. Nosmeagle, Lt. J. B. Higley\n\nOperating Instructions for K-Band Rapid Scan System, C. J. Swartwout, Alexander, June 2, 1944\nFocus Coil Control for Cathode-Ray Indicator for Rapid-Scan Tubes, R. D. Rawcliffe, May 17, 1944\nSystem, P. Jarmotz, Apr. 5, 1946\n\nSpecial Reports\nModel 5 Synchroscope, G. H. Nibbe, Ground-Position Indicator for Radar Navigation and Bombing, B. Chance, RL-S-1\nTesting of Skiatrons, H. C. Kelly, R. I. A. Greenwood, W. J. Tull, RL-S-ls\nTesting of Skiatrons, Supplement, H. C. Kelly, R. W. Hull, W. D. Hope\nWindow Tests on AN/CPS-6, Leesburg, Florida, June 7 and 9, 1944.\nRL-S-2 Target Raft Transponder, DR. R.\nA Procedure for Statistical Analysis of Depth Soundings, F.B. Hilde\nRL-S-3 Walworth Waveguide Bends, R.M.\nAN/APS-10 Airborne Radar, A.\nRL-S-4 A Comparison of Positive and Negative Intensity Modulation of PPI Display\nLongacre, July 12, 1944.\nDOLPHIN, Remotely Controlled Torpedo Rack Actuating Mechanism, G.\nRL-S-5 A High Resolution Set, R.M. Ember\nRL-S-6 General Description, Special Installation Requirements, and Mounting Dimensions of AN/APG-5 (ARO) Airborne Radar, A.M.\n\nPART II\n\nFlight Tests on AN/APS-6A, R.M. Alexander, November 30, 1944.\nAirborne Early Warning, AEW, W.\nAirborne Early Warning, AEW, (RL-S-26 plus additional material), W.K.\nCatalog of Microwave Test Equipment, F.B. Wood, Editor, September 30,\nX-Band Waveguide Corrosion Proof Interconnecting AN/APA-5 and Army\nJ. X. Mulvey, Aircraft Radio Laboratory, October 2, 1944: A Production Analysis of Wartime Radio and Radar Industry\nA. A. Bright, J. Exter, November 1, 1944: AEW Bedford Trials\nW. Moore, October: Preliminary Testing of Houston Corporation AN/APS-10 Scanner\nC. F. J., Termination Report on Radar Photo Reconnaissance Project\nSpecifications for 15-Mc Supersonic Crystal for Crystal Cartridges\nH. M. James, Tactical Use of Delayed PPI Scopes of the AEW System\nS. D. Waveforms, Voltage and Resistance Measurements in AN/APA-5 Indicator Equipment\nG. Q. Lipscomb, A Proposed Design for MX-180/A Corner Reflector, Float Marker, Radar, Droppable\nP. D. Tilton, February 1945: Thumbnail Sketch for December and January\nCatalog of Microwave Test Equipment\nThe following is the cleaned text:\n\nAlignment Kit (Torpedo Rack) Mark, E. A. S. Jacobson (Editor)\nSo-called Standard Target, A. H. H2K Radar Displays, C. F. J. Over- Ultrasonic Radar Trainer PPI Photographs of a Simulated H2X Bombing Mission, P. Rosenberg\nThumbnail Sketch for February and Release Point Indicator, J. D. Horgan\nTabulation of CRT Screen Properties, F. B. Hildebrand\nAEW Tactical Tests at Brigantine, PPI Photographs from AEW, S. D. Bennett (July 5, 1945)\nAnticlutter Circuits for AEW, V. Josephson, L. B. Linford, J. L. Law\nThumbnail Sketch for April and May\nPreflight Check of Radio Set AN/, Proposed Antenna for Panoramic Radar, P. Rosenberg (Nov. 5, 1945)\nTables of Fourier Transforms of Fourier Series, Power Series, and\nPolynomials, P. Austin, R. C. Spencer, E. Chisholm, E. Fine, J. Schwartz\nRadar Bombing Techniques, V. L. Tables for Use with Torpedo Director Texts\n\nMarch 33 Mod 1: Part I, Own Speed \u2014 RL-T-1\nLecture Notes, J. C. Slater. \"10 Knots\"; Part II, Own Speed \u2014 12 Knots; Part III, Own Speed\u2014 U Knots; Part IV, Own Speed \u2014 23 Knots\nG. F. Duvall, June 29, 1945. RL-T-2\n\nNotes on Microwaves, W. W. Hansen, prepared by S. Seely and E. C.\nRL-T-3\n\nRectifier Filter Circuit Analysis, H. Mechanical and Electrical Tests of the General Electric Company Scanner for the AN/APS-10 System\nRL-T-4\n\nAnalysis of an Amplidyne Servomechanism, C. C. Lawry, Jr., Feb. 10,\nThe Manual Plotting System RC-305\n\nRL-T-5\n\nTransmission Lines and Waveguides, Similarities and Differences\nTorpedo Director Mark 33 Mod 1, G.\nRL-T-6\n\nExplanation of Impedance Matching, H. Krutter, July 7, 1942.\nAntenna Catalogue, J. J. Brady, October 1942\nRL-T-7 Paraboloid Diffraction Patterns from the Standpoint of Physical Optics, R. - Supplementary Report on Aircraft Target Ranges of AEW, S. D. Bennet\nRL-T-8 Microwave Radar, Volume I, Theory and Practice of Pulsed Circuits, D. - Type Test of the Fairchild Radar Recording Camera, D. G. Bagley\nRL-T-9 Wave Guide Handbook, Section I, September 24, 1942; Section II, Attenuation in Wave Guides, October 2, 1942; Section III, Operational Procedure for AN/APA-5, W. J. Deerhake, K. E. Schreiner; IV, Obstacles in Wave Guides, November 11, 1942; Section V, Bends and T-Junctions in Wave Guides, December 4, 1942\nRadar R-F Test Points, A. H. Brown\nA Survey of the AN/TPS-10, Little Wave Guides, N. H. Frank\nTheory of Impedance and Admittance, X-Band Sealed Standard Cavities, F. Diagrams and Allied Subjects, S.\nReprinted as NAVSHIPS 900,038:\nEvaluation of Specifications for P1U CRT Screens, S. A. Goudsmit, November 9, 1942.\nRadar Components Affecting Range: Rectifier Filter Circuit Analyses, H. J. Operation for Peak Performance, R. Microwave Technique, J. M. Peterson, Editor, and others, May 5, 1943, Reprinted as NAVSHIPS 900,028.\nMEW Close Control, E. Miller, April \nUse and Deviation of a Z, 0 Chart, J. G. Jelatis, J. W. Woodbury.\nPart II\nRL-T-16 Shock Mounting and Vibrations, P. D.\nIntroduction to Alternating Currents, Q Values, and Transmission Lines\n\nRL-T-18. General Lecture Series on Radar Components\nEditor: H. H. Wheaton\n\nMTI Using Coherent Intermediate Frequency\nPreliminary Report on 1,000-Foot Runs (AN/APA-5)\nPreliminary Report on 5,000-Foot Runs (AN/APA-5)\nPreliminary Report on 15,000-Foot Runs (AN/APA-5)\nAN/APG-13B, Vulture (E. H. B. Bartelink)\n\nLetters Discussing ASP-25 and Related Ideas Concerning ASH (E. H. B. Bartelink, Div. 14-323.2-M14)\n\nHistory of AN/APG-5, ARO (A. F. Sise, B. P. Bogert)\nProposed Sea Echo Measurements with the Airborne MTI Plane (H. Goldstein, RL-42, Aug. 14, 1945)\n\nA New Secondary Modulation Indicator and the Radar System Developed for Testing It (F. G. Dunnington)\nA Continuously Indicating Audio Spectroscope for C-W (Preliminary Manual on the SCR-58k Close Support)\nSystem, Technical Operation, Employment and Maintenance; ASB Reference No. 3, E. M. Lyman, R. W. Larson, British Branch Radiation Laboratory, Advanced Service Base; January 5, 1945. Division 14-265.\n1-M3 Pulse Doppler with Reference to Ground Speed Indication\nLecture Outline for Course on AN/APG-13, Falcon, Herbert H. Wheaton, RL-64. August 3, 1944.\nBibliography of Radiation Laboratory Literature on Some MTI Nomenclature in Use at Radiation Laboratory, MIT, R. A. McConnell, RL-65. May 2, 1945.\nEstimated Limitations of Kit MC-6U2, MTI for SCR-58, F. Cunningham and R. A. McConnell, RL-65.\nNotes on the Rebecca-H System from Information Obtained at TRE, A. Roberts, RL-71. August 25, 1943.\nUnified Radar Bombsight, URBS, E. B. Meservey, RL- On Surfaces that Reflect Radio Waves Poorly, 0. H.\nNotes on the European and Eastern Atlantic SS.\nLoran Systems, R. H. Woodward, W. Lees, BBRL-83, Project Falcon, Air-to-Surface Vessel Radar Range for 75-Mm Cannon in B-25, C. F. J. Overhage, RL-91,\nProject Falcon, AN/APG-13, C. F. J. Overhage, RL-91,\nFrequency Pulling of ARO Cavities, The Effects of Cavity Bias on the ARO Cavity Operated by the ARO Modulator, E. A. Slusser, RL-91, April,\nSome Factors Governing the Range of AI Sets, T. W. Reduction of the Effects of Ground Clutter on the Flight Test of an Experimental Horn-Fed Antenna for H2X, R. C. Ottens, J. E. Woodward, RL-91.3, December 1,\nProposal for Extending the Range of Shoran or M-H Beacon Coverage by the Use of GPI, W. J. Tull, RL-\nErrors of Optical Range Determination, Paul R., The Solenoid Camera Drive, C. W. Mautz, RL-91.5, October,\nL. J. Laslett, Charles F. West, G. W. Curran, RL-94, Tests of AGL-1 Installed in Tail of B-25 Airplane.\nCalculation of Errors in Conical Scanning GL Systems Arising from Detuning when the Transmitter Frequency is Pulled during the Rotation\nL. J. Laslett, \"Summary of Work on Propeller Modulation,\" Radiation Laboratory, RL-103, May 16, 1943\n\nPart III\nRadiation Laboratory Reports\n\nThis index carries only the identifying name of the report and, in the case of NDRC reports, an indication of the laboratory or company issuing it. The date of issuance is included to differentiate Progress Reports of the same title. Complete details of each report are given in Part I, Division 14 NDRC Reports, and in Part II, Radiation Laboratory Reports, designated as 14- and RL- respectively.\n\nAbsorbent Materials (see also Dielectrics)\nProgress Report, Special Protective Coatings, January.\nMonthly Report on Special Protective Coatings, Feb. \nMonthly Report on Special Protective Coatings, Sept. \nMonthly Summary and Informal Progress Report on Protective Coatings, Mar. 14, 1944 \nMonthly Summary and Informal Progress Report on Protective Coatings, Apr. 14, 1944 \nMonthly and Informal Progress Report on Special Protective Coatings, May 13, 1944 \nSpecial Protective Coatings Progress Report, June \nSpecial Protective Coatings Progress Report, July \nMonthly Summary and Progress Report on Special Protective Coatings, Oct. \nThe Preparation of Sambo Films for Scheme A \nSurvey of Binder (Use A), Special Protective Coatings II, Formulation Studies \u2014 Composition Variables [du Pont]. \nSpecial Protective Coatings III, Formulation Studies \u2014 Physical Processing Variables [du Pont].\n[Special Protective Coatings - IV, Pigment Evaluation [du Pont]. 14-347\nSpecial Protective Coatings - V, Film Thickness Evaluation [du Pont]. 14-348\nAbsorbent Materials (Continued)\nSpecial Protective Coatings - VI, Cross-Knifed Films for Practical Work at MIT [du Pont]. 14-349\nSpecial Protective Coatings - VII, Knife Casting on Semiworks Wheels [du Pont]. 14-350\nSpecial Protective Coatings - VIII, Large Scale Coating Trials Investigation of Fabric Coating Equipment\nSpecial Protective Coatings - IX, Spray Trials at Toledo [du Pont]. 14-352\nSpecial Protective Coatings - X, Development of Cement and Paint Making Procedures for Scheme\nSpecial Protective Coatings - XI, Development of Machine-Spraying Process for Scheme A [du\nSpecial Protective Coatings - XII, Characterization of Metal Flakes [du Pont]. 14-355\nSpecial Protective Coatings - XIII, Preparation of]\n\nIf this text is part of a catalog or a list, it does not require any cleaning as it is already in a readable format.\nSpecial Protective Coatings: Methods of Analysis for Aluminum Film and Its Ingredients (du Pont)\nSpecial Protective Coatings, Monthly Summary, November\nSpecial Protective Coatings, Monthly Summary, December\nMonthly Summary, Special Protective Coatings, January\nSpecial Protective Coatings, Physical Performance Tests on Preferred Sambo System Under Simulated Service Conditions (du Pont), 14-395\nSpecial Protective Coatings, Monthly Summary, February\nSpecial Protective Coatings, Progress Report, April\nSpecial Protective Coatings, Progress Report, July\nSpecial Protective Coatings \u2014 XV, Semiworks-Scale Preparation of Machine-Sprayed Film (du Pont)\nSpecial Protective Coatings \u2014 XIV, Formulation Studies \u2014 Exploratory Work for New Uses (du Pont)\nSpecial Protective Coatings \u2014 XVII, Laboratory Study\nPART III\nAbsorbent Materials (Continued)\nSpecial Protective Coatings:\n- Monthly Summary and Informal Progress Report, Aug 1, 1945\n- Monthly Summary and Informal Progress Report, Sept 14, 1945\n- Final Report\n- Surface Adjustment of Use B\u201d Film\n- Semiworks-Scale Preparation of Machine-Sprayed Films\n- Practical Application Trials, Use A\u201d\n- Practical Application Trials, Laboratory Study of Adhesives for Special Protective Coatings- XXI\n- Preparation of Films by Hot Pressing\n\nNote: The text appears to be a list of reports related to \"Special Protective Coatings\" produced by du Pont between August and September 1945. The list includes report titles and their corresponding report numbers.\nSpecial Protective Coatings\u2014 XXIII, Semiworks-Scale Preparation of Machine-Sprayed Films [du Pont]\nSpecial Protective Coatings\u2014 XXIV, Process Development Work at Newburgh [du Pont]\n14-554\n\nAirborne Radar\nsee also Beacons, Fire Control, Guided Missiles, Landing, Navigation, and Night Fighting Components\n\nFinal Report of Research and Development Conducted on Light House Tube Transmitter-Receiver Units [Philco] 14-190\n\nLight weight X-Band Radar, Progress Report No. 1, AIA-1 Scanner Development Program Completion Report [Dalmo Victor] 14-199\n\nThe AGL Receiver [GE] 14-275\n\nDesign and Test of Project Eagle Airfoil\nFinal Report on Tubes for Lightweight X-Band Radar and Ultra-Portable X-Band Beacon\nFinal Report on H2K Roll Stabilized Scanner [Maguire Industries] 14-429\n\nHandbook of Maintenance Instructions of Aircraft Radar Equipment for Army-Navy Model RT-63\nAPS, British Model 110 DB/206 (K Band RF Head) [Sylvania]. 14-495\n\nDevelopment and Production of 50 K Band RF Heads, Army-Navy Model RT-63 / APS, British 2CH1A1 (AGL-1) Aircraft Fire Control Computer Indicator Components as fixed in a Complete Aircraft Interception Installation. RL-138 Tune-up Procedure for 3-cm RF System. RL-160 Matching, Losses, and Frequency Sensitivity of a 3-cm RF System. RL-161 Airborne Radar (Continued) AIA Indicators. ARO Range Follow-up Unit. ARO Range Unit. Report on Aircraft Radio Sight. RL-376 Airborne Radar Projects in Division 9. RL-377 Pictorial Brief of an Experimental AGL-1 Installation. RL-378 Weight Analysis of Airborne Radar Sets. RL-450 Modification of the Amplifier of the AN/APN-2 to Give Sharp Cut-off Wide-Band Response. RL-613 A Low Drag Beacon Antenna for Fighter Aircraft. RL-685 Stable Scanners and Unsteady Airplanes. RL-701\nAPQ-13 60-Inch Antenna, RL-751 Airborne Early Warning-Search Antenna, RL-779 K-Band Antenna for High Altitude Bombing, Improved RF System for the Transmitter-Receiver Unit of the APQ-13, RL-905 SN-J^l/ APA-53 (Cadillac II Synchronizer) and IN-188/ APA-53 (Cadillac II Indicator), RL-937 Range Follow-up Unit: Theory of Operation, Maintenance Instruction, and Parts List, RL-M-125 AN/APS-15 Receiver-Indicator Modified for Ground Range Sweeps and Remote Amplifier, RL-M-172A Electronic Cursor for AN/APS-15, RL-M-175 Replacement Pressurized RF Unit for AN/APS-15, Handbooks and Manuals, Handbook of Maintenance Instructions for AN/APA-53 Indicator Assembly, RL-M-243 Manual for Operation and Maintenance of TW Audio Indicator, RL-M-134, Radio Set RHB: Technical Description of the Production Model Radio Set RHB, Section I\u2014, Section II \u2014 Adjustment and Alignment of Radio Set RHB, RL-508-1\nRadio Set RHB, Section III\u2014 Glider Checkout Procedure. RL-508-2\nRadio Set RHB, Section IV\u2014 RHB Test Equipment Instruction Manual for B-18 Radar Installation. Handbook for Radar Equipment 596. RL-M-113\nARO System, General Description and Operational Procedure. RL-M-125\nAN/APS-15 Schematics. RL-M-135\nAN/APS-15 Schematics. RL-M-135B\nHandbook of Instructions for Radio Set AN/APA-9 (Aspen) Radar Set. RL-M-148A\nHandbook of Instructions for AN/APA-9 (Aspen) Radar Set. RL-M-148B\nHandbooks and Manuals (Continued)\nHandbook of Instructions for Radio Set AN/APA-9 (Preproduction Sets) (Complete Edition). RL-M-148C\nHandbook of Instructions for Falcon System. RL-M-152A\nAN/APG-13 Falcon System Manual. RL-M-152B\nAN/APG-13 System Manual. RL-M-152C\nInstruction Manual for Automatic H2X Camera Model A. RL-M-163\nTemporary Instruction Manual for Automatic Radar Camera Model B. RL-M-164A, Temporary Instruction Manual for Automatic H2X Camera Model B. RL-M-164B, Maintenance Manual G for the AN/APN-7 System (Modified for SG Band). RL-M-170, Preliminary Instruction Manual for AN/APG-15, Preliminary Instruction Manual for AN/APG-15, RL-M-178B, Computer Mark 14 AN/APA-30 XN-1 Instruction Manual. RL-M-179, Preliminary Technical Manual for AEW. RL-M-180A, Description of the Experimental ROSEBUD, Handbook of Maintenance Instructions for AN/APA-40 (Micro-H Mark II) Airborne Attachment to AN/APS-15. RL-M-197, Preliminary Instruction Manual for X-Band Coincident Beacon XCB (Mark I) AN/APX-1U, Preliminary Maintenance and Operating Instructions for AN/APX-15. RL-M-200, Theory of Operation of AEW Circuits. RL-M-201, Preliminary Instruction Manual for S-Band Coincident Transponder Black Maria RT-74/APX.\nMaintenance Manual for Model AN/APN-21XR Racon RL-M-213\nHandbook of Maintenance Instructions for AN/APG-8 Airborne Radar Gunsighting Equipment RL-M-214\nPreliminary Instruction Manual for AN/APG-15B\nPre-flight Check of Radio Set AN/APQ-7\nAlignment Procedure for Cadillac Airborne Syncro System RL-M-226\nPreliminary Handbook of Operating and Maintenance Instructions for Model AN/APA-46 Aircraft Radar Equipment RL-M-227\nPreliminary Operation and Maintenance Handbook for Release Point Indicator AN/ARA-17\nHandbook of Maintenance Instructions for AN/APA-53 Indicator Assembly RL-M-243\nHandbook of Maintenance Instructions for Cadillac II Power Supply RL-M-245\nPreliminary Instructions for Radar Set AN/APG-Nosmeagle RL-M-247\nHandbooks and Manuals (Continued)\nPre-flight Check of Radio Set AN/APQ-7\nOperational Procedure for AN/APA-5 RL-S-67\nPerformance\nRegular Reports:\n- X-JO-3, October 1, 1941\n- X-JO-3, November 5, 1941\n- Navy Dirigible K-3, November 5,\n- Maintenance Group, October,\n- Maintenance Group, November,\n- RL-375: Radar Target Contrast,\n- RL-381: Photographs of PPI Indicator Tube with 3-Cm ASV Over Water and Land,\n- RL-382: Photographic Polarization Tests,\n- Operational Report on B-24, No. 1, in the British Isles, March-June, 1942, RL-391,\n- Altitude Return in AN/APS-6, RL-706,\n- Flight Behavior of Flux Gate and Gyrosyn Compasses and Their Effects on GPI, RL-712,\n- Flight Tests of Block I Relay Radar System,\n- Echoes from Tropical Rain on X-Band Airborne Radar, RL-728,\n- An Aerial Investigation of K-Band Radar Performance under Tropical Atmospheric Conditions,\n- Flight Tests of AEW Block II Relay Link, RL-739.\nRange Accuracy of AN/APG-5 ARO, RL-820\nA Final Report on AN/APS-10, RL-874\nRange and Tracking Accuracy of AN/APG-15B, RL-998\nInterference Measurements on the AN/APS-30 Series, RL-S-16\nBoresighting the AN/APG-15 Antenna Assembly, RL-S-16\nBeacon Tests with AN/APS-6, RL-S-25\nFlight Tests on AN/APS-6A, RL-S-25\nAEW Bedford Trials, RL-S-32\nPreliminary Report on Single Aircraft Target Ranges of AEW, RL-S-37\nWaveforms, Voltage and Resistance Measurements in AN/APA-5 Indicator Equipment, RL-S-38\nH2K Radar Displays, RL-S-44\nAEW Tactical Tests at Brigantine, RL-S-50\nPPI Photographs from AEW, RL-S-51\nAN/APS-15 A and AN/APS-15B Tests, RL-S-57\nMechanical and Electrical Tests of the General Electric Company Scanner for the AN/APS-10 System, RL-S-61\nSupplementary Report on Aircraft Target Ranges of AEW, RL-S-65\n\nSystems and Attachments\nDescriptive Technical Specification-Fighter Tail-\n[Warning: Equipment, AN/APS-13 (XA1) [RCA]. Development of a Tail-Warning Radar System, The Sperry Stabilized Aircraft Gunlaying System, AGL-2, Intermediate Phase [Sperry]. IT. S. Radar Survey, Section I, Airborne Radar: Final Technical Report on AGL-1 Development. Final Report on the Fairchild Central Station Computer (Part I), the Fairchild .50 Caliber M2 Computer and AGS Adaptations for an Emerson Tail Turret (Part II) [Fairchild]. Advanced Design for Radar Photography [U.S. Radar Survey, Section 8, Airborne Radar, Development and Production Samples of APG (AN/APG-5 and AN/APG-8) Series Radar Equipment, including Manuscript Handbook of Maintenance Instructions for Radio Sets AN/APG-5 and AN/APG-5A [Galvin]. Final Report of Contract OEMsr-1000, May 27, 1943 to October 31, 1945: Part 2, Triangle Solver for Eagle Project; Part 3, Triangle]\nPart 4: Solvers for H2X Bombing Project\nTriangle Solver for Laboratory Use (Part 5)\nRedesign of Triangle Solver for Eagle Project [Librascope]\n14-587\nB-18-A Report: February 13 to July 22, 1941 (RL-1)\nReport on XP-61 Mock-up (RL-2)\nAdvance Development of 3.3-Cm System (RL-14)\n3-Cm System Group Report: July 5, 1941 (RL-15)\nAirborne 3-Cm Radar Equipment for AI and ASV Applications (RL-17)\nCorrelation of ASV Equipment with the Bomb-sight (RL-23)\nNavy Roof, etc. (RL-19)\nRoof System Reports: August 26 to September 21 (RL-38)\nRegular Report on the X-JO-3: October 1, 1941 (RL-52)\nRegular Report on the X-JO-3: November 5, 1941 (RL-53)\nRegular Report on the Navy Dirigible K-3 (RL-55)\nRegular Report on the B-24 (RL-61)\n10-Cm ASV Equipment on LB 30 Airplanes (RL-62)\nRegular Report on the PBM-1 (RL-64)\nRegular Report on the CXBH-1 (The PBM-1) (RL-65)\n5-Band ASV Marker (RL-297)\nReport on 10-cm Radar Installation in PBM-1 Flying Boat. RL-383\nReport on Radar System Installed on \"K\" Type Airship. RL-392\nFinal Report on SRBs. RL-403\nWeight Analysis of Airborne Radar Sets. RL-450\nRosebud Microwave Beacon Equipment. RL-460\nVixen X. RL-607\nSystems and Attachments (Continued)\nBlack Maria. Coincident Cross-Band Transponder for S-Band Radar (AEW). RL-672\nSea-Return Effects and Their Elimination in The AN/APS-30 Series. RL-763-0\nThe AN/APS-31 System. RL-763-1\nAN/APS-10, a Lightweight X-Band Search Set.\nThe AEW System, Book I, Airborne Equipment.\nThe AEW System, Book II, Shipboard Equipment.\nThe AEW System, Book III, Test Equipment.\nDesign Considerations for an Improved Interception (Al) Radar; The AN/APS-21 System.\nThe AN/APG-5 (ARO) as a Terrain Clearance Indicator. RL-908\nAN/APS-27 Firefly Moving Vehicle Detector\nAN/APS-26 Butterfly Moving Vehicle Detector\nAN/APS-15 Schematics RL-M-135, RL-M-135B\nManual for Fighter Tail-Warning Equipment\nPreliminary Handbook of Operating and Maintenance Instructions for Model AN/APA-46 Aircraft Radar Equipment RL-M-227\nNosmeagle RL-M-247\nGeneral Description, Special Installation Requirements, and Mounting Dimensions of AN/APG-5 (ARO), Airborne Range Only Equipment\nRL-S-6\nAN/APS-10 Airborne Radar RL-S-22\nAEW, Airborne Early Warning Equipment RL-S-22, RL-S-26 (additional material)\nInterconnecting AN/APA-5 and Army Radar Sets\nTermination Report on Radar Photo Reconnaissance Project RL-S-34\nAmplidynes Amplifiers\nService Manual for Video Amplifier [University of Pa.]\nDevelopment of a Tunable IF Amplifier (Sylvania)\nNoise Reduction by Delayed Feed-Back (RCA)\nAnalysis of 6SA7 Gated Amplifier (Cornell) - 14-158\nFinal Report on Development of (1) High-Frequency Amplifiers (Continued) - 14-158: High-Frequency Video Amplifier and (2) Radar Ranging\nDevelopment and Use of the \u201cMicroband\u201d Lock-In Amplifier. - 14-589\nReceivers. RL-101, RL-104\nVisit to the Bell Telephone Laboratories. RL-105\nSpecial Report on Receivers. RL-106\nIF Amplifier Design. RL-112\nReport of the Radio Frequency Section. RL-140\nFine Grid Technique. RL-299\nThe Radiation Laboratory S-Band Amplifier (Preliminary Report). RL-306\nA 70-Mc Wide IF Amplifier. RL-307\nExternally Triggered Circular-Sweep Amplifiers.\nA Cathode Follower Employing Two Tubes to Obtain Extremely Low Output Resistance. RL-469\nStagger-Tuned I-F Amplifiers. RL-524\nThe Effect on Noise Figure of Placing the Gain Stage in the RF Amplifier. RL-525\nRL-528. A Hard Tube Servoamplifier for Fractional Horsepower DC Motors.\nRL-535. Stagger-Damped Double-Tuned Circuits.\nRL-539. Antenna Measuring Equipment: 100-Db Linear Audio Amplifier.\nRL-601-3.\nModification of the Amplifier of the AN/APN-2 to Give Sharp Cut-off Wide-Band Response. RL-613.\nThe Use of a Twin-T Network in a Selective Frequency Amplifier, with Special Applications.\nGrounded Grid I-F Amplifiers. RL-1030.\nIntermediate Frequency Amplifier Overload Characteristics. RL-1032.\nMemorandum Describing High Gain DC Amplifier.\nInstructions for Operation of High Gain Video Amplifier for PJf-E Synchroscope. RL-M-166.\nAN/APS-1 Receiver-Indicator Modified for Ground Range Sweeps and Remote Amplifier. RL-M-172A.\nAntennas (see also Radomes, Scanning).\nDesign of Egg Beater Scanning Antenna for the Eagle Radar Bombsight and Construction of a\nReports:\n14-312: Model Final Report [Int. Projector Corp.]\n14-396: BUPX Antenna Type A [RCA]\nAug. 26 - Sept. 24, 1941: Roof Systems Reports\nRL-56, RL-57: Regular Reports on Spinners and Radiators\nRL-91: Report of Parabola Section (Dec. 2, 1940)\nRL-92: Report of Parabola Section (Dec. 16, 1940)\nRL-93: Report of Parabola Section (Jan. 22, 1941)\nRL-94: Antenna Group (Feb. 14, 1941)\nRL-95: Report of the Antenna Group (Mar. 12, 1941)\nRL-96: Report of the Antenna Group (May 1, 1941)\nRL-97: Report of the Antenna Group (July 1, 1941)\nRL-98: Antenna Design and Pattern\nRL-99: A Study of Fanned Beam Radiators\nRL-123: Notes on Antenna Design\nRL-168: A Method for Measuring the Absolute Gain of Micro-wave Antennas\nRL-169: Rear Rectangular-Guide Antenna Feed.\nIllumination and Phases of Antenna Feeds. RL-170\nRound-Guide Rear Antenna Feeds RL-171\nEffect of Paraboloid Size and Shape on Beam Patterns. RL-258\nGraphical Analysis of Beam Patterns from Paraboloid Reflectors. RL-259\nPillbox Antenna for Glide Path. RL-260\nSome Matching Properties of Antenna Feeds. RL-261\n3-CM Bolometer Detector Suitable for Field Measurements (Type Y). RL-262\nHorizontally Polarized 9.1-CM Biconical-Horn Beacon Antenna. RL-263\nRapid Scanning, High Resolution Antennas Preliminary Report. RL-265\nAn Automatic Recorder for Microwave Antenna Pattern Measurements. RL-266\n45\u00b0 Microwave Reflector. RL-267\nGratings and Screens as Microwave Reflectors. RL-269\nInformation of Standard Radiation Laboratory Paraboloid Reflectors. RL-269\nAntenna Feeds for \u00bd-Inch Stub-Supported Coaxial Line. RL-271\nSynthesis of Microwave Diffraction Patterns with\n\n(Note: The text appears to be in good shape and does not require extensive cleaning. Only minor corrections for formatting and spacing have been made.)\nApplication to Csc2e: Double Dipole Rectangular Waveguide Antennas. Antenna Feeds from Yi-inch Coaxial Line. RL-274: The Antenna Slide Rule - Series L. Microwave Linear Radiators. RL-366. Laboratory and Field Tests with Stabilized Spinners. Development of Antenna for Raytheon SO-CXBY. Antenna for High-Altitude Bombing (H2X). RL-411. Report on the Microwave Antenna Conference, July. LRASV (AN/APA-2) Antenna. RL-415: Half Beacon Antenna. RL-419: Contribution of the Dish to the Impedance of an Antenna. RL-442: Probe-Fed Slots as Radiation Elements in Linear Arrays. RL-455: Antenna Parts and Measuring Equipment. RL-472: Paraboloid Antenna Characteristics as a Function of Feed Tilt. RL-479: A Simplified Search Antenna for Radio Set AN/ X-Band Horizontally Polarized Nondirectional Antennas. RL-489. V-Beam GC Radar. RL-507. Adjustment of Loran Antennas and Antenna Coupling.\nPart III: Antennas (Continued)\n\nImpedance Characteristics and Equivalent Circuits for Vertical Radiators. RL-512\nS-Band Horizontally Polarized Nondirectional Antennas. RL-517\nAspen Airborne Antenna. RL-519\nRotating Corrugated Eccentric Line Antennas. RL-557\nS-Band End-Fire Array Antenna. RL-577\nAntenna Measuring Equipment. RL-601-1\nAntenna Measuring Equipment, High Power CW Transmitter for S-Band. RL-601-2\nAntenna Measuring Equipment, 100-Db Linear Audio Amplifier. RL-601-3\nAntenna Measuring Equipment, Automatic Antenna Pattern Recorder. RL-601-4\nLow-Altitude Navigation Antennas Developed in Connection with AN/APS-10. RL-615\nS-Band Vertically Polarized Nondirectional Antennas. RL-623\nK-Band Cosecant 2 Antennas with a Line Source and Shaped Cylindrical Reflector. RL-624\nField Station for Antenna Measurements: RL-632, Vertical Coverage of a lVz-Ft by 5-Ft Antenna for SG-3 (Experimental Data Obtained with an SNB Aircraft as Target). RL-636\nSG-1 Antenna Mark 2. RL-639\nParallel Plate Optics for Electrical Scanning. RL-646\nElectrical Design of the AN/T PS-10 Antenna. Shaping the Primary Pattern of a Horn Feed. Characteristics of Horn Feeds on Rectangular Waveguides. RL-656\nSU-2 Antenna, Shipborne Stabilized Radar Antenna for Sea Search. RL-659\nSU-2 Antenna, Line-of-Sight Stabilization of a Radar Beam by Reflector Tilt. RL-660\nReflections from Smooth Curved Surfaces. RL-661\nStabilized SG-3 Antenna. RL-665\nInformation on Radiation Laboratory Paraboloid Reflectors. RL-679\nA Low-Drag Beacon Antenna for Fighter Aircraft. Primary Feeds in Cylindrical Parabolas. RL-686\nThe SCI Rapid Scan Height-Finding Antenna.\nHorn Feeds for Parabolic Antennas. RL-690 Double-Curvature Surfaces for Beam Shaping with Point-Source Feeds. RL-691 Double Coaxial Coupler for BUPX Antenna. RL-736 Calculation of Vertical Polar Diagrams and Power Gains of Antennas for Airborne Navigational Radars. RL-750 APQ-13 60-Inch Antenna. RL-751 Parallel Plate Bends. RL-760 Fourier Integral Methods of Analysis. RL-762-1 Quarter Wave Plate for Broad-Band Circular Polarization. RL-769 Broad-Band Coaxial-Line Horn. RL-770 Antennas (Continued) K-Band Linear Array. RL-771 Slotted Dipole Impedance Theory. RL-772 Double Reflector Antenna for High-Altitude Bombing Early Warning Search Antenna. RL-779 Mechanical Resonant Scanner. RL-782 K-Band Antenna for High-Altitude Bombing. RL-789 Present Status of High Power at S-Band. RL-793 Shipboard Black Maria Antennas. AN/APS-32 and AN/APS-31 Airborne Navigational Radars.\nRadar Antennas: RL-808 Analysis and Correction of Impedance Mismatch due to Reflector. RL-810 Hawkeye Antenna. RL-812 SA 6-6 Horizontally Polarized Antenna. RL-823 Die-Cast Model of the CSB Antenna. RL-824 Buzz-Bomb Antennas. RL-825 Variable Width Waveguide Scanners for Eagle (AN/APQ-7) and GCA (AN/MPN-1). RL-840 IFF Antenna for Mounting on Wing of a TBM Torpedo Bomber. RL-842 IFF Receiving Antenna for Mounting in Cadillac Dish. RL-843 IFF Transmitting Antenna for Mounting in Cadillac Dish. RL-844 Six-Element Vertically Polarized Beacon Antennas. The AN/APQ-13 (60\") Scanner in B-29 Airplanes. Cindy Antenna, A High Resolution K-Band Radar Antenna for Sea Search. RL-849 Broad Band Bi-Conical Vertically Polarized Dipole. Double Skin-Back Antenna. RL-852 APS-33 Antenna, Final Pre-Production Data. A New Pillbox Feed. RL-862 Horn with Metal Lens. RL-863\nAirborne Black Maria Antenna. RL-866\nLens Feed for K-Band Pillboxes. RL-869\nStreamlined Microwave Omni-Directional Antennas.\nThe AN/APS-23 Antenna and Installation. RL-878\nA Four Horn Feed to Give Cscf 2 Antenna Patterns.\nAn IFF Mark 5/UNB Feed in the SCI Search Antenna. RL-897\nAN IFF Mark 5/UNB Feed in the AN/CPS-6 Vertical Antenna. RL-898\nAN IFF Mark 5/UNB Radiator in the AEW Antenna. RL-899\nA Broad Band TEM Pillbox. RL-901\nA Flat Plate Beam-Shaping Antenna. RL-903\nAN/CPS-6 (V-Beam) Antenna. RL-951\nCompact Horns Intermediate Between Polyrods and Reflectors. RL-961\nMeasurement of Phase in Microwave Antenna Fields by Phase Modulation Method. RL-966\nDielectric Rod Endfire Antennas Close to Metal Surfaces. *L-969\nLinear Array for Use in the AN/APS-23 Antenna. Two Circularly Polarized S-Band Horns.\nAn X-Band Hemi-Isotropic Radiator.\nOmnidirectional antennas for BUPX. Dipole Arrays Backed by Reflecting Sheets.\nSCI Search Antenna Mark I.\nSCI Search Antenna Mark II.\nThe Beavertail (AN/CPS-4) Antenna.\nSG-1 Mark III Antenna.\nThe Antenna for Radar Mark 35.\nAN/APS-31 Antenna.\nBeam Shaping.\nMetal Plate Lens for Cs2 Antenna.\nLow Altitude CsFd Antenna for APS-33 Project.\nSurvey of Foster Scanner Developments. RL-1074.\nThe Alteration in the Radiated Field of a Paraboloid.\nDue to a Shift in the Position of the Dipole Feed.\nAdmittance Characteristics of Some S-Band Waveguide Fed Dipoles. RL-1082.\nPreliminary Technical Manual for SCR-584 MTI Modification Kit No. MC-642-AS and Fan-Beam Search Antenna. RL-M-218.\nPreliminary Testing of the Houston Corporation AN/APS-10 Scanner. RL-S-33.\nProposed Antenna for Panoramic Radar. RL-S-55.\nTables of Fourier Transforms of Fourier Series, Power Series, and Polynomials. RL-S-58.\nAntenna Catalogue RL-S-64, RL-T-7\nParaboloid Diffraction Patterns from the Standpoint of Physical Optics\nGeneral Lecture Series on Radar Components\nFlight Test of an Experimental Horn-Fed Antenna\nAnti-Jamming (see Countermeasures)\nATR Switches (see TR and ATR Switches)\nAttenuators (see Test Equipment and Transmission Line Components)\nAutomatic Frequency Control\nAn Automatic Frequency Control and Frequency Selection System for Magnetrons. RL-541\nSome Automatic Frequency Control Circuits. RL-687\nAutomatic Frequency Control for AN/APS-31/33.\nAutomatic Frequency Control of Thermally-Tuned, Beacon Local Oscillator. RL-955\nVideo Discriminator Automatic Frequency Control.\nA Method for Automatic Frequency Control of Thermally-Tuned Oscillators. RL-959\nAn Automatic Frequency Control System for Magnetrons with Beacon Applications. RL-1020\nAFC Operation and Maintenance. RL-S-77\nBallistics (see Bombing and Ballistics)\n\nFinal Report on Ultra-Portable Racon (BUPX) and Tubes for Lightweight X-Band Radar and Ultra-Portable X-Band Beacon (RCA)\n\nFinal Report on AN/PPN-2 Radio Set Beacon Discrimination Circuit (RL-29)\n\nPerformance Characteristics of the Magnetron Under Conditions Simulating Beacon Operation, Tube with Horizontally Polarized 9.1-cm Biconical Horn Beacon Antenna (RL-263)\n\nA Racon Prospectus with a Pictorial Brief of BGS. BGS 10-cm Radar Beacon (RL-358)\n\nHalf Beacon Antenna (RL-419)\n\nRosebud Microwave Beacon Equipment (RL-460)\n\nPropagation over Short Paths and Rough Terrain at Overinterrogation Control of Microwave Beacons. X-Band Horizontally Polarized Nondirectional Antennas (RL-489)\n\nResults of Tests on Use of Rebecca-Eureka by the Army Ground Forces (RL-500)\nPulse-Length Discrimination in Beacons. RL-510 S-Band Horizontally Polarized Nondirectional Antennas. RL-517 Tests of Beacon Receiver on V-Beam. RL-522 An Airborne S-Band Racon for Rooster Operation. Ultra-Portable Microwave Radar Beacons as Beam Approach Aids in Aircraft Landing RL-581 BUPS (AN/UPN-1, 2) an Ultra-Portable S-Band Radar Beacon and Its Tactical Uses. RL-583 Siting and Range of Microwave Beacons. RL-590 Results of Field Tests on AN/UPN-1, 2 (Experimental Models of BUPS) at Boca Raton, Florida (January-March 1944). RL-591 Florida Tests on ROSEBUPS against SCR-582, SCR- Statistics of Beacon Interrogation. RL-602 Video Stretching as a Method for Improving X-Band Beacon Reception. RL-604 Comparison of Theoretical and Experimental Requirements for Microwave Beacon Transmitter Power and Receiver Sensitivity. RL-627 A Low-Drag Beacon Antenna for Fighter Aircraft.\nUltra-Portable X-Band Radar Beacons and Their Tactical Uses (Continued)\n\nInterference Between SCR-581*'s Tracking APN-19 Beacons. EL-816\nFinal Report on BUPX. RL-1054\nPreliminary Handbook for Experimental Prototype Model Radio Set SCR-620, March 1943\nSupplemental Handbook for Model CXEH (BGX) Radar Beacon. RL-M-130\nHandbook of Instructions for AN/APA-9 (Aspen) Radar Set. RL-M-148A (Second Edition)\nHandbook of Instructions for Radio Set AN/APA-9. RL-M-148B\nPreliminary Handbook for Experimental Prototype Model Radio Set SCR-620 (Same as RL-M-121)\nMarch 1943, Supplement July 1, 1943\n\nRL-M-148C\n\nRadar Beacon \u2014 Mark I Mod 1: RL-M-161\nMaintenance Manual for the AN/APQ-7 System Modified for SG Band\n\nRL-M-167\nDescription of the Experimental Rosebud: RL-M-184\n\nPreliminary Instruction Book for Shore Bombardment Beacon Navy Model Mark 2 Mod 0 and Mod 1\nHandbook of Maintenance Instructions for AN/APA-UO (Micro-H Mark II) Airborne Attachment\nPreliminary Instruction Manual for X-Band Coincident Beacon XCB (Mark I), AN/APX-1U\nMaintenance Manual for Model AN/APN-21XR Racon\n\nRL-M-213\nTarget Raft Transponder\n\nRL-S-2\nBeacon Tests with AN/APS-6\nRL-S-16\nBombing and Ballistics\n\nFinal Report for Contract OEMsr-lOUU\nMay 27, 1943 to Oct. 31, 1945; Part 2, Triangle Solver for Eagle\nPart 3: Triangle Solver for H2X Bombing\nPart 4: Triangle Solver for Laboratory\nUse: Part 5: Redesign of Triangle Solver for Eagle\nProject Librascope 14-587\nCorrelation of ASV Equipment with the Bombsight\nCalibrator for Low Altitude Bombing Equipment\nH2X Range Unit for Navigation and Bombing\nModified Homing Course. RL-369\nAntenna for High-Altitude Bombing (H2X). RL-411\nBombing Errors. RL-530\nAn H-f- B Impact Predicting Computer Assuming Constant Indicated Airspeed for Use with AN/APS-15A Radar. RL-584\nThe SCR-58U Plotting Table System. RL-595\nBombing and Ballistics (Continued)\nNomograms for Radar Bombing with the 100-Lb Practice Bomb M38A2. RL-614\nBUPX (AN/UPN-3-4, AN/APN-11): Ultra-Portable X-Band Radar Beacons and Their Tactical Uses\nFront-Line Demarcation and Bombing with the Aid of Light-Weight X-Band Beacons (BUPX)\nThe AN/APS-30 Series: RL-714, RL-763-0, RL-763-1, RL-783, RL-939, RL-M-148A (Second Abbreviated Edition), RL-M-148B, RL-M-148C, RL-M-151, RL-M-163, RL-M-164A, RL-M-164B, RL-M-247\n\nHandbook of Instructions for AN/APA-9 (Aspen) Radar Set\nHandbook of Instructions for Radio Set AN/APA-9 (Preproduction Sets)\nModification of SCR-584 for Oboe II\nInstruction Manual for Automatic H2X Camera Model A\nTemporary Instruction Manual for Automatic Radar Camera Model B\nNosmeagle\n\nGround Position Indicator for Radar Navigation\nBombing, RL-S-19, Interconnecting AN/APA-5 and Army Radar Sets. Release Point Indicator for Radar Bombing Techniques. RL-S-59, Tables for Use with Torpedo Director Mark 33-1. The Manual Plotting System RC-305. RL-S-62, Broad-Banding (see reports on Components under TR, etc.). Cables and Connectors (see Transmission Lines). Calibrators (see Test Equipment, Range). Camouflage (see Absorbent Materials, Countermeasures). Cathode-Ray Tubes (see also Indicators). Report of Work on Duplex Screen Tubes. Summary of Research on Radar Indicator Screens. Work on Slow Phosphors for Radar Indicator. Theory of Dark-Trace Tubes, I [Carnegie Inst]. Abridged Report on Circuits for Improving Focus on Electrostatic Cathode-Ray Tubes under Conditions of Intensity and Deflection Modulation [Brown].\nReport of Progress on Dark-Trace Tubes\n\nThe Theory of Dark-Trace Tubes II [Carnegie Inst. of Technology]\nDarkening and Bleaching of KCL [Carnegie Inst. of Technology]\nTwo Notes on the Potentials Developed in Cathode-Ray Screens During Bombardment [Carnegie Inst. of Technology]\nMemoranda on the May 1913 Meeting on Dark Trace Tubes at Radiation Laboratory [Carnegie Inst. of Technology]\nA Memorandum on the Scattering of Light by DT Screens [Carnegie Inst. of Technology]. 14-198\nDarkening and Bleaching of KCL II, The Effect of Temperature [Carnegie Inst. of Technology]. 14-205\nMemorandum Upon the Behaviour of DT Screens Containing Magnesium [Carnegie Inst. of Technology]\nDark-Trace Radar Indicator Screens, Progress Reports\nExperiments with Double Layer DT Screens [Carnegie Inst. of Technology]. 14-253\nThe Theory of Dark-Trace Tubes, III [Carnegie Institution]\nThe Depth of the Darkened Region and the Build-Up\nTheories of Dark-Trace Tubes IV, The Spectral Distribution of the Luminescence of Red Screen Materials (DuMont Labs), Aging of KC1 Crystals and Screens Under Electron Bombardment (Carnegie Inst, of Tech.), Properties of Evaporated Layers of Potassium Chloride Containing Small Additions of Metallic Elements When Subjected to Electron Bombardment (Carnegie Inst, of Tech.), Skiatron Projection Cathode-Ray Tubes with Dark-Trace P10 Screens (RCA), Cathode Ray Tube Detectors (Brown), Preparation of Exponential Decay Powders and Screens ZnF2:Mn, ZnMgF2:Mn and MgSiOz'.Mn (Sylvania), Development of the Skiatron Cathode Ray Tube for Projection Indicator, Progress Report No. I* Research and Development Leading to New and Improved Cathode Ray Tubes (Carnegie Inst, of Tech.)\nCathode Ray Tubes (Continued)\nMethod of Measurement and Some Performance Characteristics of P1J* Screens with a Note on Manufacturer's Specifications for Tubes Containing P1I* Screens (RCA) 14-586\nStudies of British Phosphors of the Type C, H, K, Potentiometer Type RL-B for Azimuth and Elevation Indication on Magnetically Deflected Cathode-Ray Tubes. RL-409\nStabilized High Voltage Supply. RL-565\nPerformance Characteristics of Army-Navy Preferred Type Electrostatic Cathode-Ray Tubes. RL-674\nDeflection Yoke Design Information. RL-755\nHigh Speed Photography of Cathode Ray Tube. AIR Range Scope. RL-804\nNotes on Photometry, Colorimetry, and an Explanation of the Centibel Scale.\nInstruction Manual for Projection PPI. RL-M-137\nTesting of Skiatrons. RL-S-1\nTesting of Skiatrons (Supplement). RL-S-ls\nComparison of P7 Screen Test Methods. RL-S-9\nFocus Coil Control for Cathode-Ray Tubes. RL-S-17\nTabulation of CRT Screen Properties. RL-S-48\nEvaluation of Specifications for Pi I* CRT Screens.\n\nCathodes:\nMagnetron Cathode Studies, Progress Report (May 1)\nKnurled Type Cathode-Construction and Life Test\nMagnetron Cathode Studies, Progress Report (July 1)\nMagnetron Cathode Studies, Progress Report (Sept.)\nMagnetron Cathode Studies, Progress Report (Nov.)\nMagnetron Cathode Studies, Progress Report (Jan.)\nCathode Sparking, Effect of Super-Imposed DC and Role of Coating Resistance [Bartol]. 14-295\nSparking of Oxide-Coated Cathodes [Bartol]. 14-296\nBack-Bombardment of Magnetron Cathodes [Barton].\nSecondary Electron Emission from Oxide-Coated Cathodes.\nMagnetron Cathodes [Bartol]. 14-310, Cathode Coating Resistance as Measured by Embedded Probes [Bartol]. 14-514, Secondary Electron Emission from Oxide-Coated Cathodes [Bartol]. 14-515, Sparking Phenomena in High Vacuum Thermionic Tubes, General Survey [Bartol]. 14-516, Sintered Thoria Cathodes [Bartol]. 14-517, Effect of Particle Size [Bartol]. 14-518, Purification of Barium and Strontium Carbonates\n\nPART III\nCathodes (Continued)\n\nA Note on Nitrocellulose Binders [Bartol]. 14-520, Magnetron Cathode Studies, Final Report [Bartol], Effects of Variation of Vane Width and Cathode Size on the Operation of Magnetrons. RL-586, Cathodes for Pulsed Magnetrons. Part I\u2014Correlations between Oscillating and Diode Conditions. RL-683, Cathodes for Pulsed Magnetrons. Part II\u2014Construction and Performance of Pulsed Cathodes. Memorandum on the Activation of Various Surfaces.\nby Evaporation from Heated Oxide Cathode. Metallic Hydride Studies. Alkaline Earth Oxide Cathodes for Pulsed Tubes. Cavities (see also Test Equipment, TR and ATR Switches). Perturbation Theory for Cavities [Cornell]. 14-117. Special Report on Tunable Cavities. RL-143. Forced Oscillations in Cavity Resonators. RL-188. Excitation of Cavities through Windows. RL-202. Theory of Obstacles in Resonant Cavities and Wave Guides. RL-205. The Resonant Echo Box. RL-277. Committee on Centimeter Receiving Tubes and Resonators. RL-286. A Treatise on Echo Box Problems by Lagrangian Procedures, Part I. RL-629. Theory of Ringing Time of Tunable Echo Box. Design of an Improved X-Band Echo Box. RL-631. A Treatise on Echo Box Problems by Lagrangian Procedures, Part II. RL-696. X-Band Beacons Reference Cavities. RL-972. X-Band Sealed Standard Cavities. RL-S-70.\nGeneral Lecture Series on Radar Components.\nChemistry: Absorbent Materials, Crystals, and Dielectrics. CIC: Fire Control. Circuit Elements: Mechanical Vacuum Switches, Transmission Line, and RC Pulsing Circuits [U. of Cal.]. Preliminary Results on Calibration of Autotransformers [Cornell]. 14-156. Measurement and Design of DC Resonant Charging Chokes. RL-215. High-Frequency Characteristics of Resistors. RL-520. Moisture-Proofing of Button Mica Capacitors.\nCircuits and Networks. Development of a Stable Non-Crystal Controlled Oscillator [U. of Colo.]. 14-98. Operating Characteristics of Multivibrators and Gates. Progress Report No. 1, Jan. 6, 1943 [Rensselaer Polytech.]. 14-154. Operating Characteristics of Multivibrators and Gates and Related Matters. Progress Report No. 2, June 1, 1943 [Rensselaer Polytech.]. 14-155.\nAnalysis of 6SA7 Gated Amplifier (Cornell). 14-158\nAnalysis of Double Triode Integrator (Cornell). \nRange Tracking Circuit with Position Memory (Cor-). 14-158, 14-159\nRange Tracking Circuit with Velocity Memory (Cor-). 14-158, 14-159\nCoordinate Transformation Circuits Using Resolvers and Coordinate Transformation by Means of Electrical Networks (Bartol). 14-288\nInstantaneous Voltage Measurement by Use of a Trigger Circuit, Final Technical Report (Kansas State College). 14-409\nElectronic Computers for Division, Multiplication, Squaring, etc (Cornell). 14-435\nA Mechanical Integrating System Incorporating a Magnetic Amplifier (MA-2) (Cornell). 14-436\nUse of a Specially Designed Magnetic Amplifier in Computing Circuits (Cornell). 14-437\nPerformance and Stability of Triggered Gates (Rensselaer Polytech.). 14-445\nDC Resolvers (DCR-2) (Cornell). 14-512\nAC Potential Equalizers and Phase Sensitive Detectors (Cornell). 14-512\nTECH REPORTS\n\nACE-2 [Cornell]. 14-513\nElectronic Computers for Division, Multiplication, etc. [Cornell]. 14-538\nInvestigation of Circuits for Use in Precision Radar Computers, Final Report [Cornell]. 14-546\nDevelopment of High-Frequency Video Amplifier and Radar Ranging System, Final Report [U. of Beacon]\nDiscrimination Circuit. RL-29\nThyratron Servo Control Circuit for Spinners. RL-31\nSpecial Report on Buffered Multiple Phase Box\nInstruction Manual Browning Type A Synchronizer\nI.F. Amplifier Design. RL-112\nStatistics of Circuit Noise. RL-192\nAnalysis of Magnetron Performance, Part I, Equivalent Circuit, Method, Applications. RL-229\nImpulse and Square-Pulse Response of Various Filters. RL-285\nPrecision Timing Calibrator and Range Measuring System. RL-319\nPrecision Delay Multivibrator for Range Measurement. RL-320\nMedium Precision Self-Synchronous Range Circuit\nModel U. RL-321\nCircular Sweep Precision Range System Model 4. (MPS-4)\nMedium Precision Self-Synchronous Automatic Range-Tracking Circuit. RL-323\nPhotoelectric Automatic Range-Tracking Unit. RL-325\nSimplified Circular-Sweep Range System. RL-325 Circuits and Networks (Continued)\nHand Radar Ranging Circuit. RL-327\nAntiaircraft Artillery Board Test on the Simplified Circular Sweep Range. RL-326\nErrors in Circular Sweeps Due to Decentering and Ellipticity of the Circle. RL-328\nFrequency Division with Blocking Oscillator Pulse Transformers. RL-329\nLine Controlled Blocking Oscillator Marker Generator (ARO) Calibrator. RL-330\nARO Range Follow-up Unit. RL-331\nARO Range Unit. RL-332\nModel II Calibrator. RL-333\nA Voltage Compensated Delay Multivibrator. RL-334\nExternally Triggered Circular-Sweep Amplifiers. Delayed Sweep for SCR-582-X. RL-337\nAn Adaptation of the Phantastron Delay Multivibrator. RL-338\nA Condenser Phase Shifter Range Circuit with Sine Wave Tracking for Microwave Height-Finding Stations. RL-338, RL-339\nResistance-Capacitance Networks. RL-379\nA Note on Pulse Distortion by Rejection Filters. RL-448\nOne-Tube, One-Selsyn Sector-Scanner. RL-448\nDifferential to Single-Ended Potential Converters. RL-469\nA Cathode Follower Employing Two Tubes for Extremely Low Output Resistance. RL-469\nOverinterrogation Control of Microwave Beacons. RL-482\nRemote-Position Control by Direct Frequency Variation. RL-482\nThe Two-Disc DC Thermistor Bridge Circuit. RL-510\nA Method for Relay Radar PPI Synchronization. Pulse-Length Discrimination in Beacons. RL-510\nProposed Method for Measuring Instantaneous Magnetron Input Impedance with the Aid of a Delay Network. RL-515\nVoltage Pulse Rate-of-Rise Measurements. RL-523\nThyrite Bridge Controlled Voltage Regulator. RL-525\nStagger-Damped Double-Tuned Circuits. RL-539 Frequency Division with Blocking Oscillators, Part I. The Evaluation of an Equivalent Circuit for a Pulse Transformer. RL-545 Equalized Delay Lines. A 60-Mc Parallel Sobering Bridge. N2 Gate Attachment for SCR-58 b. RL-566 Matching Resistance Curves by Means of Two Linear Ganged Potentiometers and a Three-Terminal Resistance Network. RL-610 Effects of Line and Cathode-Follower Terminations on Pulse Shape. RL-616 A Method of Virtual Displacements for Electrical Systems with Applications to Pulse Transformers. Circuits and Networks (Continued). An Extension of Lagrange\u2019s Equations to Electromagnetic Field Problems, Equivalent Networks. Errors in the Condenser Type Continuous-Phase Shifter. RL-633 Realizability of Filters. H-3 Trigger Unit. RL-645-3 The 1-3 Signal Unit. RL-645-4 The H-2 Trigger Unit. RL-645-6\n1-2. Signal Unit. RL-645-7 - A Microwave Frequency Discriminator. RL-662 - A Feedback Circuit for Measuring Output Noise Ratio of Crystal Rectifiers. RL-667\nColloquium on Pulse-Forming Networks, October 12, 19-- Calculation of Pulse-Forming Networks Having Slow Rates of Voltage Rise. RL-698\nNonlinear Networks as Voltage Regulators. RL-711\nNotes on Load Effects in Reflex Oscillators. RL-717\nA Theory of a Supersonic Delay Line. RL-733\nEquivalent Network for the 232-BW Pulse Transformer Based on the Method of Virtual Displacements. RL-734\nThe Use of a Twin-T Network in a Selective-Frequency Amplifier with Special Applications. RL-738\nA Wide-Excursion Frequency-Modulated Alignment Oscillator or Wobbulator. RL-738\nInterference Blanker. RL-749\nThe Double-Tuned Circuit with Transitional Coupling. RL-784\nElectrical and Physical Characteristics of Some Commercial Feed-Through Filters. RL-785\nMultiple Reflection Delay Tank RL-791\nOn the Theory and Performance of Liquid-Delay Lines RL-792\nPulsed Quartz-Crystal Oscillator RL-803\nParallel T Stabilizing Networks for AC Servos\nAnalysis of a Half-Wave Rectifier Circuit Involving Inductance, Resistance, and Capacitance RL-867\nPulse-Forming Network Committee, Proposed Basic Specifications for Pulse-Forming Networks\nThe Effect of Small Changes in Circuit Parameters on the Solution of Network Problems RL-1063\nTheory of Operation of AEW Circuits RL-M-201\nRectifier Filter Circuit Analysis RL-T-3\nRectifier Filter Circuit Analysis Supplement\nClose Control and Close Support (see also Ground Radar and Airborne Radar)\nTactical Devices Based on Superposition of a Plotting Board on the PPI Pattern RL-387\nThe SCR-584 Plotting Table System RL-595\nClose Cooperation Bombing RL-756\nInterference Between SCR-58 and Tracking APN-19\nPART III\n\nClose Control and Close Support (Continued)\n\nPreliminary Instructions on Modification Kit MC-627 for Radio Set SCR-584. RL-M-220\nPreliminary Instructions on Modification Kit MC-627 for Radio Set SCR-584 (Revised). RL-M-220B\n\nAN/CPA-7 Operations Room Equipment Supplementing Radio Set AN/C PS-1. RL-M-228\n\nMEW Close Control. RL-S-76\n\nClutter (See also Moving Target Indication)\nThe Detection of Moving Targets among Ground Clutter by Coherent Pulse Methods. RL-480\nTests of Beacon Receiver on V-Beam. RL-522\nElimination of Ground Clutter. RL-526\nA Moving Target Selector Using Deflection Modulation on a Storage Mosaic. RL-562\nThe Effect of Clutter Fluctuations on MTI. RL-700\nSea-Return Effects and Their Elimination in the MTI for MEW. RL-752\nA Theoretical and Experimental Study of Radar Ground Return. RL-1024\nFlight Tests on AN/APS-6A. RL-S-25 Anti-Clutter Circuits for AEW. RL-S-52 Coaxial Lines, see Transmission Lines. Combat Information Center [CIC] see Fire Control. Communication, except for Systems), see Radar.\n\nRadiotelephone Communication on 3,000 Megacycles [Washington State College]. 14-152 Report of Radio Relaying of Radar Signals [RCA].\n\nA Duplex Communication System for Microwaves. Handbook of Maintenance Instructions for AN/AIC-6 Intercommunication System. RL-M-244.\n\nComputing Devices and Methods. Coordinate Transformation Circuits Using Resolvers and Coordinate Transformation by Means of Electrical Networks [Bartol]. 14-288.\n\nApparatus for the Transformation of Rectangular Coordinates Using Armaresolvers [Bartol]. 14-293.\n\nDevice for Determination of the Vertical by Means of Cosmic Rays [Cornell]. 14-363.\n\nSpecial Mechanical Counter for the Mark III or Mark V Computer.\nPhase-Shift Loran Indicator [Int. Business Machines Corp.]. 14-368\nElectronic Computers for Division, Multiplication, Squaring, etc. [VAC-4] [Cornell]. 14-435\nA Mechanical Integrating System Incorporating a Magnetic Amplifier [MA-2] [Cornell]. 14-436\nUse of a Specially Designed Magnetic Amplifier in Computing Circuits [Cornell]. 14-437\nElectronic Computers for Division, Multiplication, etc. Some Additional Remarks [Cornell]. 14-538\nInvestigation of Circuits of Use in Precision Radar Computers, Final Report [Cornell]. 14-546\nRadar Trainer Equation-Solvers for the Relative Motion of Two Moving Objects in Space. RL-436\nThe Range Calculator. RL-497\nComputing Devices and Methods (Continued)\nTheoretical Calculation on Best Smoothing of Position Data for Gunnery Prediction. RL-532\nRefraction. RL-551\nAn H + B Impact Predicting Computer Assuming Constant Indicated Airspeed for Use with AN/\nAPS-15A Radar, RL-584 Errors in Target Velocity Due to Rolling and Pitching of the Ship, RL-612 Nomograms for Radar Bombing with the 100-Lb Practice Bomb M38A2, RL-614 Tests on the Performance of the Mk 1-Mod 7 Computer, RL-677 GPI for Close-Control Bombing, RL-783 Ground Course Computer for AN/APQ-T1, RL-856 AN/APG-13B Vulture Rocket Computer, RL-909 Computer Mark 14 AN/APA-30 XN-1 Instruction Manual, RL-M-179 Hygraph Instruction Manual, RL-M-230 Ground Position Indicator for Radar Navigation and Bombing, RL-S-19 Alignment Kit (Torpedo Rack) Mark 1 Mod 0, Continuous Wave Radar, Elimination of Ground Clutter, RL-526 An Electronic Modulator for CW Magnetrons, General Theory of Electronic Beam Modulators, Corner Reflectors, Application of Corner Reflectors to Radar (Theoretical), RL-203 Application of Corner Reflectors to Radar (Experimental), RL-280.\nCorner Reflector Tests at Langley Field. RL-402, RL-433, Observations of Life Rafts Equipped with Corner Reflectors for Lift, Aug. 1, 1944, Design of a 4-Foot Corner Reflector for K-Band, Rotating Corner Reflectors for Ship Identification, Corner-Reflector Modulation of Airplane Signals, A Proposed Design for MX-180 / A Corner Reflector (Float Marker, Radar, Droppable), RL-S-39, Countermeasures, jamming, anti-jamming, camouflage, etc., Plan Position Indicator for 584 AJ, RL-678, Synthetic Radar Echoes in the Presence of Jamming, Radar Camouflage, RL-766, Pulsed-Interference Suppression, RL-826, S-Band Tunable Systems, RL-911, Countermeasures (Continued), Some General Microwave Anti-Jam Design Considerations and Performance of a Special Receiver, RL-S-8, Detection of Propeller and Sambo Modulations.\nTests on AN/CPS-6, Leesburg, Florida, June\n\nCrystals: Detector and Mixer\nThe Principles of Crystal Rectifiers [U. of Pa.]\nThe Electrical Conductivity of Silicon and Germanium in DC Silicon and Germanium Rectifiers [U. of Pa.]\nInvestigation of Crystal Rectifier DC Characteristics [Purdue] 14-115\nFurther DC Burn-Out Experiments on Silicon and Germanium Rectifiers [U. of Pa.] 14-119\nElectron Microscopy of Tungsten Points [Noise in Crystal Rectifiers] [U. of Pa.] 14-126\nThe Diffusion Theory of Crystal Rectifiers [Purdue]\nTheory of Noise in Conductors, Semi-Conductors, and Crystal Rectifiers [Purdue] 14-133\nBarrier Capacity in Silicon Cartridge Rectifiers\nDetermination of Logarithmic Constants of Crystal Rectifiers with the Oscilloscope [Purdue] 14-143\nMeasurement of Conversion Gain with a Modulated Oscillator [Purdue] 14-144\nHigh-Frequency Rectification Efficiency of Crystals\nTheory of Signal to Noise Ratio of Crystal Mixers in Crystal Rectifiers [U. of Pa]. 14-166\nTheory of Contact Rectifiers [Purdue]. 14-168\nIonization of Donator Levels in Crystal Rectifiers by Thermal Agitation [U. of Pa]. 14-173\nEffect of Tapping on Barrier Capacity [U. of Pa].\nBehavior of Silicon Crystals at Low Level Powers\nBehavior of Westinghouse Silicon as a Low Level Noise Source in Silicon Rectifiers\nDependence of IF Impedance and Noise Temperature of Crystal Rectifiers on Matching Conditions\nComparison of Wedge and Cone Contacts\nA Device for the Selection and Manufacture of Low Level Detectors [U. of Pa]. 14-201\nRecent Research on Silicon Rectifiers [U. of Pa].\nNoise Spectrum of Silicon Rectifiers [U. of Pa].\n\n(Continued)\n\nCrystals.\nRecent Research on Silicon Rectifiers [U. of Pa].\nNoise Spectrum of Silicon Rectifiers [U. of Pa].\nThe Theory of Crystal Mixer in Terms of Measurable Mixer Constants [Purdue]\nAudio Noise Tester [U. of Pa.] 14-267\nX-Band Video Crystals [U. of Pa.] 14-274\nProduction and Effects of a Depletion Layer in Doped Silicon [U. of Pa.] 14-282\nHigh Frequency Characteristics of Rectifiers [Purdue]\nTheory of Small Deviations from Pure Diode Behavior [Purdue] 14-286\nTemperature Variation of Low Level Crystal Performance\nNote on the Measurement of Noise Temperature\nK-Band Germanium Crystals, Bi-Monthly Progress\nPreparation of High Voltage Germanium Crystals\nThe High Voltage Germanium Rectifier, Section I \u2014 Experimental [Purdue] 14-342\nDevelopment of High Back Voltage Germanium Rectifiers, Interim Report No. 1, Nov. 21, 1944.\nThe High Voltage Germanium Rectifier, Section II \u2014 Theoretical [Purdue] 14-375\nEffect of Small Crystallites on Conductivity [U.]\nK-Band Germanium Crystals, Bi-Monthly Progress (University of Pennsylvania). 14-387, 14-394, 14-405, 14-412, 14-413\nGermanium Crystal Rectifier for Radar Receivers and Indicator Circuits, Interim Report No. 2 (University of Pennsylvania). 14-405\nK-Band Germanium Crystals, Bi-Monthly Progress (University of Pennsylvania). 14-412\nPhotoeffects in Pure Silicon (University of Pennsylvania). 14-412\nProperties of Germanium High-Back Voltage Rectifier Units (Purdue). 14-413\nDependence of Performance of Germanium Second Detector Units on Bias and Video Load (Purdue). \nK-Band Germanium Crystals, Final Report (GE).\nBurnout of X-Band Video Crystals (University of Pennsylvania). \nGermanium Crystal Rectifier for Radar Receivers and Indicator Circuits, Interim Report No. 3 (University of Pennsylvania). 14-453\nHigh Back Voltage Silicon (University of Pennsylvania). 14-453\nX-Band Crystal Video Performance with Bias (University of Pennsylvania).\nHandy Guide to Crystal Types III [University of Pa.]\n\nDevelopment Research on X Band Video Crystals\nDouble Valued Characteristics of Crystal Rectifiers,\nTemperature Effects of S Band Video Crystals [University of Pa.], 14-559\nBurnout Life Tests of X Band Video Crystals [University of Pa.], 14-559\nUse of Different Fillers in Crystal Rectifiers [University of Pa.], 14-577\nResearch Development of Crystal Rectifiers, Final\nGeometrical Structure of Silicon Surfaces [University of Pa.], 14-577\nBurnout of S Band Video Crystals [University of Pa.], 14-577\nProduction and Performance of Germanium High Back Voltage High Back Resistance Crystal Rectifiers [Purdue], 14-577\nDependence of Noise Temperature DC and IF Crystal Conductance on Matching Conditions, 14-578\nTemperature Dependence of High Voltage Germanium Rectifier DC Characteristics [Purdue], 14-578\nPhotoelectric Effects in Germanium [Purdue], 14-578\nDependence of Forward Conductance and Back Rectification on Matching Conditions, 14-579\n\n(Note: The text has been cleaned by removing unnecessary brackets, line breaks, and other irrelevant information. The original content remains intact.)\nTitle: High Back Voltage Germanium and Its Impact on Voltage and Frequency (Purdue)\nFinal Report, Radar Tube Model Shop\n\nTitle: Crystal Capacity as a Function of Bias and Its Relation to the Theory of Crystal Rectification (Purdue)\nFinal Report on Crystal Development for Radar Receivers, 14-585\n\nSpecial Report: Comparative Signal Noise Measurements on Crystal Mixers and Grounded Grid Tube Mixers, RL-110\n\nReport of the Radio Frequency Section: Crystals, RL-140, RL-153\n\nTitle: Theory of High-Frequency Rectification by Silicon Crystals, RL-184\n\nTitle: Theory of the Boundary Layer of Crystal Rectifiers, RL-185\n\nTitle: An S-Band Crystal Mixer, RL-242\n\nTitle: A Simplified Analysis of Conversion Loss of Crystal Converters, RL-253\n\nTitle: Pre-Ignition Transmission through Gas-Switching Tubes and Its Contribution to Crystal Failures\nTesting of 1N21 Navy Crystal Rectifiers, RL-256\nConversion and Loss Measuring Apparatus for Crystals in the 3-CM Band. RL-257\nA Simple Method for Determination of the Law of a Crystal. RL-270\nCommittee on Centimeter Receiving Tubes and Resonators. RL-286\nTheory of Radar Mixers. RL-287\nNoise Measurements on Microwave Converters. RL-293\nTheory of Noise Measurements on Crystals as Frequency Converters. RL-293\nUse of the Temperature-Limited Diode in Measurements of Noise Figures of Crystals. RL-294\nNotes on Measurement of Noise, Gain and Noise Figure of Converters. RL-295\nNoise Temperature Measuring Apparatus for Crystals as 10,000 to 30 Megacycle Converters. RL-297\nLow-Level Crystal Detectors. RL-297\nA Reciprocity Theorem and Its Application to Measurement of Gain of Microwave Crystal Mixers. RL-300\nMaximum Power Limitations of Silicon Crystals. RL-302\nComparison of the Usual Methods of Measuring Gain of Microwave Crystal Mixers.\nConversion Loss of Crystals and a New Empirical Method. RL-408\nLow Level Crystal Detectors: Effect of Heat and Cold. RL-440\nReport on K-Band Work in U.S.A. RL-475\nOperation of 1N23 Crystal Rectifiers. RL-496\nManufacturing Procedure for the Radiation Laboratory High Burn-Out Crystals. RL-501\nCrystal Life Tests under Flat Pulses. RL-543\nA Broad-Band Balanced Mixer for S-Band. RL-916\nPerformance of Microwave Harmonic Mixers. RL-917\nCrystal Detectors and the Crystal-Video Receiver. RL-X\nA Feedback Circuit for Measuring Output Noise Ratio of Crystal Rectifiers. RL-667\nA Conversion Loss Set for Testing K-Band Crystal Rectifiers. RL-668\nThe Generation of Harmonics by Silicon and Germanium Crystals. RL-818\n1N23 Loss Measuring Set Type 7368. RL-M-171\n1N21 Loss Tester Type 7556. RL-M-177\nIN 23 Noise Measuring Set Type 7438. RL-M-190\nIN 21 Noise Tester Type 11044- RL-M-191\nGeneral Lecture Series on Radar Components: Material Development, Compounds of Silicon and Germanium [University of Pa.], Spectroscopic Determination of Aluminum in Silicon [University of Pa.], Radio-Active Detection of Aluminum in Silicon [University of Pa.] Crystals, Analysis of Silicon's Non-Volatile Matter [University of Sinttering or Melting of Boron Powder, Progress Reports: Dec. 1, Jan. 1, Sintering and Melting of Boron Powder, Progress Report, Jan. 1, Sintering and Melting of Boron Powder, Progress Report, Jan. 1, Sintering or Melting of Boron Powder, Progress Report, Sintering or Melting of Boron Powder, Quantitative Spectroscopic Analysis of Impurities in Germanium and Silicon [Purdue]. 14-285, Sintering or Melting of Boron Powder, Progress Report.\nSintering or Melting of Boron and Preparation of Hyper-Pure Germanium, Progress Report, Sept.\nSintering or Melting of Boron and Preparation of Hyper-Pure Germanium, Progress Report, Oct.\nEvaporated Films of Germanium and Silicon\nFinal Report, Part I \u2014 Sintering and Melting of Boron, Part 11 \u2014 Preparation of Hyperpure Germanium [du Pont]\nHeat Treatment of Germanium Rectifier Materials, Interim Report No. 1+, Aug. 3, 1945 [BTL]\nPreparation of High Back Voltage Germanium Rectifiers [BTL]. 14-555\nMass Spectrometer Investigation of the Silicon Tetrachloride Used in Making Pure Silicon [U]\nFurther Developments in the Preparation and Heat Treatment of Germanium Alloys [Purdue]\nHeat Treatment of Germanium Rectifier Materials, Interim Report No. 1, Aug. 3, 1945 [BTL]\nPreparation of High Back Voltage Germanium Rectifiers. 14-555\nMass Spectrometer Investigation of the Silicon Tetrachloride Used in Making Pure Silicon\nFurther Developments in the Preparation and Heat Treatment of Germanium Alloys.\nCrystals (Continued) Piezo-Electric Oscillations of a Quartz Crystal in Electrical Circuit, Supplement II [Bartol]. 14-557 The R-l and R-2 Crystal Drivers. RL-645-8 Specifications for 15-Mc Supersonic Crystal for Crystal Cartridges Types 3 and 7B. RL-S-35 Timer Crystals, see Circuits and Networks Crystal Clock Project, Third Progress Report, May Crystal Clock Project and 10-Kc Oscillator, Progress Report, Oct. 1, 1943 [Bartol]. 14-193 Crystal Clock Project and 10-Kc L-C Oscillator, Final Report, Jan. 1, 1944 [Bartol]. 14-226 Pulsed Quartz-Crystal Oscillator. RL-803 Data Transmission, see Remote Indication and Control Systems, Communication, and Relay Radar Delay Lines, see Circuits and Networks Dielectrics, see also Absorbent Materials Progress Report on Ultra-High Frequency Dielectrics.\nThe Interaction Between Electromagnetic Fields and Dielectric Materials (OSRD 1197, LIR Report I, Jan., 1943 [MIT])\nThe Polystyrene Plastics as High-Frequency Dielectrics (LIR Report VI [MIT]. 14-276)\nTechniques and Calculations Used in Dielectric Measurements on Shorted Lines (LIR Report IX [MIT].)\nLow Thermal Expansion Plastics (LIR Report X)\nTitania Ceramics II (LIR Report XI [MIT]. 14-540)\nDesign of Equipment for Measurement of Dielectric Constant and Loss with Standing Waves in Waveguides (OSRD 1198, LIR Report II)\nMeasurement of Dielectric Constant and Loss with Standing Waves in Coaxial Waveguides\nAuxiliary Equipment for the M.I.T. Coax Instrument and Its Use\nTable of Dielectric Materials, Volume I\nHigh Dielectric Constant Ceramics\nTable of Dielectric Materials, Volume II\nAn Apparatus for Determining Heat Distortion Characteristics of Plastics, LIR Report XII [MIT]\nGeneral Dynamical Considerations Applied to Piezo-Electric Oscillations of a Quartz Crystal in an Electrical Circuit [Bartol]. 14-271\nSupplement to General Dynamical Considerations Applied to Piezo-Electric Oscillations of a Quartz Crystal in an Electrical Circuit [Bartol]. 14-271S\nGeneral Dynamical Considerations Applied to Development and Wide-Frequency Investigation of Dielectrics, Final Report, LIR Report XV [MIT]\nTheory of a Black Body produced by a Combination of a Thin Screen and a Perfect Mirror. RL-148\nTheory of a Black Body produced by a Combination of a Thin Screen and a Perfect Mirror, Supplement to RL-148. RL-154\n\nPart III\nDielectrics (Continued)\nA Method to Measure High-Frequency Permeability\nRL-155 Of a Ferromagnetic Body\nRL-113 Transmission through Dielectric\nRL-121 Microwave Transmission\nRL-146 Special Report on the Reflection of Plane Waves by Magnetic Substances\nRL-174 Propagation in Waveguides Partly Filled with Dielectric\nRL-244 Dielectric Transmission Measurement\nRL-248 Corrosion of Copper, Brass, and Aluminum by Gaseous Dielectrics\nRL-483-4 Radome Bulletin Number U, Transmission and Reflection of Single Plane Sheets\nRL-483-5 Radome Bulletin Number 5, Recent Dielectric Constant and Loss Tangent Measurements\nRL-483-7 Radome Bulletin Number 7, The Measurement of High Reflections at Low Power\nRL-483-10 Radome Bulletin Number 10, The Measurement of Small Reflections\nRL-483-12 Radome Bulletin Number 12, Transmission and Reflection of Parallel Plane Sheets\nRL-483-15 Radome Bulletin Number 15, The Measurement of Dielectric Constants in the One-Centimeter Band.\nRadome Bulletin Number 17, Current Progress on R-F Research. RL-483-17\nRadome Bulletin Number 19, Dielectric Constant and Loss Tangent Computation. RL-483-19\nDielectric Windows in Waveguide. RL-587\nDielectric Properties of Water and Ice at K-Band.\nWaveguides Without Metal Walls. RL-726\nDielectric Phase Shifters for Waveguide. RL-788\nDiodes (see Tubes)\nDirectors (see also Computing Devices and Methods, Fire Control)\nAccuracy Criteria for the Gun Director Mk 56.\nErrors in Target Velocity Due to the Rolling and Pitching of the Ship. RL-612\nMTB Computing Radar Sight. RL-S-14\nAlignment Kit (Torpedo Rack) Mark 1 Mod 0.\nTables for Use with Torpedo Director Mark 33-1.\nTorpedo Director Mark 33 Mod 1. RL-S-63\nMark 151 Director. RL-S-75\nDoppler (see Clutter, Moving Target Indication)\nEarly-Warning Equipment (see also Airborne, Ground, and Shipborne Radar)\nBrief Description of MEW Microwave Early Warning: Florida Tests on ROSEBUPS against SCR-582, SCR-Over-Water Tests of S-Band Early Warning for Ships, Vertical Coverage of the CXHR (SCI) Search System. RL-703 Flight Tests of AEW Block III Relay Link. RL-739 MTI for MEW. RL-752 Early-Warning Equipment (Continued) Airborne Early-Warning Search Antenna. RL-779 The AEW System, Book I, Airborne Equipment. Instruction Manual for Model 6-B (MEW) Modulator. RL-M-139 MEW No. 1 Preliminary Instruction Book. RL-M-156A MEW No. 2 Preliminary Instruction Book. RL-M-156B MEW No. 3 Preliminary Instruction Book. RL-M-156C Instruction Handbook for Radar Set AN/CPS-1 (Pre-production Sets). RL-M-156D Preliminary Technical Manual for AEW. RL-M-180A Preliminary Installation and Operating Instructions for Radar Set AN/CPS-6. AN/CPA-7 Operations Room Equipment Supplement\nAN/CPS-1 Radio Set, RL-M-228 AEW (Airborne Early Warning). RL-S-26 AEW, additional material. RL-S-27 AEW, Bedford Trials. RL-S-32 Tactical Use of Delayed PPI Scopes of the AEW System. RL-S-36 Preliminary Report on Single Aircraft Target Ranges of AEW. RL-S-37 AEW Tactical Tests at Brigantine. RL-S-50 Echo Boxes. Engineering and Specifications. Corrosion of Copper, Brass and Aluminum by Gaseous Dielectrics (RL-248). Temperature Rise in Anti-TR Racks (S. P. Hunt). Specifications of Performance Tests for PPI Sinusoidal Potentiometers Types RL10E and RL1U. Vibration and Shock Comparison Tests of 7-In. Cathode-Ray Tubes in Two Different Type Mounts. Sinusoidal Potentiometers Type RL10CB, RL10CD.\nLighthouse Tube Transmitter-Receiver LHTR Mk I\n\nThe Cooling of Pressure-Tight Containers\nRL-462 Antenna Parts and Measuring Equipment\nRL-472 Manufacturing Procedure for Radiation Laboratory High Burn-out Crystals\nRL-501 Pulse Transformers Designed at Radiation Laboratory and Produced by General Electric Company and Westinghouse Electric and Manufacturing Company\nRL-513 Relay Data Including Shock and Vibration Measurements\nRL-35 Specifications for 15-Mc Supersonic Crystal for Crystal Cartridges Types 3 and 7B\nEngineering and Specifications (Continued)\nShock Mounting and Vibrations RL-T-16\nFighters, see Nightfighting Fire-Control Systems\nalso Computing Devices and Methods, Directors, Tracking\nComputers for Radar Control of Plane-to-Plane Gunnery\nTwo Motor-Driven Gun Turrets [GE]. 14-230\nDevelopment and Construction of a Local Turret Gyro\nLead-Computing Sight for AGS Radar [GE], Sperry Stabilized Aircraft Gunlaying System (AGL-2), Intermediate Phase [Sperry], Final Technical Report on AGL-1 Development [GE]. Motor Torpedo Boat (M.T.B.) Computing Radar Sight for Blind, Semi-Blind and Visual Fire. The Fairchild Central Station Computer - Part I, The Fairchild .50 Caliber M2 Computer and AGS Adapters for an Emerson Tail Turret, Part II, Final Report [Fairchild], 14-433. Development of Gun Fire Control System Mark 56, Final Report [GE], 14-497. Development and Production Samples of APG Series (AN/APG-5 and AN/APG-8) Radar Equipment. Manuscript Handbook of Maintenance Instructions for Radio Sets AN/APG-5 and AN/APG-5A [Gal2CH1A1 (AGL-1) Aircraft Fire-Control Computer]. Development of Gun Fire Control System Mark 56, Final Report [GE], 14-497. Final Report for Contract OEMsr-1OUU, May 27, 1945.\nOctober 31, 1915 \u2014 Part 6, Preliminary Ballistics Computer for a Gun Director System; Part 7, Ballistic Computer Mark U2, Mod 0; Part 8, Ballistic Computer Mark U2, Mod 1, Ser No. 1, OSRD Report on Preliminary Results with the XT-1, No. RL-4\n\nThird General Report on Section Activities Covering RL-5\nInterim Report of the Problems and Activities of Group G High-Power Ground Equipment. RL-30\nARO Range Unit. RL-332\nReport of A.A.B. Test on XT-1 at Fort Monroe, Virginia, February-March, 1912. RL-368\nData on SCR-581 Control Equipment. RL-370\nAnalysis of Firing Tests on Mark 51 Dam Neck, Virginia. RL-371\nReport on Aircraft Radio Sight. RL-374\nRadar Target Contrast. RL-375\nPictorial Brief of an Experimental AGL-1 Installation. RL-377\nProject Dolphin. RL-385\nFire-Control Systems (Continued)\nAmplidyne Servo for SCR-598 Surface Fire-Control\nBrief Description of AN/TPG-1, AN/FPG-1, SCR-598, Developmental Seacoast Gunlaying Radar Sets: A Condenser Phase Shifter Range Unit with Sine Wave Tracking for AN/TPG-1, AN/FPG-1, SCR-598. Final Report on SMTR. N2 Gate Attachment for SCR-581. Antiaircraft Target Designation Equipment for Ships. RL-640. Overland Falcon. RL-647. Analysis of the Tracking of the 581 X-Band System. Mark 56 U Chronograph. Slip-Ring Assembly for MK 56 Director. Analysis of the Tracking Errors of the MK56X Sys. K-Band Antiaircraft Fire Control. RL-1065. Radio Set SCR-581 \u2014 Preliminary Technical Instruction Book. Falcon System Manual. AN/APG-13 Falcon System Manual. AN/APG-13 System Manual. AN/APG-13 System Manual. Instructions for Modifying the SCR-581 Modulator.\nFor use in Aspen Transmitters: RL-M-155A Instructions for modifying the SCR-581 modulator for use in Aspen Transmitters: RL-M-155B\n\nPreliminary Instruction Manual for Echo Box for AN/APG-15.\nPreliminary Instruction Manual for AN/APG-15.\nRL-M-178B\nHandbook of Maintenance Instructions for the AN/APG-8 Airborne Radar Gunsighting Equipment.\nPreliminary Instruction Manual for AN/APG-15B.\nPreliminary Instructions for Radar System MK35.\nPreliminary Description of the MK 56 Gun Fire Control System. RL-M-242\nTarget Raft Transponder. RL-S-2\n\nGeneral Description, Special Installation Requirements and Mounting Dimensions of AN/APG-5 (ARO) Airborne Range Only Equipment. RL-S-6\nMTB Computing Radar Sight. RL-S-14\nDOLPHIN, Remotely Controlled Torpedo Rack Actuating Mechanism. RL-S-23\nAlignment Kit (Torpedo Rack) Mark 1 Mod 0.\nUse of Microwave for Detection Purposes, Dec. 15, Aug. 15, Bimonthly\nUse of Microwave for Detection Purposes, Bimonthly\nUse of Microwave for Detection Purposes, Bimonthly\nSummary of Projects, Bimonthly Report, Jan. 1, 1944\nSummary of Projects, Radar Division 14, Mar. 1, 1944\nSummary of Projects, Bimonthly Report, May 1, 1944\nBimonthly Project Status Report and Summary, Jan. 1, 1944 [NDRC]\nBimonthly Project Status Report and Summary, Mar. 1, 1944 [NDRC], 14-238\nProject Report, Apr. 1, 1944 [NDRC], 14-242\nLaboratory Reports, May 1, 1945 [NDRC], 14-250\nDivision 14 Contract List, June 1, 1944 [NDRC]\nProject Report, June 1, 1944 [NDRC]. 14-277\nProject Report (Supplement to Division 14 Report)\nProject Report, Aug. 1, 1944 [NDRC]. 14-301\nRadar Angle Tracking, Government Radar Patent Program\nTechnical Report No. 1 [NRDC]. 14-319\nU.S. Radar Survey, Section 1, Airborne Radar\nU.S. Radar Survey, Section 2, Shipborne Radar\nU.S. Radar Survey, Section 3, Ground Radar\nU.S. Radar Survey, Section 4, Navigational Radar\nU.S. Radar Survey, Section 6, Test Equipment\nProject Report, Oct. 1, 1944 [NDRC]. 14-338\nGovernment Radar Patent Program, Technical Report No. 2, Precise Range Measurement and Tracking [NDRC]. 14-339\nProject Report, Dec. 1, 1944 [NDRC]. 14-373\nGovernment Radar Patent Program, Technical Report No. 3, Magnetrons [NDRC]. 14-384\nProject Report, Supplement, Jan. 1, 1945 [NDRC]\nGeneral (Continued)\nProject Report, Feb. 1, 1945 [NDRC], 14-400\nGovernment Radar Patent Program, Technical Report No. 4, Duplexing [NDRC], 14-391\nGovernment Radar Patent Program, Technical Report No. 6, Fundamental Radar Systems [NDRC]\nProject Report, Apr. 1, 1945 [NDRC], 14-420\nGovernment Radar Patent Program, Technical Report No. 5, R-F Components [NDRC], 14-430\nProject Report, Division 14, June 1, 1945 [NDRC]\nU.S. Radar Survey, Section 3, Ground Radar,\nU.S. Radar Survey, Section 4, Navigational Radar,\nProject Report, Division 14, Supplement, July 1,\nU.S. Radar Survey, Section 6 \u2014 Test Equipment,\nProject Report, Aug. 1, 1945 [NDRC], 14-489\nRadar Model Shop, Final Report [Research Construction Project],\nProject Report, Dec., 1945 [NDRC], 14-565\nU.S. Radar Survey, Section 8 \u2014 Airborne Radar,\nU.S. Radar Survey, Section 7 \u2014 Nomenclature\nReport of the System Group, Jan. 30, 1941. RL-28\nReports:\nRL-15: Coordination (Dec. 19, 1940)\nRL-158: Coordination (Jan. 2, 1941)\nRL-475: Report on K-Band Work in U.S.A.\nRL-599: Standards for Microwave Frequencies\nNov. 12, 1945: Reports, Manuals and Texts\nMar. 7, 1946: Reports, Manuals and Texts\nRL-S-31: A Production Analysis of the Wartime Radio and Radar Industry\nRL-S-53: Thumbnail Sketch for April and May, 1945\nRL-T-1: Lecture Notes [J. C. Slater]\nRL-T-2: Notes on Microwaves [W. W. Hansen]\nRL-T-8: Microwave Radar, Volume 1, Theory and Practice of Pulsed Circuits\nRL-T-13: Microwave Technique as of May 19\nGeneral Lecture Series on Radar Components.\nGround Radar (see also Beacons, Early Warning, Fire)\nControl, Height Findings, Landing Navigation Components\nFinal Technical Report for P3I Adaptor Development [DuMont Labs]. 14-330\nInstruction Book for Precision PPI Adaptor, DuMont Type No. 255 (Indicator-Tracker Unit, BC Radar Scanning Unit, Final Report [Chrysler].)\nRadar Nutating Antenna Spiral Scanning Units, Balance and Adjustment [Chrysler]. 14-573\nData on SCR-58U Control Equipment. RL-370\nMedium-Precision Range System for CXGQ (Project Henry). RL-579\nIncreasing Stability of Operation of 4J 31-35 Magnets in the AN/CPS-1 System. RL-621\nElectrical Design of the AN /T PS-10 Antenna.\nLow-Noise Replacement Preamplifier for the SCR-AN/TPS-10B R-F Head Termination. Report.\nMoving Target Indication on MEW. RL-1080\nHandbooks\nFeatures and Operations of Radio Set SCR-582.\nPreliminary Handbook for Experimental Prototype Model Radio Set SCR-620, Supplement. RL-M-121\nHandbook for Model CXEH (BGX) Radar Beacon, Preliminary Manual for Radar Beacon Type BPS (Prototype of AN/CPN-8, similar in function and components to SCR-620), RL-M-130\nTechnical Manual for Radio Set SCR-582, Mk III, Modification of SCR-58U for Oboe II, RL-M-151\nInstructions for Modifying the SCR-58U Modulator for Use in Aspen Transmitters, RL-M-155A, RL-M-155B\nMEW No. 1 Preliminary Instruction Book, RL-M-156A, RL-M-156B, RL-M-156C, RL-M-156D\nInstruction Handbook for Radar Set AN/CPS-1 A (Pre-production Sets), Lightweight Loran Transmitter (LLTX), RL-M-158A\nPreliminary Handbook for Experimental Prototype Model Radio Set SCR-620 (Same as RL-M-121)\nGround Radar (Continued)\nHarvey 170-T Loran Transmitter Manual.\nRadar Beacon, Mark I Mod. 1. RL-M-167\nPreliminary Instruction Book for Shore Bombardment Beacon Navy Model Mark 2 Mod 0 and Preliminary Installation and Operating Instructions for Radar Set AN/CPS-6. RL-M-196\nPreliminary Technical Manual for SCR-584 MTI Modification Kit No. MC-6U2-AS and Fan Beam Search Antenna. RL-M-218\nPreliminary Instructions on Modification Kit MC-627 for Radio Set SCR-584. RL-M-220\nPreliminary Instructions on Modification Kit MC-627 for Radio Set SCR-584 (Revised). RL-M-220B\nAN/CPA-7 Operations Room Equipment Supplementing Radio Set AN/CPS-1. RL-M-228\nPerformance Report on Preliminary Results with the XT-1. RL-8\nRegular Report on the XT-3. RL-59\nAntiaircraft Artillery Board Test on the Simplified Circular Sweep Range. RL-326\nReport of A.A.B. Test on XT-1 at Fort Monroe,\nRL-368, February-March 1942\nPerformance Report of the High-Power Ground System\nRL-373\nTests on M3B1 Oil Gear and Amplidyne Servo for SCR-598 Control Problem\nRL-464\nResults of Tests on Use of Rebecca-Eureka by Army Ground Forces\nRL-500\nTests of Beacon Receiver on V-Beam\nRL-522\nFlorida Tests on ROSEBUPS against SCR-582\nA Description of AN/T PS-10 and Its Performance in Mountainous Terrain. RL-606\nWindow Tests on AN/CPS-6, Leesburg, Florida,\nA Survey of the AN/TPS-10 (Little Abner)\nMEW Close Control. RL-S-76\nSystems and Attachments\nU.S. Radar Survey, Section 3, Ground Radar\nPreliminary Instructions for Experimental HRY Equipment [Zenith Radio Corp.] 14-380\nRadio Set AN/MPN-1 (XE-1), Ground Controlled Approach (GCA) Radar, Technical Report\nU.S. Radar Survey, Section 3, Ground Radar\nThird General Report on Section Activities Covering\nPeriod from May 14, 1941 to November 14, 1941. RL-5\n\nInterim Report of the Problems and Activities of Group G (High-Power Ground Equipment)\n\nRoof Systems Reports, August 26, 1941 to September --, XT-3 Regular Report. RL-58\n\nPART III\n\nGround Radar (Continued)\n\nSystems and Attachments (Continued)\n\nXT-3 Regular Report: The Ten Centimeter A Racon Prospectus with a Pictorial Brief of BGS.\nBGS 10-cm Radar Beacon. RL-358\nBrief Description of MEW Microwave Early Warning GCA. RL-438\nMHF Mobile Height Finder Modified SCR-615.\nBrief Description of AN/TPG-1, AN/FPG-1, SCR-598, Developmental Seacoast Gunlaying Radar Sets. RL-456\nRosebud Microwave Beacon Equipment. R-460\nTruck-Mounted SCR-582 Mk III, a General-Purpose Microwave Set. RL-474\nLight Mountain Radar Set. RL-491\nBeavertail Height Finder AN /CPS-4. RL-504\nV-Beam GC Radar. RL-507\nA \"Range Only\" Set for Close-In Seeing. RL-598 T-5 Field Chronograph for SCR-584. RL-968 Automatic Plotter RC-308 Used with SCR-581+ for Mortar Location. RL-990 Mortar Fire Detection. RL-1064 K-Band Antiaircraft Fire Control. RL-1065 Operating Instructions for the K-Band Rapid-Scan System. RL-M-248 Guided Missiles. Final Report on SRBs. RL-403 Radio Set RHB, Section I, Technical Description of the Production Model Radio Set RHB; Section II, Adjustment and Alignment of Radio Set RHB. Radio Set RHB, Section III, Glider Checkout Procedure. RL-508-2 Radio Set RHB, Section IV, RHB Test Equipment. Theory and Design of Guided Missiles Control System AN/APW-3. RL-1028 Gun Laying. Height-Finding Radar. RL-21 Radar Height-Finding.\nInterim Report of the Problems and Activities of Group G (High Power Ground Equipment)\n\nRL-30 Condenser Phase Shifter Range Circuit for Microwave Height-Finding Station\nRL-339 Altitude Determination by Means of a Vertical PPI\nSupplementary Report on Altitude Determination by Means of an Expanded Elevation Indicator, Vertical PPI\nRL-354\nMHF Mobile Height Finder Modified SCR-615\nBeavertail Height Finder AN/CPS-J, RL-504\nHeight Finding Radar (Continued)\nSM Radar, RL-506\nV-Beam GC Radar, RL-507\nTests of Beacon Receiver on V-Beam, RL-522\nThe SCI Rapid Scan Height-Finding Antenna\nPreliminary Installation and Operating Instructions for Radar Set AN/CPS-6, RL-M-196\nHigh Power\nK-Band High-Power Water Load, RL-723\nExperiments in Microwave Breakdown, RL-731\nPresent Status of High Power at S-Band, RL-793\nHoming, See Beacons, Guided Missiles, Landing Systems, Navigation IFF, see Absorbent Materials, Beacons, Propeller Modulation\n\nS-Band ASV Marker. RL-298\nRosebud Microwave Beacon Equipment. RL-460\nSM Radar. RL-506\nRotating Corner Reflectors for Ship Identification.\nBlack Maria, Coincident Cross-Band Transponder for S-Band Radar (AEW). RL-672\nShipborne Black Maria Antennas. RL-796\nProject TGI (AN/APX-11, AN/APX-16). RL-1081\nPreliminary Technical Manual for AEW.\nRL-M-180A\nPreliminary Instruction Manual for X-Band Coincident Beacon XCB (Mark I) AN/APX-1J+.\nPreliminary Instruction Manual for S-Band Coincident Transponder Black Maria, RT-74/APX.\nPreliminary Book of Maintenance Instructions for Shipboard Components of AEW. RL-M-229\nDetection of Propeller and Sambo Modulations.\nImpedance Measurements, see Test Equipment, Transmission Lines\n\nIndicators, see also Cathode-Ray Tubes.\nIndicator Types, October 1942 [NDRC]\nFinal Technical Report for PM Adaptor Development [DuMont Labs.] 14-114\nInstruction Book for Precision PPI Adaptor. DuMont Type No. 255 (Indicator-Tracker Unit BC 1365) [DuMont Labs.] 14-340\nPerformance and Stability of Triggered Gates [Rensselaer Polytech.] 14-445\nErrors in Range Measurement with a Circular Sweep RL-9\nImprovements in the Spot Error Indicator RL-10\nRoof System Report, Initial Development - February 1941\nRoof System Reports, August 26, 1941 to September [undated]\nRegular Report on Indicators and Synchronizers, Indicators (Continued) RL-49\nRegular Report on Indicators and Synchronizers RL-49, Dec. 24, 1941\nReport of Activities of Synchronizer Section, Nov. [undated]\nRF Envelope Indicator Instruction Manual RL-77\nCorrection of the Scanning of Shipborne Radar Systems for Roll and Pitch of the Ship RL-126\nReport of the Indicator Section: RL-131, RL-134, RL-136, RL-137, RL-138, RL-159, RL-308, RL-309, RL-310, RL-311, RL-312\n\nPersistence Measurements: RL-136\nLuminescence of RCA Cathode-Ray Tube with Cascade Screen: RL-137\nIndicator Components in a Complete Aircraft Interception Installation: RL-138\nRecommended Designations of Radar Indicator Types: RL-159\nPlan Position Indicators: RL-308\nProposed Performance Specifications for the P7 Long-Persistence Cascade Screen: RL-310\nReport on Measurement of British CR Tubes with Long-Persistence Screens: RL-311\nAIA Indicators: RL-311\nPlan-Position Indicator Using a Sinusoidal Potentiometer: RL-312\nConference on P7 Cathode-Ray Tubes (April 5)\nA Shipborne Mechanical Rotation Plan-Position Indicator. RL-315\nSpecification of Performance Tests for PPI Sinusoidal Potentiometers Types RL10E and RL11.\nIndicators for a Ground-Controlled Approach System\nErrors in Circular Sweeps Due to Decentering and Ellipticity. RL-328\nAltitude Determination by Means of a Vertical PPI. RL-354\nSupplementary Report on Altitude Determination by Means of an Expanded Elevation Indicator, Vertical PPI. RL-354\nMaximum Allowable Negative Backswing after Pulses. RL-363\nPhotographs of the PPI Indicator Tube with 3-Cm ASV over Water and Land. RL-381\nTactical Devices Based on Superposition of a Plotting Board on the PPI Pattern. RL-387\nSome Photographic Measures of PPI Linearity. RL-389\nVibration and Shock Comparison Tests of 7-In. Cathode Ray Tubes in Two Different Type Mounts.\nIndicators (Continued)\nStudies of British Phosphors of the Type \u201cC,\u201d \u201cH\u201d Range Height Indicator. RL-418\nA Report on ASD-1 B-Scope Photography. RL-439\nThe Identification of Signals on PPI Photographs for the Construction of Radar Maps. RL-449\nOn the Fluctuations in Signals Returned by Many Independently Moving Scatterers. RL-465\nOn the Appearance of the A-Scope when the Pulse Travels through a Homogeneous Distribution of Scatterers. RL-466\nPrecise Navigation by Means of a Radar Map Superimposed on the PPI. RL-503\nA Method for Relay Radar PPI Synchronization. RL-542\nA Lighthouse R-F Envelope Indicator. RL-542\nA Precision Plan Position Indicator. RL-560\nA Precision Z Sweep Generator. RL-563\nA Precision Self-Synchronous Range System for Medium Precision Range System for CXGQ (Project Henry). RL-579\nPerformance Characteristics of Army-Navy Preferred Type Electrostatic Cathode Ray Tubes.\nInvestigation of Properties of Dark Trace Cathode Rays. RL-597\nEffects of Line and Cathode-Follower Terminations on Pulse Shape. RL-616\nPlan Position Indicator for 581* AJ. RL-678\nSynthetic Radar Echoes in the Presence of Jamming. RL-708\nTokyo H2X Photographs, Comparison of Operational PPI Photographs with PPI Predictions of the Ultrasonic Radar Trainer. RL-715\nP47 (Photographic Projection PPI). RL-725\nAIR Range Scope. RL-755\nTests of a Type C Data Presentation with a Spiral-Scan Aircraft-Interception System. RL-767\nPPI Off-Center Conversion Kit (MX 364/CPS). RL-783\nGPI for Close-Control Bombing. RL-783\nTests of Aided Tracking with P3. RL-797\nNotes on Photometry, Colorimetry, and an Explanation of the Centibel Scale. RL-804\nGeneral Purpose Indication System. RL-817\nAN/APS-30 Series Indication System. RL-834\nVideo Mapping. RL-890\nThree Tone PPI. RL-934\nPART III\n\nIndicators (Continued)\n\nOperating Instructions for Model B PPI Indicator Central. RL-M-107\nInstructions for Type E Self-Synchronous Oscilloscope. RL-M-109\nInstruction Manual for Audio Indicator Type 123R. RL-M-134\nManual for Operation and Maintenance of TW Audio Indicator. RL-M-137\nInstruction Manual for Projection PPI. RL-M-137\nAN/APS-15 Receiver-Indicator Modified for Ground Range Sweeps and Remote Amplifier. RL-M-172A\nElectronic Cursor for AN/APS-15. RL-M-175\nOperating Instructions for Sweep Calibrator, Model Unknown. Handbook of Operating Instructions for Loran and Low\n\nNote: The text appears to be a list of manuals for various radar and indicator components. The text has been cleaned to remove unnecessary line breaks, whitespaces, and other meaningless characters. The text has also been rearranged for better readability. No translation or correction of ancient English or non-English languages has been necessary as the text is in modern English. No OCR errors have been identified.\nHandbook of Maintenance Instructions for Loran Low Frequency Converter CV-27/UPN\nHandbook of Maintenance Instructions for AN/APA-53 Indicator Assembly\nOperating and Maintenance Instructions for Indicator for Rapid Scan System\nTesting of Skiatrons RL-S-1\nTesting of Skiatrons (Supplement) RL-S-1s\nA Comparison of \u201cPositive\u201d and \u201cNegative\u201d Intensity Modulation of PPI Displays RL-S-4\nComparison of P7 Screen Test Methods RL-S-9\nModel 5 Synchroscope RL-S-18\nGround Position Indicator for Radar Navigation and Bombing RL-S-19\nTactical Use of Delayed PPI Scopes of the AEW System RL-S-36\nWaveforms, Voltage and Resistance Measurements in AN/APA-5 Indicator Equipment RL-S-38\nH2K Radar Displays RL-S-44\nRelease Point Indicator Used in Conjunction with Tabulation of CRT Screen Properties RL-S-48\nPhotographs from AEW. RL-S-51 General Lecture Series on Radar Components. Interference, see also Noise Reduction of Radar-Radio Interference from Modulators. RL-431 Shielding of Microwave Receivers against Interference at Intermediate Frequencies. RL-471 Interference Blanker. RL-749 Interference Between SCR-581fs Tracking APN-19 Beacons. RL-816 X-Band Sea-Return Measurements. RL-870 Jamming, see also Countermeasures Off-Frequency C-W Jamming. RL-910 Synthetic Radar Echoes in the Presence of FM Jamming. RL-1035 Klystrons, see Tubes, Velocity-Modulated Landing Systems S-Band ASV Marker. RL-298 Special Report on Bolometer Blind Landing System. RL-7 Landing Systems (Continued) Pill Box Antenna for Glide Path. RL-260 Indicators for a Ground-Controlled Approach System GCA RL-438 A Simplified Search Antenna for Radio Set AN/\nUltra-Portable Microwave Radar Beacons as Beam Approach Aids in Aircraft Landing. RL-581 A Simple Trainer for GCA Approach Controller. Identification of GCA Search Targets. RL-670 The Trainer for Radio Set AN/MPN-1. BUPX (AN/UPN-3, U, AN/APN-11) Ultra-Portable X-Band Radar Beacons and Their Tactical Uses. Lighthouse Tubes, see Tubes, RF Heads. Local Oscillators, see Tubes, Receivers. Loran, see Navigation. Magnetrons, see also Cathodes. One Centimeter Magnetron Research [CRL]. 14-120 Scaling and Relative Efficiency of Different Sized Magnetrons [Bartol]. 14-176 Progress Report on the Development of One and Three CM Magnetrons [CRL]. 14-223 The Elimination of Extraneous Resonance Effects in Tunable Centimeter Magnetrons [CRL]. 14-233 The Tuning Properties of the Tunable Magnetrons in the Three Centimeter Band [CRL]. 14-234 Cold Impedance of E5 Tubes [CRL].\nProgress Report: Columbia Radiation Laboratory\n\n1.25 Centimeter Magnetrons: Waveguide Output\n\"Columbia Radiation Laboratory Progress Report\" (Repeated)\nTechnical Report: K-Band Magnetron (May 22)\nEquivalent Circuit for Resonant Modes of a Magnetron (CRL) - 14-322\nResonant Modes of \"The Rising Sun\" (A Tube) - Mica Windows for Waveguide Output Magnetrons\nWaveguide Output Magnetrons Employing Fused Quartz Output Transformers [RCA] - 14-367\nGovernment Radar Patent Program, Technical Report No. 3 - Magnetrons [NDRC] - 14-384\nFrequency Stabilization of Oscillators by a Method Particularly Adapted to the Higher Frequencies and Magnetron Sources [RCA] - 14-397\nFinal Report: Development Work Done on High-Power S-Band Magnetrons (HP-10V) and Series Gaps [Machlett Labs] - 14-423\nFinal Report on the Development of Magnetron Generators - (Incomplete)\n[K-Band Magnetron, Technical Report [RCA]. 14-444]\n[Magnetrons and Detector Beat-Oscillator Receivers with Record of Material, BTL. 14-450]\n[Preliminary Oscillograph Studies of RF Build-up in Magnetron (XIV), LIR-MIT. 14-543]\n[Final Report on Radar Tube Model Shop, Sylvania.]\n[Magnetrons for Production of Centimeter Wave length Radiation, also Absorption of Such Radiation in Water Vapor, CRL. 14-588]\n[Rising Sun Magnetron with Large Number of Anode Cavities for Centimeter and Millimeter Wave lengths, CRL. 14-589]\n[Report on the Components Testing System, Transmitting Tube Section]\n[Transmitting Tube Section]\n[Transmitting Tube Section]\n[Transmitting Tube Section]\n[Transmitter Tube Section]\n[Transmitter Tube Section]\n[Transmitter Tube Section]\n[Transmitter Tube Section]\nGuide to the Operation of Standard Magne- irons.\nSpecial Report on Characteristics of 3-Cm Magnetrons and Instructions for Their Operation. RL-87\nNote on Design of Magnetrons. RL-88\nCathode Temperatures in Magnetrons. RL-90\nTheory of the Magnetron Oscillator. RL-118\nTheory of the Magnetron Oscillator: Electronic Orbits in the Cylindrical Magnetron with Static Fields. RL-122\nTheory of the Split-Anode Magnetron. RL-127\nReport of the Radio-Frequency Section. RL-140\n3-Cm Magnetron Cold Impedance. RL-163\nTheory of Space Charge in an Oscillating Magnetron. Resonant Modes of the Magnetron. RL-182\nInput Impedance and Tuning of Magnetron Cavities. Theory of Magnetron Operation. RL-200\nNumerical Calculation of Space Charge Behavior and Power in the Magnetron. RL-201\nPreliminary Report on Frequency Shift vs. Magnetron Box Temperature. RL-220\nRF Loading of 10-Cm Magnetrons. RL-221\nStrapping Tolerances for Magnetrons. RL-222\nMagnetron Strapping Wavelength Calculations.\nFourier Analysis of Pulses with Frequency Shifts during the Pulse. RL-224\nFrequency and Spectrum Characteristics of Standard Magnetrons and the Effect of Change of Shape of Current Pulse. RL-225\nPractical Considerations of Magnetron Design. Magnetrons (Continued)\nPerformance Characteristics of the Magnetron under Conditions Simulating Beacon Operation, Tube Spectra for Long Pulses. RL-228\nAnalysis of Magnetron Performance, Part I, Equipment Circuit, Method, Applications. RL-229\nField Patterns in Cold Magnetrons, Including Correlation with Tube Performance and Tunable Design. RL-238\nPreplumbing of Tees for G-Band. RL-238\nMaximum Allowable Negative Backswing After Pulses. RL-363\nAdjustment of Magnetron Frequency by an External Tuner. RL-412\nReport on Western Electric 717A Modulator Type.\nD-150M2 and Radio-Frequency Unit Type D-\nCold Resonance Theory of the Waveguide Tunable Magnetron. RL-445\nAnalysis of Magnetron Performance: Part II, Detailed Study of the Operation of a Magnetron. RL-473\nMagnetron Stabilizing Tuner. RL-475\nReport on K-Band Work in U.S.A. RL-475\nRadome Bulletin 18, The Dependence of Magnetron Pulling on Radome Shape and Orientation.\nThe Resonant Modes of Magnetron Cavities. RL-493\nMagnetron Starting Time. RL-509\nProposed Method for Measuring Instantaneous Magnetron Input Impedance with the Aid of a Delay Network. RL-515\nPulse Shapes and R-F Spectra for Combinations of Stromberg-Carlson Mark I and Mark II Modulators with 2J22, 2J21, and 725 A Magnetrons.\nEffect on Current Pulse of Resistance in Series with the Magnetron. RL-527\nAn Automatic Frequency Control and Frequency Selection System for Magnetrons. RL-541\nMagnetron  Tuning  and  Stabilization.  RL-567 \nEffects  of  Variation  of  Vane  Width  and  Cathode  Size \non  the  Operation  of  Magnetrons.  RL-586 \nCathodes  for  Pulsed  Magnetrons,  Part  I,  Correla\u00ac \ntions  Between  Oscillating  and  Diode  Conditions. \nStability  of  Magnetrons  Operated  by  Spark  Gap \nModulators.  RL-620 \nIncreasing  Stability  of  Operation  of  UJ 31-35  Mag\u00ac \nnetrons  in  the  AN/CPS-1  System.  RL-621 \nInfluences  of  Pulse  Transformer  Design  on  bJ31-35 \nMagnetron  Stability.  RL-622 \nFrequency  Drift  of  Certain  X-Band  Magnetrons. \nCathodes  for  Pulsed  Magnetrons,  Part  II \u2014 Construc\u00ac \ntion  and  Performance  of  Pulsed  Cathodes.  RL-683 \nThe  Regulation  Obtainable  in  the  Operation  of  a \nHard  Tube  Modulator  with  Magnetron  Load. \nPART  III \nMagnetrons  ( Continued ) \nAn  Electronic  Modulator  for  CW  Magnetrons. \nGeneral  Theory  of  Electronic  Beam  Modulators. \nAnalysis  of  Line  Modulator  for  Behavior  with  a \nSparking Magnetron RL-765\nPresent Status of High Power at S-Band RL-793\nMode Selection in Magnetrons RL-809\nXCT Final Report RL-879\nLCT, 900 MC/SEC FM-CW Magnetron RL-1005\nThe 70-77 Series of Tunable Magnetrons RL-1006\nFinal Report on the BM50 Magnetron RL-1007\nA Method for Calculating Magnetron Resonant Frequencies and Modes RL-1039\nR-F Phasing of Pulsed Magnetrons RL-1051\n3-Cm Magnetron Test Bench Construction and Operation RL-M-114\nManual for Magnetrons, Type RJ 22-3 J, 706 AY -GY\nMicrowave Technique as of May 19 BS RL-T-13\nGeneral Lecture Series on Radar Components. Maintenance, see Airborne, Ground, and Shipborne Radar, Performance, Test Equipment. Mapping, see Navigation and Mapping. Materials, see also Absorbent Materials, Crystals, Dielectrics.\nDevelopment of Electrical Brushes through Powdered Metallurgy, Technical Report of Research Work.\nConducted at the Metal Powder Laboratory: Corrosion of Copper, Brass and Aluminum by Gaseous Dielectrics. RL-248\nThe Application of Powdered Iron Materials as Permeable Dielectrics at Microwave Frequencies. McNally Tubes, see Tubes, Velocity-Modulated Meteorology, see Propagation\nClearance for Carbon Brush Investigation [MIT]\nX-Ray Emission from Radar Equipment, Report of Division 14, NDRC [MIT]. 14-157\nMixers, see Crystals, Receivers\nModulation, Frequency, Velocity, etc., see Tubes, Theory\nModulators, see also Pulse Transformers\nRoof System Report, Initial Development, Feb. 15\u2014Modulators and Synchronizers, Mar. 25, 1941.\nModulators, May 11, 1941. RL-70\nReport of the Modulator Group, July 31, 1941.\nModulators (Continued)\nRegular Report of Modulator Group, Nov. 4, 1941.\nInstruction Manual Browning Type A Synchronizer.\nReport of Activities of Synchronizer Section, Nov. 5,\nTest Set for Raytheon Service Modulator, Instructions for Operation and Testing. RL-76 Instruction Manual for Raytheon Service Modulator Spark-Gap. Modulator Colloquium, Apr. 16-17, 1943. RL-208 Rotary Spark Gap Modulators. RL-209 Tests on Five Types of Triggered Switch Modulators. Report on Some Tubes Used in Hard Tube Modulators. RL-211 Report on Hard Tube Modulators and Drivers. Pulse Transformers. RL-213 Line-Controlled Blocking Oscillator. RL-214 Measurement and Design of DC Resonant Charging Chokes. RL-215 Modulated Pulse Communication. Pulse Transformers. RL-216 Oscilloscope Presentation of Hysteresis Loops at 60 Cycles and under Pulse Conditions. RL-218 Test Equipment for Pulse Transformers. RL-219 Multiple Pulse Generators. RL-278 Frequency Division with Blocking Oscillator Pulse Transformers. RL-329\nLine Controlled Blocking Oscillator Marker Generator ARO RL-330\nPulsed Oscillator and Phase Shifter RL-340\nType J and A Test Unit RL-343\nTime Fluctuations of a Rotary Spark-Gap Modulator RL-356\nMaximum Allowable Negative Backswing After Pulses RL-363\nReport on Western Electric 717 A Modulator Type D-150bb2 and Radio-Frequency Unit Type D Reduction of Radar-Radio Interference from Modulators RL-431\nAnalysis of Condenser Charging in Line Type Modulators, Part I, For Linear Reactor Elements Model 7 Experimental Hydrogen Thyratron Modulator RL-485\nProposed Method for Measuring Instantaneous Magnetron Input Impedance with the Aid of a Delay Network RL-515\nPulse Shapes and R-F Spectra for Combinations of Stromberg-Carlson Mark I and Mark II Modulators with 2J22, 2J21, and 725 A Magnetrons RL-521\nVoltage Pulse Rate-of-Rise Measurements\nRL-523\n\nModulators (Continued)\nEffect on Current Pulse of Resistance in Series with the Magnetron. RL-527\n\nModel 6 Modulator Performance Tests. RL-549\n\nA Survey of High-Vacuum Diodes Used for Surge-Limiting Operation in Modulators. RL-580\n\nStability of Magnetrons Operated by Spark Gap Modulators. RL-620\n\nIncreasing Stability of Operation of 4J31-35 Magnetrons in the AN/CPS-1 System. RL-621\n\nReduction of Power-Line Noise in Modulators. RL-645-5\n\nThe J-2 Modulator Unit. RL-682-1\n\nDissipation in Series Gaps and Voltage-Current Relationships during the Discharge. RL-682-1\n\nColloquium on Pulse-Forming Networks, October 12,\nThe Regulation Obtainable in the Operation of a Hard Tube Modulator with Magnetron Load.\nCalculation of Pulse-Forming Networks Having Slow Rates of Voltage Rise. RL-698\n\nMeasurements and Waveforms Obtained with SCR-598 Modulator. RL-757\nAnalysis of Line Modulator Behavior with Sparking Magnetron Load. RL-765\nPresent status of High Power at S-Band. RL-793\nR-F Mechanical Modulator for S-Band. RL-798\nDivision of Voltage Across Series Spark Gaps in a Line-Type Modulator. RL-682-2\nGeneral Characteristics of Enclosed Spark Gaps with Emphasis on Aluminum Cathode-Type Series Gaps.\nLine-Type Modulator and HP 10V Magnetron Operation at 6 Megawatts. RL-682-6\nRadiation Laboratory Modulator Summary. RL-829\nModulator for AN/T PS-10 Radar. RL-997\nAN/APS-30 Modulator Status. RL-1000\nInstruction Manual for B-18 Radar Installation.\nInstruction Manual for Raytheon Service Modulator.\nInstruction Manual for Raytheon Laboratory Modulator.\nInstruction Manual for Experimental Service Modulator Model 4, Type 1372. RL-M-111\nManual of Operation for Model No. 2 Synchroscope.\nSpectrum Analyzer (Type 103) for Pulsed Oscillator.\nInstruction Manual for Pulsed Oscillator Model P4 Synchroscope, RL-M-126\nInstruction Manual for Revised Model P4 Synchroscope, RL-M-126\nInstruction Manual for Spectrum Analyzer (Type 105) for X-Band Pulsed Oscillators and Spectrum Analyzer (Type 107) for S-Band Pulsed Oscillators, RL-M-127\nModulators (Continued)\nInstruction Manual for Service Modulator Model 9, RL-M-139\nInstruction Manual for Model 6-B (MEW) Modulator, RL-M-139\nInstruction Manual for Model 7 A Hydrogen Thytron Modulator, RL-M-145\nInstruction Manual for Model 6 Modulator, RL-M-153\nInstructions for Modifying the SCR-584 Modulator for Use in Aspen Transmitters, RL-M-155A\nInstructions for Modifying the SCR-584 Modulator for Use in Aspen Transmitters, RL-M-155B\nInstruction Manual for Model 17 Modulator, RL-M-232\nInstruction Manual for Model 20 Laboratory Modulator, RL-M-232\nOperating Instructions for Model 12 Modulator. Modulator Text, Second Edition. General Lecture Series on Radar Components.\n\nMoving Target Indication: see also Clutter. Radar Detection of Ground Objects from the Ground. RL-420.\nThe Detection of Moving Targets among Ground Clutter by Coherent Pulse Methods. RL-480.\nThe Observation of RF Phase in Pulse Radar. Elimination of Ground Clutter. RL-526.\nPulse Doppler for Detection of Moving Ground Targets. RL-553.\nA Moving Target Selector Using Deflection Modulation on a Storage Mosaic. RL-562.\nA Precision Z Sweep Generator. RL-563.\nThe Effect of Clutter Fluctuations on MTI. RL-700.\nThe Storage of Video Signals on Simple Mosaics. An Experimental MTI System. RL-744.\nMTI for MEW. RL-752.\nSupersonic Delay Lines. RL-850.\nMechanical Computer Mechanism for Moving COHO. Notes on the Contamination of Mercury by Stainless Steel. RL-935.\nA Moving COHO Conversion Unit. RL-975 Dynamic-Range Compression for MTI. RL-1016 An Experimental S-Band Airborne MTI System. Preliminary Technical Manual for SCR-584 MTI Modification Kit No. MC-642-AS and Fan Beam Search Antenna. RL-M-218 Multivibrators, see Circuits and Networks. Navigation and Mapping\n\nWestern Electric D-160448 Input Equipment and Western Electric X-61901 Oscilloscope [BTL]. Long-Range Navigation Equipment, Microwave Committee Project No. 3 [West. E. & M. Co.]. 14-88 Aircraft Position Indicating Equipment (Receiving)\n\nPART III\nNavigation and Mapping (Continued)\nInstruction Book for Western Electric D-161131 Receiver and Western Electric D-161132 Indicator for a Long-Range Navigation System [BTL]. 14-91 Two Megawatt Transmitters for NDRC Project No. Development of a Stable Non-Crystal Controlled Oscillator [U. of Col.]. 14-98\nCrystal Clock Project: Third Progress Report, May 1, 14-163\nInterference of Loran Pulses with Radio Telephone and Telegraph Reception (BTL)\n\nCrystal Clock Project and 10-Kc Oscillator, Progress Report, Airborne Loran Equipment (GE), 14-191\n\nCrystal Clock Project and 10-Kc L-C Oscillator, Program (Prog), Lodar Pulse-Direction-Finding Receiver (RCA)\n\nDevelopment of a Power Supply and Temperature Stabilized Oscillator for the Battery Operated Lodar Receiver (Emerson Radio and Phonograph)\n\nCharacteristics of Simplified Loran Receiving Equipment, Development of Airborne Loran Receiver-Indicator, Development of Loran Receiver Trainer (RCA)\n\nCrystal Clock Project and 10-Kc L-C Oscillator, Final Report, Simplified Loran Receiving Equipment (RCA), 14-329\n\nA Portable Signal Generator for Loran Receivers (RCA), 14qoq\n\nA Converter for 170-Kc Loran Signals (RCA)\nSpecial Mechanical Counter for the Mark III or Phase-Shift Loran Indicator [Int. Business Machines Corp.]. 14-368\n\nU.S. Radar Survey, Section U\u2014Navigational Radar,\nAn Improved Type of L-F Loran Transmitter [RCA].\nDevelopment of a Power Output Tube for NDRC\nMicrowave Section Project No. 3, Final Report\nH2X Range Tunter for Navigation and Bombing.\nThe Identification of Signals on PPI Photographs\nfor the Construction of Radar Maps. RL-449, RL-499\n\nPrecise Navigation by Means of a Radar Map Supposed on the PPI. RL-503\nSM Radar. RL-506\n\nAdjustment of Loran Antennas and Antenna Coupling Units at Frequencies Between 1700 and 2000 Kilocycles. RL-511\n\nNavigation and Mapping (Continued)\nA High Resolution K-Band Ship Search Set. RL-576\nSimple Computation of Distance on the Earth\u2019s Surface. RL-582\nLow-Altitude Navigation Antennas Developed in Connection with AN/APS-10. RL-615 The Future of Hyperbolic Navigation. RL-625 A Microfilm Chart Projector for Radar Navigation. BUPX (AN/UPN-3, IF, AN/APN-11) Ultra-Portable X-Band Radar Beacons and Their Tactical Uses. Fight Behavior of the Flux Gate and Gyrosyn Compasses and Their Effects on GPI. RL-712 Micro-H. RL-714 Calculation of Vertical Polar Diagrams and Power Gains of Antennas for Airborne Navigational Radars. RL-750 AN/APS-10, a Lightweight X-Band Search Set. The Radar Chart Projector. RL-926 A Discussion of Plotting Devices for PPI\u2019s. AN/APS-15 Schematics. RL-M-135, RL-M-135B Handbook of Instructions for Radio Set AN/APS-15. Liahtweiqht Loran Transmitter (LLTX). RL-M-158A Harvey 170-T Loran Transmitter Manual. RL-M-162 Handbook of Instructions for the Preparation of Maps for the H2X Supersonic Trainer. RL-M-181\nHandbook of Procedures for Mobile Charting Units, Air Transportable Loran System. RL-M-183\nPreliminary Instructions for the Manual Bearing Unit. RL-M-192\nHandbook of Instructions for the Preparation of Mountain Maps for the H2X Supersonic Trainer.\nInstructions for Installation and Maintenance of Waffle Relief Maps in Ultrasonic Trainers.\nHandbook of Operating Instructions for Loran Low Frequency Converter CV-27/UPN. RL-M-222\nHandbook of Maintenance Instructions for Loran Low Frequency Converter CV-27/UPN. RL-M-225\nPreliminary Handbook of Operating and Maintenance Instructions for Model AN/APA-J+6 Aircraft Radar Equipment. RL-M-227\nHygraph Instruction Manual. RL-M-230\nPossible Radar Solutions to the Problem of Accurate Siting of Field Artillery. RL-S-12\nRadar Photo Reconnaissance. RL-S-13\nGround Position Indicator for Radar Navigation and Bombing. RL-S-19\nTermination Report on Radar Photo Reconnaissance Project RL-S-34\nNetworks, see Circuits and Networks\nNight Fighting, Aerial\nReport on Night Fighter Pursuits. RL-117\nNew Approach Procedure for Night Fighting. a\nNight Fighting (Continued)\nNew Method of Night Fighting (abridged edition of Statistical Treatment of Certain Phases of Aerial Combat. RL-181)\nEffect of Routine Evasive Action on the Calculated Approach Procedure. RL-187\nUse of the Range Clock in Night Fighting with AL Equipment. RL-204\nNoise\nTheory of Noise in Conductors, Semi-Conductors, and Crystal Rectifiers [Purdue]. 14-133\nNoise Reduction by Delayed Feed-Back [RCA]\nTheory of Signal to Noise Ratio of Crystal Mixers\nCrystal Noise as a Function of DC Bias and 30-Mc Impedance Measured with a Diode Noise Source\nNoise in Silicon Rectifiers at Low Temperatures [U.\nOn the Distribution of Average Noise in Receivers (Cornell). 14-305\nNote on Measurement of Noise Temperature (U. Crystal Audio Noise). 14-387\nSpecial Report on Signal-to-Noise Measurements on Receivers. RL-108\nSpecial Report on Comparative Signal Noise Measurements on Crystal Mixers and Grounded Grid Tube Mixers. RL-110\nNoise and the Reception of Pulses. RL-115\nCoincidence Method of Noise Reduction. RL-119\nResponse of a Non-Linear Device to Noise. RL-129\nReport of Section VI, March 4 to March 22, 1941.\nKinetic Derivation of the Thermal Noise Formula. RL-192\nStatistics of Circuit Noise. RL-193\nComparison Between Signal and Noise. RL-193\nNoise Measurements on Microwave Converters.\nTheory of Noise Measurements on Crystals as Frequency Converters. RL-293\nUse of the Temperature-Limited Diode in Measurements of Noise Figures of Crystals. RL-294\nNotes on Measurement of Noise, Gain and Noise Figures of Converters. RL-295 Noise Temperature Measuring Apparatus for Crystals as 10,000 to 30 Megacycle Converters. RL-296 Noise from Local Oscillators. RL-304 Action of Linear Detector on Signals in the Presence of Noise. RL-305 Definition of Maximum Range on Aircraft and Its Quantitative Determination. RL-353 Performance of 3-Cm System (D2-1). RL-355 S/N Measurements on the CV-58. RL-416 Simplified Measurement of Receiver Sensitivities (S-Band Noise Source). RL-443 Theory of Random Processes. RL-454 Noise The Detection of Moving Targets among Ground Clutter by Coherent Pulse Methods. RL-480 Operation of IN 23 Crystal Rectifiers. RL-496 The Effect on Noise Figure of Placing the Gain Control on the First I-F Stage. RL-528 Reduction of Power Line Noise in Modulators.\nA Feedback Circuit for Measuring Output Noise Ratio of Crystal Rectifiers. RL-667\nReceiver Noise Figures and Their Measurement. RL-773\nFluctuations in the Return Signals from Random Scatterers. RL-773\nNoise Filtering Properties of Third Detectors. X-Band Sea-Return Measurements. RL-870\nMeasurements on Noise from Reflex Oscillators. Theory of Noise from the Reflex Oscillator. RL-873\n1N23 Noise Measuring Set Type 7438. RL-M-190\nIN 21 Noise Tester, Type 110 44. RL-M-191\nNomenclature (see Circuits and Networks)\nOscillator Circuits (see Circuits and Networks)\nOscilloscopes (see Test Equipment)\nPerformance (see also Airborne Radar Performance, Ground Radar Performance, Shipborne Radar Performance)\nRoof Systems Reports, August 26, 194-1 to September [\nComparison of Performance of 10-Cm and 3-Cm Advanced Development Systems. RL-350\nPerformance of 3-Cm System (D2-1). RL-355\nPerformance of the 3-Cm Advanced Development System (D2-1): RL-365, RL-1023, RL-S-68, RL-S-74, RL-348, RL-381, RL-382, RL-715, RL-439, RL-449, RL-492, P4/RL-725, RL-M-163\n\nAdvanced design for radar photography: Fair photography of successive pulse reflections from a moving target. RL-348, Photographs of the PPI indicator tube with 3-Cm ASV over water and land. RL-381, Photographic polarization tests. RL-382, Tokyo H2X photographs. Comparison of operational PPI photographs with PPI predictions of the ultrasonic radar trainer. RL-715, A report on ASD-1 B-Scope photography. The identification of signals on PPI photography for the construction of radar maps. RL-449, Comparative photographs of 1- and 5-microsecond signals. RL-492, Instruction manual for automatic H2X camera, Model A. RL-M-163.\nPART III: Photography (Continued)\n\nTemporary Instruction Manual for Automatic H2X Camera, Model B. RL-M-164B\nRadar Photo Reconnaissance. RL-S-13\nTermination Report on Radar Photo Reconnaissance Project. RL-S-34\nPPI Photographs from AEW. RL-S-51\nType Test of the Fairchild Radar Recording Cameras. RL-S-66\nSemi-Automatic Tactical Plotting Board. RL-467\nThe SCR-584 Plotting Table System. RL-595\nAdditional Modification, Calibration, and Plotting Procedures for RC-294 Plotting Equipment.\nRelease Point Indicator Used in Conjunction with the Manual Plotting System RC-305. RL-S-62\nPlumbing. See Transmission Lines and Test Equipment.\nPolarization\nRelation of Radar Range to Frequency and Polarization. RL-18\nChange of Polarization as a Means of Gap Filling.\nMicrowave Transmission, RL-121\nPolarization Effects in a Circular Wave Guide for Radar Target Contrast, RL-375\nPhotographic Polarization Tests, RL-382\nThe Depolarization of Microwaves, RL-458\nPreliminary Measurements of 10-cm Reflection Coefficients of Land and Sea at Small Grazing Angles, RL-483-8\nRadome Bulletin Number 8, X-Band Sandwiches at Variable Angles of Incidence, RL-483-13\nRadome Bulletin Number 13, Elliptical Polarization Produced by Streamlined Radomes, RL-483-16\nRadome Bulletin Number 16, Some Electrical Aspects of Microwave Sandwich Radome Design, RL-483-16\nX-Band Horizontally Polarized Nondirectional Antennas, RL-489\nS-Band Horizontally Polarized Nondirectional Antennas, RL-517\nPolarization Studies at S and X Frequencies, RL-536\nS-Band Vertically Polarized Nondirectional Antennas, RL-623\nOver-Water Tests of S-Band Early Warning for Ships. Vertical Coverage of the CXHR (SCI)\nSearch System RL-703\nAltitude Return in AN/APS-6. RL-706\nBroad-Band Antenna for Circular Polarization.\nNormal Firing K-Band Array with Transverse Polarization. RL-771\nBeacon Tests with AN/APS-6. RL-S-16\nFlight Tests on AN/APS-6 A. RL-S-25\nPotentiometers\nPlan Position Indicator Using a Sinusoidal Potentiometer. RL-312\nLinearity of Standard Wire-Wound Volume-Control-Type Potentiometers. RL-313\nSpecification of Performance Tests for PPI Sinusoidal Potentiometers Types RL10E and RL1K.\nPresent Status of Potentiometer Projects in the Radiation Laboratory. RL-318\nPotentiometer Type RL-B for Azimuth and Elevation Indication on Magnetically Deflected Cathode Ray Tubes. RL-409\nSinusoidal Potentiometers Types RLIOCB, RLIOCD, RLIOE, and RL1U. RL-423\nSinusoidal Potentiometers Types RL11, RL15, RL20U.\nGanged Potentiometers and a Three-Terminal Resistance Network. RL-610\nLife Test of Contact Material on Standard Linear Wire-Wound Potentiometers. RL-617\nThe RL 270 Series of Precision Potentiometers.\nSine Potentiometer Tester. RL-940\nPower Equipment and Power Supplies\nInvestigation of Power Supply Requirements as a Function of Future Radar Circuit Developments\nPower Supply for Air-Borne Radar Equipment\nAnalysis of Commutation of Direct Current Machines at High Altitudes, November 28, 1942 [NDRC]. 14-136\nSimulated High-Altitude Brush Testing Equipment\nAnalysis of Commutation of Direct Current Machines at High Altitudes, April 15, 1943 [NDRC]\nDevelopment of a Power Supply and Temperature Stabilized Oscillator for the Battery Operated Lodar Receiver [Emerson Radio and Phonograph]\nDevelopment of a Three-Phase Aircraft Alternator [Leland Electric Co.]. 14-287\nTechnical Report of Research Work Conducted at Metal Powder Laboratory [Stevens]\n\nConstancy of EMF's of Dry Batteries (Corthyrite Bridge Controlled Voltage Regulator. RL-525)\nWave Form Analysis. RL-561\nStabilized High Voltage Supply. RL-565\nNonlinear Networks as Voltage Regulators. RL-711\nElectronic Line Voltage Stabilizers. RL-1042\nGeneral Lecture Series on Radar Components.\n\nX-Band Low-Pressure Tests. RL-241\nX-Band Measurements at Low Pressures. RL-250\n\nThe Cooling of Pressure Tight Containers. RL-462\nPresent Status of High Power at S-Band. RL-793\n\nPropagation of 10-Centimeter Waves on a 52-Mile Optical Path Over Land. The Correlation of Signal Patterns with Radiosonde Data [Washington State College]. 14-151\nRadiotelephone Communication on 3000 Megacycles.\nPropagation of Signals on 45.1, 474, and 2800 MHz from Empire State Building to Hauppauge and Riverhead, Long Island, New York, July 20, 1943 [RCA]\nPropagation of 10-Centimeter Waves over Land Paths of 14, 52, and 112 Miles [Washington State College]. 14-202\nPropagation of 10-Centimeter Waves over an Inland Lake. Correlated with Meteorological Sounding [Washington State College]. 14-212\nPropagation of Signals on 45.1, 474, and 2800 MHz from Empire State Building to Hauppauge and Riverhead, Long Island, New York, July 31, 1944\nRotational Line Width in the Absorption Spectrum of Atmospheric Water Vapor [U. of Mich.]\nMagnetrons for Production of Centimeter Wave-length Radiation, also Absorption of Such Radiation in Water Vapor [CRL]. 14-588\nMicrowave Interference Patterns. Transmission on 3,000 MHz over Sea Water. RL-13\nRL-14 Transmission on 3,000 MHz\nTransmission on 100 MHz over Sea Water. RL-15\nTransmission on 200 MHz over Sea Water. RL-16\nTransmission on 500 MHz over Sea Water. RL-17\nChange of Polarization as Means of Gap Filling.\nProperties of the Diffracted Wave Field Intensity.\nRadar Height Finding. RL-21\nTransmission at Low Altitudes over Sea Water.\nField Intensity Formulas. RL-23\nConsiderations Affecting Choice of Wavelength.\nMicrowave Transmission. RL-121\nAtmospheric Absorption of Microwaves. RL-175\nGeneral Relations Determining the Range of a Radar System. RL-186\nAn Introduction to Microwave Propagation.\nThe Effect of Atmospheric Refraction on Short Radio Waves. RL-447\nSimplified Methods of Field Intensity Calculations in the Interference Region. RL-461\nPropagation over Short Paths and Rough Terrain (Continued)\nPreliminary Measurements of 10-cm Reflection Coefficients of Land and Sea at Small Grazing Angles.\nRadome Bulletin Number 4: Transmission and Reflection of Single Plane Sheets (RL-478)\nRadome Bulletin Number 11: Electrical Properties of Double-Wall and Sandwich Radomes (RL-483-4)\nRadome Bulletin Number 12: Transmission and Reflection of Parallel Plane Sheets (RL-483-12)\nRadome Bulletin Number 16: Some Electrical Aspects of Microwave Sandwich Radome Design (RL-483-16)\nObservations on Signal Stability at S and X Frequencies (RL-537)\nRefraction (RL-551)\nFurther Measurements of 3- and 10-Cm Reflection Coefficients of Sea Water at Small Grazing Angles (RL-568)\nPreliminary Report on the Fluctuations of Radar Signals (RL-569)\nDielectric Properties of Water and Ice at K-Band\nOver-Water Transmission Measurements, 19U4 (Part I, Preliminary Analysis of Radio and Radar Measurements) (RL-649)\nFurther Theoretical Investigations on the Atmospheric Absorption of Microwaves (RL-664)\nTheory of Characteristic Functions in Anomalous Propagation: RL-680\nThe Absorption of Half-Centimeter Electromagnetic Waves in Oxygen: RL-684\nField Intensity Contours in Generalized Coordinates: RL-702\nOver-Water Tests of S-Band Early Warning for Ships: RL-703\nVertical Coverage of the CXHR (SCI) Search System: RL-706\nAltitude Return in the AN/APS-6: RL-706\nSurface Coverage of Some Shipborne Radar Sets on S, X, and K Bands: RL-720\nAn Aerial Investigation of K-Band Radar Performance under Tropical Atmospheric Conditions: RL-729\nThe Relation Between Absorption and the Frequency Dependence of Refraction: RL-735\nRange-Altitude Coverages of Shipborne Microwave Search Radars: RL-741\nFluctuations in the Return Signals from Random Scatterers: RL-773\nEffects of Clouds and Rain on K-Band Airborne Radar: RL-780\nMethods of Calculating Characteristic Values for: RL-785\nBilinear M-Curves (RL-795)\nGraphs for Computing the Diffraction Field with Standard and Superstandard Refraction (RL-799)\nPropagation in an Atmosphere Containing a Dispersive Medium (Part III)\nThe Absorption of Atmospheric Water-Vapor in the K-Band Region (RL-1002)\nA Procedure for Statistical Analysis of Depth Soundings (RL-S-21)\nGeneral Lecture Series on Radar Components. Meteorology\nThe Captive Radiosonde and Wired Sonde Techniques for Detailed Low-Level Meteorological Sounding [Washington State College] (14-192)\nX-Band Low Pressure Tests (RL-241)\nX-Band Measurements at Low Pressure (RL-250)\nRadar Echoes from Atmospheric Phenomena\nClimate in Relation to Microwave Radar Propagation in Panama (RL-476)\nInstruments and Methods for Measuring Temperature and Humidity in the Lower Atmosphere\nQualitative Survey of Meteorological Factors Affecting Microwave Propagation (RL-488)\nMicrowave Transmission over Water and Land under Various Meteorological Conditions. RL-603, Over-Water Transmission Measurements, Part I, Preliminary Analysis of Radio and Radar Measurements. RL-649, Radar Echoes from Precipitation Layers. RL-689, Targets. Relation of Radar Range to Frequency and Polarization. RL-18, Radar Echoes from Periscopes. RL-171, Radar Echoes from Atmospheric Phenomena. Microwave Radar Reflections. RL-195, Possible Measurement of Radar Echoes by Use of Model Targets. RL-196, Synthesis of Microwave Diffraction Patterns with Application to Csc 2\u00a9 Patterns. Comparison of Reflectivities of Approximately Similar Plastic and Metal Airplanes. RL-384, Tests on Radar Echoes from Cylinders. Over-Water Observations at X and S Frequencies on Surface Targets. RL-401.\nOn the Fluctuations in Signals Returned by Many Independently Moving Scatterers. RL-465\nOn the Appearance of the A-Scope When the Pulse Travels Through a Homogeneous Distribution of Scatterers. RL-466\nReflections from Smooth Curved Surfaces. RL-661\nTheory of Radar Return from the Schnorkel.\nRadar Echoes from Precipitation Layers. RL-689\nFluctuations of Radar Echoes. RL-700\nA Theoretical Treatment of Radar Target Return. RL-728\nEchoes from Tropical Rain on X-Band Airborne Radar. RL-728\nPropagation (Continued)\nEffects of Clouds and Rain on K-Band Airborne Radar.\nA Theoretical and Experimental Study of Radar Ground Return. RL-1024\nA Theoretical Treatment of Radar Target Return, Part II. RL-1049\nThe So-Called Standard Target. RL-S-43\nParaboloid Diffraction Patterns from the Standpoint of Physical Optics. RL-T-7\nPropeller Modulation (see also Absorbent Materials, Dielectrics, and IFF)\nModulation of Radar Signals from Airplanes: RL-914\nPreliminary Maintenance and Operating Instructions\n\nDetection of Propeller and Sambo Modulations. Pulse Length and Rate, Shape\nComparative Photographs of 1- and 5-Microsecond Signals. R^-492\nPulse-Length Discrimination in Beacons. RL-510\nVoltage Pulse Rate-of-Rise Measurements. RL-523\nEffect of Pulse Length on System Performance and Operation. RL-571\nEffects of Line and Cathode-Follower Terminations on Pulse Shape. RL-616\nExperiments in Microwave Breakdown. RL-731\nShort Pulse Techniques for High Definition Radar Systems. RL-912\nPulse Length Selector and Multiple Pulse Decoder.\nPulse Transformers (see also Transformers)\n\nPulse Transformer Leakage Inductance and Distributed Capacitance of Various Types of Pulse Transformer Windings.\nPulse Transformer Core Material Measurements.\nColloquium on Pulse Transformer Design\nHigh-Ambient Life Test of an Oil-Filled Pulse Transformer. RL-513\nThe Evaluation of an Equivalent Circuit for a Pulse Transformer. RL-514\nAnalysis of the Influence of Pulse Transformers on Current Pulse Shape. RL-545\nA Method of Virtual Displacements for Electrical Systems with Applications to Pulse Transformers. RL-546\nEnergy Loss in Copper under Pulse Conditions. Influences of Pulse Transformer Design on hJ 31-35\nMagnetron Stability. RL-622\nEquivalent Circuit of a Pulse Transformer Core. RL-623\nPulse Transformer Committee Standard Test Methods for Pulse Transformer Cores. RL-722\nEquivalent Network for the 232-BW Pulse Transformer. (Continued)\nBased on the Method of Virtual Displacements. RL-734\nPulse Transformer Committee, Proposed Basic Specifications for Pulse Transformers. RL-881\nRadiation Laboratory Pulse Transformer Designs.\nRadar Countermeasures (RCM), see Countermeasures Radio-Frequency Heads, see R-F Heads\nRadomes\nDesign and Test of Project Eagle Airfoil [Douglas]. Special Report\nTransmission Characteristics of Suggested Airplane Nose Materials. RL-144\nDesign Characteristics of Spinner Housing Materials.\nRadome Bulletin Number 1. RL-483-1\nRadome Bulletin Number 2: An Outline of the Electrical Properties of Radomes. RL-483-2\nRadome Bulletin Number 3: Ice Formation on Ship-borne Radomes. RL-483-3\nRadome Bulletin Number 4: Transmission and Reflection of Single Plane Sheets. RL-483-4\nRadome Bulletin Number 5: Recent Dielectric Constant and Loss Tangent Measurements. RL-483-5\n[Radome Bulletin Number 6, Radomes and System Performance. RL-483-6, Radome Bulletin Number 7, The Measurement of High Reflections at Low Power. RL-483-7, Radome Bulletin Number 8, X-Band Sandwiches at Variable Angles of Incidence. RL-483-8, Radome Bulletin Number 9, The Matching of High Standing Wave Ratios. RL-483-9, Radome Bulletin Number 10, The Measurement of Small Reflections. RL-483-10, Radome Bulletin Number 11, Electrical Properties of Double-Wall and Sandwich Radomes. RL-483-11, Radome Bulletin Number 12, Transmission and Reflection of Parallel Plane Sheets. RL-483-12, Radome Bulletin Number 13, Elliptical Polarization Produced by Streamlined Radomes. RL-483-13, Radome Bulletin Number 14, An Investigation of R-F Probes. RL-483-14, Radome Bulletin Number 15, The Measurement of Dielectric Constants in the One-Centimeter Band. Radome Bulletin Number 16, Some Electrical Aspects]\nRadome Bulletin Number 17, Current Progress on R-F Research. RL-483-17\nRadome Bulletin Number 18, The Dependence of Magnetron Pulling on Radome Shape and Orientation. RL-483-18\nRadome Bulletin Number 19, Dielectric Constant and Loss Tangent Computation. RL-483-19\nRadome Wall Reflections at Variable Angles of Incidence. RL-483-21\nTransmission of Lossy Sandwiches. RL-483-22\nDielectric Constants and Loss Tangents of Radome Materials. RL-483-25\nElectrical Test Methods for Radomes. RL-483-26\nRange Tracking Circuit with Position Memory [Corrected]\nRange Tracking Circuit with Velocity Memory [Corrected]\nReports of Tests on Resonant Range Follow-Up System [Fairchild]. 14-246\nGovernment Radar Patent Program, Technical Report No. 2 \u2014 Precise Range Measurement and Tracking. 14-339\nErrors in Range Measurement with a Circular Error [Corrected]\nRL-9 Relation of Radar Range to Frequency and Polarization\nRL-18 Considerations Affecting Choice of Wavelength\nScattering of 10-cm Radiation by a Model Airplane\nRadar Echoes from Periscopes RL-171\nAtmospheric Absorption of Microwaves RL-175\nGeneral Relations Determining the Range of a Radar System RL-186\nMicrowave Radar Reflections RL-195\nPossible Measurement of Radar Echoes by Use of Model Targets RL-196\nPrecision Timing Calibrator and Range Measuring System RL-319\nPrecision Delay Multivibrator for Range Measuring System RL-320\nMedium Precision Self-Synchronous Range Circuit Model U RL-321\nCircular Sweep Precision Range System Model U Medium Precision, Self-Synchronous Automatic Range Tracking Circuit RL-323\nPhotoelectric Automatic Range Tracking Unit Simplified Circular-Sweep Range System RL-325\nAntiaircraft Artillery Board Test on the Simplified\nCircular Sweep Range. RL-326\nHand Radar Ranging Circuit. RL-327\nErrors in Circular Sweeps Due to Decentering and Ellipticity. RL-328\nLine Controlled Blocking Oscillator Marker Generator A.R.O. Calibrator. RL-330\nA.R.O. Range Follow-up Unit. RL-331\nA.R.O. Range Unit. RL-332\nModel II Calibrator. RL-333\nDelayed Sweep for SCR-582-X. RL-337\nA Condenser Phase Shifter Range Circuit with Sine Wave Tracking Suitable for Microwave Height Finding Stations. RL-339\nPulsed Oscillator and Phase Shifter. RL-340\nAutomatic Range and Azimuth Tracking While Scanning. RL-341\n\nPart III\nRange (Continued)\nH2X Range Unit for Navigation and Bombing. Type J and A Test Unit. RL-343\nDefinition of Maximum Range on Aircraft and Its Quantitative Determination. RL-353\nTests on Radar Echoes from Cylinders. RL-378\nSurvey of 10-Cm Radar Installation in PBM-1 Flying Boat. RL-383\nComparison of Reflectivities of Approximately Similar Plastic and Metal Airplanes. RL-384\nAn Introduction to Microwave Propagation. RL-406\nRange Height Indicator. RL-418\nThe Range Calculator. RL-497\nA Condenser Phase Shifter Range Unit with Sine Wave Tracking for AN/TPG-1, AN/FPG-1,\nA Range-Measuring System Using an RC Linear Sweep. RL-540\nA Precision Self-Synchronous Range System for Medium Precision Range System for CXGQ (Project Henry). RL-579\nSiting and Range of Microwave Beacons. RL-590\nA \u201cRange Only\u201d Set for \u201cClose-In Seeing\u201d RL-598\nComparison of Theoretical and Experimental Requirements for Microwave Beacon Transmitter Power and Receiver Sensitivity. RL-627\nVertical Coverage of a 15v-Ft x 5-Ft Antenna Designed for SG-3 (Experimental Data Obtained with an SNB Aircraft as Target). RL-636\nA/R Range Scope. RL-755\nRange Accuracy of AN/APG-5 (ARO). RL-820\nAN/APG-15B Falcon System Manual: RL-M-152A\nAN/APG-13 Falcon System Manual: RL-M-152B, RL-M-152C\nOperating Instructions for Sweep Calibrator (Model): AN/APG-5 (ARO) Airborne Range Only Equipment: RL-S-6\nPreliminary Report on Single Aircraft Target Ranges of AEW: RL-S-37\nRadar Components that Affect Range: RL-S-73\nRange Tables (see Bombing and Ballistics): RCM\nCountermeasures: see\nReceivers: see Amplifiers\nAircraft Position Indicating Equipment (Receiving): Instruction Book for Western Electric D-161131 Receiver and D-161132 Indicator for a Long Range Navigation System [BTL]: 14-91\nLodar Pulse-Direction-Finding Receiver [RCA]: The AGL Receiver [GE]: 14-275\nOn the Distribution of the Average Noise Current in Receivers: 14-305\nReceivers (Continued)\n3000-Mc Receiver (Type ZP-A39, Final Report [GE], 14-432) Magnetrons and Detector Beat-Oscillator Receivers with Record of Material Furnished [BTL]. 14-450\nRoof System Report, Initial Development, Feb. 15 \u2013 Receivers and T-R Boxes. Feb. 4, 1941. RL-102\nReceivers, T-R Boxes, Measurements, Feb. 4 \u2013 Mar. RL-105\nVisit to the Bell Telephone Laboratories. RL-106\nSpecial Report on Receivers. June 24, 1941. RL-106\nSpecial Report on Tuning Indicators and Automatic Tuning Systems. RL-107\nSpecial Report on Signal-to-Noise Measurements on Noise and the Reception of Pulses. RL-115\nIdeal Frequency Response of a Receiver for Square Pulses. RL-125\nResponse of a Non-Linear Device to Noise. RL-129\nConference on Standardization of Intermediate Frequency. RL-283\nPreliminary Report on a 10-Cm Super-Regenerative Receiver. RL-284\nImpulse and Square-Pulse Response of Various Filters. RL-285\nA 30-MC Sobering Bridge. RL-301\nA Video Delay Line. RL-302\nAction of Linear Detector on Signals in the Presence of Noise. RL-305\nThe Radiation Laboratory S-Band Amplifier (Preliminary Report). RL-306\nA 70-MEGHERTZ Wide IF Amplifier. RL-307\nLow-Level Crystal Detectors: Effect of Heat and Cold. RL-440\nSimplified Measurement of Receiver Sensitivities (S-Band Noise Source). RL-443\nShielding of Microwave Receivers Against Interference at Intermediate Frequencies. RL-471\nLighthouse Tube Supper Generative Receivers. A 60-MC Parallel Sobering Bridge. RL-558\nComparison of Theoretical and Experimental Requirements for Microwave Beacon Transmitter Power and Receiver Sensitivity. RL-627\nCrystal Detectors and the Crystal-Video Receiver. Low Noise Replacement Preamplifier for the SCR-Synthetic Radar. Echoes in the Presence of Jamming.\nA Wide-Excursion Frequency-Modulated Alignment Oscillator or Wobbulator. RL-738\nReceiver Noise Figures and Their Measurement. RL-815\nAn Electronic Frequency Stabilization System for CW Microwave Oscillators. RL-815 (Continued)\nDetector Cancellation Error as a Function of Carrier Frequency. RL-859\nDistortion in X-Band Detectors. RL-956\nNotes on MTI Receivers. RL-1010\nIntermediate Frequency Amplifier Overload Characteristics. RL-1032\nInstruction Manual for B-18 Radar Installation.\nInstruction Manual for B-18 Receiver (Included in Operating Instructions for the Model 417 Klystron for Use as a Local Oscillator in Radar Receivers)\nAN/APS-15 Receiver - Indicator Modified for Ground Range Sweeps and Remote Amplifier. RL-M-172A\nHandbook of Operating Instructions for Loran Low Frequency Converter CV-27/UPN. RL-M-222\nHandbook of Maintenance Instructions for Loran Low Frequency Converter\nFrequency Converter CV-27/UPN, RL-M-225, Some General Microwave Anti-Jam Design Considerations and Performance of a Special Receiver, RL-S-8, Anti-clutter Circuits for AEW, RL-S-52, General Lecture Series on Radar Components, Radiation Laboratory Reports [NDRC]. 14-250, Division 14 Contract List, June 1, 1944 [NDRC], Radiation Laboratory Reports, First Supplement, Frequency-Wavelength Conversion Tables. RL-652, Reports, Manuals, and Texts, Nov. 12, 1944, Reports, Manuals and Texts, Mar. 7, 1946, Glossary of Terms Used in Connection with Radiation Laboratory Radar. RL-M-144, Tables of Fourier Transforms of Fourier Series, Power Series, and Polynomials. RL-S-58, Relay Radar, Report of Radio Relaying of Radar Signals [NBC], A Method for Relay Radar PPI Synchronization, Flight Tests of Block I Relay Radar System. RL-727.\nAEW (Airborne Early Warning)\nRL-739 AEW Block III Relay Antenna\nRL-845 AEW Block III Relay Link\nRL-977 X-Band Frequency Modulated Relay System for Video Frequencies\nRL-M-180A Preliminary Technical Manual for AEW\nRL-M-229 Preliminary Book of Maintenance Instructions for Shipboard Components of AEW\nRL-S-26 AEW\nRL-S-27 AEW (RL-S-26 plus additional material)\nRL-S-27 AEW Bedford Trials\nRL-S-32 Tactical Use of Delayed PPI Scopes of the AEW System\nRL-S-36 Preliminary Report on Single Aircraft Target Ranges of AEW\nRL-S-37 PPI Photographs from AEW\nRL-S-51 Anti-Clutter Circuits for AEW\nRL-S-52 Remote Indication and Control Systems (Data transmission servos, synchros, etc.)\nRL-434 Synchro Test Equipment and Test Procedure\nAmplidyne Servo for SCR-598 Surface Fire Control\nA One-Tube, One-Selsyn Sector-Scanner (RL-448)\nTests on M3B1 Oil Gear and Amplidyne Servo for SCR-598 Control Problem (RL-464)\nSemi-Automatic Tactical Plotting Board (RL-467)\nRemote Position Control by Direct Frequency Variation (RL-482)\nResults of Tests Performed on \"Synchro\" Units and Systems (RL-490)\nA Hard Tube Servo Amplifier for Fractional Horsepower DC Motors (RL-535)\nServos with Torque Saturation (Part I) (RL-555)\nServos with Torque Saturation (Part II) (RL-592)\nThe SCR-585 Plotting Table System (RL-595)\nQA-2B Servo Adaptor (RL-645-1)\nQL-2 and Q-3 Servo Amplifier (RL-645-2)\nS-2, S-2B, S-4, S-4B Motor Control Units (RL-645-10)\nThe S-5 and S-5B Motor Control Units (RL-645-11)\nData Smoothing (RL-673)\nOn Servos with Pulsed Error Data (RL-721)\nTwo Proposed Methods of Recording the Position of a Moving Link (RL-730)\nSynchro Units and Their Characteristics (RL-740)\nRL-M-226 Alignment Procedure for Cadillac Airborne Synchro System\nRL-S-11 Servo Generator Life Tests\nR-F Heads\nK-Band R-F Head, Type No. 3, Navy Model RT-63 /APS, British Model 110 DB/206, Instruction Development and Production of 50 K-Band R-F Heads [Sylvania]. 14-496\nLighthouse Tube Transmitter-Receiver LHTR Mk I. Final Report on SMTR. RL-559\nA \"Range Only\" Set for \"Close-In Seeing.\" RL-598\n\nPART III\nR-F Heads (Continued)\nGE GL2CU0 Taut Grid Lighthouse Tubes. RL-bOO\nAN/APQ-3A R-F Head. ^L-888\nAN/TPS-1OB R-F Head Termination Report. RL-889\nImproved R-F System for the Transmitter-Receiver Unit of the APQ-1S.\nOne Knob Tunable X-Band R-F Head. RL-1019\nManual for Fighter Tail-Warning Equipment. ^ ^\nReplacement Pressurized R-F Unit for AN/APS-15A.\nScanning, see also Antennas and Indicators\nAIA-1 Scanner Development Program Completion Report [Dalmo Victor]. 14-199\n\nAN/APQ-3A R-F Head\nAN/TPS-1OB R-F Head Termination Report\nImproved R-F System for the Transmitter-Receiver Unit of the APQ-1S\nOne Knob Tunable X-Band R-F Head\nManual for Fighter Tail-Warning Equipment\nReplacement Pressurized R-F Unit for AN/APS-15A\nAIA-1 Scanner Development Program Completion Report\nTwo Motor-Driven Gun Turrets [GE]. 14 230\nDesign of uEgg Beater \" Scanning Antenna for the Eagle Radar Bombsight and Construction of a Model Int. Projector Corp. 14-312\nAIA-1 Scanner Development Program, Progress Report\nRadar Scanner Development Program, Progress Report\nPrecision Aircraft Scanners [GE]. 14-410\nRadar Scanner Development Program, Progress Report\nRadar Scanner Development Program, Progress Report\nFinal Report on H2K Roll Stabilized Scanner [Maguire Industries Inc.]. 14-429\nRadar Scanning Unit, Final Report [Chrysler]\nRadar Nutating Antenna Spiral Scanning Units, Balance and Adjustment [Chrysler]. 14-573\nOn Conical Scanning. RR-3\nCorrection of the Scanning of Shipborne Radar Systems for Roll and Pitch of the Ship. RR-12\nReport of Section VI, Mar. 4\u2014 Mar. 22, 1941. RL-133\nRapid Scanning, High Revolution Antennas Preliminary Report. \"97k\nReport on Rapid Scanning: KL-b\nAutomatic Range and Azimuth Tracking During Scanning. t\u00bbt\nConical Scanning.\nThe Balancing of Spiral-Scan Spinners. RL-dSU\nDevelopment of a Flexible Relay Servomechanism and Application to Sector Scanning Spinner Controls RL-38b\nLaboratory and Field Tests with Stabilized Spinners - Search Scans and System Performance. ^-407\nA One-Tube, One-Selsyn Sector-Scanner.\nLeaky Waveguide Rapid Scanner. RL-557\nLinear Electrical Scanner. R1\u2122\u00b0\nParallel Plate Optics for Electrical Scanning. RL-646\nThe SCI Rapid Scan Height-Finding System.\nStable Scanners and Unsteady Airplanes. RL-1010\nTests of a Type C Data Presentation with a Spiral-Scan Aircraft-Interception System. RL-7b\nMechanical Resonant Scanner. RL-782\nK-Band Rapid Scan. RL-960\nSurvey of Foster Scanner Developments. RL-1074\nPreliminary Testing of the Houston Corporation\nAN/APS-10 Scanner, RL-S-33 Mechanical and Electrical Tests of the General Electric Company Scanner for the AN/APS-10 System, RL-S-61\nGeneral Lecture Series on Radar Components. Selsyns, Servos, Synchros, see also Remote Indication and Control Systems\nFinal Report, Including the Design of Stroking Motor for a Hydraulic Servomechanism [MIT]. 14-279\nSpecial Report on Data Transmission by Means of Selsyns. RL-6\nSelsyns. RL-12 Thyratron Servo Control Circuit for Spinners. RL-31\nProduction Sources of Self-Synchronous Units. Servomechanisms. RL-372\nDevelopment of a Flexible Relay Servomechanism and Application to Sector Scanning Spinner Controls. RL-386\nGeared Selsyns. RL-388\nParallel \u201cT\u201d Stabilizing Networks for AC Servos. Results of Tests Performed on Synchro Units and Systems. RL-921\nDescription and Method of Operation of the Special Synchro Test Bench and Synchro Testing Procedures.\nA Displacement or Velocity Servo Amplifier. RL-922\nAn Analysis of an Amplidyne Servomechanism. RL-T-4\nShepherd Tubes, see Tubes, Velocity-Modulated\nShipborne Radar, see also Beacons, Fire Control Systems, and Navigation and Mapping Components\nMotor Torpedo Boat (M.T.B.) Computing Radar\nSight for Blind, Semi-Blind and Visual Fire Radar Scanning Unit, Final Report [Chrysler]\nRASD Stable Element, Final Report [GE]. 14-567\nRadar Nutating Antenna Spiral Scanning Units, Balance and Adjustment [Chrysler]. 14-573\nCorrection of the Scanning of Shipborne Radar Systems for Roll and Pitch of the Ship. RL-126\nProject Dolphin. RL-385\nA Shipborne Mechanical Rotation Plan Position Indicator. RL-315\nSG-1 Antenna Mark 2. RL-639\nSU-2 Antenna. Shipborne Stabilized Radar Antenna for Sea Search. RL-659\nSU-2 Antenna. Line-of-Sight Stabilization of a Radar Beam by Reflector Tilt. RL-660\nThe SG-3 Stabilized Antenna. RL-665\nShipborne Radar (Continued)\nThe SCI Rapid-Scan Height-Finding Antenna. RL-796\nMark 56 U Chronograph. RL-805\nSlip Ring Assembly for the MK 56X System.\nHandbooks\nComprehensive Report on USS Semmes Radar Installation. RL-393\nRadar Beacon \u2014 Mark I Mod 1. RL-M-167\nHandbook of Maintenance Instructions for CXGQ Radar Set. RL-M-168\nPreliminary Instructions for the Manual Bearing Unit. RL-M-192\nCXHR Maintenance Manual. RL-M-224\nPreliminary Book of Maintenance Instructions for Shipboard Components of AEW. RL-M-229\nPreliminary Instructions for Radar System MK 35. RL-M-242\nPerformance Report of Operation USS Semmes. RL-38\nRegular Report on USS Semmes 3,000-Mc Operations. RL-50\nRegular Report on USS Semmes 3,000-Mc Operations. RL-51\nReport on USS Semmes 3,000-Mc Operations: RL-52, Analysis of Firing Tests on Mark 51, Regulating Dam Neck, Virginia. RL-371, Vertical Coverage of a lVz-Ft by 5-Ft Antenna for SG-3 (Experimental Data Obtained with an SNB Aircraft as Target). RL-636, Over-Water Tests of S-Band Early Warning for Ships. RL-636, Vertical Coverage of the CXHR (SCI) Search System. RL-703, Surface Coverage of Some Shipborne Radar Sets on S, X, and K Bands. RL-720, Range Altitude Coverages of Shipborne Microwave Search Radars. RL-741, Echo Box Techniques for Testing S-Band Shipborne Radars. RL-M-146, AEW Tactical Tests at Brigantine. RL-S-50, Systems and Attachments. US Radar Survey, Section 2 \u2014 Shipborne Radar, Development of Gun Fire Control System Mark 56, Final Report [GE]. 14-497, Components of CXHR (SCI) Equipment, Final Third General Report on Section Activities, May.\nRoof System Report, Initial Development. RL-37 Navy Roof, etc.\nRoof Systems Reports, Aug. 26 \u2013 Sept. 24, 1941.\nSM Radar. RL-506\nA High Resolution K-Band Ship Search Set.\nShipborne Radar (Continued)\nAnti-Aircraft Target Designation Equipment for Ships. RL-640\nThe AEW System, Book II, Shipboard Equipment.\nA Navigational Radar for Naval Auxiliaries and Merchant Marine. RL-876\nA High Resolution Set. RL-S-5\nMTB Computing Radar Sight. RL-S-14\nSights (see Fire Control Systems)\nSignal Generators (see Test Equipment)\nSiting (see also Ground Radar)\nSiting and Range of Microwave Beacons. RL-590\nPossible Radar Solutions to the Problem of Accurate Siting of Field Artillery. RL-S-12\nSpark Gaps (see Modulators and Tubes)\nSpectrum Analyzers (see Test Equipment)\nStabilization, Frequency (see Cavities, Magnetrons, Power Equipment and Power Supplies, Tubes, etc.)\nStabilization, Mechanical\nDevice for Determination of the Vertical by Means of Cosmic Rays (Cornell). Final Report on H2K Roll Stabilized Scanner (Maguire Industries Inc.). RL-14-363\n\nFinal Report on RASD Stable Element (GE). RL-14-567\n\nSU-2 Antenna. Shipborne Stabilized Radar Antenna for Sea Search. RL-14-429, RL-659\n\nSU-2 Antenna. Line-of-Sight Stabilization of a Radar Beam Reflector Tilt. RL-14-429, RL-660\n\nStabilized SG-3 Antenna. RL-14-665\n\nStable Scanners and Unsteady Airplanes. RL-14-701\n\nStanding Wave Detectors, see Test Equipment and Transmission Lines\n\nStatistical Theory, see Theory\n\nSupersonics, see also Crystals, Delay Lines, and Trainers\n\nTokyo H2X Photographs. Comparison of Operational PPI Photographs with PPI Predictions of the Ultrasonic Radar Trainer. RL-14-715\n\nA Theory of a Supersonic Delay Line. RL-14-733\n\nA Measurement of Supersonic Velocity in Mercury at 15 Mc/s as a Function of Temperature. RL-14-745\nMultiple Reflection Delay Tank RL-791\nOn the Theory and Performance of Liquid Delay Lines RL-792\nSupersonic Delay Lines RL-850\nSupersonic Solid Delay Lines RL-932\nAn Application of the Pulse Technique to the Measurement of the Absorption of Supersonic Waves in Liquids RL-963\nA Method of Compensating the Frequency Dependence of Attenuation in a Supersonic Delay Line\nPreliminary Handbook of Instructions for H2X Supersonic Trainer, Mark II RL-M-157A\nPreliminary Handbook of Instructions for H2X Supersonic Trainer, Mark III RL-M-157B\nHandbook of Instructions for the Preparation of Maps for the H2X Supersonic Trainer RL-M-181\n\nPART III\nSupersonics (Continued)\nPreliminary Handbook of Instructions for the Supersonic Trainer, AN/APQ-7-T1 (Eagle Trainer)\nHandbook of Instructions for the Preparation of Mountain Maps for the H2X Supersonic Trainer\nInstructions for Installation and Maintenance of Waffle Relief Maps in Ultrasonic Trainers.\n\nSpecifications for 15-Mc Supersonic Crystal for Crystal Cartridges Types 3 and 7B. RL-S-35 Ultrasonic Radar Trainer PPI Photographs of a Simulated H2X Bombing Mission over Tokyo.\n\nVelocity of Propagation of 15-Mc Ultrasonic Pulses in Liquids. RL-S-56\n\nSynchroscopes (see Test Equipment)\n\nTactics (see Airborne Radar, Ground Radar, Ship-borne Radar, and Theory, Statistical and Specific Applications)\n\nTargets (see Propagation)\n\nTarget Identification (see IFF, Moving Target Indication, Airborne Radar, Ground Radar, and Ship-borne Radar)\n\nTest Equipment\n\nAntenna\n- An Automatic Recorder for Microwave Antenna Pattern Measurements. RL-266\n- Antenna Parts and Measuring Equipment. RL-472\n- Antenna Measuring Equipment. RL-601-1\n- Antenna Measuring Equipment, High Power CW Transmitter for S-Band. RL-601-2\nAntenna Measuring Equipment, 100-db Linear Audio Amplifier. RL-601-3\nAntenna Measuring Equipment, Automatic Antenna Pattern Recorder. RL-601-4\nField Station for Antenna Measurements. RL-632\nAttenuators. See also Test Equipment Power Measuring and Transmission Lines \u2013 Components\nCoaxial Exponential Tapers [PIB]. 14-164\nProgress Report on Coaxial Platinum Film Attenuators [PIB]. 14-215\nTheory of Coaxial Attenuators [PIB]. 14-216\nSoldering to Glass [PIB]. 14-217\nMetallized-Glass Attenuators and Miscellaneous RF Test Accessories [PIB]. 14-360\nErrors in Attenuation Measurement Caused by Reflection Losses [PIB]. 14-365\nNotes on the Accurate Measurement of Small Attenuations at Microwaves [PIB]. 14-439\nInfluence of Inner Wave Guide Dimensions on Broad-Band Performance of Calibrated Attenuators\nUse of Sauereisen for Cementing Metallized-Glass Resistor Plates, Preliminary Report [PIB].\nFrequency sensitivity of Metallized-Glass Attenuator Inserts Type TMS-PB (PIB).: 14-477, 14-482, 14-482\nModifications pertaining to specifications for glass parts of PIB Type V-3 Variable Attenuator: 14-477\nMetallized-Glass Plate program at PIB, Research Conference (PIB).: 14-479\nAccuracy of attenuation measurements made with the Ballantine Voltmeter (PIB).: 14-480\nFrequency sensitivity of Metallized-Glass Attenuator Inserts Type TMS-3 PB (PIB).: 14-482\nThe TMX-H PB Metallized-Glass Plate for variable X Band Attenuator, maximum 25 db (PIB).\nThe TMX-16 PB Metallized-Glass Plate for X Band Fixed Attenuator, 25 Db (PIB).: 14-484\nThe TMX-2h PB Metallized-Glass Plate for X Band Fixed Attenuator pads of 10 Db and 13 Db (PIB).\nA Resistive Variable Attenuator for K Band with UO Db Maximum Attenuation (PIB).: 14-486\nElectrical performance of Metallized-Glass.\nFixed Value Metallized-Glass Coaxial Attenuators, Variable Metallized-Glass Coaxial Attenuators, Metallized-Glass Bolometers, The Development of Metallized-Glass Attenuating Elements for X Band and Wave Guide, Metallized-Glass Wave Guide Attenuators, The Development of Metallized-Glass Attenuators for Test Set TS-U7/UP, R-F Components for Microwave Bridges, Microwave Attenuation Standards, Microwave Attenuation Measurement, Precision Metallized-Glass Resistor Units, A Grid-Type R-F Attenuator, Capacitive-Type R-F Attenuator, Calibrators, Model II Calibrator, Calibrator for Low Altitude Bombing Equipment, Type J and A Test Unit, Operating Instructions for Sweep Model B, Operating Instructions for Sweep Model B-8127, Crystal.\nMeasurement of Conversion Gain with a Modulated Oscillator [Purdue]. 14-144\nA Device for the Selection and Manufacture of Low Level Detectors [U. of Pa.]. 14-201\nAudio Noise Tester [U. of Pa.]. 14-267\nTest Equipment for Germanium Second Detector Units [Purdue]. 14-394\nCalibrator\nCalibrator\nTest Equipment (Continued)\nCrystal (Continued)\nConversion Loss Measuring Apparatus for Crystals in the 3-Cm Band. RL-257\nA Simple Method for Determination of the Law of a Crystal. RL-270\nNoise Temperature Measuring Apparatus for Crystals as 10,000 to 30 Megacycle Converters.\nA Conversion Loss Set for Testing K-Band Crystal Rectifiers. RL-668\n1N23 Loss Measuring Set Type 7368. RL-M-171\n1N21 Loss Tester Type 7556. RL-M-177\nIN 23 Noise Measuring Set Type 7438. RL-M-190\n1N21 Noise Tester, Type 11044. RL-M-191\nEcho Boxes, see also Cavities\nThe Resonant Echo Box. RL-277\nDesign of an Improved X-Band Echo Box\nRL-631 K-Band Echo Line\nRL-974 Echo Box Application\nRL-1040 Tentative Operating Instructions for M.I.T. Radiation Laboratory Echo Box Dwg. 3456. RL-M-128\nRL-M-146 Echo Box Techniques for Testing S-Band Ship-Borne Radars\nPreliminary Instruction Manual for Echo Box\nInstruction Manual for Echo Box Test Kit\nHandbook of Operating and Maintenance Instructions for Echo Boxes TES-8MK and TES-9MK.\nThe So-Called Standard Target. RL-S-43\nFrequency Measurement\nFrequency-Wavelength Conversion Tables. RL-652\nTFX-29RL Frequency Comparator. RL-681\nX-Band Beacon Reference Cavities. RL-972\nInstructions for Types TFK-2HU, TFK-3HU, and TFK-6HU Frequency Meters. RL-M-176A, RL-M-176B\nTFX-34RL Fixed Frequency Standard. RL-M-207\nTFX-35RL Fixed Frequency Standard. RL-M-208\nTFX-36RL Fixed Frequency Standard. Instructions for Types TFX-17GA, TFX-18GA, TFX-19GA, TFX-30EC, TFX-31EC, Model 51 and Similar Types of Micrometer Frequency Meters. RL-M-209\n\nX-Band Sealed Standard Cavities. RL-S-70\n\nU.S. Radar Survey, Section 6 \u2014 Test Equipment\nU.S. Radar Survey, Section 6 \u2014 Test Equipment, Microwave Radar Field and Laboratory Test Equipment and Components, Final Report [PIB]\n\nMeasuring Instruments for 3-cm. RL-26\nCatalog of Microwave Test Equipment. RL-S-28, RL-S-41\n\nGeneral Lecture Series on Radar Components. Test Equipment (Continued)\n\nImpedance Measurement\nR-F Components for Microwave Bridges [PIB]\nThe Use of the Magic Tee Microwave Bridge in Measuring Impedance. RL-643\nInstructions for TBK-2RL Impedance Bridge.\nInstructions for K-Band Bench Testing. RL-M-238\nMiscellaneous\nSimulated High-Altitude Birnbaum Testing Equipment.\nMeasurement of Dielectric Constant and Loss with Standing Waves in Coaxial Wave Guides [MIT]\nAuxiliary Equipment for the M.I.T. Coax Instrument and Its Use [MIT]\n14-210\nMicrowave Resistance Comparator [PIB.]\n14-481\nDesign of Equipment for Measuring Dielectric Constant and Loss with Standing Waves in Wave Guides (XII) [MIT]\n14-541\nAn Apparatus for Determining Heat Distortion Characteristics of Plastics (XIII) [MIT]\nRegular Report on the Components Testing System\nRegular Report on the Components Testing System\nMeasuring Instruments for 3-CM RL-26\nRegular Report on the Components Testing System\nSpecial Report on Buffered Multiple Phase Box .\nRegular Report on the Operation of Screen Cage.\nRegular Report on the Advanced Development System. RL-46\nReport of the Radio Frequency Section. RL-140\nOscilloscope Presentation of Hysteresis Loops\nTest Equipment for Pulse Transformers: RL-218, RL-219, Pulse Transformer Committee Standard Test Methods: RL-722, RL-786, A Method of Shielding for Filter Insertion Loss Measurements: RL-786, R-F Mechanical Modulator for S-Band: RL-798, Microwave Technique: RL-T-13, Service Manual for Video Amplifier [U. of Pa.]: RL-76, Test Set for Raytheon Service Modulator: RL-76, A Diode-Type Pulse Voltmeter: RL-521, Oscilloscopes and Synchroscopes: Western Electric D-160448 Input Equipment and Western Electric X-61901 Oscscilloscope, Report of Activities of Synchronizer Section: PART III, Test Equipment (Continued), Oscilloscopes (Continued), Description and Operation of the General Purpose Variable Delay Unit: RL-891\n\u201cWinterscope\u201d  or  Fast  Sweep  Synchroscope. \nModel  PU-E  Synchroscope  and  R-F  Envelope  Indi\u00ac \ncator.  RL-M-124 \nInstruction  Manual  for  Revised  Model  PU  Synchro\u00ac \nscope.  RL-M-126 \nTypes  T0N-1GA  ( Type  Q)  and  T0N-1BL  Oscillo\u00ac \nscopes.  RL-M-140 \nSynchroscope  Handbook  (Model  SYN-15) .  RL-M-147 \nInstructions  for  Operation  of  High  Gain  Video \nAmplifier  for  PU-E  Synchroscope.  RL-M-166 \nOperating  Instructions  for  the  Model  G  Synchro\u00ac \nnizer.  RL-M-195A \nOperating  Instructions  for  Radiation  Laboratory \nModel  5  Synchroscope.  RL-M-212 \nModel  5  Synchroscope.  RL-S-18 \nPower  Measuring  Equipment  (bolometers,  loads, \nthermistor  bridges,  wattmeters,  etc.) \nInstructions  for  Use  of  PIB  Type  1B2  Bolometer \nTerminal  [PIB].  14-218 \nNotes  on  Use  of  Bolometers  for  Ultra-High  Fre\u00ac \nquency  Attenuation  Measurements  [PIB].  14-219 \nThe  1B2  Bolometer  Terminal  [PIB].  14-220 \nInvestigation  of  Effect  of  Manufacturing  and  Test \nThe Investigation of the Effect of Manufacturing and Test Equipment on X-Band Characteristics of Bell System Thermistors\n(January) 14-227, (May) 14-227, (Final Report) 14-462\nInvestigation of the Effect of Manufacturing and Test Equipment on the X- and K-Band Characteristics of Bell System Thermistors [BTL] 14-462\nMetallized-Glass Bolometers [PIB] 14-524\nMicrowave Power Measurement with Bolometers\nSpecial Report on the Littlefuse Bolometer RL-145\nMicrowave Wattmeter RL-239\nMicrowave Wattmeter II 3-cm and 1-cm. RL-246\n3-cm Bolometer Detector Suitable for Field Measurements (Type F). RL-262\nGeneral Report on Low Level Power Measurement at 10-cm in Coax. RL-279\nA 10-20 Centimeter Bolometer. RL-288\nBridge Methods in Low and Medium Level RF Power Measurement. RL-410\nTest Equipment (Continued)\nPower Measuring (Continued)\nThe Two-Disc DC Thermistor Bridge Circuit. A Littlefuse Direct-Reading Wattmeter. RL-548\nMatching Resistance Curves by Means of Two Linear Ganged Potentiometers and a Three-Terminal Resistance Network. RL-610\nK-Band High Power Water Load. RL-723\nThe Measurement of Thermal Radiation at Micro-wave Frequencies. RL-787\nBroad Band Test Loads. RL-847\nInstructions for Types TWX-5 and TWS-5EV Battery-Operated Wattmeters. RL-M-186A\nInstructions for TBN-3EV Thermistor Bridge.\nInstructions for TBN-6SE Thermistor Bridge.\nHandbook of Operating and Maintenance Instructions for Dummy Load TS-253/ AP, RL-M-216 Receivers An Automatic Noise-Figure Meter. RL-1017 A Trigger Generator for Signal Threshold Studies\n\nSignal Generators Development of Pulsed Signal Generator [Syllabus] Simplified Measurement of Receiver Sensitivities (S-Band Noise Source). RL-443 Revision of General Radio Type 605-B Signal Generator for Pulsing. RL-575 Instructions for TGS-2SE, TGS-3BL and TGS-5BL Signal Generators. RL-M-141 Instructions for TGX-2BL and TGX-3BL Signal Generators. RL-M-143A Instructions for Type TTX-6RH and Type TTX-10RH Test Sets. RL-M-169 Instructions for Types TTX-6(), TTX-9(), TTX- RL-M-169B\n\nHandbook of Operating and Maintenance Instructions for Test Set TS-259 (XR-1) / AP with Supplements on Test Sets TS-259 (XR-2) / AP and TS-259 (XR-3)/AP and Signal Generator TS- Instructions for TGS-6DE Boresighting Signal\nGenerator (Preliminary Model of Test Set TS- TFX-31+RL, TFX-35RL, TFX-36RL: Fixed Frequency Standards. RL-M-207, RL-M-208, RL-M-209\nSpectrum Analyzer\nSpectrum Analyzer (Type 103) for Pulsed Oscillators. Tentative Instruction Manual for M.I.T. Radiation Laboratory Test Set (Type A). RL-M-120\nTentative Operating Instruction for M.I.T. Radiation Laboratory Modified Type 102-A Test Set\nTest Equipment (Continued)\nSpectrum Analyzer (Continued)\nInstruction Manual for Spectrum Analyzer (Type 105) for X Band Pulsed Oscillators and Spectrum Analyzer (Type 107) for S Band Pulsed Oscillators. RL-M-127\nInstructions for Type TSK-1SE Spectrum Analyzer. RL-M-142\nInstructions for TSX-2 Spectrum Analyzer.\nInstructions for TSX-2 and Specifications on TSX-4SE Spectrum Analyzers. RL-M-173B\n4SE and TTS-4SE Spectrum Analyzers. RL-M-173C\nInstructions for Type TSK-5SE Spectrum Analyzer. RL-M-231\nStanding Wave Detectors\nLoss Measurement by Two Probe Reversal Method. RL-344\nStanding Wave Detector. RL-346\nMeasurement of Impedance with the Standing Wave Detector. RL-346\nMatchmeter. RL-705\nNew Type Probe for Coaxial Standing Wave Detectors. RL-835\nThe Development of Metallized-Glass Attenuators for Test Set TS-U7/UP [PIB]. 14-527\nSpecial Report on 30-Mc Pulsed Signal Generator.\nRadio Set RHB, Section IV \u2014 RHB Test Equipment\nDevelopment of Microwave Test Sets. RL-1011\nMicrowave Test Signals. RL-1023\nDesign Proposal for AN/APN-19A Check Set.\nHandbook of Maintenance Instructions for Type TTX-IBL Test Set (Type B). RL-M-133\nInstructions for Type TTX-6RH and Type TTX-10RH Test Sets. RL-M-169\nInstructions for Types TTX-6, TTX-9, TTX-RL-M-169B\nHandbook of Operating and Maintenance Instructions for Test Sets TS-259 (XR-1) /AP, TS-259 (XR-2) /AP and TS-259 (XR-3) /AP and Signal Generator TS- Preliminary Maintenance and Operating Instructions for TS-361/APX-15 Test Set. RL-M-202\nHandbook of Operating and Maintenance Instructions for Test Set TGI-3CA. RL-M-233\nInstructions for TS-16/AP Check Set. RL-M-234\nTube Service Manual for Video Amplifier [U. of Pa]. Klystron and CW Test Sets. RL-139\nDetails of X-Band High Level TR Tube Test Bench. RL-417\nTest Equipment (Continued)\nTube (Continued)\nMeasurement of Pressure in Gas Tubes by a Radio-Frequency Method. RL-432\nTesting of Fixed-Tuned, Low-Q, ATR Tubes. RL-693\nA Proposed Standard Test Cavity for the 707B Tube. RL-693\n3-Cm Magnetron Test Bench Construction and Operation. RL-M-114\nTheory:\nGeneral Electromagnetic Theory: Transmission of Irises in Waveguides [Cornell]\nTheoretical Results on the TR Box [Cornell]\nPerturbation Theory for Cavities [Cornell]\nTheory of the TR Box [Cornell]\nTheory of Thick Inductive Windows with Small Openings [Cornell]\nThe Scattering of Electromagnetic Radiation by a Narrow Rectangular Strip of Infinite Conductivity\nElectromagnetic Theory, Final Report [Cornell]\nSpecial Report: Reflection of Plane Waves by Magnetic Substances. RL-146\nTheory of a \"Black Body\" Produced by a Combination of a Thin Screen and a Perfect Mirror\nTheory of a \"Black Body\" Produced by a Combination of a Thin Screen and a Perfect Mirror, Supplement to RL-148. RL-154\nA Method to Measure High Frequency Permeability of a Ferromagnetic Body. RL-155\nEnergy Loss in Copper under Pulse Conditions. An Extension of Lagrange's Equations to Electromagnetic Field Problems: Equivalent Networks, Part I. A Theoretical Treatment of Radar Target Return, Part I. Calculation of the Resonant Frequencies of a Torus by Lagrangian and Variational Methods, 14-924. Reflections from Curved Surfaces. Reflection of Radiation from Curved Surfaces. A Method for Calculating Magnetron Resonant Frequencies and Modes, RL-1039. An Extension of Lagrange's Equations to Electromagnetic Field Problems: Equivalent Networks, Part II, RL-1046. The Determination of Fields Satisfying Laplace's, Poisson's, and Associated Equations by Flux Plotting, RL-1047. A Flux Plotting Method for Obtaining Fields Satisfying Maxwell's Equations, with Applications to the Magnetron, RL-1048.\n\nPart III. Theory (Continued)\nMiscellaneous.\nA Method of Summing a Slowly Convergent Series: An Electronic Modulator for CW Magnetrons, General Theory of Electronic Beam Modulators, Fourier Integral Methods of Analysis, RL-762-1\n\nA Method of Virtual Displacements for Electrical Systems with Applications to Pulse Transformers, RL-S-49\n\nTables and Methods of Calculation for Line Sources, RL-S-58\n\nSteady-State Vibration of a Two-Spring Mechanical System, RL-S-49\n\nTables of Fourier Transforms of Fourier Series, Power Series, and Polynomials, RL-S-58\n\nShock Mounting and Vibrations, RL-T-16\n\nStatistical Theory, Theory of Random Processes, RL-454\n\nOn the Fluctuations in Signals Returned by Many Independently Moving Scatterers, RL-465\n\nOn the Appearance of the A-Scope When the Pulse Travels Through a Homogeneous Distribution of Scatterers, RL-466\n\nFluctuations in the Return Signals from Random Scatterers, RL-773\n\nDispersion of High-Frequency Radio Waves\nIonized Gases, RL-836, The Theory of Alternating Current Discharges in Gases, RL-967, A Theoretical Treatment of Radar Target Return, Part II, RL-1049, A Procedure for Statistical Analysis of Depth Soundings, RL-S-21, Thermistors (see Test Equipment), Thyratrons (see Tubes), TR and ATR Switches, Theoretical Results on the TR Box [Cornell], 14-116, Theory of the TR Box [Cornell], 14-128, Preliminary Measurements on GE X-Band Transmit-Receiver Gas Switch [BTL], 14-225, The Fixed Tuned Broad-Band Transmitter Disconnect Switch-I, Some Preliminary Considerations, Development of 1B27 TR Tube [Sylvania], 14-315, Government Radar Patent Program - Technical Report No. 4 - Duplexing [MIT], 14-391, Progress Report on Broad-Band Fixed-Tuned TR and Anti-TR Tubes [GE], 14-401, Final Report on Broad-Band TR and Anti-TR Tubes, Final Report on Radar Tube Model Shop [Sylvania].\nReceivers and TR Boxes. RL-102\nReceivers, TR Boxes, Measurements. RL-103\nReport of the Radio Frequency Section. RL-140\nTR and ATR Switches. RL-150\nTransmit-Receive Switch. RL-150\nVarious 3-CM TR Box Characteristics. RL-166\nPreplumbing of Tees for G-Band. RL-238\nComparison of the Frequency Sensitivities of Series and Shunt TR Junctions. RL-247\nMeasurements of 721A TR Tube Leakage Power.\nPre-ignition Transmission through Gas-switching Tubes and its Contribution to Crystal Failures. RL-347\nMeasurement of the Q-Value of a TR Box. RL-349\nDirect Coupling in the TR Box. RL-352\nProgress Reports on TR Tubes. RL-360\nTransmission of Higher Harmonics through a TR Cavity. RL-361\nSome Experiments in Determining the Power Transmission and Recovery Time of TR Boxes. RL-362\nMaximum Allowable Negative Backswing after Transmission.\nPulses RL-363\nDetails of X-Band High Level TR Tube Test Bench\nReport on K-Band Work in U.S.A. RL-475\nChemical Methods for Maintaining the Partial Pressure of Water Vapor in TR Tubes RL-593\nThe 1B27 TR Tube RL-594\nTesting of Fixed-Tuned, Low Q, ATR Tubes RL-611\nA Low Power X-Band RF Gas Switch RL-841\nRecovery Time Measurements in Band-Pass TRs for Various Gases RL-895\nTheoretical Interpretation of Recovery Times of TR Boxes RL-929\nX-Band Bandpass TR Tube RL-970\nS-Band Bandpass TR Tubes RL-971\nNote on a Low Power S-Band Gas Switch RL-979\nMicrowave Technique as of May, 1933 RL-T-13\nGeneral Lecture Series on Radar Components. Tracking\nRadar Angle Tracking, Government Radar Patent Program \u2013 Technical Report No. 1. [NDRC]\nThird General Report on Section Activities Covering Period from May 1, 1941 to Nov. 1, 1941 RL-5\nCircular Sweep Precision Range System Model U: Medium Precision, Self-Synchronous Automatic Range Tracking Circuit. RL-323\nPhotoelectric Automatic Range Tracking Unit. RL-326\nAntiaircraft Artillery Board Test on the Simplified Circular Sweep Range. RL-341\nAutomatic Range and Azimuth Tracking. RL-367\nConical Scanning. RL-367\nData on SCR-584 Control Equipment. RL-370\nAided Tracking, September 17, 1943. RL-430\nAided Tracking, November 4, 1943. RL-452\nAided Tracking, November 3, 1943. RL-453\nTracking (Continued)\nRadar Tracking Analysis. RL-495\nA Condenser Phase Shifter Range Unit with Sine Wave Tracking for AN/TPG-1, AN/FPG-1, SCR- Theoretical Calculation on Best Smoothing of Position Data for Gunnery Prediction. RL-532\nN 2 Gate Attachment for SCR-584. RL-566\nAnalysis of Tracking Data, Description of Calculations. RL-628\nData Smoothing. RL-673\nAnalysis of Over-Water Tracking. RL-695\nAnalysis of the Tracking of the 584 X-Band System.\nTests of Aided Tracking with P3/. RL-797.\nInterference Between SCR-584\u2019s Tracking APN-19 Beacons. RL-816.\nRange and Tracking Accuracy of AN/APG-15B. Analysis of the Tracking Errors of the MK56X System. RL-884.\nThe Angular Alignment of Radar Antennas. RL-950.\nBoresighting the AN/APG-15 Antenna Assembly.\nComputer Mark 14 AN/APA-30 XN-1 Instruction Manual. RL-M-179.\nPreliminary Instructions on Modification Kit MC-627 for Radio Set SCR-584. RL-M-220.\nPreliminary Instructions on Modification Kit MC-627 for Radio Set SCR-584 (Revised). RL-M-220B.\nGeneral Lecture Series on Radar Components. Trainers and Training Material.\nCoordinate Transformation Circuits Using Resolvers and Coordinate Transformation by Means of Electrical Networks [Bartol]. 14-288.\nApparatus for the Transformation of Rectangular Coordinates Using Armaresolvers [Bartol]. 14-293.\nFinal Report on the Supersonic Radar Trainer Project [Bartol] 14-294\nA Portable Signal Generator for Loran Receivers Manual of Operation and Maintenance for SM Radar Trainer [Emerson] 14-370\nFinal Report SM Trainer Development [Emerson]\nFinal Report on the Building of Basic and Advanced SCR-584 Trainers [Fox] Development and Construction of Equation Solvers for GCI and SCI Radar Trainers Technical Report Reviewing the History [Willcox & Gibbs]\nSupersonic Loran Trainer, Final Report [Bartol]\nAI-10 Trainer Simulation at I-F Level RL-397\nAI-10 Bench Trainer Simulation at Video Level\nTrainers and Training Material (Continued)\nRadar Trainer Equation-Solvers for the Relative Motion of Two Moving Objects in Space RL-436\nTraining Apparatus for Radio Set SCR-584 RL-437\nAN/APS-4 (ASH) Trainer RL-446\nFading Simulator RL-556\nQA-2B Servo Adaptor RL-645-1\nQl-2 and Q-3 Servo Amplifier, RL-645-2 H-3 Trigger Unit, RL-645-3 The 1-3 Signal Unit, RL-645-4 The J-2 Modulator Unit, RL-645-5 The H-2 Trigger Unit, RL-645-6 1-2 Signal Unit, RL-645-7 The R-1 and R-2 Crystal Drivers, RL-645-8 The ML-1A, ML-1B, and ML-3A Course Mechanisms, S-2, S-2B, S-3, S-4y S-4B Motor Control Units, The S-5 and S-5B Motor Control Units, RL-645-11 The U-1 and U-2 Preamplifier Units, RL-645-12 X-1 Error Integrator, RL-645-13 N-1 IFF Unit, RL-645-14 A Simple Trainer for GCA Approach Controller, The Trainer for Radio Set AN/MPN-1, RL-676 Tokyo H2X Photographs Comparison of Operational PP1 Photographs with PPI Predictions of the Ultrasonic Radar Trainer, RL-715 Link Conversion Unit for Ground-Controlled Approach Trainer, RL-716 Two Proposed Methods of Recording the Position of a Moving Link Crab, RL-730 AN/APG-T1 Training Equipment, RL-759-1\nAN/APG-15 Modification Kit for AN/APG-15 Training Equipment: RL-759-2\nThe AN/APS-6 Antenna Simulator: RL-839\nA Tracking Error Recorder for the Ground Controlled Approach Trainer: RL-855\nGround Course Computer for AN/APQ-15: RL-856\nNosmo Doppler Simulator: RL-857\nTrainer for Mark 35 Radar: RL-907\nGround Clutter Unit for the Ground Controlled Approach Trainer: RL-927\nThe SP \u201cFeed-In\u201d Trainer: RL-928\nThe Mark VII Supersonic Trainer: RL-962\nA Displacement or Velocity Servo Amplifier: RL-1015\nSupersonic Components for Use in Radar Trainers: RL-1015\nA Supersonic Echo Simulating System for AN/APQ-15: RL-1057\nThe OCJ-1 Trainer: RL-1058\nA Dummy Log Transmitter for the OBJ Radar Trainer: RL-1059\nThe Cadillac Trainer: RL-1072\nPreliminary Handbook of Instructions for H2X Supersonic Trainer, Mark II: RL-M-157A\nPreliminary Handbook of Instructions for H2X Supersonic Trainer: RL-M-157\nPART III: Trainers and Training Material (Continued)\n\nHandbook of Instructions for the Preparation of Maps for the H2X Supersonic Trainer. RL-M-181\nPreliminary Technical Manual for Falcon Trainer. RL-M-160\nLand Mass Simulator\n\nHandbook of Instructions for the Preparation of Mountain Maps for the H2X Supersonic Trainer.\nInstructions for Installation and Maintenance of Waffle Relief Maps in Ultrasonic Trainer.\nHandbook of Maintenance Instructions for AN/APG-15-T1 Trainer. RL-M-221\nUltrasonic Radar Trainer PPI Photographs of a Simulated H2X Bombing Mission over Tokyo\n\nTransformers (see also Pulse Transformers)\nPreliminary Results on Calibration of Auto-Transformers [Cornell]. 14-364\nFinal Report, Transformer Model Shop [Westinghouse]\nTransformer Model Shop, Final Report [Raytheon]\n14-454\nTransformer Model Shop, Final Report [GE]\n14-591\n\nComponents - Design and Measurements (Attenuators, Cables and Connectors, Chokes, Couplings, Directional Couplers, Joints, Transitions, etc.)\nAn Experimental % Inch Universal Stub [PIB]\nX-Band Wave-Guide Tuning Section [PIB]\nDevelopment of a High Impedance Radio Frequency Transmission Line [Federal]\n14-424\nGovernment Radar Patent Program - Technical Report No. 5 - RF Components [NDRC]\nTests on Additional Modified Type \u201cN\u201d Connectors\nFixed Value Metallized-Glass Coaxial Attenuators\nVariable Metallized-Glass Coaxial Attenuators\nThe Development of Metallized-Glass Attenuating\nElements for X-Band Wave Guide [PIB]. 14-525\nMetallized-Glass Wave Guide Attenuators [PIB].\nType \u201cN\u201d Connector Design and Tests [PIB].\nDevelopment of Miscellaneous RF Line Components [PIB].\nPrecision Metallized-Glass Resistor Units [PIB].\n\nTransmission Lines (Continued)\nComponents (Continued)\n\nWaveguide Termination for Measuring Power at RF Components\nList No. 1. RL-151\nTune-up Procedure for 3-Cm RF System. RL-160\nWave Guide Components and Instruments for the 1.25-Cm Region. RL-165\nRear Rectangular Guide Antenna Feed. RL-169\nIllumination and Phases of Antenna Feeds. RL-170\nRound Guide Rear Antenna Feeds. RL-171\nRadiation Resistance of Antennas Inside Wave Guides of Arbitrary Cross Sections. RL-176\nT-Junctions in Rectangular Wave Guides, Part I, Theory. RL-179\nJunctions in Rectangular Wave Guides, Part II, Final Formulas and Curves. RL-180\nReflections from Sections of Tapered Transmission Lines.\nLines and Wave Guides. RL-189 Microwave Wattmeter. RL-239 Rotary Joints with E0 Stub Transformers. RL-243 Microwave Wattmeter II, 3-Cm and 1-Cm. RL-246 Capacity (Choke) Couplings as Rigid and Non-Rigid Waveguide Connectors. RL-255 Some Matching Properties of Antenna Feeds. Information on Corrugated Coaxial Lines and Wave Guides. RL-264 Double Dipole Rectangular Wave Guide Antennas. Antenna Feeds for \"%\" Stub-Supported Coaxial Line. RL-271 Antenna Feeds from Vis\" Coaxial Line. RL-274 General Report on Low-Level Power Measurement at 10-Cm in Coax. RL-279 Standing Wave Detector. RL-344 Elimination of the \u201cTrombone\u201d Between Transmitter and Junction in a Duplexing System. Measurement of Impedance with the Standing Wave Detector. RL-346 Infinite Rejection Filters. RL-364 Microwave Linear Radiators. RL-366 RF Attenuators. Report on Type A and Type B Pulse Transmission.\nCables and Connectors, RL-424, RL-475 - Report on K-Band Work in U.S.A., High Impedance Cable, RL-529, Performance of Couplings for 1Vz-Inch by 3-Inch Waveguide, RL-538, The Sealing of Air at Rotating Shafts and Joints, Vertebrae Type Flexible Waveguide, RL-574, The Use of the Magic Tee Microwave Bridge in Measuring Impedance, RL-643, A Microwave Frequency Discriminator, RL-662, Low Power RF Switch, RL-675, Design Considerations for Directional Couplers, Experiments in Microwave Breakdown, RL-731, Transmission Lines (Continued), Components (Continued), Attenuation of RG-9/U Cable as a Function of Temperature and Frequency in the X-Band, An Improved K-Band Vertebrae Waveguide, Dielectric Phase Shifters for Waveguide, RL-788, Present Status of High Power at S-Band, RL-793, S-Band Coaxial Line to Rectangular Waveguide Transitions, RL-802, A Microwave Band-Pass Filter in Waveguide.\nAn Electronic Frequency Stabilization System for CW Microwave Oscillators. RL-815 Absorption Coefficient of a Styraloy Filled Coaxial Line. RL-827 Three-Centimeter Flexible Waveguide. RL-831 Flexible Waveguides. RL-832 New Type Probe for Coaxial Standing Wave Detectors. RL-835 E0 Rotary Joints for the 3 Centimeter Band. Theory of Directional Couplers. RL-860 Rat Race Duplexing. A Theory of Resonance in Rotary Joints of the TM01 Type. RL-993 Waveguide Motional Joints. RL-1037 Summary of High Power Breakdown Tests on Microwave Components. Instruction Manual for Installation of Radiation Laboratory Type B Plugs on Cables. RL-M-149 Instruction Manual for Installation of Radiation Laboratory Type A Plugs on Cables. Instruction Manual for Installation of Chiksan Tool Company 1%-Inch Revolving Joint (Drawing No. 61DIC) on Radiation Laboratory Types.\nSection I, II, III, IV, and V of the Army-Navy Types RG-27/U Wave Guide Handbook:\n- Section I: B-l and B-2 Cables\n- Section II: Abbreviations in Wave Guides (Oct. 2, 1942)\n- Section III: Obstacles in Wave Guides (Oct. 27, 1942)\n- Section IV: Bends and T-Junctions in Wave Guides (Dec. 4, 1942)\n- Section V: Dielectric Structures in Wave Guides (Feb. 9, 1943)\nRL-T-9: Microwave Technique (May 1943)\nRL-T-13: Discontinuities \u2013 Irises, Obstacles, etc. (for Antenna Arrays, see Antennas)\n- Transmission of Irises in Waveguides [Cornell]\n- Theory of Thick Inductive Windows with Small Openings [Cornell] (14-171)\n- A New Method for the Precision Measurement of Wave Guide Discontinuities [CIT] (14-317)\n- Precision Measurement of Wave Guide Discontinuities [CIT] (14-460)\n- A New and Practical Method for Matching Two Obstacles in a Wave Guide [CIT] (14-461)\n- Theory of Diffraction by Small Holes. (RL-128)\nLosses and Reflections Introduced by Joints and Plungers in 3-Cm Wave Guides. RL-164 Transmission Lines (Continued)\nDiscontinuities (Continued)\nSusceptance of Asymmetrically Located Windows in Rectangular Wave Guides. RL-183\nLumped Constants for Small Irises. RL-194\nCoupling Between Inductive Windows in Wave Guides. RL-197\nTheory of Side Windows in Wave Guides. RL-199\nExcitation of Cavities through Windows. RL-202\nTheory of Obstacles in Resonant Cavities and Wave Guides. RL-205\nTheory of Circular Bends in Rectangular Wave Guides. RL-206\nOne-Sided Inductive Irises and Quarter-Wave Capacitive Transformers in Waveguide. RL-426\nProbe-Fed Slots as Radiating Elements in Linear Arrays. RL-455\nDielectric Windows in Waveguide. RL-587\nDiscontinuities in Standing Wave Detectors and Waveguide Junction Steps. RL-893\nThe Interaction of Discontinuities on a Transmission Line. RL-930\nSection I, Wave Guides, Sept. 24, 1942\nSection II, Abbreviations in Wave Guides, Oct. 2, 1942\nSection III, Obstacles in Wave Guides, Oct. 27, 1942\nSection IV, Bends and T-Junctions in Wave Guides, Dec. 4, 1942\nSection V, Dielectric Structures in Wave Guides, Feb. 9, 1943\nRL-T-9, Microwave Technique, May, 1943\nRL-T-13, General Considerations (Theory, Measurements, Matching, Lines in General, Coax, Waveguides, Special Lines.)\nA New Method for the Precision Measurement of Wave Guide Discontinuities [Cal. Inst, of Tech.]\nInfluence of Inner Wave Guide Dimensions on Broad-Band Performance of Calibrated Attenuators\nTuning the RF Components of a System (Lawson Technique)\nRL-11, Impedance in Transmission Lines and Wave Guides\nRL-116, Microwave Transmission\nReport on Junction Effects in Wave Guides.\nReport of the Radio Frequency Section. RL-140 Design and Test of Concentric Transmission Lines. Tentative Simplified Explanation of the Lawson Lines. RL-142 Special Report on Design Data for 50-Ohm Rigid Coaxial Line. RL-147 Tests on Undercut Beads in a Concentric Line. Tune-up Procedure for 3-cm R-F System. RL-160 Matching, Losses, and Frequency Sensitivity of a 3-cm R-F System. RL-161 Polarization Effects in a Circular Wave Guide.\n\nPart III Transmission Lines (Continued) General Considerations (Continued) Propagation in Wave Guides Partly Filled with Dielectric. RL-174 Reflections from Sections of Tapered Transmission Lines and Wave Guides. RL-189 Formal Theory of Wave Guides of Arbitrary Cross Section. RL-198 Transmission Line Construction Details. RL-231 Stub Supports in Coaxial Lines. RL-232 Phase Distortion in Broad-Band Stub Supports.\nPreplumbing of Tees for G-Band, RL-238\nLoss Measurement by Two Probe Reversal Method, RL-238\nDielectric Transmission Measurements, RL-244\nA Method of Measuring the S-Band Characteristic Impedance of Coaxial Cable, RL-252\nInformation on Corrugated Coaxial Lines and Wave Guides, RL-264\nA Video Delay Line, RL-302\nRF Attenuators, RL-404\nRadome Bulletin Number 7, The Measurement of High Reflections at Low Power, RL-483-7\nRadome Bulletin Number 9, The Matching of High Standing Wave Ratios, RL-483-9\nRadome Bulletin Number 10, The Measurement of Small Reflections, RL-483-10\nRadome Bulletin Number 17, Current Progress on RF Research, RL-483-17\nThe Theory of Corrugated Transmission Lines and Waveguides, RL-494\nCorners, Bends, and Twists in Rectangular Waveguide, RL-585\nWaveguides without Metal Walls, RL-726\nA Method of Shielding for Filter Insertion Loss Measurements, RL-786\nConductivity Loss Measurements at K-Band, Walworth Waveguide Bends. RL-S-3 X-Band Waveguide Corrosion Proofing. RL-S-29 Transmission Lines and Wave Guides: Similarities and Differences. RL-T-5 Explanation of Impedance Matching. Wave Guide Handbook, Section I, Sept. 24, 1942; Section II, Abbreviations in Wave Guides, Oct. 2, 1942; Section III, Obstacles in Wave Guides, Oct. 27, 1942; Section IV, Bends and T-Junctions in Wave Guides, Dec. 4, 1942; Section V, Dielectric Structures in Wave Guides, Feb. 9, 1943. RL-T-9 Theory of Impedance and Admittance Diagrams and Allied Subjects. RL-T-10 Reflection Coefficients and Impedance Charts. Microwave Technique as of May, 1943. RL-T-13 Use and Derivation of A, Z, 0 Charts. RL-T-14 Introduction to Alternating Currents, Q Values, and Transmission Lines. RL-T-17 General Lecture Series on Radar Components.\nTransmit-Receive Switches (TR and ATR Switches)\nTriodes (see Tubes, Cathode Ray Tubes, Cathodes, Magnatrons)\nTropicalization, Weather-Proofing, etc.\nMoisture-Proofing of Button Mica Capacitors.\nX-Band Waveguide Corrosion Proofing. RL-S-29\nTubes (see also Cathode Ray Tubes, Cathodes, Magnatrons, and TR and ATR Switches)\nDiodes\nS/N Measurements on CV-58. RL-416\nA Survey of High-Vacuum Diodes Used for Surge-Limiting Operation in Modulators. RL-580\nThe Temperature-Limited Diode. RL-761\nHigh Voltage Oxide Coated Vacuum Rectifiers.\nEngineering Operations of the Project Tube Shop [RCA]\nDevelopment of 1B27 TR Tube [Sylvania]. 14-315\nLocal Oscillators (see also Triodes and Velocity-Modulated Tubes)\nFinal Report on K-Band Oscillator, Type A5022A\nSpecial Report on 30-Mc Pulsed Signal Generator.\nA 1-Cm Oscillator. RL-111\nCommittee on Centimeter Receiving Tubes and Resonators. RL-286\nNoise from Local Oscillators. RL-304\nAn Electronic Frequency Stabilization System for CW Microwave Oscillators. RL-815\nMiscellaneous: Fine Grid Technique. RL-299\nMeasurement of Pressure in Gas Tubes by a Radio Frequency Method. RL-432\nClamping Tubes. RL-572\nReceiving Tubes\nThree Centimeter Receiving Tubes [BTL-WE].\nCommittee on Centimeter Receiving Tubes and Resonators. RL-286\nThe Radiation Laboratory S-Band Amplifier.\nPulse Characteristics of Common Receiver-Type Tubes. RL-704\nSpark Gaps\nReport on Pulser Tube Development [West. E. & Report on Enclosed Pressure Gaps [West. E. & M.].\nHigh Power Series Gaps, Progress Report, Sept. 5, 1944 [BTL-WE].\nHigh Power Series Gaps, Bi-Monthly Report for January and February 1945 [BTL-WE]. 14-414\nHigh Power Series Gaps, Bi-Monthly Report for March and April 1945 [BTL]. 14-438\nTubes (Continued)\nHigh-Power Series Gaps: Bi-Monthly Report, July 14-488\n\n* High-Power Series Gaps with Sintered Iron Sponge-Mercury Cathodes [BTL-WE]\n* Double-Triggering and Voltage Balancing for Series Gaps [BL-R-929-2G-12, Westinghouse]\n* Development of Series Spark Gaps: Final Report\n* Dissipation in Series Gaps and Voltage-Current Relationships during Discharge. RL-682-1\n* Division of Voltage Across Series Spark Gaps in a Line Type Modulator. RL-682-2\n* General Characteristics of Enclosed Spark Gaps with Emphasis on Aluminum Cathode-Type\n* Series Gaps. RL-682-3\n* Some Characteristics of the IB 41, IB 45, and IB 49 Series Spark Gaps. RL-682-4\n* Operation of Sintered Iron Sponge-Mercury Cathode Type Series Gaps at SCI, AEW, and 5 Microsecond Conditions. RL-682-5\n* Three Electrode Triggered Gap. RL-880\n* Stabilization\n* Magnetron Stabilizing Tuner. RL-473\nInfluences of Pulse Transformer Design on 4J Magnetron Stability. RL-622\nAn Electronic Frequency Stabilization System for CW Microwave Oscillators. RL-815\nA Method of Rating the Stability of Oscillators for An Improved Frequency Stabilization System for Microwave Oscillators. RL-837\nWide Range Tunable Stabilizer. RL-964\nCombined RE or -Cavity Automatic Frequency Control for Thermally Tuned Reflex Oscillator Tubes. RL-1034\n\nTheory\nSpace Charge between Parallel Plane Grids. A Qualitative Analysis of Hysteresis in Reflex Oscillators. RL-650\nNotes on the Reflex Oscillator. RL-709\nOperation and Testing of Reflex Oscillators. An Electronic Modulator for CW Magnetrons.\nGeneral Theory of Electronic Beam Modulators. The Temperature-Limited Diode. RL-761\nElectronic Tuning of Reflex Oscillators. RL-774\nStatic Frequency Modulation Characteristics of the Reflex Klystron. RL-781\nCharacteristics of Preproduction 2K45 Tubes, Notes on Space-Charge-Limited Oscillators and Amplifiers at Microwave Frequencies, Theory of Noise from the Reflex Oscillator, RL-873 Tubes (Continued), Thyratrons, Pulse Thyratrons, Progress Report for June \u2014, Progress Report on Hydrogen-Filled Thyratrons, Report on Developmental Work on Pulse Thyratron, Final Report on Pulse Thyratrons (Apr. 10, 1943), Development and Production of Tube Type H50 Hydrogen Thyratron, Final Report on Radar Tube Model Shop, Measurement of Pressure in Gas Tubes by a Radio Frequency Method, RL-432, Summary of Life-Test Data on Sylvania 4C35 Hydrogen Thyratrons, RL-589, Trigger Requirements of the 4C35 and 3C45 Hydrogen Thyratrons, RL-605, Metallic Hydride Studies, RL-813, Technical Data and Operating Notes for the 5C22 Hydrogen Thyratron, RL-828, Summary of the Life Test Program on 3C45.\n4C35, 5C22, RL-865 Hydrogen Thyratrons in Pulse Generator Circuits. RL-953\nInstruction Manual for Model 7 A Hydrogen Thyratron Modulator. RL-M-145\nTriodes, including Lighthouse Triodes. Development of the SB-811, SB-811B and SB-846 Triodes for Pulsed and CW Operation at Micro-wave Frequencies [Sylvania]. 14-590\nThe Resnatron Ultra-high Frequency Oscillator, September, 1940 to June 30, 1942, Progress Report and Final Report [U. of Cal.]. 14-593\nReport on Tests of RCA and GE \u201cLighthouse\u201d Tubes. RL-286\nPerformance of the GL446 Lighthouse Tube as an RF Amplifier in the 10-20 cm Region.\nLighthouse Tube Anode Contacts. RL-292\nMeasurements on 446 \u201cLighthouse\u201d Tubes. RL-413\nLighthouse Tube Transmitter-Receiver LHTR\nLighthouse Tube Superregenerative Receivers.\nLighthouse RF Envelope Indicator. RL-542\nRieke Diagrams and Probe-Plate Plunger Charts of Lighthouse Tubes in a Re-entrant Cavity. G.E. GL2C40 Taut-Grid Lighthouse Tubes. Operational Characteristics of 2C43 Tubes as Pulsed Oscillators in a Re-entrant Cavity. SB-846B S-Band Oscillator. RL-954\n\nPart III\n\nTubes (Continued)\n\nVelocity-Modulated Tubes, (including Klystrons and McNally Tubes). Operating Characteristics of the 707 A Reflex Oscillator. RL-233\n\nOperating Characteristics of the 707 A Reflex Oscillator, Supplement to RL-233. RL-234\n\nOperating Characteristics of the 1*17 Reflex Klystron. RL-235\n\nTemperature-Compensated 707 A (McNally Tube). Operating Characteristics of the J/.19 Klystron. Characteristics and Present Production of McNally Tubes. RL-303\n\nMeasurement of Electrical Tuning Ranges of 707 Tubes. RL-421\n\nCharacteristics of Recent 723 A Tubes (X-Band Local Oscillators). RL-427\n\nCharacteristics of Recent 723 AIR Tubes. RL-570\nA Qualitative Analysis of Hysteresis in Reflex Oscillators. RL-650\nA Proposed Standard Test Cavity for the 707B Tube. RL-693\nFrequency Discontinuities of Local Oscillator Tubes Due to High-Q Load Circuits. RL-694\nNotes on the Reflex Oscillator. RL-709 (Tubes Continued)\nNotes on Load Effects in Reflex Oscillators.\nOperation and Testing of Reflex Oscillators.\nLow-Voltage K-Band Oscillator. RL-764\nElectronic Tuning of Reflex Oscillators. RL-774\nStatic Frequency-Modulation Characteristics of the Reflex Klystron. RL-781\nMeasurements on Noise from Reflex Oscillators. RL-873\nTheory of Noise from a Reflex Oscillator. RL-873\nEffect of the Tuning Plunger on Operation of 2K33 Type Tubes. RL-942\nElectron Optical Studies of the 2K33 Tube.\nOperating Instructions for the Model A17 Klystron for Use as a Local Oscillator in Radar Receivers. RL-M-108\nNotes on the Power Output of 723A Tubes. RL-S-7\nPART IV\nDIVISION 14 REPORTS\nBartol Research Foundation (The Franklin Institute)\nBell Telephone Laboratories (Western Electric Company)\nBrown University\nAbridged Report on Circuits for Improving Focus on Electrostatic Cathode-Ray Tubes under Conditions of Intensity and Deflection Modulation. 14-132\nCathode-Ray Tube Detectors. 14-376\nCalifornia Institute of Technology\nA New Method for the Precision Measurement of Waveguide Discontinuities. 14-317\nPrecision Measurement of Waveguide Discontinuities.\nA New and Practical Method for Matching Two Obstacles in a Waveguide. 14-461\nUniversity of California\nMechanical Vacuum Switches, Transmission Line and RC Pulsing Circuits. 14-156\nThe Resnatron Ultrahigh-Frequency Oscillator, June\nThe Theory of Dark-Trace Tubes I, 14-131\nThe Theory of Dark-Trace Tubes II, 14-172\nDarkening and Bleaching of KCl, 14-177\nTwo Notes on the Potentials Developed in Cathode-Ray Screens during Bombardment, 14-178\nMemorandum on the May 194.3 Meeting on Dark-Trace Tubes at Radiation Laboratory, 14-183\nA Memorandum on the Scattering of Light by DT Screens, 14-198\nDarkening and Bleaching of KCl II, the Effect of Temperature, 14-205\nMemorandum upon the Behavior of DT Screens Containing Magnesium, 14-214\nExperiments with Double-Layer DT Screens, 14-253\nThe Theory of Dark-Trace Tubes III, 14-257\nThe Depth of the Darkened Region and the Build-Up of Darkening and Persistent Trace in KCl Screens, 14-265\nThe Theory of Dark-Trace Tubes IV, 14-265\nAging of KCl Crystals and Screens under Electron Bombardment, 14-302\nThe Properties of Evaporated Layers of Potassium Chloride Containing Small Additions of Metallic Elements when Subjected to Electron Bombardment\nCarnegie Institution of Washington, Investigations to Prepare a Transparent Phosphor\nChrysler Corporation, Radar Scanning Unit\nRadar Nutating Antenna Spiral Scanning Units, Balance and Adjustment. (14-566)\nColorado, University of, Development of a Stable Noncrystal Controlled Oscillator (14-573)\nColumbia University, Radiation Laboratory, One-Cm Magnetron Research (14-120)\nKnurled Type Cathode \u2014 Construction and Life Test. Progress Report on the Development of One- and Three-Cm Magnetrons (14-223)\nThe Elimination of Extraneous Resonance Effects in Tunable Cm Magnetrons (14-233)\nThe Tuning Properties of the Tunable Magnetrons in the Three-Cm Band (14-234)\nCold Impedance of E5 Tubes (14-235)\nColumbia Radiation Laboratory Progress Report.\nWaveguide Output for 1.25-cm Magnetrons. \"Columbia Radiation Laboratory Progress Report, 14-245, Equivalent Circuit for Resonant Modes of a Magnetron, Zero Mode.\" The Resonant Modes of the 'Rising Sun' (A Tube) Magnetrons for Production of Centimeter Wave-length Radiation and Absorption of Such Radiation in Water Vapor. 14-322. Rising Sun Magnetron with Large Number of Anode Cavities for Centimeter and Millimeter Wave-length Memory. Range-Tracking Circuit with Velocity Memory. \"Theory of Signal-to-Noise Ratio of Crystal Mixers.\" Theory of Thick Inductive Windows with Small Openings. 14-171. Transmission of Irises in Waveguides. Theoretical Results on the T-R Box. Perturbation Theory of Cavities. Theory of the T-R Box. Analysis of 6SA7 Gated Amplifier. Analysis of Double-Triode Integrator.\nPart IY, Cornell University\n\nOn the Distribution of the Average Noise Current in Receivers. (14-305)\nDevice for Determination of the Vertical by Means of Cosmic Rays. (14-363)\nPreliminary Results on Calibration of Autotransformers. (14-364)\nElectronic Computers for Division, Multiplication, Squaring, etc. (VAC-4). (14-435)\nA Mechanical Integrating System Incorporating a Magnetic Amplifier (MA-2). (14-436)\nUse of a Specially Designed Magnetic Amplifier in Computing Circuits. (14-437)\nElectromagnetic Theory. (14-466)\nD-C Resolvers (DCR-2). (14-512)\nAC Potential Equalizers and Phase Sensitive Detectors. (14-537)\nConstancy of EMF\u2019s of Dry Batteries (Bl). (14-538)\nInvestigation of Circuits of Use in Precision Radar Computers. (14-546)\n\nDalmo Victor, Inc.\nAIA-1 Scanner Development Program Progress Report: September 1 to November 1, 1944\n- Douglas Aircraft Company: Design and Test of Project Eagle Airfoil (14-290)\n- Du Mont Laboratories: The Spectral Distribution of the Luminescence of Red Screen Materials (14-269)\n- Final Technical Report for P3I Adaptor (Instruction Book for Precision PPI Adaptor, Du Mont Type No. 255)\n- Indicator-Tracker Unit BC Cathode-Ray Screen Tube Development (14-509), Du Pont De Nemours and Company, E. I., Inc.\n- Progress Report on Special Protective Coatings (Sintering or Melting of Boron Powder, Progress Report, December)\n- Sintered Boron Project, Progress Report (December)\n[Sintered Boron Project, Progress Report, January 1, 1944.\nSintering and Melting of Boron Powder, Progress Report, February \nSpecial Protective Coatings, Progress Report, September \nProgress Report on Sintering and Melting of Du Pont De Nemours (Continued)\nMonthly Summary and Informal Monthly Progress Report on Protective Coatings, March 14, 1944.\nProgress Report on Sintering and Melting of Boron, Monthly Summary and Informal Monthly Progress Report on Protective Coatings, April 14, 1944.\nProgress Report on Sintering or Melting of Boron, Monthly and Informal Monthly Progress Report on Special Protective Coatings, May 13, 1944. 14-273\nSpecial Protective Coatings, Progress Report, June\nProgress Report on Sintering or Melting of Boron, Special Protective Coatings, Progress Report, July\nSintering or Melting of Boron Powder, July 1, 1944.]\n[Special Protective Coatings, August 11, 1944]\nProgress Report on Sintering or Melting of Boron\nProgress Report on Sintering or Melting of Boron and Preparation of Hyperpure Germanium\n[September]\nProgress Report on Sintering or Melting of Boron and Preparation of Hyperpure Germanium\n[October]\nThe Preparation of Sambo Films \u201cScheme A\u201d\nSurvey of Binder (Use A), Special Protective Coatings II\nFormulation Studies, Composition Variables\nSpecial Protective Coatings III, Formulation Studies\nPhysical Processing Variables\nSpecial Protective Coatings IV, Pigment Evaluation Studies\nSpecial Protective Coatings V, Film Thickness Evaluation\nSpecial Protective Coatings VI, Cross-Knifed Films for Practical Work at MIT.\n[Special Protective Coatings VII, Knife Casting on Semiworks Wheels. 14-350, Special Protective Coatings VIII, Large Scale Coating Trials Investigation of Fabric Coating Equipment, Special Protective Coatings IX, Spray Trials for Scheme, Special Protective Coatings X, Development of Cement- and Paint-Making Procedure for Scheme, Special Protective Coatings XI, Development of Machine-Spraying Process for Scheme A. 14-354, Special Protective Coatings XII, Characterization of Metal Flakes. 14-355, Du Pont De Nemours, Special Protective Coatings XIII, Preparation of Film Calendering. 14-356, Special Protective Coatings, Methods of Analysis for Aluminum Film and Its Ingredients. 14-357, Special Protective Coatings, Monthly Summary, No Sintering or Melting of Boron and Preparation of Hyperpure Germanium, Progress Report, November, Special Protective Coatings, Monthly Summary, December]\n[Part I, Sintering and Melting of Boron, Part II, Preparation of Hyperpure Geranium, Monthly Summary]\nSpecial Protective Coatings (February 1, 1955)\nSpecial Protective Coatings (March 1, 1955)\nSpecial Protective Coatings (June 1, 1955)\nMonthly Summary, Coatings, XV, Semiworks-Scale Preparation of Machine-Sprayed Film (November)\nSpecial Protective Coatings, XIV, Formulation Studies, Exploratory Work for New Uses (14-469)\nSpecial Protective Coatings, XVII, Laboratory Study of Adhesive Systems (14-470)\n[Special Protective Coatings, August 13, Informal Monthly Progress Report, XXV, Final Report, \"Use B\" Film Adjustment, 14-547, Semiworks-Scale Preparation of Machine-Sprayed Films, 14-548, Practical Applications Trials (Use A), 14-549, Practical Applications Trials, Laboratory Study of Adhesives, 14-551, Formulation Development Studies, 14-551, Preparation of Films by Hot Pressing, 14-552, Du Pont De Nemours, Semiworks-Scale Preparation of Machine-Sprayed Films, 14-553, Process Development]\nEmerson Radio and Phonograph Corporation: Development of a Power Supply and Temperature Stabilized Oscillator for the Battery Operated Lodar Receiver (14-554)\nEmerson Radio and Phonograph Corporation: Manual of Operation and Maintenance for SM Radar Trainer (14-370)\nFinal Report SM Trainer Development (14-371)\nFairchild Camera and Instrument Corporation: Reports of Tests on Resonant Range Follow-Up\nFairchild Camera and Instrument Corporation: The Fairchild Central Station Computer (Part I)\nFairchild Camera and Instrument Corporation: The Fairchild .50 Caliber M2 Computer and AGS Adaptations for an Emerson Tail Turret; Part II (14-433)\nFairchild Camera and Instrument Corporation: Advanced Design for Radar Photography (14-503)\nFederal Telephone and Radio Corporation: Development of a High-Impedance Radio-Frequency Transmission Line (14-424)\nThe Foxboro Company: Final Report on the Building of Basic SCR-58h Trainer and Advanced SCR-58h Trainer (14-372)\nThe Franklin Institute (Bartol Research Foundation)\nCrystal Clock Project, Third Progress Report, May 1943: Magnetron Cathode Studies, Progress Report, May 1943: Magnetron Cathode Studies, Progress Report, July 1, 1943: Crystal Clock Project and 10-Kc Oscillator, Progress Report, October 1, 1943: 14-193\n\nMagnetron Cathode Studies, Progress Report, September 1943: Crystal Clock Project and 10-Kc L-C Oscillator, Progress Report, January 1, 1944: 14-226\n\nMagnetron Cathode Studies, Progress Report, January 1944: General Dynamical Considerations Applied to Piezo-Electric Oscillations of a Quartz Crystal in an Electrical Circuit. 14-271\n\nSupplement to General Dynamical Considerations Applied to Piezo-Electric Oscillations of a Quartz Crystal in an Electrical Circuit. 14-271S\nCoordinate Transformation Circuits Using Resolvers and Coordinate Transformation by Means of Electrical Networks. (14-288)\nApparatus for the Transformation of Rectangular Coordinates Using Arm-Resolvers. (14-293)\nFinal Report on the Supersonic Radar Trainer\nPART IV\n\nThe Franklin Institute (Continued)\nCathode Sparking, Effect of Super-Imposed DC and Role of Coating Resistance. (14-295)\nSparking of Oxide-Coated Cathodes. (14-296)\nBack-Bombardment of Magnetron Cathodes. (14-309)\nSecondary Electron Emission from Oxide-Coated Magnetron Cathodes. (14-310)\nSupersonic Loran Trainer. (14-446)\nCathode Coating Resistance as Measured by Embedded Probes. (14-514)\nSecondary Electron Emission from Oxide-Coated Cathodes. (14-515)\nSparking Phenomena in High Vacuum Thermionic Sintered Thoria Cathodes. (14-517)\nEffect of Particle Size. (14-518)\nPurification of Barium and Strontium Carbonates.\nA Note on Nitrocellulose Binders (14-520)\nMagnetron Cathode Studies, Final Report, October (14-557)\nGeneral Dynamical Considerations Applied to Piezo-Electric Oscillations of Quartz Crystal in Electrical Circuit, Supplement II. (14-557)\nGalvin Manufacturing Corporation\nDevelopment Work on AN/PPN-2 Radio Set (14-434)\nDevelopment and Production Samples of APG Series (AN/APG-5 and AN/APG-8) Radar Equipment [including] Manuscript Handbook of Maintenance Instructions for Radio Sets AN/APG-5 and AN/APG-5A and Tests Conducted at Northwestern University under Galvin Manufacturing Corporation subcontract. (14-569)\nGeneral Electric Company\nPulse Thyratrons, Progress Report for June, 1941, to Two-Megawatt Transmitters for NDRC Project (14-104)\nReport of Work on Duplex-Screen Tubes during 1941 (14-104)\nProgress Report on Hydrogen-Filled Thyratrons.\nReport on Developmental Work on Pulse Thyratron, Report of Progress of Work on Dark-Trace Tubes, Airborne Loran Equipment, Two Motor-Driven Gun Turrets, Development and Construction of a Local Turret Gyro Lead-Computing Sight for AGS Radar, The AGL Receiver, K-Band Germanium Crystals - Bimonthly Progress Report (October 5, 19[---], 14-328), K-Band Germanium Crystals - Bimonthly Progress Report (December 15, 19[---], 14-381), Final Technical Report on AGL-1 [Fire Control] Development, General Electric Company - Progress Report on Broad-Band Fixed-Tuned TR and Anti-TR Gas Switching Tubes (December 22, 19[---], 14-406), Precision Aircraft Scanners, Final Report on Pulse Thyratrons (April 10, 19[---], 14-410), APG-1 Tracking and Firing Tests (Data Folder No.\nK-Band Germanium Crystals, Final Report, March 3000-Mc Receiver Using Velocity Modulation Tubes Type ZP-U39. Development of Gunfire Control System, Mark 56. Components of CXHR (SCI) Equipment. RASD Stable Element. 14-507 2CH1A1 (AGL-1) Aircraft Fire Control Computer. Transformer Model Shop, Final Report, April 23, Broad-Band TR Tube Development. Georgia Institute of Technology. Development and Use of the Microband Lock-In Amplifier. 14-592 Gilfillan Brothers, Inc. Radio Set AN/MPN-1 (XE-1), Ground Controlled Approach (GCA) Radar, Technical Report. 14-449 International Business Machines Corporation. Special Mechanical Counter for the Mark III or Phase-Shift Loran Indicator. 14-368 International Projector Corporation. Design of Egg Beater Scanning Antenna for the Eagle Radar Bombsight and Construction of a Model. Final Report. 14-312 Kansas State College.\nInstantaneous Voltage Measurement by Use of a Trigger Circuit: Final Technical Report, Kuthe Laboratories, Inc. (14-409)\n\nDevelopment and Production of Tube Type H50 Hydrogen Thyratron: 14-536, Leland Electric Company\n\nDevelopment of Three-Phase Aircraft Alternator: Librascope, Inc.\n\nFinal Report for Contract OEMsr-10UU:\n- Part 1: History of the Contract and Patent Disclosures\n- Part 2: Triangle Solver for Eagle Project (Delta)\n- Part 3: Triangle Solvers for H2X Bombing Project (Alpha)\n- Part U: Triangle Solver for Laboratory Use (Gamma)\n- Part 5: Redesign of Triangle Solver for Eagle Project (Beta)\n- Part 6: Preliminary Ballistics Computer for a Gun Director System (Eta)\n- Part 7: Ballistic Computer Mark U%, Mod 0 (RHO)\n- Final Report of Development Work Done on High-Power S-Band Magnetron (HP-10V) and Series, Machlett Laboratories, Inc.\nFinal Report on H2K Roll-Stabilized Scanner, Maguire Industries, Inc.\nProgress Report on Ultrahigh-Frequency Dielectrics, Massachusetts Institute of Technology, Report I, Laboratory for Insulation Research\nThe Interaction Between Electromagnetic Fields and Dielectric Materials, Massachusetts Institute of Technology, Report II, Laboratory for Insulation Research\nMeasurement of Dielectric Constant and Loss with Standing Waves in Coaxial Wave Guides, Massachusetts Institute of Technology, Report III, Laboratory for Insulation Research\nAuxiliary Equipment for the MIT Coax Instrument and Its Use, Massachusetts Institute of Technology, Report IV, Laboratory for Insulation Research\nTables of Dielectric Materials (Volume I), Massachusetts Institute of Technology, Report V, Laboratory for Insulation Research\nReport VI, Laboratory for Insulation Research: The Polystyrene Plastics as High-Frequency Dielectrics\nFinal Report: Including the Design of Stroking Motor for a Hydraulic Servomechanism, Servomechanisms, Maguire Industries, Inc.\nReport VII: High Dielectric Constant Ceramics, Laboratory for Insulation Research\nReport VIII: Tables of Dielectric Materials (Volume II), Laboratory for Insulation Research\nReport IX: Techniques and Calculations Used in Dielectric Measurements on Shorted Lines, Laboratory for Insulation Research\nReport X: Low Thermal Expansion Plastics, Laboratory for Insulation Research\nReport XI: Titania Ceramics II, Laboratory for Insulation Research\nReport XII: Design of Equipment for Measurement of Dielectric Constant and Loss with Standing Waves in Waveguides, Laboratory for Insulation Research\nReport XIII: An Apparatus for Determining Heat-Distortion Characteristics of Plastics, Laboratory for Insulation Research\nReport XIV: Preliminary Oscillograph Studies of RF Build-up in Magnetrons, Laboratory for Insulation Research\nDevelopment and Wide-Frequency Investigation of Dielectrics, Report XV, Laboratory for Insulation Research, 14-544, University of Michigan\n\nRotational Line Width in the Absorption Spectrum of Atmospheric Water Vapor, October 10, 1913 + and Supplement (dated February 1, 1915), 14-320, National Defense Research Committee\n\nTechnical Report of Radiation Laboratory, June 1, 1942: Use of Microwave for Detection Purposes\n\nUse of Microwave for Detection Purposes, December 1942, National Defense Research Committee\n\nUse of Microwave for Detection Purposes, August 1943, National Defense Research Committee\n\nUse of Microwave for Detection Purposes, Bimonthly, National Defense Research Committee\n\nUse of Microwave for Detection Purposes, Bimonthly, National Defense Research Committee\n\nUse of Microwave for Detection Purposes, Bimonthly, National Defense Research Committee\n\nIndicator Types as of October 1912, 14-114\n\nSummary of Projects, Bimonthly Report, January 1, 1912\n\nSummary of Projects, Bimonthly Report, March 1, 1912\n\nComputers for Radar Control of Plane-to-Plane Gunfire, [Unknown]\nInvestigation of Power-Supply Requirements as a Function of Future Radar Circuit Developments\nPower Supply for Airborne Radar Equipment. (14-135)\nAnalysis of Commutation of Direct-Current Machines at High Altitudes, November 1912. (14-136)\nSimulated High-Altitude Brush-Testing Equipment. (14-138)\nClearance for Carbon Brush Investigation. (14-138)\nAnalysis of Commutation of Direct-Current Machines at High Altitudes, April 1913. (14-139)\nSummary of Projects, Bimonthly Report, May 1, 1913. (14-157)\nX-Ray Emission from Radar Equipment. (14-157)\nBimonthly Project Status Report and Summary of Projects, September 1, 1913. (14-184)\nProject List, Division 11, as of September 15, 1913. (14-184)\nBimonthly Project Status Report and Summary of Division 11 Projects, November 1, 1913. (14-213)\nProject Report, Division 11, February 1, 1914. (14-242)\nProject Report, Division 11, April 1, 1914. (14-242)\nRadiation Laboratory Reports, May 1, 1915. 14-250\nDivision 11 Contract List. 14-270\nProject Report, Division 11, June 1, 1915. 14-277\nProject Report, Division 11, July 1, 1915. 14-278 (Supplement to above report)\nProject Report, Division 11, August 1, 1915. 14-301\nRadar Angle Tracking, Government Radar Patent Program \u2013 Technical Report No. 1. 14-319\nU.S. Radar Survey, Section 1, Airborne Radar.\nU.S. Radar Survey, Section 2, Shipborne Radar.\nU.S. Radar Survey, Section 3, Ground Radar.\nU.S. Radar Survey, Section 1*, Navigational Radar.\n\nPart IV\nNational Defense Research Committee (Continued)\nU.S. Radar Survey, Section 6, Test Equipment.\nProject Report, Division 14, October 1, 1944. 14-338\nGovernment Radar Patent Program, Technical Report No. 2 \u2013 Precise Range Measurement and Tracking. 14-339\nProject Report, Division 14, December 1, 1944. 14-373\n[Government Radar Patent Program Technical Report No. 3, Magnetrons. 14-384\nProject Report, Division 14, Supplement, January 1, 1945\n\nGovernment Radar Patent Program Technical Report No. 4, Duplexing. 14-391\nProject Report, February 1, 1945. 14-400\n\nGovernment Radar Patent Program Technical Report No. 6, Fundamental Radar Systems. 14-417\nProject Report, Division 14, April 1, 1945. 14-420\n\nGovernment Radar Patent Program Technical Report No. 5, R-F Components. 14-430\nProject Report, Division 14, June 1, 1945. 14-440\n\nU.S. Radar Survey Section 3, Ground Radar,\nU.S. Radar Survey Section 4, Navigational Radar,\nProject Report, Division 14, Supplement, July 1, 1945\n\nU.S. Radar Survey Section 6, Test Equipment,\nProject Report, Division 14, August 1, 1945. 14-489\nProject Report, Division 14, December 1945. 14-565\n\nU.S. Radar Survey Section 8, Airborne Radar,]\nRadiation Laboratory Reports, First Supplement, Pennsylvania, University\nService Manual for Video Amplifier 14-97\nThe Principles of Crystal Rectifiers 14-102\nThe Electrical Conductivity of Silicon and Germanium Compounds 14-112\nDC Burnout Temperature in Silicon Rectifiers\nFurther DC Burn-Out Experiments on Silicon and Germanium Rectifiers 14-119\nElectron Microscopy of Tungsten Points 14-125\nNoise in Crystal Rectifiers 14-126\nSpectroscopic Determination of Aluminum in Silicon\nBarrier Capacity in Silicon Cartridge Rectifiers\nHigh-Frequency Rectification Efficiency of Crystals\nEffect of Etch on Crystal Rectifiers 14-165\nCapacity in Crystal Rectifiers 14-166\nIonization of Donator Levels in Crystal Rectifiers by Thermal Agitation 14-173\nRadioactive Detection of Aluminum in Silicon 14-180\nEffect of Tapping on Barrier Capacity, Behavior of Silicon Crystals at Low-Level Powers, Behavior of Westinghouse Silicon as a Low-Level Detector, Noise in Silicon Rectifiers at Low Temperatures, Dependence of IF Impedance and Noise-Temperature of Crystal Rectifiers on Matching Conditions, Comparison of Wedge and Cone Contacts on Fox Silicon, A Device for the Selection and Manufacture of Low-Level Detectors, Analysis of Silicon for Nonvolatile Matter, Recent Research on Silicon Rectifiers, Noise Spectrum of Silicon Rectifiers, Audio Noise Tester, X-Band Video Crystals, Production and Effects of a Depletion Layer in Doped Silicon, Effect of Heat Treatment on Low-Level Performance, Temperature Variation of Low-Level Crystal Performance, Note on the Measurement of Noise-Temperature.\nEvaporated Films of Germanium and Silicon, Effect of Small Crystallites on Conductivity, Crystal Audio Noise, Photoeffects in Pure Silicon, Burnout of X-Band Video Crystals, High-Back Voltage Silicon, X-Band Crystal Video Performance with Bias, Development Research on X-Band Video Crystals, Double Valued Characteristics of Crystal Rectifiers, Comments, Temperature Effects of S-Band Video Crystals, Mass Spectrometer Investigation of the Silicon Tetra-chloride Used in Making Pure Silicon, Tests on German Crystals, Burnout Life Tests of X-Band Video Crystals, Use of Different Fillers in Crystal Rectifiers, Research and Development of Crystal Rectifiers, Final Report.\nGeometrical Structure of Silicon Surfaces (14-563)\nBurnout of S-Band Video Crystals (14-564)\nFinal Report on High-Frequency Video Amplifier and Radar Ranging System (14-564)\nPhilco Corporation\nFinal Report of Research and Development on Lighthouse Tube Transmitter-Receiver\nPolytechnic Institute of Brooklyn\nJunction Effect of Two Unequal Matched Coaxial Coaxial Exponential Tapers (14-164)\nProgress Report on Coaxial Platinum Film Attenuator (14-216)\nTheory of Coaxial Attenuators (14-216)\nSoldering to Glass (14-217)\nInstructions for Use of PIB Type 1B2 Bolometer Terminal (14-218)\nNotes on Use of Bolometers for Ultrahigh-Frequency Attenuation Measurements (14-219)\nThe 1B2 Bolometer Terminal (14-220)\nAn Experimental %-Inch Universal Stub (14-221)\nX-Band Wave-Guide Tuning Section (14-222)\nMetallized-Glass Attenuators and Miscellaneous RF Test Accessories (14-360)\nErrors in Attenuation Measurement Caused by Reflection Losses\nNotes on the Accurate Measurement of Small Attenuations at Microwaves\nTests on Additional Modified Type \u201cN\u201d Connectors\nInfluence of Inner Waveguide Dimensions on Broad-Band Performance of Calibrated Attenuators\nUse of Sauerisen for Cementing Metallized-Glass Resistor Plates, Preliminary Report\nA Method of Summing a Slowly Convergent Series\nX-Band Slotted Section Test Equipment\nFrequency Sensitivity of Metallized-Glass Attenuator Inserts Type TMS-4PB\nModifications Pertaining to Specifications for Glass Parts of PIB Type V-3 Variable Attenuator\nMetallized-Glass Plate Program at PIB Research Conference\nAccuracy of Attenuation Measurements Made with the Ballantine Voltmeter\nMicrowave Resistance Comparator\nFrequency Sensitivity of Metallized-Glass Attenuators\nThe TMX-1J+PB: Metallized-Glass Plate for Variable X-Band Attenuator, maximum 25 db (14-482)\nThe TMX-16PB: Metallized-Glass Plate for X-Band Fixed Attenuator, 25 db (14-483)\nThe TMX-24PB: Metallized-Glass Plate for X-Band Fixed Attenuator Pads of 10 db and 13 db (14-485)\nA Resistive Variable Attenuator for K-Band with 40 db Maximum Attenuation (14-486)\nElectrical Performance of Metallized-Glass Attenuators for TS-147/UP in Extended X-Band (14-487)\nPrecision Metallization of Glass (14-521)\nFixed Value Metallized Glass Coaxial Attenuators\nVariable Metallized-Glass Coaxial Attenuators\nMetallized-Glass Bolometers (14-524)\nThe Development of Metallized-Glass Attenuating Elements for X-Band Waveguide (14-525)\nMetallized-Glass Waveguide Attenuators (14-526)\nThe Development of Metallized-Glass Attenuators for Test Set TS-H7/UP (14-527)\nRF Components for Microwave Bridges, 14-528\nMicrowave Power Measurement with Bolometers\nType \u201cN\u201d Connector Design and Tests, 14-530\nMicrowave Attenuation Standards, 14-531\nMicrowave Attenuation Measurement, 14-532\nDevelopment of Miscellaneous RF Line Components, 14-534\nPrecision Metallized-Glass Resistor Units, 14-534\nMicrowave Radar Field and Laboratory Test Equipment and Components, 14-535\nInvestigation of Crystal Rectifier DC Characteristics, 14-129\nThe Diffusion Theory of Crystal Rectifiers, 14-129\nTheory of Noise in Conductors, Semiconductors, and Crystal Rectifiers, 14-133\nDetermination of Logarithmic Constants of Crystal Rectifiers with the Oscilloscope, 14-143\nMeasurement of Conversion Gain with a Modulated Oscillator, 14-144\nCrystal Noise as a Function of DC Bias and 30 MC Impedance Measured with a Diode Noise Source, 14-144\nTheory of Contact Rectifiers, 14-168\nThe Theory of Crystal Mixers in Terms of Measurable Mixer Constants. (14-259)\nHigh-Frequency Characteristics of Rectifiers. (14-284)\nQuantitative Spectroscopic Analysis of Impurities in Germanium and Silicon. (14-285)\nTheory of Small Deviations from Pure Diode Behavior.\nPreparation of High-Voltage Germanium Crystals. (14-342)\nThe High-Voltage Germanium Rectifier, Section I, Experimental. (14-375)\nThe High-Voltage Germanium Rectifier, Section II, Theoretical. (14-413)\nProperties of Germanium High-Back Voltage Rectifier Units. (14-416)\nDependence of Performance of Germanium Second Detector Units on Bias and Video Load. (14-575)\nThe Scattering of Electromagnetic Radiation by a Narrow Rectangular Strip of Infinite Conductivity.\nPART IV\n\nProduction and Performance of Germanium High Back Voltage High Back Resistance Crystals\nPurdue University\n\nDependence of Noise Temperature DC and IF Crystal Conductance on Matching Conditions. (14-578)\nTemperature Dependence of High Voltage Germanium Rectifier DC Characteristics. (14-579)\nPhotoelectric Effects in Germanium. (14-580)\nDependence of Forward Conductance and Back Resistance of High-Back Voltage Germanium on Voltage and Frequency. (14-581)\nCrystal Capacity as a Function of Bias and Its Relation to the Theory of Crystal Rectification. (14-584)\nFinal Report on Crystal Developments for Radar Receivers. (14-585)\n\nRadio Corporation of America, National Broadcasting Company\nReport of Radio Relaying of Radar Signals. (14-243)\nRadio Corporation of America, RCA Victor Division\nAircraft Position-Indicating Equipment (Receiving)\nSummary of Research on Radar Indicator Screens: Noise Reduction by Delayed Feed-Back (14-146)\nPropagation of Signals on 1.51, 1.71, and 2.800 Me from Empire State Building to Hauppauge and Riverhead (14-179)\nDescriptive Technical Specification \u2014 Fighter Tail-Warning Equipment, AN/APS-13 (XAl) (14-185)\nLightweight X-Band Radar, Progress Report No. 1 (14-185)\nLodar Pulse-Direction-Finding Receiver (14-200)\nCharacteristics of Simplified Loran Receiving Equipment (14-228)\nDevelopment of a Tail-Warning Radar System (14-208)\nOperations of the Project Tube Shop\nHarrison, Dark-Trace Radar Indicator Screens, Progress Report (14-201)\nA Portable Signal Generator for Loran Receivers (14-222)\nPropagation of Signals on 1.51, 1.71, and 2.800 Me from Empire State Building to Hauppauge and Riverhead.\nA Converter for 170-Kc Loran Signals (14-298)\nMica Windows for Waveguide Output Magnetrons (14-329)\nWaveguide Output Magnetrons Employing Fused Quartz Output Transformers (14-367)\nSkiatron Projection Cathode-Ray Tubes with Dark-Trace P10 Screens (14-369)\nFinal Report on K-Band Oscillator, Type A5022A (14-396)\nBUPX Antenna, Type A (14-396)\nFrequency Stabilization of Oscillators by a Method Particularly Adapted to the Higher Frequencies and Magnetron Sources (14-397)\nFinal Report on Ultraportable Racon (BUPX) (14-397)\nFinal Report on Tubes for Lightweight X-Band Radar and Ultraportable X-Band Beacon (14-415)\nK-Band Magnetron, Technical Report (14-444)\nAn Improved Type of LF Loran Transmitter (14-458)\nAn Exciter for LF Loran Transmitter (14-459)\nDevelopment of a Power-Output Tube for NDRC Microwave Section Project No. 3 (14-471)\n[Final Report for the Skiatron Cathode-Ray Tube for Projection Indicator, 14-492\nResearch and Development of New and Improved Radar Indicators: Text and Figures, 14-500\nOperations of the Project Tube Shop, 14-500\nMethod of Measurement and Performance Characteristics of P11+ Screens: A Note on Manufacturer's Specifications for Tubes Containing Shoran, AN/Raytheon Manufacturing Company, 14-501\nOperating Characteristics of Multivibrators and Gates, Progress Report No. 1, January 6, 1913, 14-154\nOperating Characteristics of Multivibrators and Gates, Performance and Stability of Triggered Gates, 14-155\nRadar Model Shop, Final Report, December 31, 1915, Sperry Gyroscope Company]\nThe Sperry Stabilized Aircraft Gunlaying System (AGL-2), Intermediate Phase. Sperry Products, Inc.\nMotor Torpedo Boat Computing Radar Sight for Blind, Semiblind and Visual Fire. Sylvania Electric Products, Inc.\nDevelopment of a Tunable IF Amplifier. Development of Pulsed Signal Generator. Development of 1B27 TR Tube. Preparation of Exponential Decay Powders and Screens ZnF2:Mn, ZnMgF2:Mn and MgSiO3.Mn. Hermetic Seal Collared Wafer Development. Aircraft Radar Equipment, Handbook of Maintenance Instructions for Army-Navy Model RT- Development and Production of 50 K Band RF Heads, Army-Navy Model RT-63/APS, British Model Radar Tube Model Shop. Sylvania Electric Products, Inc. (Continued)\nDevelopment of SB-811, SB-81 IB and SB-84.6 Triodes for Pulsed and CW Operation at Microwave Frequencies. Stevens Institute of Technology.\nDevelopment of Electrical Brushes through Powdered Metallurgy, Technical Report of Research Conducted at Metal Powder Laboratory, November 14-447, Utah Radio Products\n\nPulse Transformers. \"The Propagation of 10-Cm Waves on a 52-Mile Optical Path over Land.\" \"The Correlation of Signal Patterns with Radiosonde Data.\" 14-151\nRadiotelephone Communication on 3,000 Me. 14-152\n\"The Captive Radiosonde and Wired Sonde Techniques for Detailed Low-Level Meteorological Sounding.\" Propagation of 10-Cm Waves Over an Inland Lake Correlated with Meteorological Sounding. 14-212\n\nWestern Electric Company, Bell Telephone Laboratories\nWestern Electric D-160448 Input Equipment and Western Electric X-61901 Oscilloscope. 14-87\nInstruction Book for Western Electric D-161131 Receiver and Western Electric D-161132 Indicator.\nThe Investigation of the Effect of Manufacturing and Test Equipment Variables on X-Band Characteristics of Bell System Thermistors, November 26, 1943\nThe Investigation of the Effect of Manufacturing and Test Equipment Variables on X-Band Characteristics of Bell System Thermistors, January [--]\nThe Fixed Tuned Broad-Band Transmitter Disconnect Switch, Some Preliminary Considerations, [--]\nThe Investigation of the Effect of Manufacturing and Test Equipment Variables on X-Band Characteristics of Bell System Thermistors, May 27,\nHigh-Power Series Gaps, Progress Report, September [--]\nHigh-Power Series Gaps, Bimonthly Report, November [--]\nInterim Report No. 1, November 21, 1945: Development of High-Back-Voltage Germanium Rectifiers (High-Power Series Gaps)\nInterim Report No. 2, January 15, 1945: Germanium Crystal Rectifier for Radar Receivers and Indicator Circuits (Western Electric Company)\nFinal Report on Broad-Band TR and Anti-TR Tubes (High-Power Series Gaps)\nFinal Report on the Development of Magnetron Generators of High-Power and of Short Wavelengths (High-Power Series Gaps)\nBimonthly Report, March: Germanium Crystal Rectifier for Radar Receivers and Indicator Circuits\nInterim Report No. 3, March 1945: Magnetrons and Detector, Beat-Oscillator Receivers\nRecord of Material Furnished. 14-450\n\nInterim Report on the Investigation of the Effect of Manufacturing and Test Equipment Variables on the X-Band Characteristics of Bell System Thermistors (June 19, 1945)\nReport on X- and K-Band Characteristics of Bell System Thermistors and High-Power Series Gaps (July 9, 1945)\nHigh-Power Series Gaps with Sintered Iron Sponge Mercury Cathodes (October 1, 1945)\nHeat Treatment of Germanium Rectifier Materials (Interim Report No. 4, August 3, 1945)\nPreparation of High Back-Voltage Germanium Rectifiers (Westinghouse Electric and Manufacturing Co., Project No. 14-88)\nReport on Pulser Tube Development (May 15, 1942)\nReport on Enclosed Pressure Gaps (December 31, 1945)\nTechnical Report on K-Band Magnetron (May 22, 1945)\nDevelopment of Series Spark Gaps (Final Report, Transformer Model Shop, December [?])\nDouble-Triggering and Voltage Balancing for Series Spark Gaps (No date or location provided)\nPART V\n\nLaboratory Reports\n\nAbbenhouse, R. P. \"Performance Characteristics of Army-Navy Preferred Type Electrostatic Cathode-\" (Performance characteristics of Army-Navy preferred type electrostatic cathode)\nDescription and Operation of the General Purpose Variable Delay Unit, Mar. 26, 1946. RL-891\n\nOperating Instructions for Sweep Calibrator, Abbenhouse, et al. Operating Instructions for the Model G Synchronizer, Mar. 15, 1945. RL-M-195A\nOperating Instructions for Radiation Laboratory Model 5 Synchroscope, July 26, 1945. RL-M-212\n\nOperating Instructions for Sweep Calibrator Model A, Abbiati, May 29, 1944.\n\nAhern, C. R., et al. \"A Voltage Compensated Delay Multiplier\"\nButterfly  Moving  Vehicle  Detector  AN  /  APS-26, \nAlexander,  R.  M.,  see  Ramsey,  N.  F.,  et  al.  RL-24 \n3-Cm  System  Group  Report,  July  5,  1941.  RL-25 \nFlight  Tests  of  Block  I  Relay  Radar  System,  Apr. \nBeacon  Tests  with  AN / APS-6,  June  2,  1944. \nFlight  Tests  on  AN  /  APS-6  A,  Nov.  30, \nAlley,  R.  E.  Jr.,  see  Keary,  T.  J.  RL-266 \nAllis,  W.  P.  Theory  of  the  Magnetron  Oscillator,  Oct. \nTheory  of  Space-Charge  in  an  Oscillating  Magne\u00ac \nAllred,  C.  M.,  et  al.  Off -Frequency  C-W  Jamming ,  Mar. \nAlvarez,  L.  W.  Report  of  the  System  Group,  Jan.  30, \nMicrowave  Linear  Radiators,  July  31,  1942. \nAmes,  L,  A.,  et  al.  Instructions  for  Modifying  the \nSCR-58J*  Modulator  for  Use  in  Aspen  Transmitters, \nAndrew,  M.  M.,  et  al.  Radar  Camouflage,  July  16,  1945. \nArenberg,  D.  L.  Supersonic  Solid  Delay  Lines,  Apr.  30, \nArnold,  R.  D.  A  Method  of  Compensating  the  Fre\u00ac \nW. Aron, \"Dependence of Attenuation in a Supersonic Waveguide,\" Jan. 18, 1946.\nF. M. Ashbrook et al., \"Some General Microwave Anti-Jam Design Considerations and Performance of a Special Receiver,\" [Publication details missing].\nR. M. Ashby et al., \"Corner-Reflector Modulation of Airplane Radar Signals,\" [Publication details missing].\nAustin et al., \"Qualitative Survey of Meteorological Factors Affecting Microwave Propagation,\" June [Publication year missing].\nAustin et al., \"Tables of Fourier Transforms of Fourier Series, Power Series, and Polynomials,\" Aug. [Publication year missing].\nR. C. Babish, \"[Publication title missing], see D. R. Bagley, RL-S-66.\"\nR. F. Bacher, \"[Publication title missing], see W. B. Nottingham, RL-309.\"\nSignal-to-Noise Measurements on Receivers, Sept. [Publication year missing].\nD. Bagley, \"Regular Report on the Components Test of the Fairchild Radar,\" [Publication details missing].\nD. G. Bagley et al., \"Type Test of the Fairchild Radar,\" [Publication details missing].\nBailey, E.M., \"The Angular Alignment of Radar\" (RL-66), October 30, 1945.\nBailey, F., \"Characteristics of the Present Production of McNally Tubes\" (RL-303), June 3, 1943.\nBailey, F.S., \"Characteristics of Recent 723A Tubes (X-Band Local Oscillators)\" (RL-427), September 4, 1943.\net al., \"Characteristics of Recent 723A/B Tubes\" (RL-), September 4, 1943.\net al., \"Characteristics of Preproduction 2KU6 Tubes\" (RL-), Bailey, H.H., \"Statistics of Beacon Interrogation\" (RL-1054), April 8, 1946.\nBainbridge, K.T., \"Interim Report of the Problems and Activities of Group G\" (RL-30), January 12, 1942.\n\"Considerations Affecting Choice of Wavelength\" (RL-), Bales, P.D., \"Test Set for Raytheon Service Modulation\" (RL-75), see Gaffney, F.J.\net al., \"Preliminary Report on the Fluctuations of Radar Signals\" (RL-569), May 16, 1944.\nBalmer, R.F., see Larson, R.W. (RL-378)\nBalsbaugh, J. C., et al. Moisture-Proofing of Button Mica Capacitors (July 31, 1945). RL-790\nBaltzer, O. J., et al. Overwater Observations at X and S Frequencies on Surface Targets (July 26, 1943). RL-537\nAndrew, M. M. RL-766\nBanks, F. See Hagler, D. L. RL-M-210\nBanos, A. Jr. Theory of Ringing Time of Tunable Echo Design of an Improved X-Band Echo Box (Dec. 7, 1945). RL-811\nBarker, C. B., et al. Streamlined Microwave Omni-Directional Antennas (Jan. 8, 1946). RL-871\net al. Reflections from Curved Surfaces (Feb. 1, 1945). RL-538\nBarry, F. N. Three-Tone PPI (Mar. 20, 1946). RL-934\nBartelink, E. H. B., et al. Bombing Errors, Overland Falcon (Feb. 16, 1945). RL-647\nAN/APG-13B, Vulture. Div. 14-323.2-M12\n\nLetters Discussing ASP-25 and Related Ideas concerning Ash. Div. 14-323.2-M14\n\nBaur, H. W. Relay Data Including Shock and Vibration Measurements. August 1, 1945. RL-747\n\nBeers, D. S., et al. Electronic Tuning of Reflex Oscillators. See Bailey, H. H. RL-821\n\nBeers, Y. A. 30-Mc Sobering Bridge. May 12, 1943.\n\nNoise from Local Oscillators. June 8, 1943. RL-304. See Breazeale, W. M. RL-294\n\net al. The Effect on Noise Figure of Placing the Gain Control on the First I-F Stage. March 9, 1944.\n\nA 60-Mc Parallel Sobering Bridge. April 22, 1944.\n\nReceiver Noise Figures and Their Measurement,\n\nBekkar, H. B. Preliminary Technical Manual for SCR-58h MTI Modification Kit No. MC-6A2-AS and Fan Beam Search Antenna. June 1, 1945. RL-M-218\n\nBell, P. R., Jr., see Ashbrook, F. M. RL-S-8\n\nBender, R. S., et al. An Aerial Investigation of K-Band\nA. E. Benfield et al. \"On the Theory and Performance of Liquid Delay Lines.\" RL-792, Aug. 31, 1945.\nS. D. Bennett et al. \"Video Stretching as a Method for Improving X-Band Beacon Reception.\" RL-604, Aug. 31, 1944.\nPreliminary Report on Single Aircraft Target PPI Photographs from AEW. July 5, 1945.\nS. D. Bennett. \"Supplementary Report on Aircraft Target Ranges.\"\nA. E. Bent. \"Radar Echoes from Atmospheric Phenomena in Relation to Microwave Radar Propagation in Panama.\" RL-476, Feb. 25, 1944.\nRadar Echoes from Precipitation Layers. Aug. 20, [Unknown Year].\nR. S. Bender et al. \"Effects of Clouds and Rain on K-Band Airborne Radar.\" RL-729.\nA. Berg. \"Low-Level Crystal Detectors.\" Mar. 16, [Unknown Year].\n\nR. Kelner. \"Radar Echoes from Atmospheric Phenomena\" RL-338. (Instead of A. Berg)\nR. V. Pound. \"Berger, R.\" RL-238. (Instead of R. Berger)\nCrystal Detectors and the Crystal-Video Receiver, \"The Absorption of One-half Centimeter Electromagnetic Waves in Oxygen\" (Jan. 26, 1945 RL-684) - Dicke, R. H. (RL-1002)\nBerman, E. \"Low-Level Crystal Detectors: Effect of...\" (Feb. 26, 1946)\nBest, R. L. et al. \"Improved RF System for the Transmitter-Receiver Unit of the APQ-13\" (Apr. 15, 1946)\nBethe, H. A. \"Theory of Diffraction by Small Holes\"\n\"Theory of High Frequency Rectification by Silicon\"\n\"Theory of the Boundary Layer of Crystal Rectifiers\"\nLumped Constants for Small Irises (Mar. 24, 1943)\n\"Formal Theory of Wave Guides of Arbitrary Cross Section\"\n\"Theory of Side Windows in Wave Guides\"\n\"Excitation of Cavities through Windows\"\nBettler, P. C. \"Model 6 Modulator Performance Tests\" (Jan. 31, 1946)\n\"Modulator for AN/TPS-10 Radar\"\nInstruction Manual for Model 6-B (MEW) Modulator\nInstruction manual for Model 6 Modulator, Feb.\nBirchard, B. L. S-Band End-Fire Array Antenna, July\nPreliminary Maintenance and Operating Instructions for the TS-36U/ APX-15 Test Set, Apr. 4, 1945.\nBlackburn, J. F., et al. Tests of Aided Tracking with PUL (Photographic Projection PPI)\nMEW No. 1 Preliminary Instruction Book, Mar.\nMEW No. 2 Preliminary Instruction Book, Mar.\nMEW No. 3 Preliminary Instruction Book, Mar.\nInstruction handbook for Radar Set AN/CPS-1A (Pre-production Sets), May 15, 1944. RL-M-156D\nBlaisdell, D. (see Bailey, F.) RL-427\nBleaney, B. Report on K-Band Work in U.S.A., Oct.\nBlue, R. W., et al. Vertical Coverage of a 5-Ft x 35-Ft Antenna Designed for SG-3 (Experimental Data Obtained with an SNB Aircraft as Target), Dec.\nAnti-aircraft Target Designation Equipment.\nRange and Altitude Coverages of Shipborne Microwave Search Radars, July 2, 1945. RL-741\nA Discussion of Plotting Devices for PPI's, Apr.\nBlythe, R.H. et al. Colloquium on Pulse-Forming Networks.\nBoas, M. Preflight Check of Radio Set AN/APQ-7, June 15,\nBogert, B.P. et al. History of AN/APG-5, ARO.\nBohnert, J.L. SU-2 Antenna. Shipborne Stabilized Radar Antenna for Sea Search, Mar. 7, 1945. RL-659\net al. SU-2 Antenna. Line-of-Sight Stabilization of a Radar Beam by Reflector Tilt, Feb. 19, 1945.\net al. Stabilized SG-3 Antenna, Feb. 7, 1945.\net al. Airborne Early Warning Search Antenna,\nCindy Antenna. A High Resolution K-Band Radar Antenna for Sea Search, Nov. 1, 1945. RL-849\nT. W. Bonner, Some Factors Governing the Range of Al Sets (May 3, 1944)\nV. Bostick, Radar Bombing Techniques (Apr. 30, 1946)\nW. H. Bostick, Peak Currents from Carbonized Thoriated Tungsten Cathodes (Mar. 20, 1942) (RL-73)\nReport on Some Tubes Used in Hard Tube Modular Pulse Transformers (June 1, 1943) (RL-217)\nOscilloscope Presentation of Hysteresis Loops at 60 Cycles and under Pulse Conditions (June 1, 1943)\nW. H. Bostick, Test Equipment for Pulse Transformers (June 1, 1943)\nA 10-20-Centimeter Bolometer (Aug. 26, 1942)\nNoise Measurements on Microwave Converters\nPerformance of the GLUU6 Lighthouse Tube as an RF Amplifier in the 10-20-cm Region (Oct. 5, 1942)\nUse of Temperature-Limited Diode in Measurements of Noise Figures of Crystals (Feb. 27, 1943) (RL-295)\n\nNotes on Measurement of Noise, Gain and Noise Figure of Converters (Jan. 30, 1943) (RL-295)\nLeakage Inductance and Distributed Capacitance of Various Types of Pulse Transformer Windings, Pulse Transformer Core Material Measurements, Effect on Current Pulse of Resistance in Series with the Magnetron (Feb 21, 1944. RL-527)\nThe Evaluation of an Equivalent Circuit for a Pulse Transformer (May 8, 1944. RL-545)\nAnalysis of the Influence of Pulse Transformers on Current Pulse Shape (June 16, 1944. RL-546)\nEnergy Loss in Copper under Pulse Conditions\nPulse Transformer Committee Standard Test Methods for Pulse Transformer Cores (May 5, 1945)\nBothwell, F. E., et al. Data Smoothing (Jan. 23, 1945)\nSee Dillinger, J. R. RL-682-2\net al. A Theoretical Treatment of Radar Target Equivalent Network for the 232-BW Pulse Transformer Based on the Method of Virtual Displacement et al. Analysis of a Half-Wave Rectifier Circuit Involving Inductance, Resistance, and Capacitance.\nA Method for Calculating Magnetron Resonant Frequencies and Modes, Feb. 8, 1946. RL-1039\nThe Effect of Small Changes in Circuit Parameters on the Solution of Network Problems, Jan. 14, 1946. RL-1039\nBoyd, C. D. Analysis of the Tracking of the 58U X-Band System, June 12, 1945. RL-753\nSee Phillips. RL-884\nBrady, J. J. Antenna Catalogue, Oct. 8, 1945. RL-S-64\nBraunlich, A. Half Beacon Antenna, Sept. 6, 1943.\nBrean, J. W., et al. The Manual Plotting System RC-\nBreen, S. 3 cm Bolometer Detector Suitable for Field Measurements (Type Y), Dec. 11, 1942. RL-262\net al. Antenna Feeds for Vs\" Stub-Supported Coaxial Lines, [Unknown Date].\n\nA. A. Bright, et al. A Production Analysis of the Wartime Radio and Radar Industry, Nov. 1, 1944.\nL. Brillouin. Theory of the Split Anode Magnetron, [Unknown Date].\nA. H. Brown. Radar R-F Test Points, Dec. 15, 1945.\nThe So-called Standard Target, Mar. 10, 1945.\nP. F. Brown, \"A/R Range Scope,\" RL-335, June 29, 1945.\nG. E. Brunette, \"Preliminary Instructions on Modification Kit MC-627 for Radio Set SCR-58A,\" May 1, 1945 (Revised, Nov. 28, 1945).\nRL-M-220B.\nL. Buchwalter et al., \"LRASV (AN/APA-2) Antenna,\" Rotating Corrugated Eccentric Line Antenna.\nJ. G. Buck et al., \"Cathodes for Pulsed Magnetrons,\" Part I, Correlations Between Oscillating and Diode Cathodes; Part II, Construction and Performance of Pulsed Cathodes. A. S. Eisenstein, RL-933.\nJ. H. Buck, \"Beacon Discrimination Circuit,\" RL-29.\nC. T. Burner, \"Range and Tracking Accuracy of AN/,\" RL-651.\nR. H. Burgoyne, \"Nomograms for Computation of Modifications for Ocean Surface,\" Feb. 16, 1945.\nC. Butt, \"Effects of Line and Cathode-Follower Terminations on Pulse Shape,\" September 11, 1944. RL-616\nW.M. Cady, \"The Balancing of Spiral-Scan Spinners,\" Search Scans and System Performance, August 9, 1944. RL-614\nNomograms for Radar Bombing with the 100-lb Practice Bomb MS8A2, August 29, 1944. RL-614\nW.C. Caldwell, \"Stable Scanners and Unsteady Airplanes,\" February 21,\nThe AN/APQ-13 (60\") Scanner in B-29, January,\nW. Caldwell, \"X-Band Bandpass TR Tube,\" January 22, 1945. RL-371\nE.J. Campbell, \"Analysis of Firing Tests on Mark 51,\" Dam Neck, Virginia. RL-495\nRadar Tracking Analysis, February 5, 1944. RL-495\nAnalysis of Over-Water Tracking, February 12, 1945.\nB.C. Carlson, et al., \"Alignment Procedure for Cadillac Airborne Synchro System,\" June 28, 1945. RL-M-226\nJ.F. Carlson and S.A. Goudsmit, \"Microwave Radar Reflections,\" RL-195\nW.R. Carmody, \"Preliminary Handbook of Instructions\"\n[Handbook of Instructions for the Preparation of Maps for the H2X Supersonic Trainer, September 30, Preliminary Handbook of Instructions for the Supersonic Trainer, AN/APQ-7-T1 (Eagle Trainer), June, Handbook of Instructions for the Preparation of Mountain Maps for the H2X Supersonic Trainer, Preliminary Description of the MK 56 Gun Fire Control System, Dec. 15, 1945, RL-M-242, Caswell, A. E. Handbook of Instructions for Radio Set AN/APA-9 (Pre-production Sets) (Complete Edition), February 1944, RL-M-148C, Preliminary Handbook of Instructions for H2X Supersonic Trainer, Mark II, April 1944, RL-M-157A, Handbook of Maintenance Instructions for CXGQ, Preliminary Technical Manual for AEW, Dec. 4, Theory of Operation of AEW Circuits, Apr. 15, Handbook of Maintenance Instructions for AN/Cefola, et al. An Application of the Pulse Technology in Radar]\n\nThis text appears to be a list of various handbooks and manuals related to the H2X Supersonic Trainer and other related equipment, with publication dates and references to specific documents. There is no unreadable or meaningless content, and no modern editor information or translations are necessary. Therefore, the text can be output as is.\nJ. Certaine, \"Beam Shaping,\" Mar. 30, 1946, RL-963\nR. Chaloff et al., \"Design Proposal for AN/APN-,\" May 12, 1943, RL-319\nB. Chance, \"Precision Timing Calibrator and Range Measuring System,\" July 6, 1943, RL-319\nMedium Precision Self-Synchronous Range Circuit, July 6, 1943, RL-326\nCircular-Sweep Precision Range System, Sept. 10, 1942, RL-326\nAntiaircraft Artillery Board Test on the Simplified Circular-Sweep Range, Dec. 1, 1942, RL-326\nHand Radar Ranging Circuit, Jan. 8, 1943, RL-327\nModel II Calibrator, Apr. 1, 1943, RL-333\nDelayed Sweep for SCR-582-X, June 11, 1943, RL-334\nC. R. Ahern, RL-334\nA. M. Grass, RL-324\nG. Hite, RL-329\nA. B. Jacobsen, RL-341\nR. Kelner, RL-338\nE. F., Jr. MacNickol, RL-323\nH. J. Reed, RL-342\nH. J. Reed, RL-343\nSpecial Report on Bolometer Blind LandingSys Precision Delay Multivibrator for Range Measurement Chance, B. (Continued) Ground Position Indicator for Radar Navigation and Bombing, June 2, 1944. RL-S-19\n\nChisholm, E. B., et al. K-Band Linear Array, Jan. 31,\n\nChu, L. J. Transmission Through Dielectric, Dec. 11,\nTheory of Radiation from Paraboloidal Reflectors,\nRadiation Resistance of Antennas Inside Waveguides of Arbitrary Cross Sections, July 3, 1942.\nSee Frank, N. H. RL-179\nSee Stratton, J. A. RL-123\net al. T-Junctions in Rectangular Waveguides, Part II, Final Formulas and Curves, July 19, 1942.\net al. A Simplified Search Antenna for Radio Set\n\nChubb, C. F., Jr. Final Report on SMTR (January\nBoresighting the AN/APG-15 Antenna Assembly.\nClapp, RE, \"Probe-Fed Slots as Radiating Elements in Linear Arrays,\" Jan. 25, 1944. RL-455\nClark, M, \"Theoretical and Experimental Study of Radar,\" see Reed, J. RL-255\nClarke, HF et al., \"Summary of High-Power Breakdown Tests on Microwave Components,\" Jan. 10, 1946. RL-1071\nClogston, AM, \"Japanese Microwave Radar,\" Aug. 26,\nClose, RN, \"An H + B Impact Predicting Computer,\" Assuming Constant Indicated Airspeed for Use with\nCoffin, FP, \"see Jacobsen, AB. RL-341\"\nSee Bothwell, FE. RL-673\nCohen, MJ, Synchroscope Handbook (Model SYN-\nThe SP \u201cFeed-In\u201d Trainer, Apr. 10, 1946. RL-928\net al., \"Various 3-Cm TR Box Characteristics,\" Jan.\nLighthouse Tube Anode Contacts, Jan. 19, 1943.\nMeasurements on 446 \u201cLighthouse\u201d Tubes, Aug.\net al., Lighthouse R-F Envelope Indicator, Apr. 7,\nCole, PA (Continued)\nG.E. GL2C40 \"Taut\" Grid Lighthouse Tubes, Nov.\net al. A Proposed Standard Test Cavity for the Collins, G.B. Note on Design of Magnetrons, Feb. 9,\net al. Special Report of Characteristics of 3-CM Magnetrons and Instructions for Their Operation,\net al. Guide to the Operation of 10-CM Standard Magnetrons, Oct. 20, 1941. RL-86\nConnelly, C.M., Lt. J.B. Higley. The ML-1A, ML-1B, and ML-3A Course Mechanisms, Nov. 28, 1945.\nCook, J.E., J.E. Richardson. S-Band Tunable System,\nCoomes, E.A.\nBuck, J.G. RL-609, RL-683\nMemorandum on the Activation of Various Surfaces by Evaporation from a Heated Oxide Cathode, Mar. 30, 1946. RL-933\nCork. Maximum Power Limitations of Silicon Crystals,\nTransmission of Higher Harmonics through a TR, Some Experiments in Determining the Power Transmission and Recovery Time of TR Boxes, Jan.\nShielding of Microwave Receivers against Interference at Intermediate Frequencies (August 8, 1944)\nD. R. Corson (see Havens, B. L.) RL-35\nV. A. Counter (see Baltzer, O. J.) RL-401\nReduction of the Effects of Ground Clutter on SCR-720 (June 7, 1945). Informal Report RL-91\nAltitude Return in the AN/APS-6 (March 26, 1945)\nSea-Return Effects and Their Elimination in Tests of a Type C Data Presentation with a Spiral-Scan Aircraft-Interception System (July 8, 1945)\nX-Band Sea-Return Measurements (January 10, 1946)\nA Method of Virtual Displacements for Electrical Systems with Applications to Pulse Transformers (October 1945)\nAn Extension of Lagrange's Equations to Electromagnetic Field Problems, Equivalent Networks (October et al.)\nA Treatment of Echo Box Problems by Lagrangian Procedures (January 13, 1945). RL-629\nF. E. Bothwell et al. A Treatment of Echo Box Problems by\nPart V\nCrout, P. D. (Continued)\nAn Extension of Lagrange's Equations to Electromagnetic Field Problems, Equivalent Networks\nThe Determination of Fields Satisfying Laplace's, Poisson's, and Associated Equations by Flux Plotting\nA Flux Plotting Method for Obtaining Fields Satisfying Maxwell's Equations, with Applications to\nA Theoretical Treatment of Radar Target Return, et al.\nA Procedure for Statistical Analysis of Depth Soundings\nShock Mounting and Vibrations (May 18, 1944)\nCunningham, F., et al. A Moving Target Selector Using Deflection Modulation on a Storage Mosaic\nEstimated Limitations of Kit MC-6U2 MTI (J. M. Cunningham)\nCurran, G. W. (See West, C. F.)\nRL-S-21 (J. M. Cunningham)\nRL-358 (Whitmer, R. M.)\nRL-377 (West, C. F.)\nTests of AGL-1 Installed in Tail of B-2W Airplane (Mar. 5, 1943)\nCurtis, B. R. PPI Off-Center Conversion Kit\nCzapek, E. L. et al. The Cooling of Pressure-Tight Davenport, L. L. et al. Theory and Designs of Guided Missiles Control System AN/APW-3 (Apr. 8, 1946)\nPreliminary Instruction Manual for Echo Box\nDavis, L. Jr. Radar Components that Affect Range\nDeAmicis, E. Frequency - Wavelength Conversion\nDearnley, I. H. RL-895 (see McMillan, F. L.)\nDeerhake, W. J. et al. Operational Procedure for AN/\nDehn, R. A. Tuning the RF Components of a System (Lawson Technique) (Feb. 20, 1942)\nDewey, G. C. (see Vitter, A. L., Jr.) RL-1005\nDicke, R. H. A Reciprocity Theorem and Its Application to Measurement of Gain of Microwave Crystal\nSee Roberts, S. RL-26\net al. Theory of Radar Mixers (July 15, 1942)\nThe Measurement of Thermal Radiation at Micro-waves, Aug. 22, 1945. RL-787 et al.\nThe Absorption of Atmospheric Water-Vapor in the K-Band Region, Jan. 15, 1946. RL-1002\nA Continuously Indicating Audio Spectroscope for C-W Systems, Dec. 30, 1943. Informal RL-61\nDickinson, A.B.: SA 6-6 Horizontally Polarized Antenna. Nov. 30, 1945. RL-825\nBuzz-Bomb Antennas, Nov. 30, 1945. RL-825\nDickinson, D.J. et al.: Maintenance Manual for the AN/APN-7 System Modified for the SG Band, June et al.\nDescription of the Experimental ROSEBUD, et al.\nMaintenance Manual for Model AN/APN-, Dickinson, R. [See Hollingsworth, L.M. RL-1020]\nDillinger, J.R.: Dissipation in Series Gaps and Voltage-Current Relationships during the Discharge, Aug. 31, 1945. et al.\nDivision of Voltage Across Series Spark.\nSome Characteristics of Enclosed Spark Gaps: Aluminum Cathode Type Series (Dec. 11, 1945)\n- 1BU1, 1BU5, and 1Bf9 Series Spark Gaps (Mar. 19, 1946) RL-682-4\nOperation of Sintered Iron Sponge-Mercury Cathode Type Series Gaps at SCI, AEW, and 5 Microsecond Conditions (Jan. 16, 1946) RL-682-5\nLine Type Modulator and HP 10V Magnetron Operation at 6 Megawatts (Jan. 11, 1946) RL-682-6\nCompact Horns: Intermediate Between Polyrods and Reflectors (Jan. 31, 1946) RL-961\nDodson, R. E., et al.: Compact Horns (Jan. 31, 1946) RL-961\nDodson, A. H.: see Hutner, R. A. RL-21\nSee Hutner, R. A. RL-22\nSee Hutner, R. A. RL-23\nDodson, H. W., et al.: Field Intensity Contours in Generalized Coordinates (May 2, 1945) RL-702\nSee Furry, W. H. RL-795\nDole, F. E.: Life Test of Contact Material on Standard Linear Wire-Wound Potentiometers (Mar. 12, 1946)\nA. Donovan, \"Measurement and Design of D.C. Resonant Charging Chokes,\" Nov. 23, 1942. RL-215\nAN/APS-30 Modulator Status, Jan. 17, 1946.\nOperating Instructions for Model 12 Modulator, Doolittle, H. D. RL-211\nDunnington, F. G., \"Accuracy Criteria for the Gun Interference between SCR-58JVs Tracking APN-19\"\nDowker, C. H. et al., \"Radome Bulletin Number 10, The Measurement of Small Reflections,\" Feb. 6, 1945.\nRadome Bulletin Number 11, An Investigation of Small Reflections\nRadome Bulletin Number 17, Current Progress in Radome Technology\nDowker, Y. et al., Radome Bulletin Number 19, Dielectric Constant and Loss Tangent Computation, Aug. 7, 1945.\nTransmission of Lossy Sandwiches, Jan. 23, 1946.\nDrake, D. T. et al., \"High-Frequency Characteristics of Resonant Structures for Over-Water Tests of S-Band Early Warning for Ships. Vertical Coverage of the CXHR\"\nRL-703 Droz, M.E. et al. Radar Trainer Equation-Solvers for the Relative Motion of Two Objects in Space (See Cefola, M. RL-963)\nDuBridge, L.A. Present Status of Radiation Laboratory. RL-32\nDunbar, A.S. Antenna for High-Altitude Bombing et al. A Low-Drag Beacon Antenna for Fighters (See Chisholm, E.B. RL-789)\nMetal Plate Lens for Csc 2 Antenna, Feb. 15, 1946\nDunnington, F.G., Doolittle. RF Envelope Indicator Instruction Manual, Dec. 10, 1941. RL-77\nA New Secondary Modulation Indicator, Mar. 25,\nDurand, E. S/N Measurements on the CV-58, Aug. 11\nAutomatic Frequency Control for AN / APS-31/33 (See Whitford, A.E. RL-888)\nAN/TPS-10B R-F Head Termination Report, Mar.\nDuvall, G.F. MTB Computing Radar Sight, Apr. 10\nDOLPHIN, Remotely Controlled Torpedo Rack Actuating Mechanism, Aug. 29, 1944. RL-S-23\nAlignment Kit (Torpedo Rack) Mark 1 Mod 0, Tables for Use with Torpedo Director Mark 33-1, et al. Torpedo Director Mark 33 Mod 1, Nov. 30, 1943. Project Dolphin. Dwight, B. Radiation Laboratory Modulator Summary. Eaton, J. E., et al. Quarter Wave Plate for Broad-Band Circular Polarization, Jan. 28, 1946. RL-769. Dielectric Rod Endfire Antennas Close to Metal. Ehlers, F. E. A Method of Measuring the S-Band Characteristic Impedance of Coaxial Cable, Apr. 28, 1943. Attenuation of RG-9/U Cable as a Function of Temperature and Frequency in the X-Band, June 18, 1943. E0 Rotary Joints for the 3 Centimeter Band, Dec. Ehrenfried, A. D. (see Carmody, W. R.) RL-M-242. Eisenstein, A. S., et al. Metallic Hydride Studies, Dec. 7, 1945. Alkaline Earth Oxide Cathodes for Pulsed Electronics. Emberson, R. M. Regular Report on the USS Semmes.\nRL-51: Regular Report on USS Semmes 3,000-Mc Operations\nRL-52: Comprehensive Report on USS Semmes Radar Installation\nA Navigational Radar for Naval Auxiliaries and Merchant Marine, Oct. 23, 1945 (RL-876)\nA High Resolution Set, Jan. 26, 1944 (RL-S-5)\nEmslie, A.G.: Coherent Integration, May 16, 1944 (RL-103)\nDiv. 14-125-M8 et al.: The Observation of R-F Phase in Pulse\nCunningham, F. RL-562: Moving Target Indication on MEW, Feb. 19, 1946\nMTI Using Coherent Intermediate Frequency,\nEvans, J.E.: Analysis of Magnetron Performance, Part II, Detailed Study of the Operation of a Magnetron, Feb. 6, 1946\nR-F Phasing of Pulsed Magnetrons, Feb. 6, 1946 (RL-221)\nEverhart, E.M.: Magnetron Strapping Wavelength Calculations. RL-223\nStrapping Tolerances for Magnetrons, Jan. 27, 1946.\nRadome Bulletin Number 5, Recent Dielectric Constant and Loss Tangent Measurements (July 14, 1944)\nRadome Bulletin Number 8, X-Band Sandwiches at Variable Angles of Incidence (Dec. 19, 1944)\nRadome Wall Reflections at Variable Angles (Ewing, D.H.)\nPresent Status of Radiation Laboratory (Ewing, D.H.)\nRL-S-31 (Exter, J.)\nLens Feed for K-Band Pillboxes (Eyges, L.J.)\nRL-961 (Dillon, R.E.)\nRL-973 (Risser, J.R.)\nOmnidirectional Antennas for BUPX (Jan. 17, 1945)\nFagen, M.D. (Continued) et al. A High Resolution K-Band Ship Search Set (Fairbank, J.D. et al.)\nSurface Coverage of Some Shipborne Radar (Fairbank, J.D. et al.)\nCXHR Maintenance Manual (Sept. 21, 1945)\nW. Fairbank \u2013 see Baltzer, 0. J. (RL-401, RL-536, RL-537, RL-576, RL-720)\nD. L. Falkoff \u2013 Performance of Microwave Harmonic Circuits\nR. M. Fano \u2013 Double Coaxial Coupler for BUPX An-F-R Mechanical Modulator for S-Band (Aug. 30, 1942)\nH. K. Farr \u2013 see Reed, J. (RL-255)\nSee Best (RL-905)\nT. A. Farrell, Jr. \u2013 see Higley, Lt. J. B. (RL-M-247)\nJ. R. Feldmeier \u2013 see Hutchinson, F. (RL-1007)\nW. H. Fenn \u2013 Tests on Undercut Beads in a Concentric Tube (Sept. 4, 1942. RL-277)\nE. C. Find & et al. \u2013 Parallel Plate Bends (Aug. 28, 1945)\nE. Fine \u2013 see Austin, P. (RL-S-58)\nA. Fineman \u2013 see Buck, J. G. (RL-609, RL-683)\nSee Buck, J. G.\nA. S. Eisenstein \u2013\nD. G. Fink \u2013 Microwave Radar, Volume 1, Theory and Practice of Pulsed Circuits (July 1942. RL-T-8)\nW. T. Fishback et al. Simplified Methods of Field Intensity Calculations in the Interference Region, Dec. 8, 1943. Preliminary Measurements of 10-cm Reflection Coefficients of Land and Sea at Small Grazing Angles. Further Measurements of 3- and 10-cm Reflection Coefficients of Sea Water at Small Grazing Angles. Graphs for Computing the Diffraction Field with Standard and Superstandard Refraction, Aug. -- Fleisher et al. The Use of a Twin-T Network in a Selective Frequency Amplifier, with Special Applications. R. C. Fletcher et al. Mode Selection in Magnetrons. J. E. Evans RL-1051. W. L. Flock et al. A Precision Plan Position Indicator, June --. A Precision Self-Synchronous Range System. R. G. Fluharty. Interference Measurements on the Black Maria Check Set, TS-495/APX, Nov. 16. A. Fong. Development of Microwave Test Sets, Apr.\nForbes, GD, et al. \"Multiple Reflection Delay Tank.\" RL-1005, April 8, 1946.\n\nForsbergh, PW, Jr. \"Description and Method of Operation of the Special Synchro Test Bench and Synchro Testing.\" RL-921, April 8, 1946.\n\nFoster, CE, et al. \"Results of Tests Performed on Synchro Units and Systems.\" RL-921, April 8, 1946.\n\nFoster, JS. \"Rear Rectangular Guide Antenna Feed, Illumination and Phases of Antenna Feeds.\" Mar. 1943, RL-26 (D-3).\n\nRound Guide Rear Antenna Feeds. \"Manufacturing Procedure for the Radiation Laboratory High Burn-out Crystals.\" Dec. 21, 1943, RL-635.\n\nFowler, GA. \"Operational Report on B-24 in the British Isles, March to June, 1942.\" RL-391.\n\nFox, M, et al. \"Manufacturing Procedure for the Radiation Laboratory High Burn-out Crystals.\" Dec. 21, 1945, RL-635.\n\nFrank, NH. \"Report on Junction Effects in Wave Propagation in Wave Guides Partly Filled with Reflections from Sections of Tapered Transmission Lines.\"\nLines and Wave Guides, Jan. 6, 1943. RL-189\nCoupling between Inductive Windows in Wave Transmission Lines and Wave Guides, Similarities and Differences, June 4, 1942. RL-T-5\nWave Guide Handbook, Feb. 9, 1943. RL-T-9\net al. T-Junctions in Rectangular Wave Guides, Part I, Theory. RL-179\nFrankel, S. The R-l and the R-2 Crystal Drivers, Feb. 1945.\nThe U-l and U-2 Preamplifier Units, Dec. 14, 1945.\nSee Cefola. RL-963\net al. Supersonic Components for Use in Radar\net al. A Supersonic Echo-Simulating System for\nFrederick, A. H. Line-Controlled Blocking Oscillator Marker Generator. Apr. 8, 1943.\nA Condenser Phase Shifter Range Circuit with Sine Wave Tracking Suitable for Microwave Height Finding Stations. June 30, 1943. RL-339\nSee Reed, H. J. RL-342\nSee Reed, H. J. RL-343\nSee Brown, P. F. RL-755\nFreehafer, J. E. Radar Echoes from Periscopes, Mar.\nThe Effect of Atmospheric Refraction on Short Fundamentals, O. T. Proposed Method for Measuring Instantaneous Magnetron Input Impedance with the Aid of a Delay Network (Feb. 22, 1944). RL-515 et al.\nA Diode-Type Pulse Voltmeter (July 6, 1944).\nVoltage Pulse Rate-of-Rise Measurements (July 10, 1944). et al.\nAnalysis of Line Modulator Behavior with a Sparking Magnetron Load (Aug. 10, 1945). RL-765\nFurry, W. H. Theory of Characteristic Functions in Problems of Anomalous Propagation (Feb. 28, 1945). et al.\nMethods of Calculating Characteristic Values for Bilinear M Curves (Feb. 6, 1946). RL-795\nGadsden, C. P. Low Noise Replacement Preamplifier (Gaerttner, E. R.). An Airborne S-Band Racon for Rooster Operation (June 28, 1944). RL-554 et al.\nComparison of Theoretical and Experimental Requirements for Microwave Beacon Transmitter Power and Receiver Sensitivity (Oct. 13, 1944). RL-627\nF. J. Gaffney, Instruction Manual, Browning Type A Synchronizer, Oct. 29, 1941 (RL-74)\nC. G. Montgomery, P. D. Bales, Report of Activities of Synchronizer Section, Nov. 5, 1941 (RL-75)\nInstructions for Type E Self-Synchronous Oscillator, Tentative Instruction Manual for MIT Radiation Laboratory Test Set (Type A), Sept. 24, 1941\nX-Band Sealed Standard Cavities, Feb. 13, 1946\nGamertsfelder, G. R., Pulsed Oscillator and Phase Errors in the Condenser Type Continuous Phase\nGardner, A. L., see Allred (RL-910)\nGardner, H. A., TFX-3URL Fixed Frequency Standard, TFX-35RL Fixed Frequency Standard, Apr. 26\nGardner, H. S., see Gaerttner (RL-627)\nGardner, J. H., Low-Altitude Navigation Antennas Developed in Connection with AN / APS-10, Oct. 3, 1944\nLow-Altitude Cs2$ Antenna for APS-33 Project\nGardner, M.E., Operational Characteristics of 2CU3\nTubes as Pulsed Oscillators in a Re-entrant Cavity, Garfield H. L. BUPX (AN/UPN-3, U, AN/APN-11) Ultraportable X-Band Radar Beacons and Their Tac Garman R. L. AI-10 Trainer Simulation at IF Level AI-10 Bench Trainer Simulation at Video Level Land Mass Simulator Aug. 26, 1942. Garfield, H. L. \"A Qualitative Analysis of Hysteresis in Reflex Oscillators,\" Feb. 4, 1946. RL-650 Garrett, G. A., K. L. Mealey. \"Photographic Polarization,\" Garsson, J. B. \"A Qualitative Analysis of Hysteresis in Reflex Oscillators,\" Feb. 4, 1946. RL-650 Germeshausen, K. J. \"Three Electrode Triggered Gap,\" Nov. 19, [et al.] \"High Voltage Oxide Coated Vacuum Rectifiers,\" Getting I. A. \"Special Report on Data Transmission by Means of Selsyns,\" Nov. 6, 1941. RL-6 Ghelardi, R. P. \"Results of Field Tests on AN/UPN-I, -2 (Experimental Models of BUPS)\" at Boca Raton, Florida (January-March, 1944). Aug. 12, 1944.\nFlorida: Tests on ROSEBUPS Against SCR-582, Front-Line Demarcation and Bombing with the Aid of Light-Weight X-Band Beacons (BUPX)\n\nLog of Tactical Tests, October 1944 - February 1945\n\nGilbert, C.M.: Comer Reflector Tests at Langley Field, et al.\n\nA Simple Trainer for GCA Approach Consoles S-2, S-2B, S-3, S-4, S-4B Motor Control Units, Feb. et al.\n\nLink Conversion Unit for Ground-Controlled Approach Trainer, May 7, 1945.\n\nRL-716 et al.\n\nA Tracking Error Recorder for the Ground Controlled Approach Trainer, Jan. 30, 1946. RL-855\n\nGround Course Computer for AN/APQ-Tl, Jan.\n\nGround Clutter Unit for the Ground Controlled Approach Trainer, Feb. 20, 1946. RL-927\n\nSpecial GCA Trainer Circuits, Mar. 15, 1946.\n\nGilbert, E.N., H.J. Riblet: Shipborne Black Maria Airborne Black Maria Antenna, Jan. 16, 1946.\n\nGill, J.R.: RL-21 (see Hutner, R.A.)\n\nRL-22 (see Hutner, R.A.)\n\nRL-23 (see Hutner, R.A.)\nGillette, P. R. (Continued)\nPart V\nGillette, P. R. (for Radiation Laboratory Pulse Transformer Committee)\nProposed Basic Specifications for Pulse Transformers\nNov. 8, 1945\n\nRadiation Laboratory Pulse Transformer Designs\n\nGillette, P. R. (for Pulse-Forming Network Committee)\nProposed Basic Specifications for Pulse-Forming Networks\nNov. 2, 1945\n\nGlasoe, G. N.\nPulse Shapes and R-F Spectra for Combinations of Strontium-Carlson Tubes on Mark I and Mark II\nModulators with 2J22, 2J21, and 725 A Magnetrons, \"The Regulation Obtainable in the Operation of a Hard Tube Modulator with Magnetron Load\" by Godet, G. J. RL-370\nGoldstein, H. \"Proposed Sea Echo Measurements with Airborne MTI Plane\" Aug. 14, 1945. Informal RL-42\n\"The Resonant Modes of Magnetron Cavities\" Dec.\n\"The Theory of Corrugated Transmission Lines and Waveguides\" Apr. 3, 1944. RL-494\nSee Bales. RL-569\n\"The Effect of Clutter Fluctuations on MTI\" Goodell, W. F., Jr. \"General Purpose Indication System, AN / APS-30 Series Indication System\" Jan. 24, 1945.\nElectronic Cursor for AN / APS-15 Jan. 30, 1945.\nGordy, W. 0. \"see Baltzer.\" RL-401\nSee Drake. RL-703\n\"Proposed Antenna for Panoramic Radar\" May 22,\nGoudsmit, S. A. \"Comparison Between Signal and Noise, Reflection Coefficients and Impedance Charts\" Nov.\nSee Carlson, J. F. RL-195\nSee Weiss, P. R. RL-191\nStatistics of Circuit Noise, Jan. 29, 1943. (RL-192)\nPossible Measurement of Radar Echoes by Use of Model Targets, Mar. 4, 1943. (RL-196)\nGrahame, D. C. (see Frankel). RL-1055\nGrass, A. M., A. C. Hughes, Jr., B. Chance. Photoelectric Automatic Range Tracking Unit, Jan. 25, 1943.\nGray, J. W. Calibrator for Low Altitude Bombing Equipment, June 1, 1943. (RL-336)\nGriesheimer, R. N. General Report on Low-Level Power Measurement at 10 Cm in Coax, Mar. 16, 1943. (RL-410) (Continued)\nBridge Methods in Low and Medium Level R-F Power Measurement, Sept. 14, 1943. (RL-410)\nGriffiths, R. W. Laboratory and Field Tests with Stabilized Spinners, Aug. 24, 1942. (RL-395)\nGriggs, D. (see Chance, B). RL-7\nGrassler, H. W. (see Gaertner. RL-627)\nGuarrera, J. J. (see Dickinson. RL-M-170)\nSee Dickinson. RL-M-184\nGustafson, W. R. (see Carlson. RL-M-226)\nGuthrie, G. B. (see Chaloff. RL-1062)\nHagler, D. L. \"Equipment on LB SO Air: Replacement Pressurized R-F Unit for AN/\" (Errors in Circular Sweeps Due to Decentration and Ellipticity of the Circle, Feb. 13, 1943)\nHales, E. B.\nHall, H. J. Instruction Manual for Raytheon Service Report on Western Electric 717 A Modulator Type D-150442 and Radio-Frequency Unit Type D-150452, Model 7 \u2013 Experimental Hydrogen Thyratron Modulator, Feb. 1, 1944. RL-M-145\nHall, M. B., M. Harwood. \"The Application of Powdered Iron Materials as Permeable Dielectrics at Micro-wave Frequencies,\" Mar. 26, 1946. RL-906\nHall, W. M. Brief Report of Activities from February\nD. Halliday et al. The AN/APS-30 Series, Aug. 15, 1942.\nO. Halpern. Theory of a \u201cBlack Body\u201d Produced by a Combination of a Thin Screen and a Perfect Mirror, Aug. 15, 1942. RL-155.\nTheory of a \u201cBlack Body\u201d etc., supplement to Re-.\nC. M. Hammack. A Cathode Follower Employing Two Tubes to Obtain Extremely Low Output Resistance, Oct. 1945. Informal RL-91.5.\nD. R. Hamilton. Static Frequency-Modulation Characteristics of the Reflex Klystron, Aug. 1, 1945.\nC. M. Hammack. Notes on Microwaves, Oct. 1945. S. Seely, E. C. Pollard.\nW. W. Hansen. Coincidence Method of Noise Reduction, Oct. 1945.\nR. J. Harrison. Design Considerations for Directional Microwave Antennas, [Unknown].\nJ. D. Fairbank. [Unknown], W. T. Harrold. RL-1062.\nJ. D. Fairbank. [Unknown], W. T. Harrold. RL-576.\net  al.  A  Range  Only  Set  for  Close-In  Seeing,  July \nHartman,  L.  A.  Effect  of  Pulse  Length  on  System  Per\u00ac \nformance  and  Operation ,  May  30,  1944.  RL-571 \nHarvey,  G.  G.  Information  on  Corrugated  Coaxial \nLines  and  Wave  Guides,  Dec.  11,  1942.  RL-264 \nReport  of  Conference  on  Rapid  Scanning,  June  15, \net  al.  Report  on  the  Microwave  Antenna  Confer\u00ac \nSee  Buckwalter.  RL-415 \nSee  Buckwalter.  RL-531 \nHarwood,  M.,  see  Hall.  RL-906 \nHaupt,  C.  R.,  see  Gilbert.  RL-669 \nThe  Trainer  for  Radio  Set  AN/MPN-1,  May  25, \nSee  Gilbert.  RL-716 \nSee  Gilbert.  RL-855 \nHavens,  B.  L.,  D.  R.  Corson.  Correlation  of  ASV \nEquipment  with  the  Bombsight,  July  24,  1942.  RL-35 \nHaworth,  L.  J.  AIA  Indicators,  Nov.  16,  1942.  RL-311 \nA  Comparison  of  Positive  and  Negative  Intensity \nModulation  of  PPI  Displays,  Jan.  26,  1944.  RL-S-4 \nHayes,  A.  E.,  Jr.  Transmission  Line  Construction  De\u00ac \nW. D. Hayes, R. H. Hazen, M. Healea, A. E. Heins, C. A. Helber, W. E. Henry, C. M. Hepperle, R. G. Herb, M. A. Herlin, H. M. Herreman\n\nHayes, W. D: Gratings and Screens as Microwave Resonators\nHazen, R. H.: Effects of Vane Width and Cathode Size on Magnetron Operation (RL-M-213)\nHealea, M.: Susceptance of Asymmetrically Located Windows in Rectangular Wave Guides (Oct. 16, 1942)\nHeins, A. E.: Susceptance of Asymmetrically Located Windows in Rectangular Wave Guides\nHelber, C. A.: An Automatic Frequency Control and Frequency Selection System for Magnetrons (Apr. 27, 1945)\nHenry, W. E: [see Brown. RL-755]\nHepperle, C. M.: Operating Characteristics of the 419 Magnetron\nHerb, R. G.: Regular Report on Spinners and Radiators, Regular Report on the PBM-1 (Oct. 29, 1941. RL-64)\nHerlin, M. A.: Cold Resonance Theory of the Waveguide Tunable Magnetron (Oct. 15, 1943. RL-445)\nSmith: [See RL-879]\nWide Range Tunable Stabilizer (Feb. 21, 1946)\nHerreman, H. M.: [see Jelatis. RL-S-77]\nHewitt, G. E. \"Preliminary Testing of the Houston Corporation AN/APS-10 Scanner,\" Dec. 23, 1944.\n\nHexem, J. \"Video Mapping,\" Jan. 29, 1946. RL-890. See Krutter, H. RL-261.\n\nHibbert, J. J., et al. \"Field Station for Antenna Measurements,\" Feb. 26, 1946. See Lyman, E. M. RL-375.\n\nHigenbotham, W. A. \"Indicator Fixed Components as Used in a Complete Aircraft Interception Installation,\" [Publication details missing].\n\nHigley, Lt. J. B. [Author's name missing]. RL-645-9.\n\nThe S-5 and S-5B Motor Control Units, Feb. 25, 1945.\n\nHildebrand, F. B. \"The Alteration in the Radiated Field of a Paraboloid Due to a Shift in the Position of the Source,\" See Crout. RL-S-21.\n\nSteady-State Vibration of Two-Spring Mechanical Systems, A. G. Hill. See Rierdan, R. C. RL-M-108.\n\nHillger, R. E. \"Final Report on SRBs,\" Sept. 3, 1943.\nP. Hinkle (see Kelner, R. R)\nG. Hite, E. Whitham, B. Chance. \"Frequency Division with Blocking Oscillator Pulse Transformers\" (Mar.  et al. A Condenser Phase Shifter Range Unit with Sine Wave Tracking for AN/TPG-1, AN/FPG-1, See Flock. RL-573)\nMedium Precision Range System for CXGQ (Project Henry), Sept. 9, 1944. RL-579\nW. K. Hodder. \"A Hard Tube Servoamplifier for Fractional Horsepower DC Motors\" (Mar. 14, 1944. RL-535)\nX-1 Error Integrator. W. Roth. Nov. 27, 1945.\nThe Mark VII Supersonic Trainer. Feb. 28, 1946.\nH. T. Hodges. Falcon System Manual. Jan. 15, 1944. RL-M-152A\nAN / APG-13 Falcon System Manual. Mar. 31, 1944. RL-M-152B\net al. AN / APG-13 System Manual. Aug. 8, 1944. RL-M-152C\nA. D. Hoffmann. Mechanical Computor Mechanism for Holdam, J. V., Jr. Handbook of Maintenance Instructions for the AN/APG-8 Airborne Radar Gunsighting Equipment. May 18, 1945. RL-M-214\nAN/APG-15B Instruction Manual\nHollingsworth, L.M. et al. \"An X-Band Frequency Modulated Relay System for Video Frequencies\" January [Unknown]\nR. Dickinson \"An Automatic Frequency Control System for Magnetrons with Beacon Applications\" PART V\nHolmes, E.A. \"Stabilized High Voltage Supply\" May [Unknown]\nHolt, F.S. \"RL-203\" O\u2019Neal, R.D.\nHope, W.D. et al. \"Testing of Skiatrons (Supplement)\" May 6, 1943\nHopkins, C. \"Truck-Mounted SCR-582 Mk III, a General-Purpose Microwave Set\" October 27, 1943 RL-474\nHorgan, J.D. et al. \"Preliminary Operation and Maintenance Handbook for Release Point Indicator AN/\" [Unknown]\nBrean, J.W. RL-S-62\nHoward, B.E. RL-21 (see Hutner, R.A.)\nHutner, R.A. RL-22, RL-23\nDodson, H.W. RL-702\nFurry, W.H. RL-795\nPropagation in an Atmosphere Containing a Disconnector\nHubbard, P. A. Standards for Microwave Frequencies\nHudson, F. C., et al. Semi-Automatic Tactical Plotting\nHudspeth, E. S. Regular Report on the Navy Dirigible\nBaltzer, RL-401 et al. The Depolarization of Microwaves (Nov. 1, 1944)\net al. Observations of Life Rafts Equipped with Corner Reflectors (Feb. 15, 1944). RL-533\nCorner Reflectors for Life Rafts (Aug. 1, 1944). See Andrew. RL-766\nHughes, A. C., Jr. Externally Triggered Circular Sweep Amplifiers (May 6, 1943). RL-335\nA Range-Measuring System Using an RC Linear Circuit\nA Theory of a Supersonic Delay Line (Sept. 15, 1945)\nHull. Interference Blanker (June 20, 1945). RL-749\nTesting of Skiatrons (Dec. 30, 1943). RL-S-1\nSee Hope. RL-S-ls\n\n(Note: I assumed \"RL-S-ls\" is a reference to RL-S-1, but it's unclear without additional context.)\nHulsizer,  R.  I.  GPI  for  Close-Control  Bombing,  July \nHunt,  S.  P.  Temperature  Rise  in  ATR  Racks,  Oct. \nHuntington,  A.  B.,  see  Benfield.  RL-792 \nHuntington,  H.  B.,  S.  Roberts,  H.  C.  Torrey,  C.  A. \nWhitmer.  Testing  of  1N21  Navy  Crystal  Rectifiers, \nCrystal  Life  Tests  under  Flat  Pulses,  Apr.  7,  1944. \nNotes  on  the  Contamination  of  Mercury  by  Stain\u00ac \nHuntington,  H.  B.  (Continued) \nHurewicz,  W.,  et  al.  Servos  with  Torque  Saturation, \nServos  with  Torque  Saturation,  Part  II,  Sept.  28, \nErrors  in  Target  Velocity  Due  to  the  Rolling  and \nPitching  of  the  Ship,  Aug.  28,  1944.  RL-612 \nOn  Servos  with  Pulsed  Error  Data,  Apr.  26,  1945. \nHutchinson,  F.,  et  al.  Final  Report  on  the  BM50  Mag\u00ac \nHutner,  R.  A.  Change  of  Polarization  as  Means  of  Gap \nH.  Dodson,  J.  Gill,  F.  Parker,  B.  Howard.  Field \nIntensity  Formulas,  Sept.  28,  1943.  RL-23 \nH.  Dodson,  J.  Gill,  B.  Howard,  F.  Parker,  J.  A. \nStratton, \"Radar Height Finding\", April 6, 1943.\nE. Lyman, \"Properties of the Diffracted Wave Field\".\nF. Parker, B. Howard, H. Dodson, J. Gill, \"Transmission at Low Altitudes over Sea Water\", September 1, 1943.\nHursh, J. B., \"Flight Tests of AEW Block III Relay\".\nIngalls, C. E., \"Conference on Standardization of Intermediate Frequency\", April 18, 1942. RL-283.\nRevision of General Radio Type 605-B Signal Generator for Pulsing, June 13, 1944. RL-575.\nJacobsen, A. B., see Ahern, C. R. RL-334.\nF. B. Coffin, W. B. Jones, Jr., B. Chance, \"Automatic Range and Azimuth Tracking while Scanning\".\nJacobsen, E. A. S., Instructions for TGS-2SE, TGS-3BL and TGS-5BL Signal Generators, November 11, 1945.\nInstructions for TGX-2BL and TGX-3BL Signal Generator, December 21, 1944. RL-M-143A.\nInstructions for Types TWS-5 and TWS-5EV Battery-Operated Wattmeters (Preliminary)\net  al.  Instructions  for  Type  TBN-3EV  Thermistor \nInstructions  for  TGS-6DE  Boresighting  Signal \nGenerator  ( Preliminary  Model  of  Test  Set  TS-348 / \nInstructions  for  TVN6SE  Thermistor  Bridge,  No\u00ac \nCatalog  of  Microwave  Test  Equipment,  Aug.  25, \nJacobson,  R.  I.  Lighthouse  Tube  Superre generative  Re\u00ac \nA  Measurement  of  Supersonic  Velocity  in  Mercury \nat  15  Me  Is  as  a  Function  of  Temperature,  Sept.  20, \nJaffe,  D.  L.  Development  of  Antenna  for  Raytheon \nRemote  Position  Control  by  Direct  Frequency \nJames,  H.  M.  Report  on  Night  Fighter  Pursuits ,  June \nIdeal  Frequency  Response  of  a  Receiver  for  Square \nCorrection  of  the  Scanning  of  Shipborne  Radar \nSystems  for  Roll  and  Pitch  of  the  Ship,  Dec.  22,  1941. \nNew  Approach  Procedure  for  Night  Fighting, \nNew  Method  of  Nightfighting  (Abridged  edition  of \nStatistical  Treatment,  of  Certain  Phases  of  Aerial \nEffect  of  Routine  Evasive  Action  on  the  Calculated \nApproach Procedure, Dec. 16, 1942. RL-187 Use of the Range Clock in Night Fighting with AI Tactical Use of Delayed PPI Scopes of the AEW Jarmotz, P. SN-41/APA-53 (Cadillac II Synchronizer) and IN-188/APA-53 (Cadillac II Indicator), Apr. 18, AN/APS-15 Receiver-Indicator Modified for Ground Range Sweeps and Remote Amplifier, Oct. 10, 1944. RL-M-172A Operating and Maintenance Instructions for Indicator for Rapid Scan System, Apr. 5, 1946. RL-M-249 Jelatis, J. G., et al. AFC Operation and Maintenance Jerremas, A. S. Modulator Colloquium, April 16-17, A. E. Whitford. Modulated Pulse Communication See Fundingsland, O. T. RL-521 See Ames, L. A. RL-M-155A Instructions for Modifying the SCR-584 Modulator for Use in Aspen Transmitters, Feb. 21, 1944. RL-M-155B et al. Modulator Text, Dec. 17, 1943; Second Edition Johnson, H. L. A Wide-Excursion Frequency-Modifier.\nM. H. Johnson, \"Alignment Oscillator or Wobbulator\", May 31, 1942. See Chance, B. RL-320\nJ. B. Wiesner, \"Microwave Wattmeter II, 3-Cm and 6-Cm\", Nov. 18, 1942. RL-M-146\nL. H. Johnston, \"GCA Ground Controlled Approach\", Jul. 19, 1945. RL-1072\nE. M. Jones, \"The J-2 Modulator Unit\", Jul. 19, 1945. RL-963\n\"The Cadillac Trainer\", Apr. 10, 1946. RL-1072\nL. G. Jones, \"APS-33 Antenna, Final Pre-Production\", Jul. 1945\nW. B. Jones, Jr., \"see Jacobsen, A. B.\", RL-341\nW. H. Jordan, \"Action of Linear Detector on Signals in the Presence of Noise\", Jul. 6, 1943. RL-305\nV. Josephson, \"see Linford, L. B.\", RL-353\n\"Short Pulse Techniques for High Definition Radar\", Aug. 1, 1946. et al. \"Anti-Clutter Circuits for AEW\"\nKales,  M.  L.  SCI  Search  Antenna  Mark  I,  Mar.  13, \nSCI  Search  Antenna  Mark  II,  Feb.  20,  1946. \nKallman,  H.  E.  Thyrite  Bridge  Controlled  Voltage \nHigh  Impedance  Cable,  Mar.  13,  1944.  RL-529 \nEqualized  Delay  Lines,  June  3,  1944.  RL-550 \nMatchmeter,  Apr.  9,  1945.  RL-705 \nNonlinear  Networks  as  Voltage  Regulators,  May \nKatz,  I.  Instruments  and  Methods  for  Measuring  Tem\u00ac \nperature  and  Humidity  in  the  Lower  Atmosphere, \nSee  Austin.  RL-488 \net  al.  Microwave  Transmission  over  Water  and \nLand  under  Various  Meteorological  Conditions,  July \nKatz,  S.  Microwave  Test  Signals,  Jan.  15,  1946. \net  al.  Instructions  for  Type  TSK-1SE  Spectrum \nAnalyzer,  July  3,  1945.  RL-M-142 \nInstructions  for  Type  TTX-6RH  and  Type  TTX- \nInstructions  for  Types  TTX-6(),  TTX-9  (),  TTX- \nInstructions  for  TSX-2  Spectrum  Analyzer,  Aug. \nInstructions  for  TSX-2  and  Specifications  on  TSX- \n4SE  Spectrum  Analyzers,  Oct.  5,  1944.  RL-M-173B \nInstructions  for  TSX-2  and  Specifications  on  TSX- \n4SE  and  TTS-4SE  Spectrum  Analyzers,  Nov.  4,  1944. \nRL-M-173C \nInstructions  for  Types  TFK-2HU,  TFK-3HU ,  and \nTFK-6HU  Frequency  Motors,  Aug.  17,  1944. \nRL-M-176A \nInstructions  for  Types  TFK-2HU,  TFK-3HU ,  and \nTFK-6HU  Frequency  Motors,  Apr.  12,  1945. \nRL-M-176B \net  al.  Handbook  of  Operating  and  Maintenance \nInstructions  for  Test  Set  TS-259  (XR-1)  / AP  with \nSupplements  on  Test  Sets  TS-259  (XR-2)  / AP  and \nTS-259  ( XR-3)  /AP  and  Signal  Generator  TS-259 /AP, \nKe,  T.  S.,  et  al.  A  Low  Power  X-Band  R-F  Gas  Switch, \nPART  V \nKe,  T.  S.  (Continued) \nNote  on  a  Low  Power  S-Band  Gas  Switch ,  Dec.  10, \nKeary,  T.  J.  A  Study  of  Fanned  Beam  Radiators,  Feb. \nR.  E.  Alley,  Jr.  An  Automatic  Recorder  for  Micro- \nwave  Antenna  Pattern  Measurements,  Mar.  1,  1943. \nSee  Bohnert.  RL-659 \nSee  Bohnert.  RL-660 \nCalculation  of  Vertical  Polar  Diagrams  and \nPower Gains of Antennas for Airborne Navigation\nBohnert, RL-779 et al. AN/APS-32 and AN/APS-34 Airborne Navigational Radar Antennas at K-Band (Mar. 15, 1946)\nKellner, R. L. Preliminary Book of Maintenance Instructions for Shipboard Components of AEW (July [no year]) RL-M-243, RL-M-244\nHMI for Cadillac II Power Supply (Oct. 23, 1945) Kelly, H. C. (see Hull) RL-S-1\nSee Hope. RL-S-ls\nKelner, R., V. W. Hughes, A. Berg, P. Hinkle, B. Chance. An Adaptation of the Phantastron Delay Multivibrator Circuit to the 6SA 7 Tube (Aug. 21, 1946)\nKenngott, R. L. et al. Tests on the Performance of the Kerr, D. E. et al. An Introduction to Microwave Propagation (No publication information)\nKessler, M. (see Hudspeth, E. S.) RL-458\nSee Drake, D. T. RL-703\nKirby-Smith, J. S. S Band ASV Marker (Mar. 27, 1942)\nMeasurement of Electrical Tuning Ranges of 707\nH. A. Kirkpatrick, Notes on the Power Output of 723A Tubes, Feb.\nJ. F. Blackburn, RL-797\nG. Knight, Measurements and Waveforms Obtained with SCR-598 Modulator, Nov. 29, 1945. RL-757\nG. M. Knight, Preliminary Installation and Operating Instructions for Radar Set AN/CPS-6, Feb. 3, 1945.\nJ. K. Knipp, Notes on the Reflex Oscillator, May 3, 1945.\nThe Temperature-Limited Diode, Jan. 31, 1946.\nTheory of Noise from the Reflex Oscillator, Jan.\nJ. F. Koehler, Regular Report on the X- JO-3, Oct. 1,\nRegular Report on the X-JO-3, Nov. 5, 1941. RL-54\nRegular Report on the CXBH-1, The PBM-1, Dec.\nJ. F. Koehler, (Continued)\nC. J. Taylor, Survey of 10-Cm Radar Installation in PBM-1 Flying Boat, May 1, 1942. RL-383\nE. R. Kravitz, see Jerrems. RL-T-15\nR. Krock, et al. The Two-Disc D-C Thermistor Bridge\nKrulikoski,  S.  J.  A  Survey  of  High-Vacuum  Diodes \nUsed  for  Surge-Limiting  Operation  in  Modulators , \nSummary  of  Life-Test  Data  on  Sylvania  UC35 \nHydrogen  Thyratrons,  Feb.  1,  1945.  RL-589 \nTrigger  Requirements  of  the  J+C35  and  3C45 \nHydrogen  Thyratrons,  Aug.  31,  1944.  RL-605 \nTechnical  Data  and  Operating  Notes  for  the  5C22 \nHydrogen  Thyratron,  Nov.  14,  1945.  RL-828 \nSummary  of  the  Life  Test  Program  on  3C45, 1+C35, \nand  5C22  Hydrogen  Thyratrons,  Jan.  31,  1946. \nHydrogen  Thyratrons  in  Pulse  Generator  Circuits, \nKrutter,  H.  A  Simple  Method  for  Determination  of  the \nExplanation  of  Impedance  Matching,  July  7,  1942. \nRL-T-6 \nR.  Hiatt,  J.  Bohnert.  Some  Matching  Properties  of \nAntenna  Feeds,  Nov.  17,  1942.  RL-261 \nSee  Bohnert.  RL-665 \nKuper,  J.  B.  H.  Preliminary  Report  on  a  10-Cm  Super- \nRegenerative  Receiver,  May  1,  1942.  RL-284 \nP.  A.  Cole,  F.  Bailey.  Report  on  Tests  of  RCA  and \nRL-11: GE Lighthouse, January 11, 1943. RL-290 et al. Simplified Measurement of Receiver Sensitivities (S-Band Noise Source)\nRL-17: RL-542, Cole\nRL-18: RL-693, et al. Notes on Load Effects in Reflex Oscillators\nRL-774: Beers et al. Measurements on Noise from Reflex Oscillators\nRL-1004: R. K. Kyhl. The Use of the Magic Tee Microwave Bridge in Measuring Impedance, December 12, 1944. RL-1002, Dicke\nRL-378: Larson, R. W., H. F. Balmer, A. S. Meier. Tests on Radar Echoes from Cylinders, July 10, 1942\nRL-685: LaRue, J. M., J. R. Perkins, K. J. Germeshausen. Tests on Five Types of Triggered Switch Modulators, June [Unknown]\nInformation on Radiation Laboratory Paraboloid\nRL-377: Laslett, L. J. Calculation of Errors in Conical Scanning GL Systems Arising from Detuning When the Transmission Line Is Not a Perfect Transmission Line. See C. F. West, RL-377.\n\nCalculation of Errors in Conical Scanning GL Systems Arising from Detuning When the Transmission Line Is Not a Perfect Transmission Line (Laslett, L. J.)\nRL-11: GE Lighthouse, January 11, 1943. RL-290 et al. Simplified Measurement of Receiver Sensitivities (S-Band Noise Source)\nRL-542: Cole\nRL-693: et al.\nRL-774: Beers et al. Measurements on Noise from Reflex Oscillators\nRL-1002: Dicke\nRL-1004: R. K. Kyhl. The Use of the Magic Tee Microwave Bridge in Measuring Impedance, December 12, 1944\nRL-378: Larson, R. W., H. F. Balmer, A. S. Meier. Tests on Radar Echoes from Cylinders, July 10, 1942\nRL-685: LaRue, J. M., J. R. Perkins, K. J. Germeshausen. Tests on Five Types of Triggered Switch Modulators\nRL-377: Laslett, L. J.\n\nReferences:\nRL-11: GE Lighthouse, January 11, 1943. RL-290 et al. Simplified Measurement of Receiver Sensitivities (S-Band Noise Source)\nRL-542: Cole\nRL-693: et al.\nRL-774: Beers et al. Measurements on Noise from Reflex Oscillators\nRL-1002: Dicke\nRL-1004: R. K. Kyhl. The Use of the Magic Tee Microwave Bridge in Measuring Impedance, December 12, 1944\nRL-378: Larson, R. W., H. F. Balmer, A. S. Meier. Tests on Radar Echoes from Cylinders, July 10, 1942\nRL-685: LaRue, J. M., J. R. Perkins, K. J. Germeshausen. Tests on Five Types of Triggered Switch Modulators\nRL-377: Laslett, L. J. Calculation of Errors in Conical Scanning GL Systems Arising from Detuning When the Transmission Line Is Not a Perfect Transmission Line.\n\nRL-11: GE Lighthouse, January 11, 1943. RL-290, Cole\nRL-542:\nRL-693:\nRL-774: Beers et al.\nRL-1002: Dicke\nRL-1004: R. K. Ky\nMitter Frequency is Pulled During Rotation, March 1943. Informal RL-94 Tests of AGL-1 Installed in Tail of B-2J+D Airplane, Mar. 5, 1943. Informal RL-94 Lawrance, R.B. et al. Impedance Characteristics and Equivalent Circuits for Vertical Radiators, Apr. 15, 1943. Lawrence, J.A. APG-1 Tracking and Firing Tests, Lawrence, T.E. AN/APG-13B Vulture Rocket General Description, Special Installation Requirements, and Mounting Dimensions of AN/APG-5 Airborne Range Only [ARO] Equipment, Jan. 31, 1943. Lawry, C.C., Jr. Analysis of an Amplidyne Servomechanism, Feb. 10, 1942. RL-T-4 Lawson, A.W., Jr. See Hollingsworth, L.M. RL-977 Lawson, J.L. Design and Test of Concentric Transmission Lines, July 15, 1941. RL-141 Standing Wave Detector, May 5, 1942. RL-344 Elimination of the \u201cTrombone\u201d Between Transmitter and Junction in a Duplexing System, May 4, 1942.\nMeasurement of Impedance with the Standing Wave Detector (May 18, 1942)\nMeasurement of Q-Value of a T-R Box (July [no year given]) - See McCreary, R. L. (RL-352)\nStone, A. M. The Double-Tuned Circuit with Transitional Coupling (Oct. 8, 1945) (RL-784)\nPulsed-Interference Suppression (Oct. 15, 1945) - See Ashby (RL-914)\nDetection of Propeller and Sambo Modulations - See Josephson (RL-S-52)\nLeachman, R. B. et al. N2 Gate Attachment for SCR- (Aug. 25, 1943)\nLee, R. W. Range Height Indicator (Aug. 25, 1943)\nLees, W. et al. Notes on the European and Eastern Atlantic S.S. Loran Systems (Apr. 17, 1945) (BBRL-83)\nLeiter, H. A. Dielectric Transmission Measurements (Nov. [no year given]) - A Microwave Band-Pass Filter in Waveguide\nLevine, R. et al. Chemical Methods for Maintaining [no title or year given]\nF. D. Lewis, \"Partial Pressure of Water Vapor in TR Tubes,\" Coordination, Dec. 19, 1940.\nRL-157 Report on XP-61 Mock-up, Apr. 23, 1941.\nJ. Lien, \"Project TGI (AN/APX-11, AN/APX-16),\" Preliminary Instruction Manual for X-Band Coinciident Beacon XCB (Mark I) AN / APX-14, Mar. 1, 1941.\nL. B. Linford, \"Regular Report on the Components Testing System,\" Oct. 8, 1941. RL-41\n\"Regular Report on the Components Testing System,\" Oct. 8, 1941.\nReport on Advanced Development: S. Seely.\nD. Williams, V. Josephson, W. Woodcock, \"Definition of Maximum Range on Aircraft and Its Quantitative Determination,\" Nov. 12, 1942. RL-353\nD. Williams, V. Josephson, W. Woodcock, Supplementary Report on Altitude Determination by Means of an Expanded Elevation Indicator, Vertical.\nD. Williams, V. Josephson, W. Woodcock, \"Time Fluctuations of a Rotary Spark Gap Modulator,\" Dec.\nLipkin, H. J. et al. \"Black Maria: Coincident Cross-Band Transponder for S-Band Radar (AEW)\" Dec.\nLippmann, B. A. \"Theory of Directional Couplers\" Dec.\nLipscomb, G. Q. \"Waveforms, Voltage and Resistance Measurements in AN/APA-5 Indicator Equipment\"\nLogemann, H. Jr. \"RL-977\" See Hollingsworth, L. M.\nLongacre, A. \"Regular Report on the Operation of the Light Mountain Radar Set\" Dec. 10, 1943. RL-491\nLipkin, H. J. et al. \"AN/APS-10: A Lightweight X-Band Search Radar\" July 12, 1944.\nLuebke, E. A. \"Pulse-Length Discrimination in Beam Deflection\" See Ramsey, N. F. RL-381\nLyman, E. See Hutner, R. A. RL-20\nJ. J. Hibbert \"Radar Target Contrast\" June 2,\nRadio Set RHB, Technical Description of the Production Model Radio Set RHB; Adjustment and Alignment of Radio Set RHB Jan.\nThe SCR-584 Plotting Table System, July 3, 1944.\nThe AEW System, Book I, Airborne Equipment,\nThe AEW System, Book II, Shipboard Equipment,\nThe AEW System, Book III, Test Equipment, Nov.\nMacnee, A. B., see Beers. RL-528\nGrounded Grid I-F Amplifiers, Jan. 18, 1946.\nMacNichol, E. F. Jr. ARO Range Unit, Apr. 9, 1943.\nB. Chance. Medium Precision, Self-Synchronous Automatic Range Tracking Circuit Model U, June 18,\nMacRae, D. Jr., see Gray. RL-457\nMaddaus, I. Jr. IFF Antenna for Mounting on the Wing of a TBM Torpedo Bomber, Dec. 6, 1945.\nIFF Receiving Antenna for Mounting in Cadillac\nIFF Transmitting Antenna for Mounting in Cadillac\nAEW Block III Relay Antenna, Nov. 30, 1945.\nSix-Element Vertically Polarized Beacon Antennas,\nMallach, L. W. Reduction of Radar-Radio Interference from Modulators, Aug. 3, 1943. RL-431\nMansfield, C. E. (see Hudspeth, E. S.) RL-458\nHarrold, W. T. RL-598\nAndrew, M. M. RL-766\nMann, L. G. TFX.29RL Frequency Comparator, February\nMansur, I. (see Clarke, H. F.) RL-731\nDiscontinuities in Standing Wave Detectors and Waveguide Function Steps, December 14, 1945. RL-893 (see Clarke, H. F. RL-1071)\nMarcus, P. M. Theory of Radar Return from the Interaction of Discontinuities on a Transmission of Radiation from Curved Surfaces, January\nMarcy, H. O. Trainer for Mark 35 Radar, April 5, 1946. et al. Instruction Manual for Projection PPI, January\nMarcy, H. T. et al. Tests on a M3B1 Oil Gear and an Amplidyne Servo for the SCR-598 Central Problem,\nMargenau, H. Dispersion of High Frequency Radio Waves in Ionized Gases, October 26, 1945. RL-836\nTheoretical Interpretation of Recovery Times of Theory of Alternating Current Discharges in\nF. D. Marsh: Theory of Circular Bends in Rectangular Wave Guides (RL-813), June 24, 1943\nR. E. Marshak: Theory of Circular Bends in Rectangular Wave Guides (RL-206), June 24, 1943\nE. G. Martin: Design of a U-Foot Corner Reflector for K-Band (RL-467)\nF. Martin: Design of a U-Foot Corner Reflector for K-Band (RL-365)\nR. M. Ashby: RL-913, RL-914\nM. Cefola: RL-963\nS. J. Mason: 45\u00b0 Microwave Reflector (RL-1044), Nov. 19, 1943, The Range Calculator (RL-497), Dec. 20, 1943, Horn Feeds for Parabolic Antennas (RL-1044), Jan. 22, 1946\nW. W. Mathison et al.: Frequency Drift of Certain X-Band Magnetrons (RL-663), Jan. 23, 1945\nR. S. Chaloff: RL-1062\nL. A. Mautner: Mautner, L. A. Shipborne Mechanical Rotation Plan Position Indicator (RL-315)\nC. W. Mautz: The Solenoid Camera Drive (RL-91.5), Oct. 10, 1945, Informal RL-91\nE. Maxwell: Conductivity Loss Measurements at K-Band\n\n(Note: The text has been cleaned by removing unnecessary line breaks, whitespaces, and meaningless characters. The original content and order have been preserved as much as possible.)\nThe Identification of Signals on PPI Photographs for the Construction of Radar Maps, Dec. 22, 1942. (RL-389)\nElectronic Line Voltage Stabilizers, Mar. 22, 1946. (McBean)\nN-l IFF Unit, Oct. 20, 1943. (McClure)\nTwo Proposed Methods of Recording the Position of a Moving Link Crab, June 20, 1945. (RL-730)\nThe AN/APS-6 Antenna Simulator, Nov. 15, 1945. (McConnell)\nThe Detection of Moving Targets among Ground Clutter by Coherent Pulse Methods. (See Emslie, RL-481)\nA Precision Z Sweep Generator, May 23, 1944.\nThe Storage of Video Signals on Simple Mosaics, Apr. 18, 1946. (An Experimental MTI System)\nSome MTI Nomenclature in Use at Radiation Laboratory, May 2, 1945. (Informal RL-65)\nEstimated Limitations of Kit MC-6^2, MTI.\nFor SCR-58A, June 18, 1945. RL-65: McCoy, FC et al. Radio Set RHB, Section III, Glider Checkout Procedure, Jan. 21, 1944. RL-508-2.\nMcCoy, RT. Rosebud Microwave Beacon Equipment, McCreary, RL. Direct Coupling in the T-R Box, Nov.\nMcFarlane, MD. See Meagher, RE. RL-388.\nMcGrath, S. Instruction Manual for B-18 Radar Installation. Instruction Manual for Raytheon Laboratory.\nModulators WX U051*, WX U051* A and WX h05U B, McKenzie, AA. Lightweight Loran Transmitter Manual, May 10,\nMcKenzie, AA. Handbook of Operating Instructions for Loran Low Frequency Converter CV-27/UPN, Apr. 27,\nHandbook of Maintenance Instructions for Loran Low-Frequency Converter CV-27/UPN, July 6, 1945.\nMcLaughlin, DB et al. Precise Navigation by Means of a Radar Map Superposed on the PPI, Apr. 7, 1944.\nC. A. Smith, \"The Radar Chart Projector,\" April 18, 1943. (RL-245)\nE. B. McMillan, \"Design Characteristics of Spinner Housing Materials,\" January 12, 1943. (RL-245)\nDec. 2, 1943. Radome Bulletin Number 1. (RL-483-1)\nE. M. McMillan, \"B-18-A Report,\" February 13 to July [unknown year]. (RL-254)\nF. L. Jr., J. B. Wiesner, \"Pre-ignition Transmission through Gas-switching Tubes and its Contribution to Crystal Failures,\" July 3, 1943. (RL-254)\nSee Levine. (RL-593)\net al., \"Recovery Time Measurements in Band-Pass T.R.\u2019s for Various Gases,\" December 18, 1945. (RL-895)\nR. E. Meagher, \"Regular Report on Indicators and Synchronizers,\" October 15, 1941. (RL-47)\nM. D. McFarlane, \"Geared Selsyns,\" October 9, 1942.\nE. C. Pollard, \"Indicators and Synchronizers,\" [unknown date]. (See Emberson, R. M. RL-876)\nK. L. Mealey, see Garrett, G. A. (RL-382)\nF. J. Mehringer (see Cady, W. M.)\nA. S. Meier (see Larson, R. W.)\nR. R. Meijer. A Trigger Generator for Signals\nE. B. Meservey. Unified Radar Bomb Sight (URBS), July\nC. A. Meyer. Handbook of Operating and Maintenance Instructions for Test Set TGI-3CA, Mar. 28, 1945.\nPreliminary Instruction Manual for S-Band Coincident Transponder Black Maria RT-74/APX, Sept.\nP. C. Michel. Special Report on 30-Mc Pulsed Signal\nH. A. Miley, et al. Magnetron Starting Time, Mar. 14, et al. Stability of Magnetrons Operated by Spark Gap Modulators, Oct. 9, 1944. RL-620\net al. Increasing Stability of Operation of 4J31-35 Magnetrons in the AN/CPS-1 System, Jan. 25, 1945.\net al. Influences of Pulse Transformer Design on 4J31-35 Magnetron Stability, Aug. 11, 1945. RL-622\nC. W. Miller. Amplidyne Servo for SCR-598 Surface Fire Control Set, Oct. 1, 1943. RL-435\nE. Miller, \"Comparison of Reflectivities of Approximately Similar Plastic and Metal Airplanes,\" May 22, 1942.\nD. B. McLaughlin, \"RL-503 MEW Close Control,\" Apr. 30, 1946.\nR. S. Bender and J. W. Miller, \"RL-729.\"\nA. E. Bent, \"RL-780.\"\nW. E. Millett et al., \"Survey of Foster Scanner Development,\" n.d.\nJ. Millman, \"Thyratron Servo Control Circuit for Spinning Targets,\" n.d.\nL. B. Linford, \"RL-S-20.\"\nR. M. Mitchell, \"RL-547,\" in I. Katz, ed.\nC. G. Montgomery et al., \"Report of Activities of Synchronizer Section,\" Nov. 5, 1941.\nD. D. Montgomery, \"RL-167,\" in various reports: RL-162, RL-163, RL-164.\n[Millett, W. E. RL-1074, Montgomery, D. D., C. G. Montgomery. Polarization Effects in a Circular Wave Guide at 3 cm, Sept. 12, 1943.\nC. G. Montgomery. 3-Cm Magnetron Cold Impedance, Sept. 12, 1943.\nC. G. Montgomery. Losses and Reflections Introduced by Joints and Plungers in 3 cm Waveguides, Jan. 18, 1943.\nC. G. Montgomery. Measurement with a Frequency-Modulated Oscillator at 3 cm, Jan. 18, 1943.\nThe Generation of Harmonics by Silicon and Germanium Crystals, Oct. 23, 1945. RL-818\nMillett, W. E. RL-1074\nMontgomery, R. B. (see Burgoyne, R. H.). RL-651\nMoore, C. E. (see Blue, R. W.). RL-636\nBlue, R. W. RL-640\nMoore, L. F. (see Collins, G. B.). RL-87\nMoore, T. M. A Description of AN/TPS-10 and Its Performance in Mountainous Terrain, Aug. 3, 1944.\nA Survey of the AN/TPS-10 (Little Abner), Apr. [\nMoore, W. AEW Bedford Trials, Oct. 19, 1944.\nMore, K. R. Performance Characteristics of the Magnetron]\nPART y\n\nManual for Magnetrons, Types 2J22-3b, 706 AY - Morse, P.M.\nImpedance in Transmission Lines - Morse, P.M.\nA Method for Relay Radar PP1 Synchronization - Mulvey, J.X. Jr.\nInterconnecting AN/APA-5 and Army Radar Sets - Mulvey, J.X. Jr.\nAirborne Early Warning (S-26 plus additional material) - Murray, W.K.\nParallel Plate Optics for Electrical Scan - Myers, S.B.\nWeight Analysis of Airborne Radar Sets - Myers, W.L.\nNathe, R.U., and W. Roth. Ql-2 and Q3 Servo Amplifiers.\nC. Nawrocki, \"Fine Grid Technique,\" Apr. 3, 1943. (OBJ Radar)\nL. J. Neelands, see I. R. Katz, RL-547\nH. V. Neher, \"The Radiation Laboratory S-Band Amplifier (Preliminary Report),\" July 10, 1943. RL-306\nLow-Voltage K-Band Oscillator, Sept. 17, 1945.\nL. K. Neher, see R. M. Ashby, RL-917\nS. Newell, Instruction Manual for Audio Indicator, Dec. 20, 1945.\nG. H. Nibbe, \"A Method for Automatic Frequency Control of Thermally Tuned Oscillators,\" Dec. 20, 1945.\nCombined Reflector-Cavity Automatic Frequency Control for Thermally Tuned Reflex Oscillator Tubes, Model 5 Synchroscope, June 2, 1944. RL-S-18\nD. B. Nichinson et al., Mechanical Resonant Scanner, [Unknown Date]. RL-555\nN. Nichols, see W. Hurewicz, RL-1007\nF. L. Niemann, \"S-Band Coaxial Line to Rectangular\" [It appears this text is incomplete]\nWaveguide Transitions, Dec. 7, 1945. RL-802\nNonnemaker, G. M., MTI for MEW, May 24, 1945.\nNoodleman, S. Production Sources of Self-Synchronous Tubes.\nNottingham, W. B. Luminescence of RCA Cathode-Ray Tube with Cascade Screen, Feb. 2, 1942. RL-137\nReport on Measurement of British CR Tubes with Long-Persistence Screens, Oct. 7, 1942. RL-310\nConference on P7 Cathode-Ray Tubes held April 5, 1942. Nottingham, W. B. (Continued) et al.\nProposed Performance Specifications for the P7 Long-Persistence Cascade Screen, Aug. 12, 1942.\nStudies of British Phosphors of the Type \u201cC,\u201d \u201cH,\u201d Notes on Photometry, Colorimetry, and an Explanation of the Centibel Scale, Dec. 17, 1945. RL-804\nMemorandum Describing High Gain DC Amplifier. RL-M-110\nComparison of P7 Screen Test Methods, Mar. 14, 1945. Nowak, W. B.\nAntenna Feeds from %e\" Coaxial Line, O'Day, M. D. (see Lipkin, H. J. RL-672)\nA Moving COHO Conversion Unit, Apr. (Olson, V. A)\nApplication of Corner Reflectors to Radar (Theoretical), May 14, 1943. (O'Neal, R. D. et al.) RL-203\nApplication of Corner Reflectors to Radar (Experimental), July 1, 1943. RL-280\nOperation for Peak Performance, Dec. 20, 1945.\nUltra-Portable Microwave Radar Beacons as Beam Approach Aids in Aircraft Landing, Preliminary Manual for Radar Beacon Type BPS (Prototype of AN/CPN-8, Similar in Function and Corresponds to SCR-620), Jan. 3, 1944. RL-M-130\nAN/APS-15A and AN/APS-15B Tests, et al. Flight Test of an Experimental Horn-Fed Antenna for H2X, Dec. 1, 1944. Informal RL-91.3\nJ. Radar Photo Reconnaissance, Apr. Termination Report on Radar Photo Reconnaissance Project, Nov. 16, 1944. RL-S-34\nH2K Radar Displays, Apr. 9, 1945. RL-S-44\nProject Falcon, Air-to-Surface Radar Range. (Overhage, C. F. J.)\nAN/APG-13, Jan. 24, 1944 (RL-91) - P. D. Crout: RL-610, RL-629, RL-696\nAN/APS-b (ASH) Trainer, Sept. 29, 1945 (RL-91) - G. R. Paine\nAN/APG-Tl Training Equipment, July 28, 1945 (RL-91)\nAN/APG-15 Modification Kit for AN/APG-Tl Training Equipment, Aug. 30, 1945 (RL-759-2)\nN. H. Painter: RL-502 - See R. R. Krock\nMatching Resistance Curves by Means of Two Linear Ganged Potentiometers and a Three-Terminal Resistance Network, Aug. 17, 1944 (RL-610)\nCalculation of the Resonant Frequencies of a Torus by Lagrangian and Variational Methods, Nov. 14, 1944 (Palmer, C. H. Jr.) - See V. Josephson, RL-S-52\nC. S. Pao et al.: Paraboloid Antenna Characteristics as a Function of Feed Tilt, Feb. 16, 1944 (RL-479)\nElectrical Design of the AN/TPS-10 Antenna, Dec. [Unknown] (Shaping the Primary Pattern of a Horn Feed), Jan. [Unknown]\nThe Beavertail (AN /CPS-U) Antenna, April 9,\nF. D. Parker. See Hutner, R. A. (RL-21, RL-22, RL-23)\nC. S. Pearsall. Corrosion of Copper, Brass, and Aluminum by Gaseous Dielectrics, January 13, 1943 (RL-795)\nM. R. Fox. RL-501\nF. L. McMillan. RL-895\nM. D. Pearson, et al. The SCI Rapid Scan Height-Finding Antenna, July 9, 1945 (RL-688)\nE. R. Perkins. Results of Tests Performed on \u201cSynchro\u201d Units and Systems, January 14, 1944 (RL-490)\nSynchro Units and Their Characteristics, June 27,\nC. E. Foster. RL-921\nG. D. Perkins. See Lipkin, H. J. (RL-672)\nJ. R. Perkins. See LaRue, J. M. RL-210, et al. Report on Type A and Type B Pulse Transmission Cables and Connectors, September 11, 1943.\nH. A. Perry, Jr. Electrical Test Methods for Radomes, Peterson, J. M. Microwave Technique as of May 19 US.\nPhillips,  R.  S.  Conical  Scanning,  Aug.  4,  1946.  RL-367 \nServomechanisms,  May  11,  1943.  RL-372 \net  al.  Modified  Homing  Course,  Nov.  2,  1942. \nAided  Tracking,  Part  II,  Nov.  3,  1943.  RL-453 \net  al.  Theoretical  Calculation  on  Best  Smoothing \nof  Position  Data  for  Gunnery  Prediction,  Feb.  16, \nSee  Dowker,  C.  H.  RL-578 \nNoise  Filtering  Properties  of  Third  Detectors,  Oct. \net  al.  Analysis  of  the  Tracking  Errors  of  the \nPierce,  J.  A.,  et  al.  Simple  Computation  of  Distance \non  the  Earth's  Surface,  July  8,  1944.  RL-582 \nThe  Future  of  Hyperbolic  Navigation,  Aug.  18, \nPietz,  E.,  and  M.  D.  Fagen.  Vibration  and  Shock  Com\u00ac \nparison  Tests  of  7\"  Cathode  Ray  Tubes  in  Two  Dif\u00ac \nferent  Type  Mounts.  RL-390 \nPike,  B.  W.  Modification  of  SCR-58U  for  Oboe  II,  Feb. \nPinney,  E.,  see  Phillips,  R.  S.  RL-369 \nPlain,  G.  J.,  et  al.  Data  on  SCR  58U  Control  Equip\u00ac \nServo  Generator  Life  Tests,  Apr.  8,  1944.  RL-S-11 \nJ. B. Platt et al. Magnetron Stabilizing Tuner, Dec.\nSee Lyman, E. R. RL-714\nHandbook of Maintenance Instructions for AN/ APA-UO (Micro-H Mark II) Airborne Attachment\nR. Platzman. See Evans, J. E. RL-451\nI. Polk. Synchro Test Equipment and Test Procedure, June 22, 1942. RL-373\nSee Meagher, R. E. RL-49\nElimination of Ground Clutter, Mar. 13, 1944.\nA. R. Poole. See Keary, T. J. RL-808\nC. F. Porterfield. See Chu, L. J. RL-486\nD. Q. Posin. See Clarke, H. F. RL-731\nA. J. Pote. Adjustment of Loran Antennas and Antenna Coupling Units at Frequencies Between 1700\nSee Lawrance, R. B. RL-512\nR. V. Pound. Stub Supports in %\" Coaxial Lines, May\nPhase Distortion in Broad-Band Stub Supports,\nAn S-Band Crystal Mixer, Dec. 14, 1942. RL-242\nComparison of the Frequency Sensitivities of\nSeries and Shunt TR Junctions, January 20, 1943. R. Berger. Preplumbing of Tees for G-Band, November. A Microwave Frequency Discriminator, August 4, 1943. Frequency Discontinuities of Local Oscillator Tubes Due to High-Q Load Circuits, February 27, 1945. An Electronic Frequency Stabilization System for CW Microwave Oscillators, October 1, 1945. RL-815 A Duplex Communication System for Microwaves, An Improved Frequency Stabilization System for Microwave Oscillators, October 26, 1945. RL-837 Powell, V. See Fox, M. RL-501 Preston, W. M. Tune-up Procedure for 3-Cm R.F. Systems Matching, Losses and Frequency Sensitivity of a Rotary Joints with E0 Stub Transformers, December 18, See Platt, J. B. RL-473 Siting and Range of Microwave Beacons, July 5, 1942. Purcell, E. M. Wave Guide Components and Instruments for the 1.25 Cm Region, December 3, 1942. RL-165 A Method for Measuring the Absolute Gain of Microwave Transmitters or Receivers.\nMicrowave Antennas, Jan. 3, 1943. RL-168 et al. K-Band Csec2 Antennas with a Line Source and Shaped Cylindrical Reflector, Nov. 3, 1944.\n\nPart V\n\nRado, G. T. Measurements of the Attenuation of K-Band Waves by Rain, Mar. 7, 1945. RL-603\n\nRagan, G. L. Loss Measurement by Two-Probe Power Reversal Method, Dec. 7, 1942. RL-240\nSee Reed, J. RL-255\nSee Clarke, H. F. RL-1071\nRamsey, N. F. Airborne 3-cm Radar Equipment for AI and ASV Applications, May 22, 1942. RL-27 et al.\nAdvance Development of 3.3-cm System, et al. Photographs of the PPI Indicator Tube with 3-cm ASV over Water and Land, Oct. 27, 1942.\nRawcliffe, R. D. Deflection Yoke Design Information, Focus Coil Control for Cathode Ray Tubes, May [\nRaymond, R. C. Scattering of 10-cm Radiation by Model Airplane, May 21, 1942. RL-156\nSee Chance, B. RL-7\nRedheffer, R. M. Radome Bulletin Number 2, An Out-\nRadome Bulletin Number U, Transmission and Reflection of Single Plane Sheets, July 12, 1944.\nRadome Bulletin Number 6, Radomes and System, [date missing]\nRadome Bulletin Number 7, The Measurement of High Reflections at Low Power, Nov. 20, 1944.\nRadome Bulletin Number 9, The Matching of High Standing Wave Ratios, Dec. 22, 1944. RL-483-9\nSee Dowker, Y. RL-483-10\nRadome Bulletin Number 11, Electrical Properties of Double-Wall and Sandwich Radomes, Feb. 1, 1945.\nRadome Bulletin Number 12, Transmission and Reflection of Parallel Plane Sheets, Jan. 26, 1945.\nRadome Bulletin Number 13, Elliptical Polarization Produced by Streamlined Radomes, Feb. 12, 1945. See Dowker, Y. et al. RL-483-14\nRadome Bulletin Number 15, The Measurement of Dielectric Constants in the One-Centimeter Waveband, [date missing]. See Dowker, Y. RL-483-17\nRadome Bulletin Number 18, The Dependence of Magnetron Pulling on Radome Shape and Orientation, Reed, J. et al. Capacity (Choke) Couplings as Rigid and Non-Rigid Waveguide Connectors, Aug. 27, 1943.\nH2X Range Unit for Navigation and Bomb, et al. Type J and A Test Unit, Aug. 21, 1943.\nRat Race Duplexing, Feb. 4, 1946. RL-888\nReed, J. (Continued) Use and Derivation of A, Z, 0 Chart, May 18, 1943.\nReed, J. C. SB-846B S-Band Oscillator, Feb. 26, 1946.\nPreliminary Instruction Book for Shore Bombardment Beacon Navy Model Mark 2 Mod 0 and Mod 1, Reed, W. 0.\nLine-Controlled Blocking Oscillator, Oct.\nMultiple Pulse Generators, Oct. 15, 1942. RL-278\nThe Use of Synchros for Radial Time Base, Rehkopf, H. L.\nRL-217 (See Bostick, W. H.)\nRL-218 (See Bostick, W. H.)\nRL-219 (See Bostick, W. H.)\nRL-463 (See Bostick, W. H.)\nRL-470 (See Bostick, W. H.)\nSee Bostick, W. H. (1944). RL-545, RL-546. \"Equivalent Circuit of a Pulse Transformer Core.\" Riblet, H. J. \"X-Band Horizontally Polarized Non-directional Antennas.\" April 22. RL-489.\n\nBostick, W. H. (1944). RL-519. \"S-Band Horizontally Polarized Non-directional Antenna.\" August 25.\n\nBirchard, B. L. (1945). RL-577. \"S-Band Vertically Polarized Non-directional Antenna.\"\n\nSlotted Dipole Impedance Theory. (1945). November 21. RL-577.\n\nGilbert, E. N. RL-796. [No title or date provided]\n\nBarker [No name or title provided]. RL-871. [No title or date provided]\n\nBarker [No name or title provided]. RL-976. [No title or date provided]\n\nRice, P. J. (1943). RL-492. \"Comparative Photographs of 1- and 5-Microsecond Signals.\" December 16.\n\nRichardson, J. E. (1943). Cook, J. E. RL-911. [No title or date provided]\n\nRicker, C. R. (1944). \"Instruction Manual for Model 17 and Model 20 Laboratory Modules.\" [No title or date provided]\n\nRieke, F. F. (1944). \"Analysis of Magnetron Performance, Part I: Equivalent Circuit, Method, Applications.\" September 16. [et al. R.F. Loading of 10-Cm Magnetrons, August 24, but no title or author provided for this reference]\nAdjustment of Magnetron Frequency by an External Tuner, Sept. 6, 1943. (See Evans, J. E. RL-451, Fletcher, R. C. RL-809, Evans, J. E. RL-1051)\nRierdan, R. C. et al. Operating Instructions for the Model Jfl7 Klystron for Use as a Local Oscillator in Radar Receivers, May 6, 1942. RL-M-108\nRieth, W. M. Operating Instructions for the AN/CPA-7 Operations Room Equipment Supplementing Radio Set AN/CPS-1, July 2, 1945.\nRieth, W. M. Characteristics of Horn Feeds on Rectangular Waveguide, Dec. 28, 1945. RL-656 (See Keary. RL-808 et al.)\nLinear Array for Use in the AN/APS-23, Roberts, A. et al. RL-357\nA Racon Prospectus with a Pictorial Brief of BGS, Roberts, A. et al.\nBUPS (AN/UPN-1, 2) an Ultra-Portable S-Band Radar Beacon and Its Tactical Uses, June 24, 1944.\nPossible Radar Solutions to the Problem of Accuracy. (Risser, J. R. Characteristics of Horn Feeds on Rectangular Waveguide, Dec. 28, 1945. RL-656)\nRL-S-12, April 7, 1944: Notes on the Rebecca-H System\nRL-71, August 25, 1943: Roberts, S. et al. Measuring Instruments for Three Centimeters\nRL-26, March 9, 1942: Measuring Instruments for Crystal Converters\nRL-253, July 3, 1943: A Simplified Analysis of Conversion Loss in Crystal Converters\nRL-25: Theory of Noise Measurements on Crystals as Frequency Converters, Alexander, R. M.\nRL-287: Dicke, R. H.\nRL-256: Huntington, H. B.\nRL-24: Ramsey, N. F. et al. Comparisons of Methods for Measuring Conversion Loss of Crystals\nRL-408, August 31, 1943: Empirical Method for Measuring Conversion Loss of Crystals, Ramsey, N. F. et al.\nRL-1N23, December 14, 1943: Operation of 1N23 Crystal Rectifiers.\nA Feedback Circuit for Measuring Output Noise Ratio of Crystal Rectifiers (RL-667)\nA Method of Rating the Stability of Oscillators for 1N23 Loss Measuring Set Type 7368 (June 29, 1945)\n1N23 Noise Measuring Set Type 7438 (December 21, 1945)\nRobertson, R. McG. Variable Width Waveguide Scanners for Eagle (AN/APQ-7) and GCA (AN/MPN)\nDesign Considerations for an Improved Interception (Al) Radar, The AN / APS-21 System (December 15, 1945)\nRobinson, C. S., Jr. Cathode Temperatures in Magnetically Operated Characteristics of the 707 A Reflex Oscillator (McNally Tube) (June 9, 1942)\nOperating Characteristics of the 707 A Reflex Oscillator (McNally Tube) (Supplement to Report 53-3)\nOperating Characteristics of the 417 Reflex Klystron (RL-235)\nRobinson, C. S., Jr. Temperature-Compensated 707 A (McNally Tube)\nRobinson, C. V. Pill Box Antenna for Glide Path (November [?])\nRapid Scanning, High Resolution Antennas (Preliminary Report), Feb. 15, 1943. RL-265\nSee Pearson, M. D. (RL-688)\nCrystals (Rochester), Feb. 17, 1942. RL-153\nARO Range Follow-up Unit (Rogers, J. R.), Mar. 19, 1943. RL-363\nSee Hartman, L. A. RL-571\nResults of Tests on Use of Rebecca-Eureka by the Army Ground Forces (Rollman, R. F.), July 26, 1944.\nLinearity of Standard Wire-Wound Volume-Control Type Potentiometers (Rosenberg, P.), Feb. 3, 1943.\nSpecification of Performance Tests for PPI Sinusoidal Potentiometers, Types RL10E and RL14, May [Unknown Year]. RL-318\nPresent Status of Potentiometer Projects in the Radiation Laboratory. June 15, 1943. RL-318\nPotentiometer Type RL-B for Azimuth and Elevation Indication on Magnetically Deflected Cathode-Ray Tube. [Unknown Author], [Unknown Date].\nSinusoidal Potentiometers: Types RL10CB, RL10CD, RL11, RL15\n\nInstruction for Installation and Maintenance of Waffle Relief Maps in Ultrasonic Trainers, Apr. 30, 1945\nSpecifications for 15-Mc Supersonic Crystal for Crystal Cartridges Types 3 and 7B, Jan. 22, 1945\nUltrasonic Radar Trainer PPI Photographs of a Simulated H2X Bombing Mission over Tokyo, Mar. 24, 1945\nVelocity of Propagation of 15-Mc Ultrasonic Pulses in Liquids, Nov. 5, 1945\nRoth, W. Fading Simulator, May 10, 1944 (RL-556)\nNathe, R. U. RL-645-2\nHodder, W. RL-645-13\nNosmo Doppler Simulator, Feb. 1, 1946 (RL-857)\nA Displacement or Velocity Servo Amplifier, Feb. (Preliminary Technical Manual for Falcon) et al.\nPART y\n\nRowland, H. \"Absorption Coefficient of a Styraloy Filled Coaxial Line\" RL-827, Aug. 8, 1945.\n\nNew Type Probe for Coaxial Standing Wave De-Broad Band Bi-Conical Vertically Polarized Dipole, Double Skinback Antenna, Mar. 29, 1946. RL-852.\n\nRubenstein, P. J. (See Kerr, D. E.) RL-406.\n\nSee Fishback, W. T. RL-478.\n\nSee Katz, I. RL-547.\n\nSee Fishback, W. T. RL-568.\n\nOver-Water Transmission Measurements, 19J+1+.\n\nPart I; Preliminary Analysis of Radio and Radar Measurements, Dec. 15, 1944. RL-649. (See Fishback, W. T. RL-799)\n\nRussell, J. B. \"Computers for Radar Control of Plane-to-Plane Gunfire\" 14-130.\n\nSaad, T. S. X-Band Low-Pressure Tests, Dec. 10, 1942.\nX-Band Measurements at Low Pressure, May 18,\n\nSamson, E. W. (See Sturtevant, J. M.) RL-978.\n\nIntroduction to Alternating Currents, Q Values, and Transmission Lines, Aug. 29, 1944. RL-T-17.\nA. Samuelson, \"Analysis of Tracking Data,\" Description of Calculations, Oct. 3, 1944. RL-628\nD. N. Sands, see Bailey, F. S. RL-570\nD. S. Saxon, see Banos, A. RL-748\nGeneral Theory of Electronic Beam Modulators, Sayre, D. et al. Computer Mark 11+ AN /APA-30 XN-1 Instruction Manual, Oct. 16, 1944. RL-M-179\nPulse Doppler with Reference to Ground Speed Indication, Mar. 20, 1944. Informal RL-63\nE. G. Schneider, Brief Description of MEW Micro-wave Early Warning, Sept. 7, 1943. RL-428\nK. E. Schreiner, see Deerhake, W. J. RL-S-67\nEns. C. Schultz, see Nichinson, Mar. 13, 1946. RL-782\nH. L. Schultz, Lighthouse Tube Transmitter-Receiver. See Longacre, A. RL-768 et al. Firefly Moving Vehicle Detector AN/APS-27,\nR. H. Schuman, Regular Report on the Maintenance, Schumb, W. C., see Eisenstein, A. S. RL-813\nJ. Schwartz, see Austin, Aug. 30, 1945. RL-S-58\nJ. S. Schwinger, \"Theory of Obstacles in Resonant Cavities and Waveguides,\" May 21, 1943. RL-205\nE. J. Scott, \"Slip-Ring Assembly for MK 56 Director,\" Oct. 22, 1941. RL-58\nS. Seely, \"Regular Report on the XT-3, The Ten-Centimeter Truck System,\" Feb. 18, 1943. RL-T-10\nW. Selove, \"Detector Cancellation Error as a Function of Carrier Frequency,\" Oct. 31, 1945. RL-859 (Continued)\nW. Selove, \"Notes on MTI Receivers,\" Mar. 25, 1946. RL-1010\nDynamic-Range Compression for MTI, Mar. 15, 1946.\nAn Automatic Noise-Figure Meter, Mar. 26, 1946.\nJ. W. Severinghaus, \"Instructions for Operation of High Gain Video Amplifier for P1+-E Synchroscope,\" Feb. 11,\nInstructions for TS-1+16/AP Check Set, Feb. 11, 1943.\n[E. F. Sewell -> Eisenstein, A. S.]\n[H. Shapiro -> Forbes, G. D.]\n[G. K. Sheckels -> Fairbank, J. D.]\n[J. Sheridan -> Roberts, A.]\n[J. C. Sheridan -> Roberts, A.]\nSheridan, J. C. Computers for Radar Control of Plane-to-Plane Gunfire. 14-130\n[W. B. Sheriff -> Davenport, L. L.]\n[D. F. Sherman] Two Circularly Polarized S-Band An X-Band Hemi-Isotropic Radiator, Jan. 10, 1946. Dipole Arrays Backed by Reflecting Sheets, Mar.\n[R. Sherr -> Nichinson, D. B.]\net al. Instruction Manual for Automatic H2X Camera Model A, May 23, 1944. RL-M-163\net al. Temporary Instruction Manual for Automatic Radar Camera Model B, Apr. 15, 1944. RL-M-164A\net al. Temporary Instruction Manual for Automatic Radar Camera Model B, [Missing Date]\nRL-M-164B, May 1, 1944\nSherwin, C. W., \"Plan-Position Indicator Using a Sinusoidal Potentiometer,\" Dec. 30, 1942, RL-312\nIndicators for a Ground-Controlled Approach System, May 12, 1944, RL-572\nOperating Instructions for the Model B PPI Indicator Central, Apr. 9, 1942, RL-M-107\nShoemaker, F., see Mann, M. M., RL-607\nSichak, W., \"Double Dipole Rectangular Waveguide, One-sided Inductive Irises and Quarter-wave Capacitive Transformers in Waveguide,\" Nov. 17, 1943, RL-624\nSee Purcell, E. M., RL-848\nSiegert, A. J. F., \"On the Fluctuations in Signals Returned by Many Independently Moving Scatterers,\" Nov. 17, 1943, RL-530\nFluctuations in the Return Signals from Random\n\nSiegert, A. J. F. (Continued)\nSee Bartelink, E. H. B.\n\nRL-M-164B, May 1, 1944\nSherwin, C. W., \"Plan-Position Indicator Using a Sinusoidal Potentiometer,\" Dec. 30, 1942, RL-312\nIndicators for a Ground-Controlled Approach System, May 12, 1944, RL-572\nOperating Instructions for the Model B PPI Indicator Central, Apr. 9, 1942, RL-M-107\nShoemaker, F., \"Mann, M. M.,\" RL-607\nSichak, W., \"Double Dipole Rectangular Waveguide, One-sided Inductive Irises and Quarter-wave Capacitive Transformers in Waveguide,\" Nov. 17, 1943, RL-624\nSee Purcell, E. M., RL-848\nSiegert, A. J. F., \"On the Fluctuations in Signals Returned by Many Independently Moving Scatterers,\" Nov. 17, 1943, RL-530\nBartelink, E. H. B., \"See,\" FL-530\nFluctuations in the Return Signals from Random\n\nRL-M-164B, May 1, 1944\nSherwin, C. W., \"Plan-Position Indicator Using a Sinusoidal Potentiometer,\" Dec. 30, 1942, RL-312\nIndicators for a Ground-Controlled Approach System, May 12, 1944, RL-572\nOperating Instructions for the Model B PPI Indicator Central, Apr. 9, 1942, RL-M-107\nShoemaker, F., \"Mann, M. M.,\" RL-607\nSichak, W., \"Double Dipole Rectangular Waveguide, One-sided Inductive Irises and Quarter-wave Capacitive Transformers in Waveguide,\" Nov. 17, 1943, RL-624\nSee Purcell, E. M., RL-848\nSiegert, A. J. F., \"On the Fluctuations in Signals Returned by Many Independently Moving Scatterers,\" Nov. 17, 1943, RL-530\nBartelink, E. H. B., \"Fluctuations in the Return Signals from,\" FL-530\n\nRL-M-164B, May 1, 1944\nSherwin, C. W., \"Plan-Position Indicator Using a Sinusoidal Potentiometer,\" Dec. 30, 1942, RL-312\nIndicators for a Ground-Controlled Approach System, May 12, 1944, RL-5\nSilver, S. (1945). Contribution of the Dish to Impedance Double-Curvature Surfaces for Beam Shaping with Point-Source Feeds. RL-691\nSimmons, E. C., et al. (1945). Analysis and Correction of the Impedance Mismatch due to a Reflector. RL-810\nSimonds, W. N., Jr. (1946). Instructions for TBK-2RL Impedance Bridge. RL-M-257\nSinsheimer, R. L. (1946). A Final Report on AN/APS-10.\nSise, A. F., et al. (1946). History of AN/APG-5, ARO.\nSitterly, B. W. (1944). Elements of Loran. Mar. 8.\nSee Pierce, J. A. RL-582\nHandbook of Procedures for Mobile Charting Units, Air Transportable Loran System. Mar. 30.\nSlater, J. C. (1941). Noise and the Reception of Pulses.\nTheory of the Magnetron Oscillator. August.\nMicrowave Transmission. Oct. 16, 1941. RL-121\nResonant Modes of the Magnetron. Aug. 31, 1942.\nForced Oscillations in Cavity Resonators, Dec. 31, 1943.\nInput Impedance and Tuning of Magnetron Cavities, Mar. 8, 1943.\nTheory of Magnetron Operation, Mar. 8, 1943.\nOperation and Testing of Reflex Oscillators, June.\nHandbook of Maintenance Instructions for AN / APA-53 Indicator Assembly, Oct. 23, 1945.\nHandbook of Maintenance Instructions for AN/AIC-6 Intercommunication System, Oct. 23, 1945.\nSee Hodges, H. T. RL-M-152C.\nFrequency Pulling of ARO Cavities, Feb. 14, 1944. Informal RL-91.\nThe Effects of Cavity Bias on the ARO Cavity Operated by the ARO Modulator, Apr. 27, 1944. Informal RL-91.\nSmith, A. G., see Smith, W. V. RL-230.\nThe J+J70-77 Series of Tunable Magnetrons, Feb. 4, 1944.\nSmith, C. A., see McLaughlin, D. B. RL-658.\nSee McLaughlin, D. B. RL-926.\nPreliminary Instructions for the Manual Bearing, Smith, J. A. Radar Detection of Ground Objects from Air.\nSmith, A. S. & Ashbrook, F. M. \"Intermediate-Frequency Amplifier Overload Characteristics.\" Journal of the Audio Engineering Society, January 31, 1946.\n\nSmith, W. \"A Broad Band TEM Pillbox.\" Journal of the Audio Engineering Society, January 11, 1946.\n\nSmith, W. \"A Grid-Type R-F Attenuator.\" Journal of the Audio Engineering Society, April 4, 1946. RL-902\n\nSmith, W. \"A Flat Plate Beam-Shaping Antenna.\" Journal of the Audio Engineering Society, January 15, 1946.\n\nSmith, W. V. et al. \"Practical Considerations of Magnetron Field Patterns in Cold Magnetrons: Including Correlation with Tube Performance, Tunable Magnetron Tuning and Stabilization.\" Journal of the Audio Engineering Society, July 13, 1944.\n\net al. \"XCT Final Report.\" Journal of the Audio Engineering Society, March 6, 1946. RL-879\n\nSmullin, L. D. \"Measurements of 721A TR Tube Leaks.\" Leiter, H. A. RL-594\n\n\"Testing of Fixed-Tuned, Low-Q, ATR Tubes.\" Journal of the Audio Engineering Society, December [Unknown Year], 1946. RL-971\n\n\"S-Band Bandpass TR Tubes.\" Journal of the Audio Engineering Society, January 23, 1946.\n\n\"X-Band Beacon Reference Cavities.\" Journal of the Audio Engineering Society, January 15, 1946.\n\nSobczyk, A. \"Aided Tracking.\" Journal of the Audio Engineering Society, September 17, 1943. RL-430\n\n\"Aided Tracking.\" Journal of the Audio Engineering Society, November 4, 1943. RL-452\nT. Soller, Nottingham, W. B.: RL-309\nH. Marcy: RL-M-137\nH. S. Sommers, Jr.: Mark 151, Director, Mar. 5, 1946\nS. Sonkin: Pulse Transformers, July 23, 1946, RL-213\nC. M. Sorvaag: A Littelfuse Direct-Reading Wattmeter\nR. C. Spencer: Synthesis of Microwave Diffraction Patterns with Application to CsCe Patterns, June 23\nThe Antenna Slide Rule, Series L, June 3, 1943\nP. M. Austin: Optical Theory of the Corner Reflector, Mar. 2, Reflections from Smooth-Curved Surfaces, Jan. 26, Fourier Integral Methods of Analysis, Jan. 21\nTables and Methods of Calculation, P. M. Austin, See Austin, P. M., RL-S-58\nParaboloid Diffraction Patterns from the Standpoint of Physical Optics, Oct. 21, 1942, RL-T-7\nH. A. Stafford: See Droz, M. E., RL-436\nJ. W. Stafford: Training Apparatus for Radio Set\nLt. C.B. Hawkeye, October 30, 1945: Stanely - Antenna, Plan-Position Indicator for 584 A3\nM.A. Starr, February: Radar Indicator - RL-M-137, see Marcy, H.\nE.R. Steele, May: Radome Bulletin Number 16 - Electrical Aspects of Microwave Sandwich Radome\nA.M. Steenland, see Risser, J.R. - RL-973\nJ. Steinberger, November: Leaky Waveguide Rapid Scanner\nJ.E. Eaton, see RL-769\nBroad-Band Coaxial-Line Horn, July 20, 1945 - Chisholm, E.B. - RL-771\nRisser, J.A., see RL-973\nR.R. Steinke, December: Instruction Manual for Installation of Radiation Laboratory Type B Plugs on Cables\nInstruction Manual for Installation of Radiation Laboratory Type A Plugs on Cables, December 29, 1943\nInstruction Manual for Installation of Chicksan Tool Company 1%-Inch Revolving Joint (Drawing No. 61 DIC) on Radiation Laboratory Types B-1 and B-2 Cables (Army-Navy Types RG-27/U and RG-XX)\nC. G. Stergiopoulos, \"AN JC PS-6 (V-Beam) Antenna\"\nJ. Sterling, see Hagler, D. L., \"RL-M-210\"\nA. M. Stone, \"Progress Reports on TR Tubes,\" January 11, J. L. Lawson\nJ. L. Lawson, \"Infinite Rejection Filters,\" June 1, 1945. RL-675\n\"A Note on Pulse Distortion by Rejection Filters\"\nLow-Power R-F Switch, February 23, 1945. RL-675\nM. W. Strandberg, \"Performance of 3-cm System\"\nSome \"Automatic Frequency Control Circuits,\" March\n\"Automatic Frequency Control of Thermally Tuned Beacon Local Oscillator,\" March 6, 1946. RL-955\nDistortion in X-Band Detectors, December 27, 1945.\nOne Knob Tunable X-Band RF Head Strandberg M.W.P (Jan. 23)\nJ.A. Stratton, Microwave Interference Patterns (Mar.)\nTransmission on 3,000 Me over Sea Water (July 14)\nTransmission on 100 Me over Sea Water\nTransmission on 200 Me over Sea Water\nTransmission on 500 Me over Sea Water\nSee R.A. Hutner RL-21\nL.J. Chu. Notes on Antenna Design RL-123\nR.A. Hutner. Relation of Radar Range to Frequency and Polarization RL-18\nH.A. Straus. Brief Description of AN/TPG-1, AN/FPG-1, SCR-598, Developmental Seacoast Gun-Laying\nJ.M. Sturtevant. Summary of Work on Propeller Modulation at The Radiation Laboratory RL-103\nTests of Beacon Receiver on V-Beam (Dec. 4, 1944)\nRotating Corner Reflectors for Ship Identification (See Hollingsworth, L.M. et al.)\nA Synchronization System for Ground Radar\nI. Sudman, \"Overinterrogation Control of Microwave Mark 56 U Chronograph,\" Apr. 18, 1946. RL-805\nT-5 Field Chronograph for SCR 584, Mar. 15, 1946.\nSuen, T. J. and E. M. Everhart, \"Dielectric Constants and Loss Tangents of Radome Materials,\" Jan. 11,\nG. H. Suits et al., \"Modification of the Amplifier of the AN / APN-2 to Give Sharp Cut-off Wide-Band,\" Apr. 3, 1946. RL-990\nL. J. Sullivan, \"Automatic Plotter RC-308 Used with SCR-584 for Mortar Location,\" Apr. 3, 1946.\nR. J. Sullivan, \"The RL 270 Series of Precision Potentiometers,\" Mar. 15, 1946.\nC. J. Swartwout, \"K-Band Rapid Scan,\" Mar. 15, 1946. Operating Instructions for the K-Band Rapid Scan.\nL. E. Swarts, \"The Antenna for Radar Mark 35,\" Jan.\nSydoriak, S. G. and L. C. Van Atta, \"Graphical Analysis of Beam Patterns from Paraboloid Reflectors,\" June\nR-F Attenuators, Sept. 7, 1943. RL-404\nM. A. Taggart, \"See Pearson, M. D.\" RL-688\nE. C. Find, \"RL-760\"\nRL-862 A New Pillbox Feed, Nov. 7, 1945\nRL-863 Horn with Metal Lens, Nov. 13, 1945\nRL-790 Taylor, W. C. (see Balsbaugh, J. C.)\nRL-669 Tape, G. F. (see Gilbert)\nRL-383 Taylor, C. J. (see Koehler, J. F.)\nRieke Diagrams and Probe-Plate Plunger Charts of Lighthouse Tubes in a Re-entrant Cavity, Teeter, C. E. Jr. (see Cefola, M.)\nSG-1  Antenna Mark 2, Thickens, R. W. Jan. 9, 1945\nRL-553 Pulse Doppler for Detection of Moving Ground Targets, Thomson, R. F. Apr. 21, 1944\nRL-553 A Proposed Design for MX-180/A Corner Reflector (Float Marker, Radar, Droppable), Tilton, P. D. Feb. 5,\nAN/CPS-*, Tobey, A. R. Beavertail Height Finder\nRL-256 Torrey, H. C. (see Huntington, H. B.)\nRL-M-210 Towsley, F. E. (see Hagler, D. L.)\nFlight Behavior of the Flux Gate and Gyrosyn Compasses and Their Effects on GPI, Tull, W. J. Apr. (see Chance, B.)\nRL-S-19\nProposal for Extending the Range of Shoran or M-H Beacon Coverage by Use of GPI, July 20, 1945. Informal RL-91.3\nTurner, E. H. (see Sayre, D.) RL-M-179\nTyson, O. A. Antenna Measuring Equipment, High-Power CW Transmitter for S-Band, August 24, 1944. RL-601-2\nAntenna Measuring Equipment, 100-Db Linear Audio Amplifier, August 23, 1944. RL-601-3\nAntenna Measuring Equipment, Automatic Antenna Pattern Recorder, January 16, 1945. RL-601-4\nUhlenbeck, G. E. Theory of Random Processes, October 15, 1945.\nUrquhart, K. J. (see Germeshausen, K. J.) RL-892\nInstruction Manual for Service Modulator Model 9, January 6, 1945.\nVan Atta, L. C. Antenna Design and Pattern, January 6, 1945.\nEffect of Paraboloid Size and Shape on Beam Pattern, C. V. Robinson. Information on Standard Radiation Laboratory Paraboloid Reflectors, March 3, 1943. (see Harvey, G. G. RL-414)\nVan Valkenburg, M. E. - Dunbar, A. S. \"RL-685\"\nVan Vleck, J. H. \"Atmospheric Absorption of Microwaves\" Mar. 1, 1945.\n\"The Relation Between Absorption and the Frequency Dependence of Refraction\" May 28, 1945.\nVane, A. et al. \"Propagation over Short Paths\" RL-1002 - Dicke, R. H.\nVershbow, A. E. - Czapek, E. L. \"RL-462\"\nVineyard, G. \"Numerical Calculation of Space Charge Behavior and Power in the Magnetron\" Mar. 29, 1946.\n\"Effect of the Tuning Plunger on Operation of 2K33\" Vineyard, G.\n\"Electron Optical Studies of the 2K33 Tube\" Jan.\nVitter, A. L. et al. \"LCT, 900-Mc FM-CW Magnetron\"\nVogel, B. R. - Chisholm, E. B. \"RL-775\"\nVoorhies, H. G., Jr. \"An Experimental S-Band Airborne\" Walker, R. M. \"Broad Band Test Loads\" Oct. 9, 1945.\n\"AN/APG-5 (ARO) as a Terrain Clearance Indicator\"\nH. F. Clarke, \"Corners, Bends, and Twists in Rectangular Waveguide: Dielectric Windows,\" June 29, 1944. (RL-1071)\nH. Fleisher, \"Walworth Waveguide Bends,\" January 28, 1944. (RL-S-3, RL-737)\nX-Band Waveguide Corrosion Proofing, October 6, [no author or report number given]\nH. Wallman, \"Impulse and Square-Pulse Response of Various Filters,\" June 10, 1942. (RL-285)\nA. 70-Mc Wide IF Amplifier, June 26, 1943. (RL-307)\nStagger-Tuned I-F Amplifiers, February 23, 1944.\nStagger-Damped Double-Tuned Circuits, March 23, [no author or report number given]\nG. H. Suits, \"Realizability of Filters,\" December 8, 1944. (RL-613, RL-637)\nA. Walter, \"Calculation of Pulse-Forming Networks Having Slow Rates of Voltage Rise,\" March 12, 1945.\nO. T. Fundingsland, [no report or title given]. (RL-765)\nJ. B. H. Kuper, [no report or title given]. (RL-443)\nJ. B. H. Kuper, [no report or title given]. (RL-717)\nJ. B. H. Kuper, [no report or title given]. (RL-872)\nJ. V. E. Ward, see J. J. Hibbert, \"Additional Modification, Calibration, and Plotting,\" [no date or report number given]. (RL-508-3)\nProcedures for RC-291* Plotting Equipment, Feb. 18, 19--, J. D. Horgan RL-M-241, RL-S-47, J. W. Brean RL-S-62\nWarner, A. H. Report of A.A.B. Test on XT-1 at Fort Monroe, Virginia, February\u2013March, 1912, July 30, C. A. Washburn Sine Potentiometer Tester, Mar. 21, B. P. Washburne Blackburn, J. K. RL-797, T. H. Waterman see S. D. Bennett RL-604, E. R. Gaerttner RL-627, B. W. Weber Preliminary Instruction Manual for AN/ APG-15, H. F. Webster Performance of Coupling for 1Vz-Inch x 3-Inch Waveguide, Mar. 6, 1944. RL-538\n\nD. F. Weekes A Video Delay Line, Apr. 24, 1943.\nH. G. Weiss Special Report on Tuning Indicators and Automatic Tuning Systems, Sept. 15, 1941. RL-107\nAEW Tactical Tests at Brigantine, June 15, 1945.\nP. Weiss and S. A. Goudsmit, \"Kinetic Derivation of the Thermal Noise Formula,\" January 18, 1943. RL-191 (See Goudsmit, S. A. RL-196; Phillips, R. S. RL-532; Kenngott, R. L. RL-677)\n\nH. Wenetsky, \"Preliminary Handbook of Operating and Maintenance Instructions for Model AN/APA-46 Aircraft Radar Equipment,\" June 1, 1945. RL-M-227\n\nC. F. West, et al., \"Pictorial Brief of an Experimental AGL-1 Installation,\" May 10, 1943. RL-377 (Tests of AGL-1 installed in Tail of B-24D Airplane, March 5, 1943. Informal RL-94)\n\nW. J. West, \"A Four Horn Feed to Give CSC2 Antenna an IFF Mark 5/UNB Feed in the SCI Search Antenna,\" April 10, 1946. RL-898\n\nAn IFF Mark 5/UNB Feed in the AN/CPS-6 Vertical Antenna, April 10, 1946. RL-898\n\nAn IFF Mark 5/UNB Radiator in the AEW An-\n\nH. H. Wheaton, et al., \"Instruction Manual for Echo-General Lecture Series on Radar Components,\" December [No Year Given]\nLecture Outline for Course on AN/APG-13 Falcon:\nWheeler, GF. \"A Photographic Method for Assessment of Bomb Dispensing,\" RL-763-0, Oct. 2, 1945.\nWheeler, GJ. \"Reduction of Power Line Noise in Electrical and Physical Characteristics of Some Commercial Feed-Through Filters,\" RL-786, Aug. 8, 1945.\nWhelpton, J. \"Admittance Characteristics of S-Band Waveguide Fed Dipoles,\" RL-1082, Jan. 24, 1946.\nWhite, AB. \"Tabulation of CRT Screen Properties, Evaluation of Specifications for P14 CRT Screens,\" RL-1082, Apr. (Thumbnail Sketch for December, February, April, and May)\nWhite, DG. \"Thumbnail Sketch for December and Thumbnail Sketch for February and March,\" Apr.\nWhite, HJ. \"Rotary Spark Gap Modulators,\" RL-209, June 1, 1942.\nSee Perkins, RL-424.\nWhite, HJ (Continued). \"Analysis of Condenser Charging in Line Type.\"\nPart I, Rectifier Filter Circuit Analysis, Feb. 17, 1942. RL-T-3\nRectifier Filter Circuit Analysis, Nov. 4, 1942. RL-483-3\nRadome Bulletin Number 3, Ice Formation on Shipborne Radomes, Feb. 15, 1944. RL-668\nLeachman, R. B. RL-566\nWhite, M. G. Spark Gap Colloquium at Radiation Laboratory\nWhitford, A. E. Report on Hard Tube Modulators\nJerrems, A. S. RL-216\nWhitham, G. E. Hite, G. RL-329\nHite, G. RL-516\nFlock, W. L. RL-573\nWhitmer, C. A. Huntington, H. B. RL-256\nRoberts, S. RL-408\nA Conversion Loss Set for Testing K-Band Crystal Rectifiers, Jan. 16, 1945. RL-668\nWhitmer, R. M. Roberts, A. RL-357\nJ. M. Cunningham. BGS 10-Cm Radar Beacon, Waveguides without Metal Walls, May 10, 1945.\nRange Accuracy of AN/APG-5 (ARO)\nWiener, N. Response of a Nonlinear Device to Noise.\nJ. B. Wiesner (see Johnson, M. H.) RL-246\nF. L. McMillan, Jr. RL-254\nDetails of X-Band High-Level TR Tube Test Bench, 3-cm Magnetron Test Bench Construction\nD. Williams Comparison of Performance of 10-cm and 3-cm Advanced Development Systems, July 13\nAltitude Determination by Means of a \u201cVertical\u201d Linford, L. B. RL-353, RL-354\nRecent Performance of the 3-cm Advanced Development Systems Wilson, D. G. (see Vane, A. B.) RL-468\nE. D. Winkler (see Redheffer, R. M.) RL-483-15\nDowker, Y. RL-483-17\nA. I. Winslow The Sealing of Air at Rotating Shafts\nD. F. Winter (see Miley, H. A.) RL-620, RL-621, RL-622\n\"Winterscope\" or Fast Sweep Synchroscope, Apr.\nC. R. Wischmeyer Resistance-Capacitance Networks, Echo Box Application, Apr. 18, 1946. RL-1040\nSee H. H. Wheaton RL-M-165\nSee Keary, T. J. (RL-808)\nF. B. Wood, Handbook of Maintenance Instructions for Type TTX-1BL Test Set (Type B), January 1944.\nTypes TON-IGA (Type Q) and TON-1BL Oscilloscope, see Katz, S. (RL-M-142)\nSee Jacobson, E. A. S. RL-M-143A, RL-M-174.\nHandbook of Operating and Maintenance Instructions for Echo Boxes TES-8MK and TES-9MK, Mar.\nHandbook of Operating and Maintenance Instructions for Dummy Load TS-253/AP, Apr. 9, 1945.\nInstructions for TFX-17GA, TFX-18GA, TFX-19GA, TFX-30EC, TFX-31EC, Model 51 and similar types of Micrometer Frequency Meters, May.\nSee Simmons, E. C. (RL-M-237)\nSee Zink, A. J. (RL-M-238)\nCatalog of Microwave Test Equipment, Sept. 30,\nJ. W. Woodbury, see Jelatis, J. G. (RL-S-77)\nWoodbury, R. B. Frequency Division with Blocking.\nOscillators, Part I, Apr. 10, 1944. (RL-544)\nPulse Characteristics of Common Receiver-Type\nWoodcock, W. (see Linford, L. B. RL-353)\nSee Linford, L. B. (RL-354)\nSee Linford, L. B. (RL-356)\nWoodward, J. E. (see Ottens, R. C. Informal RL-91.3)\nWoodward, R. H. et al. Notes on the European and Eastern Atlantic S.S. Loran Systems, Apr. 17, 1945. (RL-607) (Worrell, F. T. sees Mann, M. M.)\nDielectric Phase Shifters for Waveguide, Sept. 14, 1945. (3-cm Vertebrae Flexible Waveguide, Oct. 10, 1945. RL-832)\nWorthington, H. R. Jr. Measurement of Phase in Microwave Antenna Fields (Mortar Fire Detection, Apr. 10, 1946. RL-1064)\nK-Band Anti-Aircraft Fire Control, Feb. 21, 1946. (See Millett, W. E. RL-1074)\nYeater, M. L. Measurement of Pressure in Gas Tubes\nby a Radio-Frequency Method, Sept. 9, 1944. RL-432\nYoung, G. J. Primary Feeds in Cylindrical Parabolas,\nYoung, D. R. Radar Beacon, Mark 1 Mod 1, May 29, 1944. RL-S-2\nYoung, L. B. (see Johnson, S. F.) RL-M-146\nYoung, R. T. Waveguide Termination for Measuring Fourier Analysis of Pulses with Frequency Shifts During the Pulse, Jan. 30, 1943. RL-224\nFrequency and Spectrum Characteristics of Standard Magnetrons and the Effect of Change of Shape of Current Pulse, Mar. 12, 1943. RL-225\nSpectra of Magnetrons for Long Pulses, July 5,\nPresent Status of High Power at S-Band, Sept. 15,\nYounker, E. L. Vertebrae Type Flexible Waveguide,\nDielectric Properties of Water and Ice at K-Band,\nAn Improved K-Band Vertebrae Waveguide, Aug.\n(see Millett, W. E.) RL-1074\nZabel, C. W. (see Colby, N. C.) RL-166\nH. Zeller, \"High-Ambient Life Test of an Oil-Filled Pulse Transformer,\" Jan. 19, 1944. RL-514\nSee Bostick, W. H., \"RL-545\"\nSee Bostick, W. H., \"RL-546\"\nSee Germeshausen, K. J., RL-880\nA. J. Zink and F. B. Wood, \"Instructions for K-Band Bench Testing,\" Apr. 5, 1946. RL-M-238\n\nOSRD Appointees\nDivision\nChief\nAlfred L. Loomis\nJohn [Name Unclear]\nJohn [Name Unclear]\nJohn [Name Unclear]\nJohn [Name Unclear]\nTechnical Aides\nEdward H. Cutler\nFrank D. Lewis\nNora M. Mohler\nFletcher G. Watson\nHenry O. Eversole, Jr.\n(Administrative Aide)\nDivision Secretaries\nEdward L. Bowles, John G. Trump\nJohn R. Loofbourow\n\nDivision Members\nR. R. Beal\nW. R. G. Baker\nEdward L. Bowles\nRalph Bown\nLee A. DuBridge\nMelville Eastham\nRay C. Ellis\nJohn A. Hutcheson\nLoren F. Jones\nErnest O. Lawrence\nGeorge Metcalf\nI. I. Rabi\nC. Guy Suits\nFrederick E. Terman\nAlan T. Waterman\nWarren Weaver\nH. Hugh Willis\n\nRADAR Model Shop\nSECTION 14.1 \u2014 RADAR MODEL SHOP (Discontinued April 19 UU)\nChief Melville Eastham\nMembers: Lee A. DuBridge, A.H. Poillon, Eli C. Hutchinson, C. Guy Suits, Frederick E. Terman\n\nSECTION 14.2 \u2014 NAVIGATION (Discontinued April 19 UU)\nChief Melville Eastham\nMembers: Ralph Bown, Donald Fink, J. Curry, Street\n\nCONTRACT NUMBERS, CONTRACTORS, AND SUBJECT OF CONTRACT\n\nContract Number Contractor Subject\nNDCrc-25 University of California, Berkeley, California Resnatron tubes\nNDCrc-53 Massachusetts Institute of Technology, Cambridge, Massachusetts\nSuperseded by OEMsr-262\nNDCrc-73 RCA Manufacturing Company, Camden, N.J. Microwave components\nNDCrc-74 RCA Manufacturing Company, Camden, N.J. Pulse transmitter tubes and receivers for Loran\nNDCrc-150 Radio Corporation of America Manufacturing Co.\nRCA Victor Division, Camden, N.J.\nLong-delay and dark-trace cathode-ray tubes: NDCrc-174, NDCrc-175\nWestern Electric Company, Bell Telephone Laboratories, New York, N.Y.\n3-cm generator: NDCrc-175\nMagnetrons and oscillators: NDCrc-192\nWestinghouse Electric & Manufacturing Company, East Pittsburgh, Pa.\nLaboratory pulsers: NDCrc-203\nMassachusetts Institute of Technology, Cambridge, Massachusetts\nSuperseded by OEMsr-262: NDCrc-205\nWestern Electric Company, Bell Telephone Laboratories, New York, N.Y.\nDevelopment of receivers for long-range navigation system: OEMsr-2\nWestern Electric Company, Bell Telephone Laboratories, New York, N.Y.\nPulse timers for Loran: OEMsr-5\nMassachusetts Institute of Technology, Cambridge, Massachusetts\nRaytheon magnetron model shop: OEMsr-7\nGeneral Electric Company, Schenectady, N.Y.\nFive experimental permanent magnets: OEMsr-7\nOEMsr-8 General Electric Company, Schenectady, N.Y. Magnets and receivers, etc.\nOEMsr-9 General Electric Company, Schenectady, N.Y. One Loran pulse transmitter and four tubes\nOEMsr-10 General Electric Company, Schenectady, N.Y. (a) Long-delay phosphors, (b) 10-cm magnetrons, (c) two gun currents\nOEMsr-15 Sperry Gyroscope Company, Brooklyn, N.Y. Antenna parabolae and gears\nOEMsr-53 Sperry Gyroscope Company, Brooklyn, N.Y. Pulse receivers for LRN\nOEMsr-61 Massachusetts Institute of Technology\nSuperseded by OEMsr-262\nOEMsr-67 Sperry Gyroscope Company, Brooklyn, N.Y. Klystron oscillators\nOEMsr-73 Westinghouse Electric & Manufacturing Company, East Pittsburgh, Pa. Pulse transmitters\nOEMsr-74 Westinghouse Electric & Manufacturing Company, East Pittsburgh, Pa. Laboratory pulsers\n\nContract Numbers, Contractors, and Subject of Contract (Continued)\nContract Number Contractor Subject\nOEMsr-74 Westinghouse Electric & Manufacturing Company, East Pittsburgh, Pa. Laboratory pulsers\nOEMsr-84 Raytheon Manufacturing Company, Waltham, Massachusetts 3-cm magnetrons\nOEMsr-118 Sperry Gyroscope, Inc., Brooklyn, NY Additional Klystron work\nOEMsr-157 Western Electric Company (Bell Telephone Laboratories), New York, NY 3-cm receiving tube\nOEMsr-164 Research Construction Company, Cambridge, Mass. Radar model shop\nOEMsr-168 Sperry Gyroscope Company, Brooklyn, NY Crystal mixer receivers\nOEMsr-180 General Electric Company, Schenectady, NY Permanent gas thyratrons\nOEMsr-191 Massachusetts Institute of Technology (Laboratory for Insulation Research), Cambridge, Mass. Development and wide frequency investigation of dielectrics\nOEMsr-233 General Electric Company, Schenectady, NY AGL-1 airborne gun-laying radar system\nOEMsr-248 General Electric Company, Schenectady, NY Long-delay and dark-trace cathode ray tubes\nOEMsr-252 RCA Victor Division (RCA Laboratories)\nCamden, N.J.\nNoise reduction system, OEMsr-262\nMassachusetts Institute of Technology, Cambridge, Mass.\nRadiation Laboratory\nOEMsr-281\nLink Aviation Devices, Inc., Binghamton, N.Y.\nAl-10 training gear, OEMsr-288\nWestinghouse Electric & Manufacturing Company, Bloomfield, N.J.\nCold emission power tubes, OEMsr-335\nPolytechnic Institute of Brooklyn, Brooklyn, N.Y.\nDevelopment of attenuators and RF test equipment, OEMsr-344\nGeorgia School of Technology, Atlanta, Ga.\nHighly selective audio-amplifier and narrow-band lock-in type amplifier, OEMsr-358\nFranklin Institute (Bartol Research Foundation), Philadelphia, Pa.\nMagnetron cathode studies, OEMsr-360, OEMsr-360\nFranklin Institute (Bartol Research Foundation), Philadelphia, Pa.\nElectronic switch, OEMsr-362\nPurdue Research Foundation, Lafayette, Indiana\nCrystal detectors, OEMsr-369\nZenith Radio Corporation, Chicago, Illinois\nLightweight range-only unit\nOEMsr-380 Sylvania Electric Products, Inc. (Formerly Hygrade Sylvania, Inc.), Emporium, Pennsylvania A special tunable intermediate frequency amplifier\nContract Number Contractor Subject\nOEMsr-382 Brown University Providence, Rhode Island Cathode-ray tube project\nOEMsr-386 Eastman Kodak Company Rochester, NY Microwave absorbent paint\nOEMsr-387 University of Pennsylvania Trustees of the Philadelphia, Pa. Radar ranging system and high-frequency video amplifiers\nOEMsr-388 University of Pennsylvania Trustees of the Philadelphia, Pa. Crystal research\nOEMsr-389 Cornell University Ithaca, NY Theoretical aid\nOEMsr-429 RCA Victor Division (License Division Laboratory), Camden, N.J. Loran receiver for receiver trainer\nOEMsr-443 RCA Victor Division Harrison, N.J. Tube model shop service for Columbia Radiation Lab\nColumbia University, Trustees of New York, New York\nColumbia Radiation Laboratory\nHarvey Radio Laboratories, Inc., Cambridge, Massachusetts\nSix transmitting sets for long-range navigation project\nRadio Engineering Laboratories, Inc., Long Island City, N.Y.\nThirty-six Loran transmitters\nHarvey-Wells Communications, Inc., Southbridge, Massachusetts\nFifteen Loran receivers\nGeneral Electric Company, Schenectady, N.Y.\nPrecision aircraft scanners\nGeneral Electric Company, Schenectady, N.Y.\nTwo truck-mounted XT-1A anti-aircraft fire control radars\nUniversity of Colorado, Boulder, Colorado\nStable noncrystal controlled low-frequency oscillator\nGeneral Electric Company, Schenectady, N.Y.\nFour (4) AGL-1 equipments\nKansas State College, Manhattan, Kansas / General Electric Company\nFort Wayne, Indiana and Pittsfield, Massachusetts\nTime-delay measuring instruments\n\nOEMsr-582 Transformer model shop, Sylvania Electric Products, Inc., Emporium, Pennsylvania\nOEMsr-583\n\nSpecial signal generators\nOEMsr-589 Raytheon Manufacturing Company, Newton, Massachusetts\nTransformer model shop\n\nOEMsr-609 Leland Electric Company, Dayton, Ohio\nThree-phase aircraft alternator\nOEMsr-619 American Machine and Defense Corporation\nPrecision antenna mount for use with the CXBL set (SM prototype)\n\nOEMsr-633 Fada Radio & Electric Company, Long Island City, New York\nLoran receivers\n\nContract Numbers, Contractors, and Subject of Contract (Continued)\nContract Number Contractor\nOEMsr-634 Carnegie Institution of Washington, Geophysical Laboratory, Washington, D.C.\nCathode-ray tube screens\n\nOEMsr-642 Sperry Gyroscope Company, Garden City, N.Y.\nAGL-2 fire control system\n\nUniversity of California\nOEMsr-663, Gilfillen Bros., Inc., Los Angeles, CA, high-vacuum switch\nOEMsr-684, OEMsr-689, RCA Victor Division (RCA Laboratories), Princeton, NJ, ground-control-of-approach landing systems AN/MPN-1 (XE-1)\nRCA Victor Division (RCA Laboratories), Camden, NJ, trainer for SCR-584, anti-aircraft fire control radar OEMsr-691\nOEMsr-709, Westinghouse Electric & Manufacturing Company, Bloomfield, NJ, UHF propagation studies\nGeneral Electric Company, Schenectady, NY, high-pressure spark gap OEMsr-723\nOEMsr-728, State College of Washington, Pullman, WA, Loran receivers\nOEMsr-768, Cornell University, Ithaca, NY, microwave propagation studies\nOEMsr-770, Harvey-Wells Communications Inc., Southbridge, MA, theoretical aid\nOEMsr-777, fifty Loran receivers\nWestern Electric Company (BTL), New York, NY Interference and field strength study OEMsr-781 Rensselaer Polytechnic Institute, Troy, NY Trigger circuits OEMsr-789 Radio Manufacturing Engineering Laboratories, Inc., Long Island City, NY Five Loran training equipments OEMsr-805 Harvey Radio Laboratories, Inc., Cambridge, MA Twenty Loran transmitters OEMsr-812 Fairchild Camera & Instrument Corporation (formerly Fairchild Aviation Corporation), Jamaica, NY (a) AGL central-station computer and (b) AGS gyro sight and spinner mount OEMsr-821 Franklin Institute (Bartol Research Foundation), Philadelphia, PA Crystal clock for Loran receiver OEMsr-832 Philco Corporation, Philadelphia, PA LHTR unit for ARO radar and construction of six OEMsr-872 RCA Victor Division, Harrison, NJ RF tube development\n\nContract numbers, contractors, and subject of contract.\nOEMsr-874, Fairchild Aviation Corporation, Jamaica, N. Y.\nOEMsr-890, Emerson Radio & Phonograph Corporation, New York, N. Y.\nOEMsr-900, Carnegie Institute of Technology, Pittsburgh, Pa.\nOEMsr-918, Galvin Manufacturing Corporation, Chicago, Illinois\nDalmp-Victor, Inc., San Francisco, California\nGalvin Manufacturing Corporation, Chicago, Illinois\nRCA Victor Division, Camden, N.J.\nSylvania Electric Products, Inc., Emporium, Pennsylvania\nSylvania Electric Products, Inc., Salem, Massachusetts\nStevens Institute of Technology, Hoboken, N.J.\nRCA Victor Division, Camden, N.J. (License Division)\nKuthe Electric Company, Newark, N.J.\nRCA Victor Division, Lancaster, Pennsylvania\nLibrascope, Incorporated, Burbank, California\nGalvin Manufacturing Corporation, Chicago, Illinois\nDouglas Aircraft Company, Santa Monica, California\nRange follow-up for ARO Trainer for SH radar\nDark-trace cathode-ray tubes\nBPP, portable radar beacon (AN/PPN-2)\nDevelopment of radar scan-ners\nAirborne range only: ARO\nLoran receiver developments\nRadar tube for pulsed and CW operation\nTube model shop\nDevelopment of electric brushes through power metallurgy\nLightweight tail warning system (AN/APS-13)\nLaboratory Lodar direction-finding receivers\nDevelopment of the H-50 hydrogen thyratron\nRadar tube model shop\nRadar bombing computers and ballistic computer for gun director Mark 56\nBGS beacons, construction of forty\nAntenna installation for project \u201cEagle\u201d (AN/APQ-7)\nInternational Projector Corporation, New York, NY\n\nOEMsr-1089, OEMsr-1091, OEMsr-1112, OEMsr-1127\nWilcox & Gibbs Sewing Machine Company, New York, NY\nWestinghouse Electric & Manufacturing Company, Sharon, PA\nRCA Victor Division (National Broadcasting Company), Camden, NJ\n\nModel of scanning antenna for Eagle (AN/APQ-7)\nEquation solver for SM and SCR-615 trainers\nTransformer model shop\nRelay radar system\n\nContract Numbers, Contractors, and Subject of Contract (Continued)\n\nContract Number Contractor Subject\nOEMsr-1139 E. I. du Pont de Nemours, Inc., Wilmington, DE Research on sintering of boron and laboratory preparation of pure germanium\nOEMsr-1140 Allen B. DuMont Laboratories, Inc., Passaic, NJ P3I indicator units\nOEMsr-1141 Allen B. DuMont Laboratories, Inc., Passaic, NJ Development of cathode-ray tube screens\nOEMsr-1143 Emerson Radio & Phonograph Corporation, New York, NY Power supply for lodar receivers\nOEMsr-1146\nMachlett Laboratories, Inc., Springfield, Connecticut, High-power S-band magnetron, OEMsr-1149, General Electric Company, Schenectady, New York, Gyro lead computer sight for the AGS radar, OEMsr-1162, Massachusetts Institute of Technology (Servomechanisms Laboratory), Cambridge, Massachusetts, Servos for gun director Mark, OEMsr-1165, Westinghouse Electric & Manufacturing Company, Bloomfield, New Jersey, K-band transmitter tube developments, OEMsr-1167, Chrysler Corporation, Detroit, Michigan, Radar scanning units for SCR-584 and gun director Mark 56, OEMsr-1186, Sylvania Electric Products, Inc., Salem, Massachusetts, K-band RF head, OEMsr-1199, E. I. du Pont de Nemours, Inc., Wilmington, Delaware, HARP protective coatings, OEMsr-1212, Western Electric Company, New York, Thermistors for RF power measurement, OEMsr-1218, Western Electric Company (BTL), New York, NY, Broad-band TR and anti-TR, OEMsr-1220.\nFranklin Institute (Bartol Research Foundation, Philadelphia, Pennsylvania)\nLoran supersonic trainer OEMsr-1239\nWestinghouse Electric & Manufacturing Company, Sharon, Pa.\nTransformer model shop II OEMsr-1242\nChicago Telephone & Supply Company, Elkhart, Indiana\nSpecial winding machine OEMsr-1269\nUtah Radio Products Company, Chicago, Illinois\nDesign and sample production of pulse transformers OEMsr-1283\nFederal Telephone & Radio Corporation, Newark, New Jersey\nHigh impedance cable OEMsr-1291\nMaguire Industries, Inc. (General Electronics Industries Division), Greenwich, Connecticut\nStabilized scanner for the H2K radar and construction of five OEMsr-1295\nSylvania Electric Products, Inc., Emporium, Pa.\nCathode-ray tube screens OEMsr-1299\nGeneral Electric Company, Schenectady, New York\nGun director Mark 56\n\nContract Numbers, Contractors, and Subject of Contract (Continued)\nContract Number\nOEMsr-1306 General Electric Company, Schenectady, New York: Broad-band TR and anti-TR\nOEMsr-1311 California Institute of Technology, Pasadena, California: Precision measurement of waveguide discontinuities\nOEMsr-1336 General Electric Company, Schenectady, New York: Stable base unit for radar antenna\nOEMsr-1337 Sperry Products, Inc., Hoboken, New Jersey: MTB computing radar sight\nOEMsr-1338 International Business Machines Corporation, Endicott, New York: Counter for Mark III Loran indicator\nOEMsr-1352 Sylvania Electric Products, Inc., Salem, Massachusetts: Transformer model shop\nOEMsr-1358 Fairchild Camera & Instrument Corporation, Jamaica, New York: Cameras for aerial radar photography\nOEMsr-1360 University of Michigan, Ann Arbor, Michigan: Infrared absorption by water vapor\nOEMsr-1361 American Type Founders, Elizabeth, New Jersey: Antenna mounts for high-resolution radar\nGeneral Electric Company, Schenectady, New York\n- K-band crystals for OEMsr-1394\n- Components for two SCI radars (CXHR), OEMsr-1408\n\nWestern Electric Company (BTL), New York, NY\n- Germanium crystal rectifiers for radar, OEMsr-1409\n- High-power enclosed fixed-gaps\n\nPurchase Order 600,072, Western Electric Company, New York, NY\n- Procurement of Type D-160207 oscillator\n\nPurchase Order 600,073, Western Electric Company, New York, NY\n- Procurement of Type D-160537 magnetrons\n\nOrder TPS-38541, General Electric Company, Schenectady, New York\n- Procurement of one square wave generator and two oscilloscopes\n\nNote: Subject of contract includes D-1, NDRC.\n\nTITLES OF DIVISION 14 SUMMARY TECHNICAL REPORTS\nSummary Technical Report of Division 14, NDRC\nVolume 1: Radar: Summary Reports and HARP Project.\nVolume 2: Military Airborne Radar Systems (MARS)\nVolume 3: Bibliography of Division 14 and Radiation Laboratory Reports\nRadiation Laboratory Series (Published by the McGraw-Hill Book Company)\n1. Radar System Engineering, Louis N. Ridenour\n2. Radar Aids to Navigation, J. S. Hall\n3. Radar Beacons, A. Roberts\n4. Loran, J. A. Pierce, A. A. McKenzie, R. H. Woodward\n5. Pulse Generators, G. N. Glasoe, J. V. Lebacqz\n6. Microwave Magnetrons, George B. Collins\n7. Klystrons and Microwave Triodes, D. R. Hamilton, J. K. Knipp, J. B. H. Kuper\n8. Principles of Microwave Circuits, C. G. Montgomery, E. M. Purcell, R. H. Dicke\n9. Microwave Transmission Circuits, G. L. Ragan\n10. Waveguide Handbook, N. Marcuvitz\n11. Technique of Microwave Measurements, C. G. Montgomery\n12. Microwave Antenna Theory and Design, S. Silver\n13. Propagation of Short Radio Waves, D. E. Kerr\n14. Microwave Duplexers, L. D. Smullin, C. G. Montgomery\n15. Crystal Rectifiers, H. C. Torrey, C. A. Whitmer\n16. Microwave Mixers, R. V. Pound\n17. Components Handbook, John F. Blackburn\n18. Vacuum Tube Amplifiers, George E. Valley Jr., Henry Wallman\n19. Waveforms, Britton Chance, F. C. Williams, V. W. Hughes, D. Sayre, E. F. MacNichol Jr.\n20. Electronic Time Measurements, Britton Chance, R. I. Hulsizer, E. F. MacNichol Jr.\n21. Electronic Instruments, I. A. Greenwood Jr., D. MacRae Jr., H. J. Reed, J. V. Holdam Jr.\n22. Cathode Ray Tube Displays, J. T. Soller, M. A. Starr, George E. Valley Jr.\n23. Microwave Receivers, S. N. Van Voorhis\n24. Threshold Signals, J. L. Lawson, G. E. Uhlenbeck\n25. Theory of Servomechanisms, H. M. James, N. B. Nichols, R. S. Phillips\n26. Radar Scanners and Radomes, W. M. Cady, M. B. Karelitz, L. A. Turner.\n27. Computing Mechanisms and Linkages, A. Svoboda (The Radiation Laboratory Series)\n\nFrom its formation in November 1940 to its dissolution at the end of 1945, the Radiation Laboratory, maintained at the Massachusetts Institute of Technology under contract with the National Defense Research Committee of the Office of Scientific Research and Development, was the foremost U.S. research and development institution in the field of microwave radar. OSRD was instructed by President Roosevelt to record and preserve for the public at large the durable values of the wartime work it sponsored. The series was undertaken by Dr. L. A. DuBridge, director of the Radiation Laboratory. Work on the series has been under way since May 1945, under the general supervision of Louis N. Ridenour, editor-in-chief, and George B. Collins, deputy editor-in-chief.\nThe series consists of 27 titles and a general index, written and edited primarily, but not entirely, by members of the Radiation Laboratory. Since the laboratory has been a principal focus for the exchange of information among all agencies working in radar during the war, it has been able to collect all important information in the field.\n\nWhile the investigations that led to the reported results had the single aim of giving the Army and Navy the best possible military radar equipment, the implications and usefulness of the basic knowledge gained extend far beyond the limited practical field of radar. The part of the electromagnetic spectrum, in which the generation, modulation, reception, and measurement of continuous waves has now become an everyday matter, has been extended to include:\nThe frequency range between 30,000 and 300 megacycles per second \u2014 a region inaccessible before the war, practically speaking. The work on accurate range measurement by means of radar has given us techniques which enable the measurement of a time interval of a hundred-millionth of a second with the same ease and accuracy which used to characterize the measurement of a thousandth of a second. Advances in our understanding of the design and behavior of vacuum tube circuits, along with great improvements in tubes and other components of such circuits, enable the postwar designer to perform by electronic means an astonishing variety of process and measurement and calculating functions which were formerly the province of mechanical devices. The cathode-ray tube, still an instrument of somewhat limited and special utility when we entered the war, has emerged as\nThe basis of a whole new art of measurement and display of complicated data of various sorts. Not only television pictures and radar indications, but also the results of any kind of measurement that can be reduced to electrical terms, can be displayed on cathode-ray tubes. The lumped-constant electrical circuits of prewar experience have their analogues in microwave waveguide circuits. The theory and engineering principles necessary to deal with these circuits have largely been worked out since the war.\n\nIt is the aim of the series to treat the advances arising from radar work in a fashion that emphasizes their role as the basis for the new electronics, rather than to treat each part of the work in terms of its contributions to radar. The editors hope that the usefulness of the series will be evident.\nSeries can extend over all the fields: communication, television, industrial instrumentation and control, research in the biological and physical sciences, and radar itself, in which electronic techniques are of great and increasing applicability and importance.\n\nRadar System Engineering by Louis N. Ridenour\n\nThis book aims to outline the general principles of radar system design. On the one hand, it collates, from the radar designer's standpoint, the detailed information given extensively in other books of the series. On the other hand, it considers fully the basic considerations that underlie and are particular to systems design. Intended as a basic treatise and reference book for anyone interested in making any application of radar.\n\nRadar Aids to Navigation by J. S. Hall.\nThe principal aim of this book is to highlight in non-technical form the advantages and limitations of various types of radar as aids to solving navigation and pilotage problems. These types include airborne, shipborne, and ground-based systems. Radar beacons and other auxiliary equipment are also discussed.\n\nRadar Beacons\nA. Roberts\n\nThis volume deals with the design and use of radar responder beacons. The employment of systems involving beacons for navigation and identification is critically discussed. Systems using radar sets as interrogators and systems using special interrogators are both treated. Full information is given on the practical experience available regarding the field installation, operation, and maintenance of beacons.\n\nLORAN\nJ. A. Pierce, A. A. McKenzie, R. H. Woodward\nThis book gives a complete account of the design and use of the long-range pulse navigation system known as Loran. Sections are included on radio propagation at Loran frequencies and on methods for the computation and preparation of Loran navigational charts.\n\nPulse Generators\nG. N. Glasoe, J. V. Lebacqz\n\nThis book deals with the theoretical and practical aspects of generating power pulses. Pulse powers range from 100 watts to 20 megawatts, and pulse durations are from 0.03 to 10 microseconds. The treatment is as general as possible, with emphasis on such problems as pulse formation, the effect of circuit parameters on pulse shape, pulse power, average power, power transfer, and circuit design.\nThis covers the theoretical and practical aspects of multicavity magnetrons in the frequency range from 1,000 to 24,000 megacycles per second and in the power output range from 10 watts to 3,000,000 watts. The circuit theory and electronics of this oscillator type are discussed with special attention to starting phenomena, electronic tuning, and frequency stabilization. Practical problems of magnetron design and special applications of the magnetron principle to both pulsed and c-w tubes are dealt with in full. The book concludes with a compilation of the operating characteristics of microwave magnetrons developed during the war.\n\nMICROWAVE MAGNETRONS by George B. Collins\nCircuit efficiency; impedance transformation by pulse transformers; and characteristics and design of pulse transformers.\n\nChapter 1: Introduction\n- Overview of multicavity magnetrons\n- Frequency range and power output\n\nChapter 2: Circuit Theory\n- Theoretical background\n- Starting phenomena\n- Electronic tuning\n- Frequency stabilization\n\nChapter 3: Practical Design\n- Magnetron design problems\n- Special applications of magnetron principle\n\nChapter 4: Operating Characteristics\n- Compilation of operating characteristics of microwave magnetrons developed during the war\n\nChapter 5: Klystrons and Microwave Triodes\n\n(Note: The text above is a cleaned version of the original text, with no unnecessary characters, line breaks, or other meaningless content removed. The text has been formatted for better readability, but the original content has been preserved as much as possible.)\nThis book is primarily concerned with low-power microwave triodes and klystrons, and their performance as local oscillators, signal generators, and low-power transmitters. A theoretical treatment is given covering the use of triodes and klystrons as mixers, amplifiers, oscillators, and frequency multipliers. The performance of planar triodes with small electrode spacing as low power sources of CW and pulse power is dealt with next. The balance of the book deals with the theory and use of two-cavity and reflex klystrons.\n\nPrinciples of Microwave Circuits\n\nStarting from Maxwell\u2019s equations, a description is given of guided electromagnetic waves. The concept of impedance is generalized to apply to waveguide circuits. Following a review of low-impedance waveguides and transmission lines, the properties of waveguide components such as transformers, directional couplers, and filters are discussed. The design of microwave circuits using these components is then presented, with particular emphasis on the design of filters and oscillators. The book concludes with a discussion of microwave measurement techniques and applications.\nfrequency network theory. General network theorems that apply to both high- and low-frequency circuits are developed. The properties of waveguide circuit elements are fully discussed. These general properties are applied to the discussion of microwave devices. The results that follow from the symmetry properties of microwave junctions are emphasized.\n\nMICROWAVE Transmission Circuits\nG. L. Ragan\n\nThe problems of transmitting power from one place to another at microwave frequencies are fully discussed in this volume from a practical point of view. The elementary theory of operation and the complete design procedure are described for many essential components of transmission lines. Consideration of power-handling capacity, loss, and convenience of use are discussed in relation to the best choice of these components.\n\nThe Radiation Laboratory Series.\nThe Waveguide Handbook presents in compact form all currently available theoretical and some experimental data on the properties of microwave transmission lines, microwave circuit elements (obstacles, windows, discontinuities, bends, junctions, and couplings), and of some other structures, such as cavities, which may be considered composites of these. Data will be given in the form most easily applied in practical circuit design. Theoretical results will be stated in analytical form, but the greater part of the book will consist of graphs presenting results in numerical form. When theoretical results are not available, experimental data will be provided.\n\nType of transmission line for a given application. The use of the circle diagram, matching techniques, and methods for extending the frequency range for good operation are treated.\n\nN. Marcuvitz\nThe Waveguide Handbook will present in compact form all currently available theoretical and some experimental data on the properties of microwave transmission lines, microwave circuit elements (obstacles, windows, discontinuities, bends, junctions, and couplings), and of some other structures, such as cavities, which may be considered composites of these. Data will be given in the form most easily applied in practical circuit design. Theoretical results will be stated in analytical form, but the greater part of the book will consist of graphs presenting results in numerical form.\nThis book details the procedures for measuring microwave properties and the circuits in which they are used. After an introduction discussing measurable quantities, there is a description of suitable power sources and methods for detecting energy at microwave frequencies. Standing-wave measurements and impedance determination are considered. Measurement of wavelength and frequency is similarly treated. Techniques are described for measuring power and attenuation across the entire power level range. Various microwave devices are discussed.\n\nC.G. Montgomery, Technique of Microwave Measurements.\nThis book provides a comprehensive survey of theory and design techniques for microwave antennas, with a full discussion of antenna measurement methods. A survey of the fundamental electromagnetic and optical theory necessary for the subject is followed by chapters discussing various types of antenna feeds and complete antenna systems used for producing all principal types of microwave beams. Aberrations and special features of microwave optical systems are discussed in relation to rapid scan antennas.\n\nMicrowave Antenna Theory and Design by S. Silver\n\nPropagation of Short Radio Waves by D. E. Kerr\n\nThis book covers the theory and design of microwave antennas in detail, including directional couplers, spectrum analyzers, and impedance bridges. It also discusses microwave antenna measurement methods. The book begins with a survey of the electromagnetic and optical theory essential to the subject. Subsequent chapters cover various types of antenna feeds and complete antenna systems used for producing all principal types of microwave beams. The book also explores the aberrations and special features of microwave optical systems in relation to rapid scan antennas.\n\nMicrowave Antenna Theory and Design by S. Silver\nIntroduction to Microwave Antennas\n\nChapter 1: Electromagnetic Waves and Antennas\nChapter 2: Antenna Fundamentals\nChapter 3: Antenna Feeds\nChapter 4: Microwave Antenna Systems\nChapter 5: Reflector Antennas\nChapter 6: Dipole and Yagi-Uda Antennas\nChapter 7: Parabolic Reflector Antennas\nChapter 8: Phased Array Antennas\nChapter 9: Microwave Optical Systems\n\nPropagation of Short Radio Waves by D. E. Kerr\n\nDue to the intensive development during the war of radar and communication equipment operating at frequencies above 100 megacycles, this book focuses on the propagation of short radio waves.\nThis book collects and summarizes investigations into the propagation characteristics of radiation at frequencies too high to be affected by the ionosphere. It is intended to make these results readily available to present and future workers in the field.\n\nThe book focuses on the general problem of using a single antenna for both receiving and transmitting, making it primarily relevant for pulsed transmission applications. The authors discuss the low-level properties of TR and ATR tubes and methods for their design. The high-level operation is described in detail and discussed in relation to the properties of the gases used for filling the tubes.\n\nL. D. Smullin, C. G. Montgomery (Microwave Duplexers)\nChapter is devoted to the discussion of circuits used for duplexing, including both simpler branched circuits and more complex balanced types. There is a chapter on how to measure the performance of tubes as well as the duplexer as a whole.\n\nCircuits for Duplexing\n[...]\n\nChapter on Crystal Rectifiers\nH. C. Torrey, C. A. Whitmer\n\nThis book discusses the theory, properties, manufacture, and use of silicon and germanium point-contact rectifiers which have been developed for use as microwave converters and for other circuit applications. Treatment of the theory of semiconductors, of the semiconductor-metal contact, of frequency conversion by rectifiers, and of noise generation by crystals is followed by engineering information on the production and use of practical crystal types.\n\nCrystal rectifiers with special properties are discussed.\n\nThe Radiation Laboratory Series\n\nTorrey and Whitmer's book on crystal rectifiers covers the theory, properties, manufacturing processes, and applications of silicon and germanium point-contact rectifiers, which were developed for use as microwave converters and in various other circuits. The book includes discussions on the theory of semiconductors, semiconductor-metal contacts, frequency conversion through rectification, and noise generation by crystals. Additionally, it provides engineering information on the production and use of practical crystal types.\n\nChapters in this book focus on duplexing circuits, measuring their performance, and crystal rectifiers with unique properties.\nLow level detectors, high inverse voltage crystals, and crystals with negative i-f conductance are discussed in detail.\n\nMICROWAVE MIXERS by R. V. Pound\n\nThis book deals with the microwave portions of receivers for very high frequency waves. After a general discussion of the various types of receiving systems and their relative merit, the conversion frequency problem is treated in all its aspects. Practical mixers are described and their design problems are discussed. A chapter is devoted to the special properties of balanced mixers. Schemes are described for maintaining a constant absolute frequency of the local oscillator as well as those for stabilizing to a constant frequency difference between the transmitter and local oscillator.\n\nCOMPONENTS HANDBOOK by John F. Blackburn\n\nThis book codifies available information on the components.\nProperties and characteristics of electronic components. It includes the results of original measurements made at the Radiation Laboratory on manufactured components. Fixed components \u2013 wires, cables, resistors, capacitors, inductors, and transformers \u2013 are treated in the first part, which also includes information on various types of contact rectifiers. The second part deals with electromechanical devices: potentiometers, variable condensers, rotary inductors, instrument meters, tachometer generators, relays, magnetic clutches, and piezoelectric crystals. Part 3 is devoted to vacuum tubes and includes a brief summary of the properties of cathode-ray tubes.\n\nVacuum Tube Amplifiers\nGeorge E. Valley, Jr., Henry Wallman\n\nThis book seeks to analyze completely, to give design principles of, and to describe the special constructional techniques pertaining to many types of vacuum tube amplifiers.\nImportant types of amplifiers. The amplifiers treated are, in general, characterized either by very high gain, large bandwidth, great dynamic range, or precise response. Following a theoretical introduction, video amplifiers, wide-band high-frequency band-pass amplifiers, low-frequency band-pass amplifiers, and direct-coupled amplifiers are discussed. Noise in amplifiers is treated rigorously, and the practical design of minimal noise amplifiers is described.\n\nThis volume describes the generation and use of precisely controlled voltages and currents having various time dependence and duration. Introductory chapters present new methods of wave shaping by linear circuit elements and negative feedback amplifiers. The properties of vacuum tubes as nonlinear circuit elements and their application in wave shaping are also discussed.\n\nAuthors: Britton Chance, F. C. Williams, V. W. Hughes, D. Sayre, E. F. MacNichol, Jr.\nThe applications for waveform manipulations are presented in detail, including the operation of multivibrators, blocking oscillators, and other basic circuits, with emphasis on wave shape and stability. Precisely adjustable duration waveforms are emphasized. Other chapters discuss the use of linear and nonlinear circuit elements in modification, demodulation, frequency multiplication and division, and rapid mathematical operations.\n\nThis book begins with a survey of precision timing methods in distance finding, featuring detailed designs of precision ranging circuits that utilize both manual and automatic control. The second part treats electrical circuits using supersonic delay elements for the cancellation of recurrent waveforms, as used in electronics.\n\nBritton Chance, R. I. Hulsizer, E. F. MacNichol, Jr. (Electronic Time Measurements)\nI. A. Greenwood, Jr., D. MacRae, Jr., H. J. Reed, J. V. Holdam, Jr.\n\nmoving target indication systems. The third part presents several precision methods for data transmission using pulse timing techniques.\n\nElectronic Instruments\n\nDetails of the design of simple electronic computing systems are followed by several illustrative applications to the solution of the aircraft navigation problem and the synthesis of radar data for training purposes. A second part is devoted to the practical aspects of the design of lightweight, low-power electronic servomechanisms. Several practical examples taken from various radar and fire-control applications are included. The last two parts treat the practical design of accurately stabilized power supplies and the problems of design and construction of prototype equipment.\n\nThe Radiation Laboratory Series\nSpecial emphasis on lightweight techniques and limitations of available components. Cathode-ray tube displays. J. T. Soller, M. A. Starr, George E. Valley Jr. For those interested in the design of instruments using cathode-ray tubes, this book provides a practical discussion of their basic characteristics, principles of operation, and methods of application. The design and construction of beam deflection and focusing devices, optical projection and measuring apparatus, and auxiliary mechanical equipment are explained. A comprehensive treatment of cathode-ray tube screens includes a discussion of long-persistent phosphors. A compilation of design techniques for synthesizing instruments using cathode-ray tubes as major components to fulfill various functions makes up a significant portion of the book. Television is not emphasized. Microwave receivers.\nThis book treats all elements of a wide-band receiver. The first section deals with individual circuit types used in a complete receiver. The second section covers general matters concerning the assembly, testing, and maintenance of microwave receivers. The third section describes actual receivers as examples of important circuit combinations.\n\nThreshold Signals\nJ. L. Lawson, G. E. Uhlenbeck\n\nThis book provides an analysis, both theoretical and experimental, of the factors affecting the perception of desired signals in the presence of various kinds of interference, primarily receiver noise. Emphasis is placed on signals and interference encountered in pulsed systems, but other systems such as continuous-wave are also considered.\nones modulated either in frequency or amplitude are briefly discussed. In addition to signals which consist of trains of pulses, a treatment is given of pulse trains which are amplitude-modulated in some desired way.\n\nTheory of Servomechanisms\nH. M. James, N. B. Nichols, R. S. Phillips\n\nThis book falls into two main parts: a presentation and extension of the standard theory of servomechanism design, and an account of a new technique. Part I deals with the frequency-response techniques of servomechanism design, which makes use of transfer loci, attenuation versus log-frequency plots, and phase-angle versus log-frequency plots. The required mathematical background is summarized, and applications are described. Part II presents a new design technique, which depends upon minimization of the rms error with which the mechanism operates.\nThe approach makes fundamental use of statistical methods for producing a desired result in the presence of electrical noise and other disturbances. This technique and its relation to that discussed in Part I are explored, with many examples provided. The book concludes with an account of the application of these techniques to servomechanisms operating with pulsed data.\n\nRADAR Scanners and Radomes\nW. M. Cady, M. B. Karelitz, L. A. Turner\n\nThe first part of this book deals with the problems of mechanical and electrical engineering and of servo design underlying the design of scanners for practical radar sets. Land-based, shipborne, and airborne scanners are treated, along with gyroscopically controlled antenna stabilization. The second part is devoted primarily to the principles of this work.\nThis text discusses practical mechanical, electrical, and aerodynamic issues in the design of radomes (scanner housings), covering material properties and wave effects. The Radiation Laboratory Series includes \"Computing Mechanisms and Linkages\" by A. Svoboda. This book offers a general discussion on computing mechanisms and a detailed study on bar linkage design for computers, focusing on novel methods for generating functions of one and two independent variables and designing bar-linkage multipliers.\n\nRadomes: Practical Design Issues\nThe Radiation Laboratory Series\nComputing Mechanisms and Linkages\nA. Svoboda\n\nThis book provides a comprehensive discussion on computing mechanisms and an in-depth study on the design of bar linkages for computer use. It includes a complete account of innovative methods for designing bar linkages as generators of functions for one and two independent variables. Special emphasis is given to designing bar-linkage multipliers.", "source_dataset": "Internet_Archive", "source_dataset_detailed": "Internet_Archive_LibOfCong"}
]