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S-L6 kK Glo BAILS F71/ BALLISTIC MISSILE GUIDANCE AND CONTROL - USSR AND PRC DST-1000S-293-76 DIA TASK NO. PT-1000-01-75 DATE OF PUBLICATION 5} 12 MARCH 1976 r™ N\ rf \yy \ - } \— Information Cutoff Date . 9 June 1975 rN NY : I} 0. y2 4) . Q . wae A ( ‘This study supersedes ST-CS-05-293-75, “Ballistic and Defensive \ Missile Guidance and Control—ECC (U),” dated 14 March 1975. \ \ \ AY \ » G, \ ar oRNGN (Reverse Blank) - / ase - REE Reckaeceoneiteenaeeemeeen SO pre at SURES SERB aR orgasm om — ee cs
. 7 . : : DST-1000S-293-76 : 12 March 1976 PREFACE & i The following definitions apply to terms used in this study: 1. Estimate - Judgment regarding the present or a historical period about which there is substantial validated information; extended to include the next 2 years, 2. Projection - Judgment regarding the time frame from 2 years hence with decreasing confidence as the time span increases, 3. Almost Certain - Indicates approximately a 90:10 chance that an event will occur. Related terms: will, shall, is expected, is anticipated, 4. Probable - Indicates approximately a 75:25 chance that an event will occur. Related term: likely. 5. 50:50 - Even chance an event will occur. 6. Unlikely - Indicates approximately a 25:75 chance or less: i.e., only one chance in four it will happen. Related term: improbable. 7. Better Than Even Chance - Greater than a 50:50 chance but less than approximately a 75:25 chance. 8. Less Than Even Chance - Less than a 50:50 chance but greater than approximately a 25:75 chance. , “ This revision contains significantly new and revised information which affects previously published assessments, A delta (A) preceding a paragraph, heading, or caption indicates that the discussion, table, or figure is reporting significantly new or revised information. , ili ee (Reverse Blank)
° DST-1000S-293-76 - 12 March 1976 METRIC CONVERSION TABLE —_—_ + | Parameters and measurements in this document are reported in metric units, to bring Department of Defense intelligence reporting into consonance with internationally accepted standards for measurement. For the benefit of users who require parametric values expressed in customary units, the accompanying table lists each metric unit applicable to this document, along with its corresponding value in customary units. The metric system used is the International System of Units (SI), along with certain non-SI metric units approved by the International Committee on Weights and Measures (ICWM) for use with the SI system. Certain non-metric, international customary units such as degree of arc, and the customary units of time also have been approved by ICWM for continued use with the SI system and will continue to be employed where appropriate. US customary units also will continue to be employed for items which are defined or named in terms of customary units, such as 1-megaton warhead, .38- caliber pistol, and two-by-four. An asterisk (*) in the Customary Unit's column indicates that the customary unit will continue to be used for the indicated parameter. VALUE IN METRIC ‘ VALUE IN CUSTOMARY PARAMETER METRIC METRIC UNIT SYMBOL CUSTOMARY UNIT ACCELERATION, SPEED, VELOCITY Acceleration 1 meter/second? m/s? . 3.280840 ft/sec? Velocity 1 meter/second m/s 3.280840 ft/sec RANGE, ALTITUDE, DIMENSION, LENGTH Range/Distance 1 kilometer km * 0.5399568 NM Altitude dimension 1 meter m 3.280840 . foot Dimension 1 millimeter mun 0.03937008 inch Thickness, wavelength 1 micrometer um 9.03937008 mil MASS (WEIGHT) Gross weight, payload 1 kilogram kg 2.204623 pound (m) Mass (bulk) 1 metric ton (tonne) t 1.102311 ton ENERGY (J=W-s=N- m), TORQUE (N +m) ‘Tarque 1 newton-meter N-m 0.7375621 Ibf.ft PRESSURE, STRESS, STRENGTH (Pa=N/m') Pressure (gage) 1 kilopascal kPa (gage) 0.1450377 psig Preasure (absolute) 1 kilopascal kPa (aba) 0.1450377 psia ANGLE Flane angle 1 radian rad §7.29579 *degree Angular velocity 1 radian/second rad/s 9.549279 “rpm Vv * ‘Reverse Blank)
° ° DST-1000S-293-76 bd 12 March 1976 TABLE OF CONTENTS Page No Preface ..ccccccsscssecscceccosscsencecceovesssssccssconsctosccsececcsscsessscessnsacessesessescsaccessacececsesacsscesaecececensanaceeseesessnseseassaaseneeaee iii Metric Conversion Table ou... ceccccsssscsossessssssecsescccceccssesessesscensseuseaceenecsssssoscoserseeecerscessssseeussstenecesreonse v SUMMALY.....ecceescseesecccceeeceecescectstsseseatecnetcacansenscesenccsessnnsesceaunerseaenenseaessasesssesssaeasescacnagaasssceeceveneseneacenseeeseeetes xiti Section I Soviet Surface-to-Surface Ballistic Missile Guidance and Control ow... 1 LT. Introduction ( ( ciccceecscsccccsccccsscseccseccscccvesesvecsssscerscceccesscuseatscesecesssscsensnassasaceanseesscueeeseeseaees 1 2. ICBM Guidance and Control! o.icccecsssssscssesssssesceesseseessesseneeneesecesseensssesnesnsseecsssees 2 B, GS-7 anaasecescecescsnscccusssccncensessscsesesesecsensaenscasausscdescadceesaceccecenesessecaccssecasesaseaaveacenasease 2 Bb. GS-8 aessssesssecsccercnccscssccssceccscscsessescescecssssssesenssssenseccaesacecssscencoascecscesacacarseessaeouanane 6 C. GGG aareececccsecscecensescsesssensctsstcatsneneesonsnecceereauevensesesesussescsecsaeseaeacsecessssersseeceeececaeons 8 GD, SSL eccceccsceccecsssccccceessscssescorsssceessesserevasensscsceesusccesacesessonnenacecueesnecevsssecessecsescueeegs 22 Cc,  SS19 avec ceclecscscsnsssssssssssssessssscecaccesssnsecessesecseceeneeseessevscersenseseusetevssesseesssecesenss 33 — fi SSK A15 cece ec cceccccnsesecessssasasncessensccuccesececeeseccecssesacseececsaesseacesecsuscacesesaenecennenes 38 Bo. GSAK-16 acess iccccesssssssnscnessessesseeeessnecssssessvssussnsscesssssessneaasseacauceasesesesesseeseeeseesceas 39 Fh. SS-17  aaceccssccacccceccssccessessorescesssssevenseraccusesecsenssecesesaseussscsrscssseescasessussesseececesseeseeovesees 43 BSS A18 _ciceccsssssccccscessscccsscsecessscelonsessssacessecsussnessauessevsensesrsssaveeseescesenscereseeecaseecsecaseeese 53 Je S19 ee eccscsssscsssssessssvscnssccusecssceesesscseeusssssestsceessrsosceevsccesseunacccssarsscesssetaneasessecses 59 3. SRBM, MRBM, and IRBM Guidance and Control) cicsscssssssssssssussssneseee «63 a. SCUDA and SCUD B cvncccicccssssssssssssscsscssscssssssasssssscsssesscatassesesseseatseseensoeeases 63 b. SS.-4 sesacescesseseceneccccsccescereseccececeassnescacecccacsasacacacesesasssccrevsesusocescascsececsvseyecsssesssessesseeses 68 C2 SSB a aiecscssecscccssccesonececceccorsscscsnenensavsesensecsecesssosueeaesseeeceusecseueesenceserercenceseacsssseseesneses 70 G. GS-12, a cecstcccccccssesccsscnesssetecseterssevecesssstecceesecenseesenseessessssuessssssssseseseasesaseeaes 72 =, GS-14 seessssstensssasssennssnntestunsenenerenepenensestseseesiseegnestanpeteerteseanstesnasti 73 4. Naval Ballistic Missile Guidance and Control ciccccccccssssccsssecsescecrecsceccesscsssersceceees 75 a. SS-N-4 ssscssssssussessssnecsonsuuesstseecesenanessecarenesnuuneeesessavecesuveetenseveseeenuesesrassssesegessseseassestusse 75 b. SS-N-5 0 ascsessssesesssssensssmsecaseessasseusssseceescasnsscesecsscacsssscensssesesaeeanas V7 C. GSN eeccciscsccsscsssssssnsssssssssescssecsscsssscsssscssevsssscescsrsesscssascsecetsesansssasssssessseseersuces 78 G.  SS-N-8 © acacccsccssecscscsssssssnscsesssetsassessesecesesssssesessesscsencesccsssnssesucaasesssescsvessacsrereeesees 79 C. SS-NX-13 —— ieccscccsccecsosevscscecssceccsecsessccssaesscanqeesvecssaesensessaseaseasensvecceresererensereraecessese 82 HB. Trends © eatscecesscscssssssscscssscssceusecssecssssssucssscstorsosscacssecucsecesecaceseesseceacscesvaccessecevaccersetesesssseseensense 87 a. Inertial Component Capabilities and Trends (ooui.e.ccccssssesssessessssssseeecacecsenes 87 b. Soviet Ballistic Missile Guidance Technology Trends © oo.eecccsesssssseseseeeesee 92 ce. SRBM Guidance and Control Trends (( oocciccecceeccccscssccecscecascscsscceseneessceererseseese 94 d. MRBM/IRBM Guidance and Control Trends (ou cccccsscscssccsscsssssscssseseesseeseeees 95 e. ICBM Guidance and Control Trends ceecccccccccccccsscscccsoscscccescssecsssassessrersesesscecee 95 f. Postulated Reentry Guidance ( icciicccsscsssccssssessscssscsscssssscsescesassescssceressesscsensseess 97
DST-10008-293-76 12 March 1976 TABLE OF CONTENTS (Cont) - Page No Section IT People’s Republic of China Surface-to-Surface Ballistic Missile Guidance and Control fo ooi.cceccessssessessssssscsccsscesscassacerecresesesacsacesecssssereussssnsessueesaces 105 / 1. Technology Background 4 oii..cccccccesssssssssssssssscscsessesecssesersestacatscsscessussesseceeucuesussecsusencen 105 a. Computer Developments ( oon..cscsssssssssssssssssssescsssssssssensuscnsessusessssssccsssvsesleseesessssssen 105 b. Missile Guidance Radar Development ( oooiociccccccsssesccsscssscssecssssessceccessnecsnsonsens 105 c. Automatic Control Components | ..cccccsccsssssscsssssssssvessecsaesecsucseccsecssecesssestceracsensens 106 d. Miniaturization and Semiconductors Development | oioccccsseccscsscscsccssessesssssessosee 106 €. PRC Commerical Trade, oo..e.secccessecssssssssssssssssssssscecececsssessassssssusssseccesecessesevcnscescusee 106 2. Systern Control Theory 4 oie ecssssssssscsscsssescssesessssssssesecseseceecaceseecasssesecsesecacaceceusavenvessea 106 3. Guidance Assessments (  ouu.scesscscssssessessssssssssescsesosssssesssessesncasacsencacsuesssusassssssecsesucarcesessees 107 4. Component Assessments —— ..n.eeesscssssssssesssssssescessesesassssesssassucassecscsesussesssssssssesesucareceessesacces 107 5. Error Analysis of the CSS-2 IRBM System Jo iccccccccccsccccccsssssssssessecsesssececesceceeseecee 107 G. Guidance Accuracies | oot. ececcessssssssssesnessssessscsssosssessesstsssesassassusssesssstesesassssssasasessusccusesees 110 Appendix I USSR and PRC Missile Guidance Systems) + .ccscsscssssssssssssssssssessesursseuee 113 Appendix II Principal Error Axis Concept / _ seseavecscenccnersecasconsensenesensessucsssessesesvenseessesanens ae 117 Appendix III Cutoff Law Mechanizationa ;” - seeeeaeeseseesaessessesseoseasasensasecsaeacssscseacsucesesensuasassave 121 Appendix IV Guidance Errors! o..cssssssesssssesssssesssssssssesseesen casessenesneaesaaesssesnesseesecees » ceseeseseseue 123 - 7 Appendix VI Soviet Naviational Aids | oo... sssssssssssssssssssscsssccesssssssssssssnsscessssssssessececersssnneesneeees 127 Appendix VII Pendulous Proportional Gyro Accelerometer | ..esssecsessssssssssssesssesesssseesenssone 131 Bibliogr aphy......ssssssssesesssssssnssssusssseesesnsesseeuntassanssssessssssstsesonsassesrsunesesseusansessssssnsusnsesuecaneeneuvecenenes 133 LIST OF ILLUSTRATIONS Figure 1 Missile Guidance Functional Diagram ! . savsececscsseesesnsentecsuaessssesssssssacesecsaconseesesvos 2 Figure 5 Miss vs Impact Range—Guidance Contribution eveeeeueesevnestnstnesnestsetnen 17 Figure 6 CEP va Impact Range—Guidance Contribution leseteseacaueacesesesesestscesseseceassennveeee 18 vill
Figure 7 Figure 8 ‘ Figure 12 Figure 15 Figure 16 Figure 17 Figure i8 7 Figure 20 Figure 21 Figure 27 (As DST-1000S-293-76 12 March 1976 LIST OF ILLUSTRATIONS (Cont) Miss vs Impact Range—Guidance Contribution CEP vs Impact Range—Guidance Contribution Variable Gain Actuation System | vececesceereees Modified PEA Guidance Mechanization { 0... Pitch Steering Loop esescccsssssssssesseseessesseesssseesteneneeseess Nominal Pitch Command | .o..cescssssessssesscesesseseeneees Stable Platform After Pitchover | wuss Accelerometer Orientations § ooowecweecccscscccsccsceseeene Guidance and Control Functional Block Diagram Guidance Coordinate System oo.eececcccssccsseecesenene er oe rer rrr rPrPrrrrrrrr TTT TP Srirerrrrrrrerer erst tien yrirr yyy PVeTPe OPTI TTT er reer rere rrerrerrrrerrrrre errr Prrrrererrerrrrererestreeriririirriririiy tee eececerscereor esse csessernasnssacseasaaraseeuse errr ertrrierr reir ror erirrs seseacusenvaneessaerseseseasssaseneateneaseenees 28 sesssesnassuseanscseenseneaeersceeestsnaeseeaty 34 aseetacscecenensesessrsreersesssenscseeceeneneee 35 35 36 40 41 ea emeesocccetecsvensenarereeeeseeseennee
DST-1000S-293-76 12 March 1976 Figure 31 Figure 34 .7 Figure 36 Figure 42 Figure 43 Figure 44 Figure 45 LIST OF ILLUSTRATIONS (Cont) Page No. Guidance System Mechanization (  cusscccccscscsccsccsscccsceccscecscsecsscecsecescesseseerescersnes 60 SCUD Guidance and Control Systerm oc sscssssssssssccsssessseecsnnseeesececcsneesccnnseseceseee 65 Terrain Navigator Used with SCUD System (0 cuceiccsccscssscscessssssscseceseceaeeee 67 Estimated Trend in Soviet Stabilization Gyro Technology. oe 93 Accelerometer Quality Trend Estimates | oc.csccccsssssssssssscssssesessssesscsescsesssacsecseene 94 MRBM/IRBM Accuracy Trend Estimate © csessssssssssssssssecssseessessssseee sosssesessseee ‘96 ICBM Inertial Guidance-Only Accuracy Trend sesseeesceensseecsesessesecsssesecrevesesersees 97 =a 4 —s, a n wd. i oF . EL —
Figure Figure Figure Figure Figure Figure Table Table Table Table Table 50 51 52 53 54 56 DST-1000S-293-76 12 March 1976 LIST ILLUSTRATIONS (Cont) Page No. Downrange Miss ve AT c—2,950-kim Trajectory ( oeseceeesessssssssessessssneseerssorsceeses 109 Cutoff Mechanization—Time Compensation System © wisciscsessssssssssecsssessessacessnee 110 Trajectory Coordination System —— o..ecccccesessscsssessssesesssscesensenssenerssnanseess ensescevaceseese 117 Principal Axis Coordinate System . ssasssssuseneununsensssenaneesecsececuesenesnancenceccenceceneneaee 118 Soviet Directional Gyroscopes ——...sessccsesscesessscceccscsecssnereeecasessessacesssgesensesssssssuaassnnee 125 Diagram of Pendulous Proportional Gyro Accelerometer (U) .........sccsscecseseseenees 131 LIST OF TABLES I Accelerometer Orientations and Pitch Attitude at Burnout (Degrees) ~~ ..e.sccsccsssssssssssccesececsscceccosescesecessessesesasssssesscsvsccecsasscssssuaussuauesseransnazenteesecers 4 II First Stage Pitch Program ow.ccccccccssssssssescensecrecssrssecesescessesnesscessnsnassnseassenecs 12 TIT Accelerometer Orientations —oo..eccssecsecscoscscecrsecscessessecsessssnscasssasssseeensensrsereens 13 XI Relative Capability of Available Navigation Aids —— ......sssessscsssssssssseensesees 76 XII Soviet Inertial Component Technology Capabilities ( oo...esssssssesereeeee 89 xi
DST-1000S-293-76 12 March 1976 Table Table Table Table Table Table XVI XVII XVIII XIX XX XXI LIST OF TABLES (Cont) Page No. Three-Sigma Parameter Uncertainties (U)......cccccccssssssssssscsscssscscscnccecessesseees 108 Guidance Errors For System Without Time Compensation (U)....... 108 Time Compensation Parameters (U) ........ccccccsssssessssesssssscscsssscesencecsecescesscseescsees 110 Guidance Errors for System With Time Compensation (U).......cccccsssssses 111 Guidance System Accuracy (U))..ccuccccsccssscsssscssssssssscssccscesceccsesscecescescececseceesarereees 111 Offensive Ballistic Missile Guidance Systems (U) o.oo. cccescccecsceecececeeesesase 115 xii
anne es en nn ee oe ae DST-10005-293-76 12 March 1976 SECTION I SOVIET SURFACE-TO-SURFACE BALLISTIC MISSILE - GUIDANCE AND CONTROL (U) 1. Iatroduction | , . | A method of improving the accuracy of an inertial guidance s:stem, especially mobile launchers, 1s to use a star tracker. A star tracker can correct for both position and azimuth errors. It can greatly reduce the need for frequent updatings of the navigation system oa the mobile Jauncher. The amount of improvement depends on the quality of the inertial components used in the inertial guidance system on the missile and in the navigational system used «+ the mobile launcher.
DST-1000S-293-76 12 March 1976 = Cy U + Cy U + Cat? Cy NORMAL ACCELERO- METER FTD A70-2102 Fig. 16 Pitch Steering Loop THRUST ANGLE (D£€G) TIME (SEC) Fig. 17. Nominal Pitch Command 35
DST-1000S-293-76 12 March 197 TILT MOTOR PLATFORM TILT TABLE FTD A72-1249 : Fig. 18 Stable Platform After vitchover 36
DST-1000S-293-76 ‘ 12 March 1976 ” . VERTICAL a 8 = HORIZONTAL CROSSRANGE O = UPPER INSTRUMENTS ORIENTATION B— LOWER INSTRUMENTS ORIENTATION - FTD A75-1883 Fig. 20 Accelerometer Orientations
DST-1000S-293.76 12 March 1976 A possible guidance system limitation does exist for any future MIRV use; ie., use against targets hundreds of miles apart. The guidance concept now employed may not easily adapt to MIRV use. The introduction of a high capacity digital computer and a change in guidance philosophy will likely have to take place to obtain the flexibility and onboard navigation capability required for advanced multiple RV delivery systems. 79
DST-1000S-293-76 12 March 1976 Gyro error sources (Table XII) can be separated into two main categories: (1) systematic torques and (2) random torques. Systematic torques are defined as torques which can be measured and whose characteristics can be correlated with some parameter. It is theoretically possible to compensate either directly or indirectly for the errors produced by the systematic torques. The drifts due to systematic torques are basically of two types: (1) acceleration-sensitive drifts generally caused by mass unbalance, and (2) acceleration-squared-sensitive drifts generally caused by structural compliance- anisoelasticity. Random or unpredicted variations will introduce uncompensated errors which must be charged to the gyro. These errors are defined as “constraint” torques and are the most significant errors. “Constraint” errors are the limiting accuracy factor affecting gyro performance, 88
wo ee Pa me Poe ed DST-1000S-293-76 12 March 1976 A TABLE XII SOVIET INERTIAL COMPONENT TECHNOLOGY CAPABILITIES The literature indicates that the Soviets have a good mastery of the theory of gas bearings, and the techniques they are reportedly investigating closely parallel European and US designs. There are many Soviet publications on gas bearings dating back as far as the early 1950's. 89
pce ae a ee DST-10008-293-76 12 March 1976 Successful developments of these instruments could lead to their use in ballistic missile guidance systems where high accuracy, low cost, ease of maintenance, and reliability are extremely important. The technical literature on the ESG has indicated the Soviets have a good understanding of its potential capabilities. Since the late 1960's, the Soviets have progressed rapidly from treating the basic operating principles of suspension to analyzing the more complex problems such as resistance to vibration and acceleration, manufacturing tolerances, deformations under rotation, residual friction effects upon duration of spin, pickoff, and control torquing; they appear to be well along in the development. It is apparent that they recognize that a drift rate of 0.0001 degree per hour can be achieved with the ESG. 91
DST-1000S-293-76 12 March 1976 A TABLE XVI THREE-SIGMA PARAMETER UNCERTAINTIES PARAMETER 3-SIGMA UNCERTAINTY Specific Impulse 2.0% Initial Weight 3.0% Mass Flow Rate 2.5% Thrust Misalignment x In-Plane 0.1 deg ‘ Cross-Plane 0.1 deg A TABLE XVII GUIDANCE ERRORS FOR SYSTEM WITH TIME COMPENSATION ' 108
DST-1000S-293-76 12 March 1976 DOWNRANGE MISS (km) FTD A75-1854 A Fig. 50 Downrange Miss vs ATs: - 2,950-km Trajectory (U) 109
”~ . oe DST-1000S-293-76 12 Murch 1976 4 TABLE XIX GUIDANCE ERRORS FOR SYSTEM WITH TIME COMPENSATION (U) IMPACT RANGE DR MISS CR MISS - (km) (cm) (km) 111 (Reverse Blank) .
one a8 we one ne ee « DST-1000S-293-76 12 March 1976 APPENDIX II PRINCIPAL ERROR AXIS CONCEPT ap en er teen mans Ne el ei i AONE at dna __. The principal error axis (PEA) concept is presented in this Appendix. Figure 52 portrays the launch centered inertial (LCI) computational coordinate system used where Y is along the geodetic vertical, X is directed downrange, and the Z axis forms a right-hand coordinate system. The vehicle thrust axis is in the X, Y plane. The range from launch to impact is a function of the position and velocity vectors at thrust termination. For the purposes of this discussion, it will be assumed that the earth is nonrotating; therefcre, a flight time dependency is not explicitly included. However, in the results to follow, flight time is implicitly included. Also, the crossrange effects will not be explicitly handled in the development of the range control. Y LAUNCH zZ . FTD A71-2515 UNCLASSIFIED Fig. 52 Trajectory Coordination System (U) (U) Taking the injection condition of a reference or nominal trajectory, a Taylor Series Expansion of the range equation can be developed as follows: oR oR OR ay OR ,Yy OR = == AX — AY —— AX — AY+..... 1 ax + aY AY + ax + ay OY + @) where AX = X — Xo = difference in X coordinate from the reference (nominal) condition Xa Other A terms are defined analogously. Only first order terms are retained. The principal position axis coordinate system is developed by defining it as a rotation about the Z axis of the LCI coordinated system as portrayed in Figure 53. “417
DST-1000S8-293-76 12 March 1976 r 4 FID A7}-2514 Fig. 53. Principal Axis Coordinate System The transformation of LCI errors into this coordinate system is OXp cos 6p sin @p] AX AYp ~—sin Op cos Opi AY The inverse transformation is Ax cos 6p —sin @p|AXp ‘ - (2) AY sin Gp cos Op AYp ' Substituting equation (2) into position elements of equation (1) results in R R . RR. OR = (23 coz. 6p + 34 sin 6>) AXp — (2% sin 6p —- ae cos 6s) AY», (3) Defining the X, axis as the principal Position axis, the angle @ pof this axis is determined by setting the component of AX» to zero. Thus . and OR/IOY oR/OX (4) sin @p = sia sh 5» cos Oo = Se V(3y) + (3x) Very) + (3x) Using these in equation (3) results in oR 118
DST-1000S.293-.76 12 March 1976 where gs o V (5x) “4 yy obtain by using (4) in (3), With the same approach, the principal velocity axis is developed, (U) Summarizing the above, the necessary formulas are: Op = tan-! ROY, Ov = tan-! ORIOY aR/aX OR/OX (5) oR oR 2 oR,? = a/(2 + -/ ge: “OP (3 x) (3¥ (ax ay) Using these in equation (1) results in the following equation for range error: oR OR where the notation AP = AX,and AV = AX, has been substituted. 119 (Reverse Blank) Ls -
DST-1000S-293-76 12 March 1976 APPENDIX HI CUTOFF LAW MECHANIZATIONS Appendix II established the concept for mechanization of thrust termination. The desired condition for cutoff is when the range equation goes to zero, Setting equation (6), Appendix II, to zero results in _ aR aR | SR = 0 = 45 AP + ay OV (1) Then equation (1) can be solved for the required cutoff velocity as: Vr = Vo — Kp (P — Po) where _ 2R/aP = QROV 2) Equation (2) forms the basis for range control by termineting thrust when the velocity along the principal axis equals the required velocity. This concept for range cor‘rol is simple, requiring only two scalar quantities (position and velocity along their respective principal axes) and equation (2) to be instrumented in order to satisfy the range control function, This concept relies on the control of the acceleration vector during powered flight to be of sufficient quality to satisfy conditions of linearity which was assumed in the development of equation (2). : To implement the concept, however, requires further approximations or more complex instrumentation than implied above. For example, the acceleration along a principal axis is Ap = a. cos (9 — Op) — gp (3) where ap acceleration along the principal axis a. = total magnitude of sensed acceleration (sum of all nonconservative forces ++ mass) @ — 8» = angle between a. and principal axis &e = component of acceleration due to gravity along the principal axis Integrating equation (3) results in Vp = Ve — Vep Pp = Pe — Pep 121
DST-1000S-293-76 12 March 1976 where Vp = velocity along principal axis Va» = integral of sensed acceleration along principal axis Ve = integral of gravity along principal axis, with analogous definitions for the position (P) terms. The sensed quantities can be measured by using inertial instruments. However, the gravity terms must be computed as a function of vehicle position which is not easily mechanized in principal axes, If it is assumed that the flight trajectory is sufficiently close to the reference trajectory that the difference in the gravity integrals from nominal is small, then only the sensed quantities need be measured, The error which results from the assumption is termed “mechanization error.” The magnitude of this contribution to the total mechanization error is a function of how well the boost system controls the flight trajectory. Therefore, to assess the magnitude requires a detailed analysis of major error sources contributing to trajectory deviations from the reference trajectory. Also, given one departure from the theoretical mechanization (i.e., neglecting explicit calculations of gravity), other than theoretical alignments or scaling constants (K,) of equation (2) could result in smaller mechanization errors. . , The position terms in equation (2) represent differences of large numbers which are hard to mechanize accurately without resorting to digital techniques. An alternate approach ia to mechanize the difference between the reference (programmed) sensed velocity along the position axis and that measured by an integrating accelerometer. This difference is small (consistent with previous assumptions) and, therefore, can be integrated quite accurately without resorting to digital integration. With this consideration, equation (2) is modified to read s bs) Vn = Va + Kp AP (4) where AP = Live — Vs) dt Vr = required sensed velocity along velocity axis 6 v Vo = reference sensed velocity along that axis ; Vp = programmed sensed velocity as a function of time along position axis 9p V. = measured sensed velocity along that axis. 122
DST-1000S-293-76 12 March 1976 APPENDIX V FTD A75-114 Fig. 54 Soviet Directional Gyroscopes 125
DST-1000S-293-76 12 March 1976 APPENDIX VI SOVIET NAVIGATIONAL AIDS (VU) re re a ne nt eae anne (U) Reference to an inertial navigation system will occur throughout the following discussion. It is necessary at this point to provide a statement concerning the meaning of inertial navigation systems in order to clarify the context of the discussion. All inertial navigation systems are dead reckoning systems. A dead reckoning system depends upon continuous operation and periodic fixes inserted as updates to correct its inherent errors and reset the system. The periodic fixes must be supplied by systems which are independent of measureable drift, platform maneuvers, and other disturbing factors. No one fixing system meets all these criteria. Therefore, any inertial system must have several different fixing methods in order to function accurately. 127
_ © DST-1000S-293-76 12 March 1976 LORAN positions are determined from the difference in the time of arrival of pulses transmitted simultaneously from a master and two slave stations. Greatest accuracy is achieved when the observer is on a line which bisects the angle formed by the two base lines from the master to the slave stations and decreases as the distance from the stations increases. | No special receiving equipment is required, but automated receivers are on the open market which would remove the basic operator errors involved in counting dots and dashes. ae ee ce 128
_ DST-1000S-293-76 12 March 1976 BIBLIOGRAPHY te . Appazov, F. R., Lavrov, F.S., and Mishin, V. P., “Ballistica of Long-Range Rockets .” Science Publishing House, Moacow USSR, April 1966. , . 2. DIA Study No. ST-CS-05-294-74, “Space Vehicle Guidance and Control - ECC . 3. FTD-MT-65-96, Rivkin, S. S., “Theory of Gyroscopic Devices, Part II ,” I:datel'stvo Sudostroyeniye, Leningrad, USSR, 1964. . 4. Slomanskiy, G. A. “On Determination of the Drift of Float Integrating Gyroscopes Without the Use of a Dynamic Stand ” izy, Vuz, Priborostrogeniye, Vol. No. 3, 1963. ( 5. Yagodkin, V. V., Khlebnikov, G. A. “Gyroscopic Devices of Ballistic Missiles * Voyennoye Izdvo Ministerstva Oborony, SSSR, Moscow, 1967. 4 &. Andreyev, U. D., “Theory of Inertial Navigation Correcting Systems " Moscow, USSR, 1967. ‘ 7. Ishlinakiv. A. Yu., “Inertial Guidance of Ballistic Missiles :" Published 1968, Translated 1971, FTD-MT-24-291-70. 133 (Reverse Blank}